GeneticGenetic mapping mapping InvitationInvitation Genetic mapping in polyploids Genetic Genetic mapping in polyploids Genetic
in polyploidsin polyploids You are cordiallyYou are invitedcordially to invited to attend theattend public the defense public defense of my PhDof thesis my PhD entitled: thesis entitled:
GeneticGenetic mapping mapping in polyploidsin polyploids
on Fridayon 15 Fridayth June 152018th June 2018 at 11:00 in at the 11:00 Aula in ofthe Aula of WageningenWageningen University, University, Generaal GeneraalFoulkesweg Foulkesweg 1, 1, Wageningen.Wageningen. Peter M. Bourke Peter M. Bourke Peter BourkePeter Bourke [email protected]@wur.nl
ParanymphsParanymphs
Michiel KlaassenMichiel Klaassen Peter PeterM. Bourke M. Bourke [email protected]@wur.nl 2018 2018 Jordi PetitJordi Pedro Petit Pedro [email protected]@wur.nl Propositions
1. Ignoring multivalent pairing during polyploid meiosis simplifies and improves subsequent genetic analyses. (this thesis)
2. Classifying polyploids as either autopolyploid or allopolyploid is both inappropriate and imprecise. (this thesis)
3. The environmental credentials of electric cars are more grey than green.
4. ‘Gene drive’ technologies display once again that humans act more like ecosystem terrorists than ecosystem managers.
5. Heritability is a concept that promises much but delivers little.
6. Awarding patents to cultivars or crop traits is patently wrong.
7. The term “air miles” should refer to one’s lifetime allowance of fossil- fuelled air travel.
8. The Netherlands’ most effective educational tool comes on two wheels with a bell.
Propositions belonging to the thesis, entitled
“Genetic mapping in polyploids”
Peter M. Bourke Wageningen, 15th June 2018 Genetic mapping in polyploids
Peter M. Bourke Thesis committee
Promotor Prof. Dr R.G.F. Visser Professor of Plant Breeding Wageningen University & Research
Co-promotors Dr C.A. Maliepaard Associate professor, Plant Breeding Wageningen University & Research
Dr R.E. Voorrips Senior scientist, Plant Breeding Wageningen University & Research
Other members Dr J. Endelman, University of Wisconsin-Madison, USA Prof. Dr M.E. Schranz, Wageningen University & Research Dr J.W. van Ooijen, Kyazma B.V., Wageningen Prof. Dr B.J. Zwaan, Wageningen University & Research
This research was conducted under the auspices of the Graduate School of Experimental Plant Sciences (EPS) Genetic mapping in polyploids
Peter M. Bourke
Thesis submitted in fulfilment of the requirements for the degree of doctor at Wageningen University by the authority of the Rector Magnificus, Prof. Dr A.P.J. Mol, in the presence of the Thesis Committee appointed by the Academic Board to be defended in public on Friday 15 June 2018 at 11 a.m. in the Aula. Peter M. Bourke Genetic mapping in polyploids, 306 pages.
PhD thesis, Wageningen University, Wageningen, the Netherlands (2018) With references, with summary in English
ISBN 978-94-6343-846-9 DOI 10.18174/444415 Table of contents
Chapter 1 General Introduction 7 Chapter 2 Tools for genetic studies in experimental populations of polyploids 27 Chapter 3 The double reduction landscape in tetraploid potato as revealed by a high-density linkage map 53 Chapter 4 Integrating haplotype-specific linkage maps in tetraploid species using SNP markers 77 Chapter 5 Partial preferential chromosome pairing is genotype dependent in tetraploid rose 109 Chapter 6 polymapR - linkage analysis and genetic map construction
from F1 populations of outcrossing polyploids 137 Chapter 7 An ultra-dense integrated linkage map for hexaploid chrysanthemum enables multi-allelic QTL analysis 153 Chapter 8 Quantifying the power and precision of QTL analysis in autopolyploids under bivalent and multivalent genetic models 177 Chapter 9 Multi-environment QTL analysis of plant and flower morphological traits in tetraploid rose 209 Chapter 10 polyqtlR – an R package to analyse quantitative trait loci in autopolyploid populations 233 Chapter 11 General Discussion 255
References 277 Summary 297
Acknowledgements 299 About the author 302 List of publications 303 Education certificate 304
Chapter 1
General Introduction
7 ______General introduction
Molecular markers and Mendel’s missing caveat
It is only relatively recently that the terms “marker” and “molecular marker” have been taken to be synonymous. In his pioneering experiments with peas, Mendel was already studying the transmission and inheritance of a now-famous set of genetic “markers” (Mendel, 1866), with the physical expression of seven different traits (what we term “phenotypes”) being the marker set itself. It took almost fifty years before it was realised that these morphological markers also represented specific locations on chromosomes which were either transmitted together (due to genetic linkage) or independently (due to lack of linkage) (Morgan, 1911). Curiously, Mendel had selected only unlinked traits for his study of peas (whether this was by accident or by design we do not know). His second law, the law of independent assortment, states that alleles of one gene sort into gametes independently of the alleles of another gene. However, because chromosomes and their connection to inheritance had not yet been discovered, Mendel missed one vital caveat to this law, namely that independence only occurs if such genes are located on separate chromosomes (or perhaps at opposite ends of a single long chromosome). Most of what follows in this thesis is based on this non-independent segregation of linked loci. One of the major milestones in genetics was the realisation that a collection of linked markers could be arranged in a linear fashion, with distances between their positions estimated from the counts of co-inherited markers (Sturtevant, 1913). In his demonstration of this fact using six linked morphological markers of the common fruit fly Drosophila melanogaster, Sturtevant created the world’s first genetic linkage map (Sturtevant, 1913;Van Ooijen and Jansen, 2013).
Nowadays, we generally rely on DNA markers (a.k.a. molecular markers) to identify positions on chromosomes. In this thesis we exclusively present data on single nucleotide polymorphism (SNP) markers. These are nucleotide positions which generally differ in the individuals being screened and are usually selected to be “bi-allelic” (i.e. alternating between two possible nucleotides in the material under study). However, the methods we develop are general to any bi-allelic marker system for which marker “dosage” counts can be accurately estimated. The term “dosage” is less commonly used in diploid studies, but is a very important concept in genetic analyses of polyploids. Dosage is generally understood to be the number of copies of the alternative allele carried by an individual at a particular locus. An illustration of the possible marker dosage scores in a tetraploid and hexaploid are shown in Figure 1.
8 ______Chapter 1
Linkage mapping and QTL analysis – part I
The principal aim of this thesis is the development and exploration of methods and tools to create linkage maps and perform quantitative trait locus (QTL) analysis in polyploids. Both of these activities combined can conveniently be termed “genetic mapping” as the title of this thesis suggests. These are not new activities – as already mentioned, the first linkage map was constructed in 1913, and the first QTL analysis was arguably conducted a decade later (Sax, 1923). The novelty of this work lies in its application to polyploids, a group of organisms that possess much more complex genomes than their diploid counterparts, and in its use of modern genotyping data which often consists of many tens of thousands of markers. a. 0 1 2
3 4
b. 0 1 2 3
4 5 6
Figure 1. Representation of the possible marker dosage scores, for a. Tetraploid (ploidy = 4) and b. Hexaploid (ploidy = 6). In general, there are ploidy + 1 possible dosage classes at a bi- allelic marker position, here shown in blue / red. The convention for assigning dosage scores is to count the number of copies of the alternative allele (coloured red), with the reference allele count (in blue) given by ploidy – dosage.
Modern plant and animal breeding has benefitted from the use of molecular markers, allowing specific traits of interest to be predicted without having to necessarily grow a plant to maturity and test the trait directly. This can have many advantages, for example by allowing a greater number of traits to be more cost-effectively combined, allowing selection among multiple progenies, or in material for which phenotyping is difficult
9 ______General introduction or expensive etc. At least, that is the intention of marker-assisted selection (MAS). In practice, MAS has met with mixed success in plant breeding programs (Collard and Mackill, 2008;Hospital, 2009). In the autotetraploid crop potato (Solanum tuberosum L.), markers have been demonstrated to be useful for certain disease resistances (e.g. potato cyst nematode (Schultz et al., 2012)) and have been shown to be a cost-effective proposition if deployed appropriately in a breeding program (Slater et al., 2013). However, in order to use markers effectively, we need to develop models to capture the relationship between a plant’s genotype and its phenotype. For polyploids, modelling these relationships is still relatively new and is fraught with added complications not encountered in diploids. Polyploid inheritance patterns are by nature more complex than diploids. Furthermore, many polyploids are outcrossing species that resist the genetic simplification achieved through inbreeding. We will first examine some of the challenges that polyploids pose to the molecular geneticist, and in particular the idiosyncrasies of polyploid meiosis, before returning to the topic of linkage mapping and QTL analysis.
Polyploidy
A polyploid is any organism that carries more than two copies of each chromosome, from the Greek “poly-” meaning much or many, and “–ploid” from “ploos”, meaning fold, thus “many-fold”. Polyploidy was discovered more than a century ago (Strasburger, 1910) and since then has been a topic of continued interest and debate. Diploidy, the state of possessing two copies of each chromosome, is considered the chromosomal “ground state” or norm for complex organisms. In diploids, parents transmit a single copy of each chromosome to each gamete, thereby re-establishing diploidy in the offspring. In polyploid organisms, more than one copy of each chromosome is transmitted, which is one of the main contributing factors to the complexity of polyploid genetics. There is a tendency for polyploid lineages to return to a diploid conformation over evolutionary timescales, a process termed “diploidisation” or “re-diploidisation” (Ohno, 1970;Le Comber et al., 2010). In the timescales of interest to breeders and researchers however, polyploidy is effectively a permanent condition. Although the definition of polyploidy is quite unequivocal, there can be some confusion over the classification of a species as polyploid or not, particularly as many complex life-forms were polyploid at some point in the past (Van de Peer et al., 2017). “Paleopolyploids” are species that were true polyploids millions of years ago but have since re-diploidised, and the term “neopolyploids” refers to newly- formed polyploids (Ramsey and Schemske, 2002;Lloyd and Bomblies, 2016), possibly artificially generated for research purposes to understand how polyploids deal with the
10 ______Chapter 1 initial “genomic shock” of having an extra genome (McClintock, 1984). Neopolyploidy may also refer to recently-formed wild polyploid populations such as Spartina anglica, an allopolyploid that arose when Spartina alterniflora was introduced outside its native range and hybridised with local Spartina species (Soltis and Soltis, 2009). Some authors further distinguish “mesopolyploids” as re-diploidised species that underwent whole- genome duplication (WGD) at a less ancient timescale than paleopolyploids and which can be detected by genetic or cytogenetic analyses (Mandáková et al., 2010;Franzke et al., 2011). In this thesis we are principally concerned with extant polyploid species that have not re-diploidised, yet have already passed the (presumed bumpy) early generations i.e. they are no longer considered neopolyploid.
Among polyploids, two distinct types are generally recognised – autopolyploids and allopolyploids. These terms can distinguish or emphasise two features, namely the origin of the polyploid (also termed the “taxonomic” definition), or how its chromosomes behave during meiosis (the “genetic” definition) (Ramsey and Schemske, 2002;Doyle and Egan, 2010). Autopolyploids are generally-speaking derived from a single species and exhibit polysomic inheritance. Polysomic inheritance means that all possible combinations of alleles are equally likely to end up in a gamete – although we will return to this question in more detail in the next section as it is one of the fundamental points of interest in this thesis. Allopolyploids on the other hand are derived from at least two species and exhibit disomic inheritance (where disomic means diploid-like inheritance, the result of exclusive pairing and recombination between homologous chromosomes and an absence of pairing and recombination between homoeologous chromosomes). Although also important, they are not the focus of study here. It should be noted that classifying a species as either autopolyploid or allopolyploid is not always straightforward, as demonstrated for example in the debate about the correct classification of the polyploid ancestor of soybean (Glycine spp.) (Barker et al., 2016;Doyle and Sherman‐Broyles, 2016). In other words, the taxonomic and genetic definitions do not always neatly overlap, particularly in species with a long history of inter-specific hybridisation among progenitor species of varying relatedness. A large body of polyploid research is aimed at understanding how different polyploid lineages arose, and how these newly-wed genomes adapted and evolved to accommodate each other and their changing environment.
There is a third category of polyploid, namely the “segmental allopolyploid” as it was originally termed (Stebbins, 1947). Again this category can be defined from a taxonomic perspective or a genetic perspective – as a hybridisation between two very closely-related species or subspecies, or as a polyploid which demonstrates a meiotic
11 ______General introduction pairing behaviour that cannot be classified as fully disomic or fully polysomic (recently termed “mixosomic” (Soltis et al., 2016)). Throughout this thesis we rely on the genetic definition, as it is the pairing behaviour that influences how homologues recombine, upon which our methods to study inheritance are ultimately based. Although it is interesting to speculate upon how or why such differences arose, in the end we are primarily interested in understanding what happens, as this is the most solid ground upon which to build a model.
Polyploidy occurs in animals, plants and fungi, with the ancestors of all angiosperms and vertebrates thought to have experienced at least two whole-genome duplications (Putnam et al., 2008;Jiao et al., 2011). In the plant kingdom there are numerous examples of extant polyploids. There are fewer known examples of polyploid animals, which some suggest is due to difficulties in re-establishing a balance in chromosomal sex-determination systems following genome duplication (Muller, 1925;Orr, 1990). However examples do exist, particularly in amphibians and fish (but much less so in other vertebrates) (Mable et al., 2011). Amphibious examples include the Bluespotted- Jefferson salamander complex (Uzzell, 1964), the grey tree-frog Hyla versicolor (Ptacek et al., 1994), the American ground frog Odontophrynus americanus (Beçak et al., 1966) and the African clawed frog Xenopus laevis (Session et al., 2016). Among fish, it is now well-established that a whole genome duplication (WGD) occurred in the ancestor of all salmonids (e.g. salmon, trout etc.) between 50 and 100 million years ago (Allendorf et al., 2015). Polyploidy is also sometimes artificially induced in animals, for example in Pacific oysters (Crassostreae gigas) (Benabdelmouna and Ledu, 2015) or the silkmoth (Bombyx mori L.) (Rasmussen and Holm, 1979). There continues to be debate about whether any polyploid mammals exist, with the initial claim that the Argentinian red vizcacha rat (Tympanoctomys barrerae) is tetraploid (Gallardo et al., 1999) being more recently challenged in light of new data (Svartman et al., 2005;Evans et al., 2017).
Polyploidy occurs widely among plant species, with recent advances in whole-genome sequencing allowing a detailed analysis of recent and ancient polyploidisation events in an increasingly large number of plant lineages (Vanneste et al., 2014;Van de Peer et al., 2017). In natural populations of plants there is always a small possibility of a new polyploid species arising (usually although not exclusively through unreduced (2n) gametes (Harlan and De Wet, 1975)). In the case of autotetraploids, one possible path for their establishment is through the initial formation of a triploid bridge (from a fusion of n + 2n gametes) (Ramsey and Schemske, 1998;Schinkel et al., 2017). These triploids, although generally infertile, may also produce 2n gametes and hence through
12 ______Chapter 1 selfing or pollination by 2n gametes from diploids, tetraploids may be formed (Ramsey and Schemske, 1998;Comai, 2005). Note that for a new polyploid lineage to establish and diversify, an even-numbered ploidy is required. An exception to this is when plants exclusively reproduce vegetatively or apomictically, thereby avoiding the disruptions that odd-numbered ploidies pose to balanced meiotic division. However such lineages would be expected to evolve more slowly than sexually-reproducing ones (McDonald et al., 2016). The fusion of unreduced pollen with an unreduced egg cell, both from diploid parents, is also theoretically possible (“one-step” tetraploids (Ramsey and Schemske, 1998)). Induced polyploidy (man-made) can also occur through somatic chromosome doubling, although its status as a means to polyploid formation in natural populations is uncertain (Harlan and De Wet, 1975). An interesting alternative pathway that has only recently been explored is the possibility of polyspermy, where more than one sperm cell fertilises an ovule (Dresselhaus and Johnson, 2018). Interestingly, stressed plants are found to produce more unreduced gametes (such stresses may relate to environmental variables like extreme temperatures, wounding, drought or nutrient deficiency (Ramsey and Schemske, 1998)). Unreduced gametes are thought to arise as a result of defective spindle fibres or cell-plate formation, both of which have been shown to regularly occur at extreme (particularly higher) temperatures (Pécrix et al., 2011;De Storme and Geelen, 2014;Bomblies et al., 2015)).
In most cases, neopolyploid plants are usually at an immediate disadvantage, being un- adapted and reproductively isolated (what is termed “minority cytotype disadvantage” (Levin, 1975;Husband, 2000)). The speed at which newly-established polyploid lineages prosper and diversify varies, with indications that there may be a significant time lag before this occurs (Schranz et al., 2012). One of the fascinating hypotheses that has emerged is the possibility that a disproportionately-high number of WGDs occurred close to the Cretaceous-Paleogene boundary (around 66 million years ago) (Van de Peer et al., 2017). Non-avian dinosaurs are thought to have disappeared around the same time, along with 60-70% of all plant and animal life, coinciding with a number catastrophic phenomena including perturbations in the global climate, increased volcano activity and the impact of a large meteor near Chicxulub, Mexico (Renne et al., 2013). Clearly this was a difficult time to be alive on planet Earth. Nevertheless, in times of severe environmental stress the increased genomic plasticity of polyploids (te Beest et al., 2011) coupled with their propensity to vegetatively propagate (Herben et al., 2017), as well as reduced competition from severely-stressed or dying diploids may have contributed to their success.
13 ______General introduction
Polyploids are particularly common among domesticated crops (Salman-Minkov et al., 2016), a fact that has helped drive interest to better understand these species. In many cases polyploidy is deliberately induced – for example modern ornamental breeding often relies on inter-specific hybrids to create novel varieties, which are often “polyploidised” (through colchicine treatment for mitotic polyploidisation, or through selection of 2n gametes) to overcome sterility in the F1 (Van Tuyl and Lim, 2003). Fruit breeders also generate seedless fruit by crossing parents of different ploidy levels, resulting in sterile fruit-bearing (usually triploid) offspring (Bradshaw, 2016). Many of the native attributes of polyploids may also have endeared them to the early agriculturalists, e.g. larger organs (tubers, fruits, flowersetc. ), also known as the “gigas” effect (Sattler et al., 2016), or their ability to be clonally propagated. We therefore find ourselves in the position of relying on some of the most genetically-complex species to provide us with the basic necessities for life. Examples of some globally-important polyploid crops include allopolyploids such as wheat (Triticum aestivum L.), cotton (Gossypium hirsutum L.), coffee (Coffea arabica L.), oilseed rape (Brassica napus L.), oats (Avena sativa L.), peanut (Arachis hypogaea L.), strawberry (Fragaria × ananassa L.) and autopolyploids such as potato (Solanum tuberosum L.), alfalfa (Medicago sativa L.), sweetpotato (Ipomoea batatas L.), leek (Allium ampeloprasum L.), blueberry (Vaccinium corymbosum L.), chrysanthemum (Chrysanthemum spp.) and rose (Rosa × hybrida L.). Despite their importance, polyploids, and in particular autopolyploids, remain an understudied and poorly-understood group. One may attribute this to their genetic complexity and the fact that few software tools are developed to analyse autopolyploid data (noting that due to the diploid-like inheritance of allopolyploids it is possible to use many of the diploid software tools for those crops). It is also only relatively recently that datasets containing sufficient marker numbers to allow investigations into their genetic properties have become available. In this thesis we aim to tackle this deficit by developing tools and methods to analyse autopolyploid genotype and phenotype data. Although the methods we develop are general, we have so far only applied them to plant datasets. Before going into more detail on how this was done, we first need to understand the process of meiosis.
Meiosis
The topic of meiosis in polyploids is central to this thesis. Indeed, one of our primary interests in markers is that they provide a detailed picture of meiosis when deployed over a population of related individuals. The inheritance information from the population allows us not only to organise these markers into ordered clusters representing chromosomes,
14 ______Chapter 1 but also to track the pairing and recombination that occurred in each parental meiosis that gave rise to a particular offspring individual. Meiosis can be defined as “two successive nuclear divisions that produce gametes carrying one half of the genetic material of the original cell” (Griffiths et al., 2012). In plants and fungi as opposed to animals, the direct product of meiosis is technically not a gamete, but rather a spore which gives rise to a gametophyte which later produces the gamete cells. However, from the perspective of inheritance, all the interesting phenomena occur during meiosis, and not in any later intermediate (mitotic) cell divisions which carry the haploid chromosomes towards their final destiny as gametes. Therefore, in this thesis the term “gamete” is often loosely used to denote the products of meiosis, when “spore” would have been more appropriate in plant-specific contexts.
Meiosis in polyploids
In describing polyploid meiosis, one can either choose to give a very detailed picture or to sketch the most important features and hope that in so doing the audience are still following. In this thesis we try to take the middle road, avoiding unnecessary terminology or technical detail where possible. Apart from lucidity, we are also only interested in meiosis from a practical perspective – it is simply a process that we model in order for us to make sense of marker data. We leverage this data to come to a better understanding of the chromosomal composition of our experimental organisms (in the fullest sense – from gene order and position to gene function and effect). One clear example of our (over) simplification is the use of the term “pairing” in meiosis. In the early stages of meiosis I (leptotene) homologues pair up – they physically align. This is followed by the formation of synaptonemal complexes during zygotene. However, in cases where this pairing is aberrant (e.g. between homoeologues) any synaptonemal complexes that may have formed are dissolved or corrected in late zygotene and pachytene, and only bivalents between homologues persist into metaphase I. In this thesis we avoid terms such as leptotene, zygotene and pachytene, and use “pairing” to describe the conformation of (recombining) homologues (or homoeologues even) that have persisted into metaphase I. If this pairing behaviour is not random but preferentially occurs between certain homologues, we call this behaviour “preferential pairing”, which is one of the main distinguishing characteristics of a segmental allopolyploid. However technically-speaking it would be better to talk about “preferential crossover formation” instead (Lloyd and Bomblies, 2016). In fact, the literature on the subject of preferential pairing appears to be written by two groups – those who are comfortable with terms like
15 ______General introduction
“leptotene” and those who are not.
Interphase I
Prophase I
Metaphase I
bivalents multivalent
Anaphase I
Figure 2. Simplified scheme of the early stages of polyploid meiosis, in this case foran autotetraploid. By the beginning of Metaphase I, pairs of sister chromatids will have associated and come to lie on the equatorial plane, either in bivalent or multivalent pairing structures.
From a simplified perspective, therefore, there are a number of aspects that are relevant for this thesis. The first concerns the early stages of meiosis which lead to the formation of different types of pairing structures (Figure 2). As already mentioned, the precise details of Prophase I are beyond the scope of this introduction, but the interested reader is directed to any number of excellent reviews on the subject of meiosis in general (Harrison et al., 2010;Da Ines et al., 2014;Hunter, 2015;Mercier et al., 2015;Zickler and Kleckner, 2015), and in particular those that look specifically at polyploid meiosis (Cifuentes et al., 2010;Zielinski and Scheid, 2012;Grandont et al., 2013;Moore, 2013;Lloyd and Bomblies, 2016).
At the onset of meiosis each homologous chromosome condenses and is replicated into pairs of sister chromatids (shown in Figure 2, Prophase I). These are held together by cohesion complexes that persist into the later stages of meiosis (Hunter, 2015). These pairs of sister chromatids then associate either as pairs, in which case they are described
16 ______Chapter 1 as bivalents, or in groups of three or more, described as multivalents (Figure 2, Metaphase I). It is now known that in order for meiosis to proceed in an orderly fashion, there must be formation of chiasma leading to at least one cross-over per chromosome (the number of cross-overs per chromosome tends to also have an upper bound, with rarely more than three observed) (Mercier et al., 2015) which occur through the formation and subsequent repair of double-strand breaks in the DNA (Henderson and Keeney, 2004). The most commonly-observed multivalents involve four homologues (also called a quadrivalent), with on average 27% of all pairing structures found to be quadrivalents in a meta- analysis of autopolyploid meiosis (Ramsey and Schemske, 2002). By contrast, only 2% of trivalent structures were observed. Uneven numbers of pairing homologues are more likely to lead to aneuploid gametes (carrying an unbalanced number of chromosomes) which rarely survive. Multivalents are more likely to be observed in autopolyploids than allopolyploids (because in the latter case there are barriers to pairing and recombination between homoeologues), but even in allopolyploids they may occur (Ramsey and Schemske, 2002).
Double reduction
It has long been suggested that multivalents are aberrant pairing structures that can often lead to aneuploidy and reduced fertility (Darlington, 1937;Kostoff, 1940;Hazarika and Rees, 1967;Lloyd and Bomblies, 2016), but this view likely stems from a bias towards neopolyploids which have been shown to produce abnormally-high numbers of multivalents in early generations, stabilising to lower frequencies in later generations (Ramsey and Schemske, 1998;2002;Santos et al., 2003;Bomblies et al., 2016). There are numerous reports of multivalents being formed in a wide range of established autopolyploids, without necessarily negatively impacting on fertility (Swaminathan and Howard, 1953;Morrison and Rajhathy, 1960;Jones and Vincent, 1994;Khawaja et al., 1997;Ramsey and Schemske, 2002). As this thesis is concerned with stable, established autopolyploids, we are primarily interested in the genetic consequences of multivalents and in particular the phenomenon of double reduction (Figure 3). Double reduction has been known about for almost a century and theories of how it should be modelled have been considered by some of the early pioneers of statistical genetics (Haldane, 1930;Mather, 1935;Fisher, 1947). It is quite common nowadays for authors to assert that double reduction is required for a complete and accurate description of autopolyploid inheritance (and by extension, that it be ignored at great peril) (Luo et al., 2004;Wu et al., 2004;Wu and Ma, 2005;Li et al., 2010;Lu et al., 2012;Xu et al., 2013). On the other
17 ______General introduction
1 2 3
6 5 4
7 8 9
Figure 3. Steps leading to double reduction in an autotetraploid. 1. During late Prophase I, pairs of sister chromatids associate. Multivalents involving four pairs of sister chromatids are also called quadrivalents, as shown. 2. For quadrivalents to be maintained from Prophase I into Metaphase I, cross-overs need to form between at least three of the four pairing partners. Here, four cross-overs are shown between all partners, leading to a ring-quadrivalent. 3. Resolved double-strand breaks leading to cross-overs, as seen in late Metaphase I. 4. During Anaphase I,
18 ______Chapter 1 spindle fibres originating from the centrosomes attach to the centromeres. 5. For proper chromosomal segregation, two of the four pairing homologues must migrate to each pole. This mechanism appears to be unregulated in neopolyploids but established polyploids often exhibit correct segregation leading to no abnormalities. For double reduction to occur, a homologue and its pairing recombination partner must migrate to the same pole, a situation that is impossible with only bivalent pairing. 6. Following interkinesis (which includes Telophase I with the division of the cell in two, and Prophase II which is rather uneventful) pairs of sister chromatids carrying recombinant homologues come to lie again at the equatorial plane in Metaphase II. 7. Anaphase II subsequently follows, with spindle fibres again attaching to the centromeres. At this stage, cohesion complexes that held chromatids together are dissolved. 8. In late Anaphase II, cell division again occurs. 9. Based on how sister homologues segregate, it is possible for gametes (spores) carrying two identical copies of part of a homologue to occur. In this example, the upper two gametes carry double reduction products (e.g. homozygous blue section), whereas the lower two gametes do not. hand, a number of recent reviews of allo- and autopolyploid meiosis completely fail to mention it (Bomblies et al., 2016;Lloyd and Bomblies, 2016). In this thesis double reduction is not ignored, but in many cases we do omit it from our models. However, we take particular care that if so doing, we do not introduce unnecessary bias. Preferential pairing
One other aspect of polyploid meiosis that requires our attention is the phenomenon of “preferential pairing” (or as pointed out already, perhaps more accurately termed “preferential crossover formation” (Lloyd and Bomblies, 2016)). Allopolyploids consist of both homologues (closely related chromosomes presumed to have derived from the same species) and homoeologues (less closely-related chromosomes, presumed to be from distinct species). During meiosis, homologues are found to pair and recombine whereas homoeologues are not. This is often under the direct control of specific genes or loci, such as the Ph1 locus in wheat (Triticum aestivum L.) (Okamoto, 1957;Riley and Chapman, 1958) or the PrBn locus in oilseed rape (Brassica napus L.) (Jenczewski et al., 2003;Nicolas et al., 2009). In such instances we refer to “fully preferential pairing” between homologues, leading to disomic inheritance. In autopolyploids on the other hand there is an equal chance of pairing and recombination between all homologues during meiosis, leading to polysomic inheritance. However, these states represent the two extremes of a supposed continuum between random and non-random pairing, with the term “segmental allopolyploid” (Stebbins, 1947) used to gather together everything in between (including the possibility of certain chromosomes behaving disomically and others polysomically). Examples where a mixture of disomic and polysomic inheritance have been observed are rainbow trout (Oncorhynchus mykiss) (Allendorf and Danzmann, 1997), peanut (Arachis hypogaea L.) (Leal-Bertioli et al., 2015;Nguepjop et al., 2016),
19 ______General introduction
Figure 4. Gametes of two hypothetical tetraploid parents (displaying homologues of a single chromosome). In the maternal meiosis (left), the red and violet-coloured homologues (and the yellow and blue homologues) pair and recombine more often than would be expected by chance. Almost all gametes sampled carry red/violet and yellow/blue homologue mosaics, with far fewer red/yellow & violet/blue or red/blue & violet/yellow combinations. In this case, we say there is preferential pairing between red and violet homologues (and also yellow and blue homologues – one pairing implies the other). In the paternal meiosis (right), no such preference exists leading to balanced numbers of gametes from each of the three possible (bivalent) pairing combinations. sugarcane (Saccharum officinarum × S. spontaneum) (Jannoo et al., 2004) and birdsfoot trefoil (Lotus corniculatus L.) (Fjellstrom et al., 2001). In these cases it is not always clear whether we are dealing with an autopolyploid that is gradually becoming re- diploidised, or an allopolyploid from two very closely-related species (Soltis et al., 2016). Diagnosing the mode of inheritance in polyploids (disomic / polysomic / mixosomic) is a challenging endeavour, but the task has been made considerably easier by the use of
20 ______Chapter 1 markers. By following the inheritance of specific types of markers in a population, it is possible to detect whether there are statistically significant deviations from the expected proportions of marker alleles. These can be tested against an initial hypothesis of disomy or polysomy, usually informed by a study of the existing literature on the subject. Suppose we cross two heterozygous tetraploid plants and consider the segregation of markers in the resulting F1. It is possible for us to uncover the parental origin of each of the homologues inherited in the population, and in this way reconstruct the parental gametes that contributed to each offspring (Figure 4). This gives us even greater clarity regarding the parental meiosis as we are in a position to map all the recombination events (and therefore also know between which pairing partners they occurred).
Linkage mapping and QTL analysis – part II
We return to the topic of linkage maps and QTL analyses now that some of the more important eccentricities surrounding autopolyploids have been laid bare. At its core, the process of linkage mapping in polyploids is analogous to that of a diploid (Figure 5.a). The first step is to genotype a set of related individuals, either using a pre-defined set of markers or by sequencing the individuals directly and determining the marker set subsequently. Based on the co-segregation of markers in the population, the markers can be clustered together into linkage groups (ideally corresponding to chromosomes), ordered within these linkage groups and spaced according to the genetic distances between them (Figure 5.a).
However, polyploid linkage mapping, and in particular autopolyploid linkage mapping, adds a further level of complexity by distinguishing between homologue linkage groups and chromosomal linkage groups. The terminology often used to describe the process of classifying a marker across homologues is phasing, that is determining whether the segregating marker alleles are on the same homologue (for which we say markers are linked in coupling phase) or whether they reside on different homologues of the same chromosome (for this we say they are linked in repulsion phase). Phase considerations in diploids are trivial if inbred parents are used; an exception is when parents are out- breeding (so-called cross-pollinating or CP populations (Van Ooijen, 2006)), for which linkage phase must also be carefully considered (Maliepaard et al., 1997). The first main challenge of polyploid linkage mapping therefore is to assign a marker not just to a linkage group and a position, but to determine precisely how its alleles are distributed across the parental genomes in relation to all the other markers (Figure 5.b). The second
21 ______General introduction
a.
b. 0
20
40 cM 60
80
100
h1 h2 h3 h4 h5 h6 h7 h8 h9 h10 h11 h12 Figure 5. Linkage mapping in polyploid species. a. Principal stages in linkage map construction. Firstly, genotype (marker) data is generated for a population. These markers are clustered into groups (this can be at the level of both chromosome and homologue, not shown here). Markers are subsequently ordering within these clusters. In the final step, map positions are assigned to the markers, usually on a centiMorgan scale. Markers may be lost in the clustering stage due to lack of linkage, possibly due to poor data quality. Some markers may also map to the same position, as indicated by the side branches in the right-hand figure.b. Example of an integrated autohexaploid linkage map (centre), with phasing of the markers on the maternal homologues h1 – h6 in red, and paternal homologues h7 – h12 in blue. Marker positions in centiMorgans (cM) are shown on the y-axis. challenge is how to best order the markers. In this thesis we do not tackle marker ordering but rely on the work of others and in particular, we apply a recent algorithm that applies multi-dimensional scaling to efficiently solve the problem (Preedy and Hackett, 2016). As with diploid CP populations, recombination frequency estimates can be of varying precision based on the informativeness of a particular marker combination (Maliepaard et al., 1997). This non-constant variance is reflected in variable LOD scores, resulting
22 ______Chapter 1 in the need for a marker ordering algorithm that performs weighted optimisation (Stam, 1993;Preedy and Hackett, 2016).
Once a linkage map has been created it is possible to test for associations between genetic positions on the parental homologues and phenotypic traits of interest. Similar to the central challenge of linkage mapping, one of the main challenges in polyploid QTL analysis is to correctly predict the parental origin of QTL alleles (Figure 6). In the case of a QTL with a single allele of positive effect, this can usually be achieved by single- marker approaches (given sufficient marker coverage in the QTL region). However, in situations where QTL are influenced by multiple allelic variants at the same locus it may not be possible to track all positive alleles using single-marker approaches. Instead,
- + + +
Figure 6. Locating and phasing QTL in an autotetraploid. As with diploids, a logarithm of odds (LOD) profile gives an indication of the strength of association between a genetic position and a particular trait. Significant associations are usually taken as those that exceed a certain threshold, shown here as a dashed red line. QTL positions are often displayed beside a link- age map with various support intervals (e.g. a LOD-1 and LOD-2 support interval) using soft- ware such as MapChart (Voorrips, 2002). However, in a polyploid we are also interested in the configuration of a QTL. In this example, two alleles with positive (+) effect originated from parent 2, and both a positive and negative (-) allele originated from parent 1. In this way, off- spring carrying optimal combinations of alleles, potentially at multiple loci, can be identified.
23 ______General introduction
QTL methods that move away from single marker information to instead use multi-locus identity-by-descent (IBD) probabilities (Hackett et al., 2013;Zheng et al., 2016) may provide additional diagnostic power (Kempthorne, 1957;Hackett et al., 2014).
The polyploid revolution
Up until relatively recently, breeding in polyploid crops has relied completely on phenotypic selection. For simple traits this may well have been sufficient, but the effectiveness of phenotypic selection for complex traits like yield is questionable (Jansky, 2009). There is increased interest among polyploid breeders in the use of molecular and genomic tools to assist with their breeding programs. The reasons why this has not so far happened were technological, methodological and financial. The technology to be able to efficiently and cheaply dissect polyploid genomes in detail is only now becoming available. The methodology to interpret this data and the software tools to run these analyses (such as described in this thesis) are following suit. We therefore stand at the dawn of a revolution in polyploid genomics and breeding, brought about by a favourable combination of these three factors.
Layout of this thesis
The central aim of this thesis is to develop and test methods to perform genetic mapping in polyploid populations. This can constitute a significant computational challenge, given the complexity and sheer size of modern genotyping datasets. We begin therefore with a review of the available software tools for the genetic analysis of polyploids in Chapter 2. This chapter explores the current options for assigning marker dosages and assembling haplotypes, performing linkage mapping and QTL analyses, genome-wide association studies and genomic selection, as well as looking at the availability of physical maps and tools for simulating polyploid populations.
The rest of the thesis can be broken down into two main subjects – linkage mapping and QTL analysis, with linkage mapping methods developed in the first half of the thesis, and QTL mapping in the second half. However, we also are interested in understanding the meiotic behaviour of polyploids (which linkage mapping can help to clarify). In Chapter 3 we generate homologue-specific linkage maps in an autotetraploid potato population and use them to investigate the frequency of double reduction events across the population. A denser set of linkage maps, consisting of all marker segregation types,
24 ______Chapter 1 is integrated in Chapter 4 using information from bridging markers (markers with alleles which reside on multiple homologues). We also perform a simulation study to test the effects of double reduction and partial preferential chromosome pairing on the accuracy of recombination frequency estimates upon which our maps are based.
In Chapter 5 we go one step further by developing a high-density SNP map for a tetraploid rose population. We perform an in-depth exploration of the meiotic pairing and recombination behaviour and in the process, develop a method to correct for mixosomic inheritance in the creation of autotetraploid linkage maps. These initial chapters culminate in Chapter 6, where we present a new software package for the creation of integrated and phased linkage maps in polyploid species, called polymapR.
In Chapter 7, we apply our mapping methodology to a large population of the popular autohexaploid cut-flowerChrysanthemum × morifolium. The integrated linkage map and marker phase information is used to detect QTL for a number of flower-related traits. Chapter 8 explores the power of QTL mapping methods in autopolyploids, comparing models which allow for double reduction with those that do not. In Chapter 9, these methods are used to perform a QTL analysis in tetraploid rose, exploring the genetic architecture of a number of economically-important physiological traits measured across multiple growing environments. In Chapter 10, we present polyqtlR, a novel software package for performing QTL analyses in autopolyploid populations, building on the work of the previous chapters. Finally, the thesis is rounded off with a discussion in Chapter 11 on how the findings presented in this thesis can contribute to improvements in polyploid breeding as well deepening our understanding of these fascinating species.
25
Chapter 2
Tools for genetic studies in experimental populations of polyploids
Peter M. Bourke1, Roeland E. Voorrips1, Richard G. F. Visser1, Chris Maliepaard1
1 Plant Breeding, Wageningen University & Research, Droevendaalsesteeg 1, 6708 PB Wageningen, The Netherlands.
Published (with modifications) as Bourke, P.M., Voorrips, R.E., Visser, R.G.F. and Maliepaard, C. (2018). “Tools for genetic studies in experimental populations of polyploids”, Frontiers in Plant Science, 9:513. doi: 10.3389/fpls.2018.00513
27 ______Polyploid genetic tools
Abstract olyploid organisms carry more t an t o copies of eac c romosome, a condition rarely tolerated in animals ut ic occurs relati ely fre uently in t e plant ingdom. ne of t e principal c allenges faced y polyploid organisms is to e ol e sta le meiotic mec anisms to fait fully transmit genetic information to t e next generation upon ic t e study of in eritance is ased. n t is re ie e loo at t e tools a aila le to t e researc community to etter understand polyploid in eritance, many of ic a e only recently een de eloped. Most of t ese tools are intended for experimental populations (rat er t an natural populations), facilitating genomics assisted crop impro ement and plant reeding. T is is ardly surprising gi en t at a large proportion of domesticated plant species are polyploid. T e current polyploid analytic tool ox includes soft are for assigning mar er genotypes (and in particular, estimating t e dosage of mar er alleles in t e etero ygous condition), esta lis ing c romosome scale lin age p ase among mar er alleles, constructing (s ort range) aplotypes, generating lin age maps, performing genome ide association studies ( ) and uantitati e trait locus ( T ) analyses, and simulating polyploid populations. T ese tools can also elp elucidate t e mode of in eritance (disomic, polysomic or a mixture of ot as in segmental allopolyploids) or re eal et er dou le reduction and multi alent c romosomal pairing occur. n increasing num er of polyploids (or associated diploids) are eing se uenced, leading to pu licly a aila le reference genome assem lies. Muc or remains in order to eep pace it de elopments in genomic tec nologies. o e er, suc tec nologies also offer t e promise of understanding polyploid genomes at a le el ic it erto as remained elusi e.
Key words
olyploid genetics, polyploid soft are tools, autopolyploid, allopolyploid, segmental allopolyploid
28 ______Chapter 2
Introduction ne of t e most fundamental descriptions of any organism is its ploidy le el and c romosome num er, generally ritten in t e form 2n 2x 10 ( ere, for t e u i uitous model plant species Arabidopsis thaliana .). lant scientists in particular ill e familiar it t is representation of t e c romosomal constitution of t e sporop yte generation (i.e. t e adult plant). T e second term in t is seemingly simple e uation descri es t e normal complement of c romosomal copies possessed y a mem er of t at species, which is generally 2x (“two times”) for diploids. Species where this number exceeds t o are collecti ely referred to as polyploids. ot unexpectedly, eac polyploid indi idual is t e product of t e fusion of gametes from t o parents, ust li e t eir diploid counterparts. n ot er ords, polyploids can also e defined as indi iduals deri ed from non aploid gametes (in t e case of triploids deri ed from diploid tetraploid crosses, only one gamete satisfies t is condition). T e transmission of non aploid gametes is one of the main “complexifying” features of polyploidy, leading to a whole range of implications for the genetic analysis of these “hopeful monsters” ( oldsc midt, 1 ).
T e ongoing genomics re olution can e seen as a rising tide ic as also lifted t e polyploid genetics oat, alt oug not uite to t e same le el as for diploids. Most genetic ad ances are made in model organisms, among ic self fertilising diploid species predominate. t is t erefore not surprising t at most tools and tec ni ues for molecular genetic studies are specific to diploids. o e er, polyploid species are particularly important to man ind in t e pro ision of food, fuel, feed and fi re (not to mention “flowers”, if ornamental plant species are also included), ma ing t e genetic analysis of polyploid species an important a enue of researc for crop impro ement.
Although a collective term such as “polyploidy” has its uses, it tends to obscure some fundamental differences et een its mem ers. or example, polyploids are generally su di ided into autopolyploids and allopolyploids ( i ara and no, 1 2 ). utopolyploids arise t roug genomic duplication it in a single species, generally t roug t e production of unreduced gametes ( arlan and e et, 1 ) and ex i it polysomic in eritance, meaning pairing and recom ination can occur et een all omologous copies of eac c romosome during meiosis. ne of t e most ell studied examples is autotetraploid potato (Solanum tuberosum .). llopolyploids, on t e ot er and, are t e product of genomic duplication et een species (usually t roug y ridisation in ol ing unreduced gametes ( arlan and e et, 1 )) and display disomic in eritance, ere more related chromosome copies (“homologues”) may pair and recom ine during meiosis, ilst less related c romosome copies (“homoeologues”, also spelled “homeologues” ( lo er et al., 201 )) do not. mong allopolyploids, allo exaploid eat (Triticum aestivum .) is pro a ly t e most ell
29 ______Polyploid genetic tools studied. f pairing and recombination between homoeologues occurs to a limited extent, the species may be referred to as “segmental allopolyploid” (Stebbins, ), traditionally deemed to have arisen from hybridisation between very closely related species (Stebbins, hester et al., 2 2) but which may also be the result of partially diploidised autopolyploidy (Soltis et al., 2 ). n many cases, a species cannot be clearly designated as one type or another, leading to uncertainty or debate on the sub ect ( ar er et al., 2 oyle and Sherman royles, 2 ). rom the perspective of genetics and inheritance, allopolyploids behave much li e diploid species and therefore ‐ many of the tools developed for diploids can be directly applied. he main challenge that faces allopolyploid geneticists is in distinguishing between homoeologous gene copies carried by sub genomes within an individual ( aur et al., 2 2 van i et al., 2 2 othfels et al., 2 ). Autopolyploids (and segmental allopolyploids) do not behave li e diploids, and are therefore in most need of specialised methods and tools for subse uent genetic studies. n this review we focus primarily on the availability of tools and resources amenable to polysomic (and “mixosomic” (Soltis et al., 2 )) species, with less emphasis on allopolyploid specific solutions. Although the development of novel methodologies for the genetic analysis of polyploids are interesting, without translation into a software tool for use by the research community they remain purely conceptual and with limited impact. e therefore try to limit our attention to the tools currently available rather than cataloguing descriptions of unimplemented methods.
Experimental populations, in use since Mendel’s ground brea ing wor ( endel, ), are traditionally derived from a controlled cross between two parental lines of interest
(either directly studying the or some later generation). e use the term here to distinguish our subject matter from “wild” or “natural” populations, which would necessitate sampling individuals from an extant population in the wild. uantitative genetics, particularly the genetics of human pathology, has greatly benefitted from the use of large panels of individuals to perform so called “genome wide association studies” (GWAS). The use of such panels offers to complement the experimental toolbox of polyploid geneticists as well, and although perhaps not strictly spea ing an “experimental” population, we consider them relevant to the current discussion.
ere, we review the current possibilities for polyploid genotyping, including the scoring of mar er dosage (allele counts) and generation of haplotypes, the availability of reference se uences, the possibilities for lin age mapping, uantitative trait locus ( ) analysis and AS, as well as tools to simulate polyploid organisms for in silico studies. e also reflect on current and future developments, and the tools that will be needed to eep pace with the innovations we are witnessing in genomic technologies.
30 ______Chapter 2
Polyploid genotyping ne of the most crucial aspects in the study of polyploid genetics is the generation of accurate genotypic data. owever it is also fraught with difficulties, not least the detection of multiple loci when only a single locus is targeted (Mason, imborg et al., ). arious technologies exist, with almost all current applications aimed at identifying single nucleotide polymorphisms (SNPs). Although many genomic “service providers” (e.g. companies or institutes that offer A se uencing) have their own tools to analyse and interpret raw data, these tools are not always suitable for use with polyploid datasets.
Genotyping technologies Although gel based mar er technologies continue to be used and have certain advantages (e.g. low costs associated with small mar er numbers, re uiring only basic laboratory facilities, multi allelism etc.), most studies now rely on S mar ers for genotyping due to their great abundance over the genome, their high throughput capacity and their low cost per data point. Targeted genotyping such as SNP arrays (a.k.a. “SNP chips”) rely on previously identified and selected polymorphisms, usually identified from a panel of individuals chosen to represent the gene pool under investigation. n contrast, untargeted genotyping generally uses direct se uencing of individuals, albeit after some procedure to reduce the amount of A to be se uenced (e.g. by exome se uencing ( g et al., ) or target enrichment (Mamanova et al., )). The disadvantages of targeted approaches have been well explored (particularly regarding ascertainment bias, where the set of targeted S s on an array poorly represents the diversity in the samples under investigation due to biased methods of S discovery) (Albrechtsen et al., Moragues et al., idion et al., achance and Tish off, ), although there are advantages and disadvantages to both methods (Mason et al., ). Apart from costs, differences exist in the ease of data analysis following genotyping, with se uencing data re uiring greater curation and bioinformatics s ills (Spindel et al., ajgain et al., ) as well as potentially containing more erroneous and missing data (Spindel et al., ones et al., ). n polyploids, S arrays have been developed in numerous species, which include both autopolyploid (or predominantly polysomic polyploids) and allopolyploid species. Examples of the former include alfalfa ( i et al., b), chrysanthemum (van Geest et al., c), potato ( amilton et al., elcher et al., os et al., ), rose ( oning oucoiran et al., ) and sour cherry ( eace et al., ). Examples of allopolyploid S arrays include cotton ( ulse emp et al., ), oat (Tin er et al., ), oilseed rape ( alton Morgan et al., lar e et al., ), peanut ( andey et al., ), strawberry ( assil et al., ) and wheat (A hunov et al., avanagh et al., Wang et al., b Winfield et
31 ______Polyploid genetic tools al. ). ntargeted approaches such as genotyping y se uencing have also een applied or e ample in autopolyploids such as al al a ( hang et al. u et al. ) lue erry ( c allum et al. ) luestem prairie grass (Andropogon gerardii) ( cAllister and iller ) cocks oot (Dactylis glomerata) ( ushman et al. ) potato ( itde illigen et al. Sverrisd ttir et al. ) sugarcane ( alsalo re et al. ang et al. ) and s eet potato (Shirasa a et al. ) and in allopolyploids such as co ee ( oncada et al. ) cotton ( slam et al. eddy et al. ) intermediate heatgrass (Thinopyrum intermedium) ( antarski et al. ) oat ( ha in et al. ) prairie cordgrass (Spartina pectinata) ( ra ord et al. ), shepherd’s purse (Capsella bursa-pastoris) ( ornille et al. ) heat (Poland et al. dae et al. ) and oysiagrass (Zoysia japonica) ( c amy et al. ) (noting that the precise classi ication o some o these species as auto or allopolyploids has yet to e conclusively determined). hatever the technology used it is clear that e are currently itnessing an e plosion o interest in polyploid genomics. o ever the critical issue o ho to make sense o this data remains starting ith the assignment o marker dosage a.k.a. “genotype calling”.
Assignment of dosage ne o the key distinguishing eatures o polysomic polyploidy is the act that there are multiple hetero ygous conditions possi le in genotyping data. e use the term marker “dosage” to denote the minor allele count of a marker; a species of ploidy q possesses q distinct dosage classes in the range to q ( igure ). course the concept o marker dosage could also e used in diploid species ut coding systems such as the lm ll nn np hk hk system ( an oi en ) predominate. arker dosage is generally understood to apply to i allelic markers (such as single SNPs) although it is conceiva le to score marker dosage at multi allelic loci. marker dosage cannot e accurately assessed genotypes ould likely have to e dominantly scored (i.e. all hetero ygous classes ould e grouped ith one o the homo ygous classes) resulting in a loss o in ormation (Piepho and och ).
Figure 1. Dosage possibilities in an autotetraploid. n a tetraploid ive distinct dosages are possi le at a i allelic marker positions ranging rom copies o the alternative allele through to copies. ere the alternative allele is coloured red ith the re erence allele coloured lue.
32 ______Chapter 2
ll a aila le dosage calling tools rely on a population in order to determine marker dosage. n other ords, cali ration et een the arious dosage classes is performed across the population for hich e are not implying any degree of relatedness in the population other than coming from the same species . ll current tools are designed to process genotyping data from arrays, in other ords using the relati e strength of t o allele specific fluorescent signals to assign a discrete dosage alue. ith increasing interest in genotyping y se uencing data, e anticipate that tools hich use read counts of potentially multiple s or multi haplotypes ill soon e de eloped, although these ha e yet to appear. ne of the current challenges under in estigation regarding ased genotype calling is the accurate determination of dosage im et al., , hich may re uire relati ely deep se uencing e.g. co erage estimated in autotetraploid potato itde illigen et al., .
eturning to the array ased tools, the t o main ser ice pro iders for high density arrays, llumina and ffymetri , oth offer proprietary soft are solutions for analysing polyploid datasets. Affymetrix’s Power Tools and Illumina’s GenomeStudio ith its olyploid enotyping odule ere de eloped ith oth diploid and polyploid datasets in mind. o e er, there ha e also een a num er of genotyping tools that ha e een put into the pu lic domain. ne of the first of these to e released as fit etra oorrips et al., , a freely a aila le package ore eam, designed to assign genotypes to autotetraploids that were genotyped on either Illumina’s Infinium or Affymetrix’s Axiom arrays. fitTetra fits mixture models to bi allelic intensity ratios either under the constraint of ardy ein erg e uili rium ithin the population, or as an unconstrained fit, using an e pectation ma imisation algorithm in fitting. his can ha e the dra ack of re uiring significant computational resources for high density marker datasets, although it is automated and can therefore process large datasets in a single run. he original release as specific to tetraploid data only. o e er, an updated ersion fit oly can process genotyping data of all ploidy le els and is soon to e made a aila le as a separate package . . oorrips, personal communication . he uper application erang et al., can also process data from all ploidy le els as it as initially de eloped to dosage score sugarcane data, notorious for its cytogenetic comple ity and is currently hosted online y the tatistical enetics a oratory in the ni ersity of o aulo, ra il. ne of the interesting features of uper is that prior kno ledge of the e act ploidy le el is not needed useful for a crop like sugarcane . nstead, the genotype configuration hich ma imises the posterior pro a ility across all specified ploidy le els is chosen. n practice, most researchers ill already kno the ploidy of their samples although aneuploid progeny in some species may occur and can constrain the model search. ma or dra ack of the current implementation is that markers are analysed one y one, and results need to
33 ______Polyploid genetic tools be opied from the webpage ea h time there is urrently no downloadable ersion of the software a ailable . or high density datasets with tens of thousands of mar ers this is learly impra ti al.
The pa age polyseg atio a er et al. generates mar er dosages for dominantly s ored mar ers using the AGS software Plummer for ar o hain onte arlo generation. ully polysomi beha iour is assumed and segregation ratios of mar er data are used to deri e the most li ely parental s ores. Although able to pro ess data from all e en ploidy le els the software only onsiders a subset of mar er types mar er that are nulliplex in one parent or simplex in both parents . owadays there is a mo e away from dominantly s ored mar ers to o dominant mar er te hnologies li e S Ps and parental samples are usually in luded in multiple repli ates and so an be genotyped dire tly with offspring rather than imputed from the offspring . The pa age is therefore of uestionable use for modern genotyping datasets. An unrelated pa age beadarray S Gids ehaug et al. was developed to handle Illumina Infinium SNP array data from “diploidising” tetraploid spe ies su h as the Atlanti salmon. The software was designed to s ore mar ers whi h target multiple lo i so alled multi site ariants or S s as well as single lo us mar ers displaying disomi inheritan e. In a omparison with fitTetra beadarray S was unable to a urately genotype autotetraploid data from potato although on ersely fitTetra performed poorly on salmon data oorrips et al. . This demonstrates that appropriate software is needed for spe ifi situations indeed in many ases spe ifi s enarios ha e moti ated the de elopment of spe ialised software .
a ing prior nowledge about the expe ted meioti beha iour of the spe ies is always ad antageous when it omes to analysing any polyploid data. This is espe ially true for the latest dosage alling software to be released the luster all pa age for S hmit arley et al. . ere prior nowledge of the meioti beha iour of the spe ies is re uired sin e the expe ted segregation ratios of an autotetraploid population are used to assign dosage s ores to the lusters identified through hierar hi al lustering. In well beha ed autotetraploids su h as potato Swaminathan and oward our e et al. this is arguably not a problem as long as s ewed segregation does not o ur and indeed an lead to in reased a ura y in genotype alling S hmit arley et al. . owe er in less well hara terised spe ies su h as lee alfalfa or many ornamental spe ies the pre ise meioti beha iour may not always follow the expe ted tetrasomi model ausing potential problems with fitting. The authors are aware of this and suggest that alternati es li e fitTetra or Super ASSA be used in ir umstan es where a tetrasomi model no longer holds. nfortunately su h prior nowledge is not always a ailable before genotyping ta es pla e – meioti beha iour an e en differ between
34 ______Chapter 2 individuals of a spe ies that as thought to display meioti homogeneity e.g. omplete tetrasomy our e et al
Haplotype assembly lthough i alleli SNP mar ers have many pra ti al advantages they arry less inheritan e information than multi alleli mar ers rop resear hers and reeders often ish to develop a simple diagnosti mar er test for a trait of interest nfortunately the han es of having a single SNP in omplete lin age dise uili rium ith a favoura le or ausative allele of a gene of interest is very small ar ers hi h have een found to uni uely “tag” a favourable allele in one population may not do so in another. For more than a de ade the in reased po er of haplotype ased asso iations have een no n and reported in human geneti studies hang et al de a er et al ith the term “haplotype” denoting a unique stretch of sequence. Translating haplotyping approa hes from diploid to polyploid spe ies has een a non trivial e er ise re uiring novel algorithms to handle the over helming range of possi ilities that an arise espe ially hen allo ing for se uen ing errors and possi le re om inations ulti SNP haplotypes an e assem led from single dosage s ored SNPs originating from SNP array data although haplotypes are more ommonly generated using overlapping se uen e reads igure num er of different polyploid haplotyping tools for se uen e reads have een developed in re ent years in luding poly ap Su et al S lotyper Neigenfind et al ap ompass guiar and Istrail ap ree erger et al S haP as and i alo S sisplus Shen et al and riPoly ota edi et al a hree of these tools ap ompass ap ree and S haP ere re ently ompared and evaluated over a range of different simulated read depths ploidy levels and insert si es for paired end reads ota edi et al he authors found that ea h of these soft are programs had parti ular advantages for e ample ap ree as found to produ e more a urate haplotypes for triploid and tetraploid data hilst ap ompass performed est at higher ploidies and higher ota edi et al oth S sisplus and riPoly have yet to e independently tested or allopolyploid spe ies the user friendly aplotag soft are has een designed to identify oth single SNPs and multi SNP haplotypes from S data in er et al . An interesting feature is the use of a simple “heterozygosity filter” that excludes haplotypes ith higher than e pe ted hetero ygosity a ross a population suggesting paralogous lo i urrently ho ever data from out rossing or autopolyploid spe ies is not suita le for this soft are
he input data of haplotyping soft are an e grouped into t o types Individual SNP genotyping data ith a no n mar er order as used y the first ave of polyploid haplotyping implementations su h as poly ap and S lotyper ore re ently
35 ______Polyploid genetic tools
Figure 2. Generation of multi-SNP haplotypes. a. n this example three possible haplotypes exist spanning polymorphic positions and . b. ingle genotyping cannot distinguish between the “A” allele originating from different haplotypes, combining them into a single allele as illustrated in the second call. c. n a haplotyping approach overlapping reads are used to re assemble and phase single genotypes. ere the no n ploidy level of the species x is used to impute the dosage of the t o haplotypes identified in this individual given a ratio bet een the assembled haplotype read depths. haplotyping tools use sequence reads as their input although some pre processing is required reads must first be aligned follo ed by extraction of their s i.e. mas ing of non polymorphic sites to generate a fragment matrix ith individual reads as ro s and positions as columns as described for ap ompass Aguiar and strail . n other ords all haplotyping tools apart perhaps from aplotag Tin er et al. require that users possess a certain level of bioinformatics s ills. n terms of applications and usage there appears to be some hesitation among the polyploid research community to ta e up these tools Figure perhaps because of the required bioinformatics qualifications. Although e expect polyploid haplotypes to become increasingly used in the future the development of user friendly and computationally efficient tools is first needed before haplotype based genotypes become truly mainstream.
36 ______Chapter 2
ne interesting de elopment is the application of haplotyping to whole genome assemblies as opposed to genotyping a population his has recently been attempted in the tuberous he aploid crop sweet potato Ipomoea batatas ang et al , a he authors first produced a consensus assembly to which reads were re mapped for ariant calling, followed by a phasing algorithm which resol ed the si haplotypes of the se uenced culti ar for about of the assembly ang et al , a ltimately, about half of the assembled genome could be haplotype resol ed uture se uencing or re se uencing efforts in polyploid species should produce more phased genomes, which will no doubt be useful for haplotyping applications for e ample in alidating predicted haplotypes
Figure 3. Cumulative number of Web of Science citations (core collection) by January 1st 2018 for the most popular polyploid haplotyping tools. ear of first citation is highlighted by a star Physical maps Arguably, one of the most important “tools” in current genomics studies is access to a high uality reference genome assembly pecies for which a reference genome assembly exists have even been classified as “model organisms” eeb et al , , such is the importance and impact a genome can bring to research on that species ithout a reference se uence a ailable, the scope of genomic research remains limited or e ample, genome wide association studies rely on nowledge of the relati e position of mar ers usually on a physical map , and many se uencing applications rely on a reference assembly on which to map reads A reference genome also facilitates the de elopment of molecular mar ers e.g. primer de elopment , the comparison of results
37 ______Polyploid genetic tools bet een different genetic studies by providing a single reference map , as ell as allo ing comparisons of specific se uences such as genes, enabling prediction of gene function across related species
olyploid genomes are by definition more complex than diploid genomes, having multiple copies of each homologous chromosome any polyploid species are also outbreeding, leading to increased hetero ygosity hich is problematic in de novo assemblies and necessitates specialised approaches a itani et al , he most common solution until no has been to se uence a representative diploid species or example in highly hetero ygous autotetraploid potato, a completely homo ygous doubled monoploid Solanum tuberosum group Phureja as se uenced otato enome e uencing onsortium, hich still represents the primary reference se uence today http solanaceae plantbiology msu edu n the case of allopolyploids, multiple diploid progenitor species are often se uenced instead e.g. peanut ertioli et al , he emergence of the pan genome concept, originally proposed for microbial species ettelin et al , , has interesting implications for ho highly hetero ygous polyploid genomes ill be presented in future e have already mentioned the arrival of phased genomics ith the s eet potato genome, hich aimed to generate six chromosome length phased assemblies for each of its chromosomes ang et al , a n future, both pan genomes and phased genomes are li ely to play a bigger role in polyploid reference genomics xample of polyploid species that have so far been “sequenced” are listed in Table 1. This is by no means an exhaustive list, nor does it describe all developments for the listed species or example, the se uence of allotetraploid Coffea arabica hich accounts for roughly of all coffee production has recently been assembled, ith a draft assembly Coffea arabica v available on the hyto ome database phyto ome net hat able highlights is that at the time of riting, there ere already a ide range of polyploid crop species that have ell developed genomic resources, despite the fact that in many cases these are from closely related or progenitor diploid species n time, ust li e for coffee, e predict that direct se uencing of polyploid species themselves ill gradually replace the haploidised reference se uences in importance and application, leading to more insights of direct relevance to polyploids Linkage maps Although the first genetic lin age map as developed over a hundred years ago turtevant, , their use in genetic and genomic studies has persisted into the “next generation” era. This can be attributed to a number of factors. A linkage map is a description of the recombination landscape ithin a species, usually from a single experimental cross of interest or breeders, no ledge of genetic distance is arguably
38 ______Chapter 2 more important than physical distance, as it reflects the recombination frequencies in inheritance studies as ell as describing the extent of linkage drag around loci of interest. any soft are for performing quantitative trait locus T analysis require linkage maps of the markers, not physical maps. This is because co inheritance of markers and phenotypes ithin a population are assumed to be coupled – a physical map gives less precise information about the co inheritance of markers than a linkage map does since physical distances do not directly translate to recombination frequencies particularly in the pericentromeric regions . Another reason hy linkage maps continue to be developed is that they are often the first genomic representation of a species, upon hich more advanced representations can be built. They provide useful long range linkage information over the hole chromosome, hich is often missing from assemblies of short sequence reads. This fact has been repeatedly exploited in efforts at connecting and correctly orientating scaffolds during genome assembly pro ects artholom et al., 1 ierst, 1 .
As mentioned in the ntroduction, polyploids can be divided into disomic or polysomic species, ith the additional possibility of a mixture of both inheritance types in the case of segmental allopolyploids. any linkage maps in polyploids have been based exclusively on 1 1 segregating markers, also kno n as simplex markers because the segregating allele is in simplex condition one copy in one of the parents only . These markers possess a number of advantages over other marker segregation types, but also some distinct disadvantages. n their favour, coupling phase simplex markers in polyploid species behave ust like they ould in diploid species, regardless of the mode of inheritance involved repulsion phase recombination frequency estimates are not invariant across ploidy levels or modes of inheritance, but exert less influence on map construction due to lo er scores . The advantage of this is clear in unexplored polyploid species for hich the mode of inheritance is uncertain, simplex markers allo an “assumption free” linkage map to be created, following which the mode of inheritance can be further explored. The only exception to this is if double reduction occurs, i.e. hen a segment of a single chromosome gets transmitted ith its sister chromatid copy to an offspring, a consequence of multivalent pairing and a particular sequence of chromatid segregation and division during meiosis aldane, 1 ather, 1 . ouble reduction occurs randomly in polysomic species and only introduces a small bias into recombination frequency estimates ourke et al., 1 . This means that, ignoring the possible influence of double reduction, diploid mapping soft are can generally be used for simplex marker sets at any ploidy level and for any type of meiotic pairing behaviour igure , opening up a very ide range of diploid specific soft are options heema and icks, .
39 ______genetic tools Polyploid 40
Table 1. Some examples of currently-available reference sequences for polyploid species. AUTOPOLYPLOIDS Target species Sequenced species (ploidy) Genome browser References lfalfa, Medicago truncatula medicagogenome org plants ensembl org oung et al , Medicago sativa ang et al , iwifruit, Actinidia chinensis bdg hfut edu cn kir uang et al , Actinidia chinensis bioinfo bti cornell edu cgi bin kiwi home cgi otato, Solanum tuberosum solanaceae plantbiolog msu edu otato enome e uencing Solanum tuberosum plants ensembl org onsortium, weet potato, Ipomoea batatus public genomes ang et al , a Ipomoea batatus ngs molgen mpg de weet otato ipomoea genome org ALLOPOLYPLOIDS anana, Musa acuminata banana genome hub southgreen fr (D’Hont et al., 2012) Musa acuminata plants ensembl org offee, Coffea canephora coffee genome org enoeud et al , Coffea arabica otton, Gossypium arboretum cottongen org i et al , a Gossypium hirsutum Gossypium raimondii ang et al , ilseed rape, Brassica napus genoscope cns fr brassicanapus halhoub et al , Brassica napus plants ensembl org eanut, Arachis duranensis peanutbase org ertioli et al , Arachis hypogaea Arachis ipaensis uinoa, Chenopodium quinoa cbrc kaust edu sa chenopodiumdb ar is et al , Chenopodium quinoa trawberr , Fragaria vesca rosaceae org hulae et al , Fragaria ananassa heat, Triticum aestivum wheat urgi ersailles inra fr nternational heat enome Triticum aestivum plants ensembl org e uencing onsortium, ______Chapter 2
Ho e e , le a e et a e o e l tat on . tl , n ele t n onl le a e , a la e o o t on o a e t e ent e e at on atte n a e not e . all e e t e a o e a e ( le n ea n t e e a e o t o t e nal et o a e a e ). o e o tantl , le a e e l te n o at on a o t l n a e n e l on a e, a t la l at e lo le el ( an ee t et al., 201 a). ean t at o olo e e a an e o e , t t e a e nl el
Figure 4. Simplex markers. e e a e a a n le o o t e e e at n a e allele an n e t la l a o all lo le el an a n e a o , allo n lo a n o t a e to e e . He e, t e ( le ) allele olo e e . to e ell nte ate et een o olo e n a n le a ent, an o le to nte ate a o a ent . n ot e o , t e o o o al n e n ll o t l el e n on tent et een a ental a onl le a e a e e . o n a on en o ll nte ate a e a le o an ea on , n l n e n a le to ete t an o el o e o le on at on t an t le . e e o e, a t l ol lo l n a e a n tool o l e a le to n l e all a e e e at on t e , not t 1 1 e e at n a e .
Polyploid linkage mapping software n a e a n an e o en nto t ee te – l n a e anal , a e l te n an a e o e n . e e a e t ll elat el e o t a e tool t at an e o all t ee o t e e te o ol o e e . e a t e o t ell no n an el e o t a e tool et a lo a o n o (Ha ett an o, 200 Ha ett et al., 200 ). ell a o n l n a e a o a totet a lo e e , t o t a e al o
41 ______Polyploid genetic tools
i.e.
42 ______Chapter 2
Figure 5. Theoretical rate of decrease in heterozygosity in polyploid species from repeated rounds of inbreeding / selfing, using expressions derived by Haldane (1930).
43 ______Polyploid genetic tools
r r –
44 ______Chapter 2
e.g.
Genome-wide association studies –
Polyploid GWAS
45 ______Polyploid genetic tools
i.e. K K K K
Arabidopsis thaliana Arabidopsis were estimated, using a ‘hide SNP’ simulation for Arabidopsis versus a ‘rule of thumb’ calculation for potato, but mainly from the difference in the extent of LD between A. thaliana S. tuberosum
46 ______Chapter 2 polyploids, which would complement the design of future S studies in polyploid species QTL analysis The term “QTL analysis” usually refers to studies that aim to detect regions of the genome so called uantitative trait loci eldermann, that have a significant statistical association with a trait in specifically constructed experimental populations These populations are most often created by crossing two contrasting parental lines (“bi parental” populations), although there is increasing interest in using more complex population designs in order to increase the range of alleles and genetic bac grounds being studied e.g. “MAGIC” populations uang et al , s already discussed, there is great difficulty in developing inbred lines by repeatedly selfing polyploids due to the sampling of alleles during polyploid gamete formation in a diploid this sampling generates combinations for a tetraploid this rises to and in a hexaploid 2 4 (combinations,) = 2 resulting in protracted hetero ygosity( ) = igure 6 , not to 1 2 6 mention( ) = 20 the problem of inbreeding depression associated with many outcrossing polyploid3 species herefore, most L analyses in polyploid species have been performed using the directly segregating progeny of a cross between hetero ygous parents (a “full sib” population). This leads to poor resolution of QTL positions when compared to the more popular diploid inbred populations li e Ls etc., as well as the fact that populations must be vegetatively propagated if replication over years or different growing environments is desired or many polyploid species, vegetative propagation is indeed possible erben et al , and populations have the added advantage of being relatively uic and simple to develop, while, because of a generally high level of hetero ygosity, many loci will be segregating in the herefore despite their drawbac s, populations remain the bi parental population of choice for mapping studies
he methods for L analysis in diploid species have become increasingly convoluted van euwi et al , in polyploid species such theoretical complexities have yet to be attempted, given the more immediate difficulties in accurately genotyping as well as modelling polyploid inheritance ust li e for lin age mapping and S, the range of software tools available for L analysis in polyploids remains rather limited, although there are a number of recent developments that are helping transform the field
ne of the only dedicated software for tetraploid L analysis is the already mentioned etraploid ap software ac ett et al , his software enables interval mapping to be performed in autotetraploid populations as well as a simple single mar er
47 ______Polyploid genetic tools
A A test), using a restricted range of mar ers ( , and mar ers only, where denotes a mar er dosage of in one parent and in the other, etc.). Although still a ailable, it has been superseded by the Tetraploid Map software ( ac ett et al., ). Tetraploid Map (T M) uses dosage data to either construct a lin age map (as already described) or perform QTL inter al mapping. In contrast to its predecessor, T M can analyse all mar er segregation types, and allows the user to e plore different QTL models at detected pea s. At its core is an algorithm to determine identity by descent (I ) probabilities for the offspring of the population, which are then used in a weighted regression performed across the genome.
An independent software tool that has been de eloped to determine I probabilities in tetraploids is Tetra rigin ( heng et al., ), implemented in the Mathematica programming language. Tetra rigin rela es the assumption of random bi alent pairing during meiosis (which T M employs) to allow for both preferential chromosomal pairing as well as multi alent formation and the possibility of double reduction. Although not programmed in a user friendly format li e T M, it is relati ely straightforward to use, ta ing an integrated lin age map and mar er dosage matri as input. It does not perform QTL analysis directly, but the resulting I probabilities can then be used to model genotype effects in a QTL scan either using a weighted regression approach li e T M, or in a linear mi ed model setting. I probabilities allow inter al mapping since they can be interpolated at any desired inter als on the lin age map.
or ploidy le els other than tetraploid, there are currently no dedicated software tools a ailable for QTL analysis or I probability estimation. ingle mar er approaches such as A A on the mar er dosages (assuming additi ity – arious dominant models could also be e plored see e.g. ( osyara et al., )) are of course possible and re uire access to basic statistical software pac ages such as (or e en cel). owe er, such approaches are not ideal – they are only effecti e if mar er alleles are closely lin ed in coupling with QTL alleles, and offer no ability to predict the QTL segregation type or mode of gene action as is done for e ample in T M ( ac ett et al., ). As interest increases in the genetic dissection of important traits in polyploid species, we anticipate that it is only a matter of time before more fle ible cross ploidy solutions are de eloped. Methodologies developed for tetraploid species often claim that “extension to higher ploidy levels is straightforward”. These sorts of disingenuous claims attempt to mark new research territory as already sol ed. If e tensions to higher ploidy le els were indeed straightforward we would already be reporting on a wider range of tools a ailable for them – as far as we can tell, so far there are none.
48 ______Chapter 2
eturning to the topic of population types we also anticipate that more powerful T analyses can e performed y com ining information over multiple populations. pproaches such as pedigree informed analyses implemented for diploids in the lex T software ink et al. could overcome some of the limitations imposed y the restrictions on population types in software for polyploids. owever it may take some time efore such tools ecome translated to the polyploid level.
Genomic prediction and genomic selection There has een much attention given to the advantages of using all marker data to help predict phenotypic performance rather than focusing on single markers or haplotypes that are linked to T as was previously advocated. The motivation ehind this is clear – many of the most important traits in domesticated animal and plant species are highly uantitative with far too many small effect loci present to e a le to tag them all with single markers ernardo . ne of the most important traits in any reeding program is also a famously uantitative trait yield. t has een suggested that despite many years of phenotypic selection crop yield in tetraploid potato has essentially remained unchanged ansky later et al. . This is a remarka le indictment of traditional selection methods yet offers much needed impetus for the development and deployment of new paradigms in reeding for uantitative traits.
enomic prediction first arose in animal reeding circles Meuwissen et al. where the concept of estimating reeding values from known pedigrees was already well esta lished. owever the estimation of reeding values in polyploid species re uires special consideration due to the complexity of polysomic inheritance and the possi ility of dou le reduction. n practice reeding values are usually estimated using restricted maximum likelihood M to solve mixed model e uations re uiring the generation of an inverse additive relationship matrix A-1 also called the numerator relationship matrix. The form of A-1 depends on among other things whether the inheritance is polysomic or disomic and whether dou le reduction occurs err et al. amilton and err . ecently the package poly inv was released which computes the appropriate A-1 as well as the kinship matrix K and the in reeding coefficients F amilton and err . owever in one study of nine common traits in autotetraploid potato the inclusion of dou le reduction or even the adoption of an autotetraploid appropriate relationship matrix was found to have a minimal impact on the results later et al. . tudies which ignore the specific complexities of autopolyploids may still enefit from genomic prediction and selection as for example was demonstrated in tetraploid potato verrisd ttir et al. . ommonly used
49 ______Polyploid genetic tools
Mode of inheritance The term “mode of inheritance” refers to the randomness of meiotic pairing processes Some “traditional” approaches to predict the mode of inheritance are summarised in
50 ______Chapter 2 and rruda or in ornamentals such as Alstroemeria uitendi et al hich ma es the diagnosis of the mode of inheritance e en more difficult s more pol ploid species egin to e genot ped the issue of un no n mode of inheritance ill li el e ert more influence further necessitating the de elopment of soft are tools that can pro ide an accurate assessment of the inheritance mode using mar er data and that can accommodate the full spectrum of pol ploid meiotic eha iours
Simulation software s ith an soft are tool de eloping standards and scenarios upon hich the performance of the tool can e udged is ital to ensure relia le results n this final section e consider the range of simulation tools currentl a aila le for pol ploids ro a l the most idel used pol ploid simulation soft are currentl a aila le is edigreeSim oorrips and aliepaard riginall de eloped to generate diploid and tetraploid populations the current release edigreeSim can simulate populations of an e en ploid le el hat ma es edigreeSim particularl attracti e is its a ilit to simulate a di ersit of meiotic pairing conditions including uadri alents hich can result in dou le reduction or preferential chromosome pairing t ta es four input files hich are relati el simple to generate that pro ide a description of the desired simulation parameters and the input mar er data The soft are then creates dosage scored genot pe data for an pedigreed population e.g. an population of specified si e oorrips and aliepaard Some authors ha e used edigreeSim to simulate multiple generations of random mating allo ing an in estigation of population structure and lin age dise uili rium in pol ploid species e.g. os ara et al os et al hich can e implemented uite easil ith some asic programming no ledge edigreeSim is ritten in a a and can run on all ma or operating s stems indo s ased soft are ol lin hich originall performed t o point lin age anal sis and simulation of tetraploid populations e et al is no longer a aila le The pac age pol Segratio a er simulates dominantl scored mar er data in autopol ploids of an e en ploid le el enerating the dosage data is straightfor ard onl the e pected proportion of mar er t pes simple duple triple as ell as the ploid is re uired o e er the mar ers are essentiall completel random ith no connection to an lin age map hich is argua l of limited use for an application that re uires some degree of lin age et een mar ers The simulation capacities of pol seg atio therefore appear to e most useful for testing functions ithin the pac age itself namel those designed to impute parental dosages gi en the o ser ed segregation ratios in offspring scores
51 ______Polyploid genetic tools
final pol ploid simulation tool that has recentl een de eloped is the aploSim pipeline hich includes the aplo enerator function ota edi et al aplo enerator is designed to generate se uence ased haplot pes in a pol ploid of an e en ploid ta ing the fasta file it is pro ided ith as a reference from hich haplot pes are uilt The soft are generates random S mutations at a specified distri ution efore simulating ne t generation se uencing S reads in formats corresponding to a num er of current se uencing technologies such as llumina or acific ios stems ac io The pipeline as originall de eloped to compare the performance of a num er of haplot pe assem l algorithms ota edi et al ut could also e useful for testing the performance of an other tool hich uses S reads as genot pes
Future perspectives n this re ie e ha e attempted to descri e the most important soft are tools that are currentl a aila le to the pol ploid genetics communit There are li el to e tools that ere missed and tools that ha e su se uentl een released – this is the danger of such a re ie o e er e ha e tried here possi le to also discuss the gaps that are apparent in the current set of a aila le tools hich ill hopefull help guide their de elopment in future ol ploid genot ping argua l remains the most critical step as ithout accurate genot pe data there is little point in uilding models for pol ploid inheritance o e er e are no itnessing the slo emergence of tools that ta e pol ploid genot pes and use them to ma e inferences on the transmission of alleles and the effects of such alleles in pol ploid populations s genot ping technologies continue to e ol e so too should the suite of tools de eloped to anal se those genot pes Tools for anal sing S dosage data from S arra s are ell esta lished ith e tensions of current tools to higher ploid le els planned i.e. fit ol The coming decade ill li el see a mo e a a from S arra ased genot ping to the use of se uence read ased genot pes although this ill re uire that all tools heretofore de eloped e updated to accommodate the ne t pe of data nformation on the mode of inheritance from mar er data is also needed for each population studied hich deser es more attention than it currentl recei es mo e from diploid ased reference genomes to full pol ploid and haplot pe resol ed reference genomes ould also help roaden the oundaries of pol ploid genetics a a from the diplo centric ie of genomics hich currentl dominates lthough there ha e een man e citing disco eries and de elopments in pol ploid genetics in the past decade or more e feel its golden age has et to arri e an age hich ill e heralded all the sooner the pro ision of ro ust and user friendl tools for the genetic dissection of these fascinating group of organisms
52 Chapter 3
The double reduction landscape in tetraploid potato as revealed by a high- density linkage map
Peter M. Bourke1, Roeland E. Voorrips1, Richard G. F. Visser1, Chris Maliepaard1
1 Plant Breeding, Wageningen University & Research, Droevendaalsesteeg 1, 6708 PB Wageningen, The Netherlands.
Published as Bourke, P. M., Voorrips, R. E., Visser, R. G. F. and Maliepaard, C. (2015). “The Double Reduction Landscape in Tetraploid Potato as Revealed by a High-Density Linkage Map”, Genetics 201 (3), 853-863 and reproduced here with permission of the Genetics Society of America
53 ______Double reduction landscape
Abstract T , T , Solanum tuberosum , T ,
Key words , , , ,
54 ______Chapter 3
Introduction , T T , T T , ,
Solanum tuberosum , , , , , , , , , , , , , , , , ,
T , , , , , T , ,
55 ______Double reduction landscape
, , ,
, , , , , , Materials and Methods
Plant material tetraploid potato varieties, cultivars ‘Altus’ (hereafter referred to as parent one, P1) and ‘Colomba’ (P2).
DNA extraction and genotyping ’s instructions (Thermo Scientific). The concentration of DNA was T , – T T , , , , T
56 ______Chapter 3 manufacturer’s protocol at ServiceXS, Leiden, the Netherlands. Each parent was genotyped in duplicate using two iological replicates. other tetraploid accessions were sampled in a similar fashion, as well as diploid accessions for use in another study as well as helping marker dosage fitting .
Assignment of dosages he X and allele signal intensities were imported from the llumina data output into the programming environment ore eam, . SNPs were initially filtered so that the average of their total signal intensity the sum of the X and allele signal intensities over all samples was greater than . . he marker intensities were converted into allele dosages using the fit etra package for oorrips et al., . hanges to the default settings of the saveMarkerModels function of fit etra were as follows p.threshold was decreased from . to . , peak.threshold was increased from . to . and sd.target was set to . , where p.threshold is the “minimum P value re uired to assign a genotype to a sample”, peak.threshold is the “maximum allowed fraction of the scored samples that are in one peak” and sd.target is used to specify the maximum non penalised standard deviation of the fit on a transformed scale oorrips et al., . ll diploid and tetraploid samples were included in the fitting ecause this generally results in a etter fit of the dosage classes. ollowing fitting with fit etra, the marker dosage scores were screened to ensure consistency etween parental and offspring genotypes. arkers with up to invalid scores scores that were not expected ased on the parental genotypes and ivalent chromosome pairing were allowed. high fre uency of many invalid scores suggests that either the marker performed poorly, there was some consistent error in dosage assignment, or one or oth of the parents had een incorrectly genotyped. ighly skewed markers p . were also removed at this stage.
Table 1. Breakdown of SNP marker numbers after quality filtering
Steps in SNP filtering #SNPs % SolS nfinium array total SNPs . osages assigned y fit etra a . oth parents ok . pattern accepta le .
monomorphic .
polymorphic . a arkers not scored were either monomorphic or not clearly resolved riteria for lack of fit presence of null alleles, invalid scores, highly skewed segregation P .
57 ______Double reduction landscape
Marker conversion arkers that segregated in a fashion were re la elled as simplex x nulliplex or nulliplex x simplex for mapping and dou le reduction analysis. onsidering markers whose segregating allele is inherited from P , these consisted of triplex x nulliplex, triplex x uadruplex and simplex x uadruplex markers. or example, a triplex x nulliplex marker is expected to produce 50% dosage ‘1’ and 50% dosage ‘2’ among the offspring, with o servable double reduction scores appearing as dosage ‘0’ (a double copy of the ‘0’ allele from P1). Re labelling ‘2’ as ‘0’ and ‘0’ as ‘2’ (with the parents re la elled as simplex and nulliplex achieves the desired result of marker conversion.
Table 2. Tetraploid marker segregation types by number Parental dosage Segregation #SNP a Simplex x nulliplex SxN Nulliplex x simplex uplex x nulliplex xN Nulliplex x duplex Simplex x simplex SxS Simplex x triplex Sx uplex x simplex xS Simplex x duplex Sx uplex x duplex x 7214 a Num er of SNP markers after simplifying marker conversions have een performed. Linkage map construction Simplex x nulliplex marker data were recoded to oin ap . cross pollinator format lm x ll . ‘Impossible’ genotypes (invalid scores) were made missing before importation into oin ap. ne pair of identical individuals was identified in the dataset similarity of . , therefore we removed individual . arkers were assigned to linkage groups with a minimum L of a higher L was used if clusters roke into large su clusters at a higher L . arker clusters were assigned to physical chromosomes ased on the position of markers on the physical se uence Potato enome Se uencing onsortium, . apping was first performed using the groupings from the roupings ree using maximum likelihood L . omologues were then identified y large gaps in the estimated map distances (≥ 60 cM), which was also often accompanied y a transition in estimated marker phase. arker data for separate homologues was exported from oin ap in .loc files and re imported for creation of the homologue maps. fter an initial mapping of the homologues, individual was found to contri ute unrealistic num ers of recom inations in many linkage groups across oth parents and
58 ______Chapter 3 was therefore removed resulting in a final mapping population of 2 5 individuals. apping was performed using with three rounds of map optimi ation using the default settings for spatial sampling thresholds. Haldane’s mapping function was used to convert recombination fre uency estimates to map distances as has previously been used for linkage map construction in tetraploid potato ( eyer et al. 1 ackett et al. 201 ). In a number of cases we used linkage information from the duplex x nulliplex and simplex x simplex markers to connect sub homologue linkage groups that had poor internal linkage among simplex x nulliplex markers. ap data was exported from oin ap as text files and imported into ap hart 2. ( oorrips 2002) for further plotting.
Comparison of genetic and physical maps he genetic positions of markers were compared with their physical positions as defined in ( os et al. 2015). It was found that some markers did not map to the same chromosome as expected from the physical map a list of such markers is included in upplementary table 1. he physical position of the centromere boundaries was initially adopted from previously published values ( harma et al. 201 ). hese were not found to coincide precisely with the points of inflection on the genetic physical map following which the approximate centromere bounds were re defined by examination of the aligned genetic physical plots (also referred to as arey aps ( hakravarti 1 1)) and calculating an approximate physical position between marker pairs flanking the points of inflection on these plots. he order of the genetic map was reversed in cases where the genetic maps were found to be inversely ordered with respect to the physical map.
Conversion rate of physical to genetic distance he conversion rate between genetic and physical distance was determined by regressing the genetic positions on their physical positions per homologue arm. he slopes of the regression lines for each homologue arm were tested for e uality in an analysis of covariance by introducing where necessary up to three dummy variables (to code for the presence or absence of a homologue) per chromosome arm per parent ( ndrade and st ve P re 201 ). n average genome wide estimation of the genetic to physical conversion rate was calculated after excluding a single outlying value from the northern arm of homologue 2 of chromosome 1 in parent 1. his genome wide recombination rate was used to convert the physical map to a pseudo integrated genetic map for use in the simulation studies.
Rates of double reduction fter recoding the 1 1 segregating marker data duplex marker scores in the offspring were taken as possible evidence for double reduction. uplex scores can also arise as a
59 ______Double reduction landscape result of genot ping errors. herefore we used a relati el strict criterion to decide if such scores were e idence of dou le reduction a string of three consecuti e duple scored mar ers on a homologue map was re uired in order to e considered strong enough e idence for dou le reduction. his could theoreticall lead to some under estimation of the rates of dou le reduction ut the simple mar er densit was sufficient that in most cases a dou le reduction region would contain at least three segregating simple nulliple mar ers.
routine was written in to identif strings of three or more duple scores. he rate of dou le reduction was determined for each mar er counting the num er of times it formed part of a dou le reduction segment and di iding this the num er of non missing alues scored for that mar er across the population. e then deri ed the a erage rate of dou le reduction per homologue for windows north and south of the centromeric ounds calculating the mean rate of dou le reduction o er all mar ers within that window. hese means were aggregated to gi e a single a erage rate of dou le reduction per homologue for each window distance from the centromeres across all chromosomes and oth parents. he a erage rate per chromosome was estimated multipl ing the homologue rates a factor of four.
Simulation of double reduction and prediction of quadrivalent formation An approximate “integrated” genetic linkage map was produced using the average cM to con ersion rate and ph sical positions of the simple mar ers. nl mar ers for which the assigned lin age group and ph sical chromosome corresponded were considered. ar er phase was determined according to the homologue assignment of all mar ers. hased mar er genot pes and a consensus genetic map position are the asic input for the simulation software edigree im oorrips and aliepaard which simulates diploid or pol ploid populations with specified le els of multi alents and or preferential pairing. ne thousand separate populations of indi iduals were generated using the same simple mar er data and appro imated map under a range of different fractions of uadri alents. he algorithm for estimating dou le reduction was applied to the simulated datasets allowing us to deduce the relationship etween the rate of dou le reduction and the fre uenc of multi alents underl ing meiosis.
Estimation of the rate of preferential pairing epulsion phase simple mar er data can e used to in estigate whether preferential pairing occurs as the estimates for recom ination fre uenc in repulsion are e pected to differ under disomic and tetrasomic inheritance u and Hancoc . e ha e adapted the approach of u and Hancoc to correct for multiple testing using
60 ______Chapter 3 the alse discover rate en amini and och erg con ining our anal sis to within chromosomes to reduce the overall num er o tests coupling or repulsion linkage have no meaning when marker pairs rom separate linkage groups are considered
or two markers A and B we de ine as the num er o individuals with dosage at oth markers as the num er o individuals with dosage at marker A and dosage 𝑛𝑛00 at marker B and so on he explicit M estimator or the recom ination re uenc r in 𝑛𝑛01 coupling phase under oth disomic and tetrasomic inheritance is invariant whereas in repulsion phase the M estimator under disomic 𝑛𝑛01+𝑛𝑛10 inheritance𝑛𝑛00+𝑛𝑛01+𝑛𝑛10 +𝑛𝑛is 11 and under tetrasomic inheritance 𝑛𝑛00+𝑛𝑛11 𝑟𝑟𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 =the𝑛𝑛00 mode+𝑛𝑛01+𝑛𝑛 o 10 inheritance+𝑛𝑛11 is tetrasomic should never𝑟𝑟𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 all= 2(𝑛𝑛00+𝑛𝑛11)−(𝑛𝑛01+𝑛𝑛10) elow𝑛𝑛00+𝑛𝑛 the01+𝑛𝑛 value10+𝑛𝑛 11o whereas in the case o disomic inheritance 𝑟𝑟𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 his orms the asis o an exact inomial test with and 𝑟𝑟𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 ∈ [0,0.5) orrection or multiple testing was per ormed using the procedure with α 𝐻𝐻0: 𝑟𝑟𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 1/3 𝐻𝐻1: 𝑟𝑟𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 < 1/3 as descri ed in en amini and och erg
Simulation of mapping under different rates of quadrivalent formation and preferential pairing ne o the h potheses we wanted to test was whether ivalent ormation predominates in tetraploid potato as is commonl assumed e also wanted to see the e ect that deviations rom this assumption could have on recom ination re uenc estimates that are ased on a ivalent model n this stud we limited our ocus to segregating markers e used edigree im to simulate new mapping populations o individuals with the raction uadrivalents var ing rom ero to one in increments o or each setting one thousand simulated populations were generated he simulated genome had a single chromosome o cM with simplex x nulliplex markers randoml distri uted at positions no closer than cM apart and the centromere at cM he true and estimated recom ination re uencies etween the irst marker and the other markers on the chromosome were recorded as well as the and assigned phase (“coupling” or “repulsion”). Recombination frequencies between marker pairs were estimated using M or which explicit estimators can e derived in the case o simplex marker pairs c.f. previous section hase was determined choosing the lowest estimate or the recom ination re uenc in the range which we term phasing the minimum recom ination re uenc M his di ers rom previous studies where the maximum o the log likelihood M was used to assign the most likel phase uo et al ackett et al egative estimates or r can occur due to
61 ______Double reduction landscape
en elian sampling ariation un er weak repulsion linkage. or strongl negati e alues (r . ) a recombination frequenc of . of ero an p ase “Unknown” were assigne an in t e case 0.05 ≤ r t e recombination frequenc was set to ero an t e an p ase were left unc ange . e recombination frequenc estimates were regresse on t eir true alues for bot coupling an repulsion p ase in or er to e aluate ow close to t e true alue t e estimates fell for eac pairing scenario. e proportion of correctl assigne p ases for coupling an repulsion p ase markers was also recor e . Results
Genotyping and dosage assignment f t e s assa e onl were foun to be acceptable an segregating in t is population ( able ). cceptable markers were t ose for w ic osages coul be assigne b fit etra for w ic parental osages were score consistentl between replicates an for w ic parental osages an offspring segregation patterns were consistent. ppro imatel of t e markers coul be assigne osages b fit etra after w ic a furt er were re ecte for a ing inconsistent parental – offspring osages or for being too ig l skewe (χ² test wit p . ). segregating markers forme t e largest group among t e segregating markers in our population ( able ) accounting for o er of useable markers.
Mapping of the 1:1 segregating markers lmost no simple nulliple markers roppe out uring t e mapping stage. f t e simple nulliple markers in were mappe an out of t e markers were mappe ( able ). e unmappe markers were lost ue to poor linkage (eit er no c romosome assignment or e tremel weak linkage wit in a linkage group) or large numbers of missing alues. arker co erage o er all c romosomes was well space wit on a erage o er markers per c romosome. nl c romosomes an a fewer t an mappe markers ( an markers respecti el ) wit c romosomes an a ing t e ig est marker co erage ( an markers mappe respecti el ). number of omologues were split up o er more t an one linkage group ue to insufficient linkage information. n t ese cases an markers were use to pro i e linkage information between omologue fragments. n e ample of t e four omologue maps of c romosome in parent is s own in igure .
62 ______Chapter 3
Figure 1. Homologue linkage maps of potato chromosome 1 for parent 2
n o e rker were o n o e re n e ween e r n en o nk e ro n o on n e r ne ro o o e on e e en e e er e o e e e wo o rker o n n o n were o n o e o on wo o on e o n e ene o on r er e rker
Figure 2. Comparison of genetic to physical distance with homologue maps of potato chromosome 1. ro e en ro ere o n re own e ne orre on n o e n e on o n n e r e er e o er n o o o e were ne r or o r n re e n n e o on ne e r
63 ______Double reduction landscape
Table 3. Composition of parental homologue maps
Parent 1 Parent 2 Chm h1a h2 h3 h4 Totalb h1 h2 h3 h4 Totalb 1 158 183 2 155 235 3 109 225 4 144 134 5 192 196 6 76 153 7 105 134 8 186 104 9 117 107 10 83 43 11 137 129 12 82 86 1544 1729 o o o o o o etc. o o o en n en or n n aldane’s mapping function, with n er o e rker n r ke o n er o e rker
were o n o e n nknown o on ro e e e o rker o on e er e o e e ro e o e e rker w e r e o on n e en r e one o e rker w owe nk e ro re n e were n e n e n o on er on r e or o e re on e were n e on e n ene e o e r n o ene o on
64 ______Chapter 3
Position of the centromeres g aphical compa ison of the aligned genetic and ph sical maps allowed an estimation of the cent ome ic ounds igu e hen compa ed to p e iousl pu lished cent ome e ounda ies ha ma et al , the esults do not co espond p ecisel fo ch omosomes , , , , , and t is possi le that the disc epancies a e due to the fact that ou estimates a e ased on a tet aploid population athe than a diploid one elche et al , ha ma et al , since the method used to dete mine the ounda ies was essentiall the same upplementa ta le p o ides ou estimates fo the cent ome e ounds, used in the calculation of elati e distance f om the cent ome e fo the dou le eduction anal sis
Conversion rate between genetic and physical distance he c con e sion ate was dete mined pe homologue a m ac oss all ch omosomes in oth pa ents linea eg ession of genetic distance on the ph sical distance igu e pa t f om one clea l outl ing alue due to insufficient ma e co e age the ecom ination ate was found to e elati el constant ac oss all ch omosomes, with an a e age alue of standa d e o of the mean
Figure 3. Average recombination rate across homologous chromosome arms ates calculated pe homologue a m no th o south of the cent ome e linea eg ession of ma e positions on the ph sical e sus genetic distance plots oints a e colo ed ch omosome, with upwa d pointing t iangles denoting no th p a ms and downwa d denoting south a ms data is shown filled t iangles, data empt t iangles
65 ______Double reduction landscape
Double reduction ou le eduction e ents we e identified on all twel e ch omosomes, suggesting that multi alent pai ing st uctu es can fo m among all potato ch omosomes f the indi iduals in the mapping population, showed e idence of dou le eduction coming f om meioses and showed dou le eduction segments f om o t si indi iduals showed e idence of ha ing inhe ited a dou le eduction segment f om oth pa ents ut not necessa il f om the same ch omosome , which co esponds well with the indi iduals e pected unde independence of pa ental meioses he dist i ution of duple st ing lengths shows that singleton duple sco es p edominate in this dataset upplementa igu e e e we ha e chosen to conside singleton duple sco es as unsuppo ted e idence fo dou le eduction which cannot e distinguished f om e o s in dosage estimation
Figure 4. Average rate of double reduction versus distance from the centromeres haded a eas ep esent confidence egions a ound the simulated mean ate of a ising f om a f action uad i alents of and he standa d de iation of the simulated mean ate of inc eases towa ds the telome es, coinciding with g eate fluctuations in the t ue ate of in these egions
e also used an algo ithm which allowed fo possi le missing sco es within a st ing of duple alues sing this app oach, we we e a le to e eal the elationship etween dou le eduction and the a e age distance f om the cent ome e igu e pooling the estimates f om all homologue maps, gi ing the a e age ate of dou le eduction as a function of distance f om the cent ome e he ate of dou le eduction close to the cent ome es app oaches e o while towa ds the telome es it inc eases su stantiall ithin the cent ome es themsel es the e we e twent two ma e s and fi e
66 ______Chapter 3 ma e s with duple sco es in the offsp ing f these, we e single occu ences which were probable errors (for example, the centromeric marker “PotVar0014900” which mapped to ch omosome , homologue in ga e fi e sepa ate duple sco es his ma e was also found to ha e missing alues, suggesting a lowe elia ilit the isolated cases would e ui e a dou le ecom ination at oth sides of the ma e s, which is highl unli el to ha e occu ed he e emained fi e cases of longe st ings of duple sco es which pa tiall ente ed the ounda ies of the cent ome ic egions upplementa ta le , suggesting that in a e limited num e of cases, ecom ination ma occu within what is conside ed to e a non ecom ining egion
Figure 5. True versus estimated r (using maximum likelihood) for coupling-phase simplex markers with fraction quadrivalents 0.2. he st aight line y = x shows the line of pe fect co espondence etween t ue and estimated alues
edig ee im has p e iousl een used to dete mine the ate of dou le eduction in simulated populations and to isualise the elationship etween genetic distance f om the cent ome e and dou le eduction oo ips and aliepaa d, n this stud we simulated phased ma e data and a mapping population si e of in o de to empi icall fit a pai ing model to the o se ed data he o se ed ates of dou le eduction and those p edicted simulation o e lap well when the f action of uad i alents was simulated in the ange – owa ds the telome es the a e age ate of dou le eduction e ceeded the e pected ates within a confidence inte al , although the confidence inte als we e found to widen g eatl in these egions his ma e due to the limited num e of ma e s at these distances f om the cent ome es, causing g eate unce taint in the estimates
Evidence for preferential pairing sing the epulsion phase ma e data, we in estigated whethe the e was an e idence fo p efe ential pai ing in this population e found almost no e idence fo p efe ential pai ing co ecting fo multiple testing using the co ection n ch omosomes and in the e we e fou ma e pai s out of and pai s, especti el which did show possi le e idence of disomic pai ing, ut this was not conside ed st ong enough e idence to suppo t a h pothesis of p efe ential pai ing n , no ma e s
67 ______Double reduction landscape
ispla e isomic like beha ior t was therefore concl e that potato follows tetrasomic inheritance as is enerall ass me
Effect of quadrivalents on mapping of simplex markers r anal sis of o ble re ction s ests that a ri alents ma acco nt for between 0 an 0 of all meiotic pairin confi rations in this pop lation i en that pre io s mappin st ies in potato ha e ass me that the rate of a ri alent formation is ne li ible, we wante to examine what effect a ri alents ha e on recombination fre enc estimates (an hence on linka e mappin e compare pairwise estimators for r to their tr e n erl in al e ( i re for ifferent rates of a ri alents erall, the effect of a ri alents on co plin phase estimates for simplex marker pairs was relati el minor, as shown b the ra al ecrease in the slope of the re ression between the tr e an estimate al es ( i re b orrect phasin in the co plin phase was also naffecte b a ri alents ( i re a or a a ri alent rate between 0 an 0 , the effect on co plin phase estimates can likel be i nore or rep lsion phase marker pairs, a reater effect was fo n altho h remarkabl , the assi nment of marker phasin act all impro es sli htl with hi her n mbers of a ri alents ( i re a f the 4 incorrect rep lsion phase assi nments in the p rel bi alent sit ation, onl 14 ha an associate score reater than one his s ests that as a preca tion a ainst incorrect phase assi nment within a linka e ro p, an “unknown” phase be assi ne in cases where the falls below a certain threshol (e.g. of one
Effect of preferential pairing on mapping of simplex markers r st on the effect of preferential pairin on estimates of r re eale that preferential pairin has no effect on these estimates in co plin phase b t has a ramatic impact in rep lsion phase ( i re b his fact has alrea been reporte ( an ancock, 001 onin o coiran et al , 01 an forms the basis for a test of preferential pairin which we also exploit in this st t is e i ent that preferential pairin can ha e a se ere impact on the correct assi nment of rep lsion phase ( i re a , re ar less of whether or is se for phase assi nment ( ata not shown ince we fo n no e i ence to s est that an s stematic preferential pairin occ rre we can be fairl confi ent that the estimates for recombination fre enc an phase were acc ratel performe , as confirme b the sim lation st
68 ______Chapter 3
Discussion
Linkage maps e en pub a on es bes he e ho s use o p o u e a h h ens nka e ap o a we s u e e ap o app n popu a on a ke e a us n he n n u o ap a a e he e a hou h we ha e no a e p e o n u e a a ke pes n he u en nka e aps we ha e appe a a e nu be o a ke s n a e ap o popu a on wh h o he bes o ou know e e s he h hes e epo e a ke ens o a e ap o po a o ap
Figure 6. Effect of quadrivalents on linkage analysis. a. opo on o n o e phase a ke s pa s un e e en e e s o ua a en o a on. b. e o ua a en s on a u a o r es a es o oup n an epu s on phase s p e a ke pa s
69 ______Double reduction landscape
h s has en us a e ua e o e a e o e o e a ho o o ous h o oso es an e e op an a u a e p u e o he oub e e u on an s ape n h s e ap o spe es e ha e p esen e sepa a e ho o o ue aps a he han a s n e onsensus n e a e ap pe h o oso e as a h e e b a ke e a epa a e ho o o ue aps e one he ab o n e he phas n o a ke s e o he ap on an e hap o p n w hou e ou se o h en a ko o e s a ke e a a hou h u a e n e a e aps an eno pe p obab es es a e us n he n e a e ap w ea o ea e powe n subse uen s u es
Figure 7. Effect of preferential pairing on linkage analysis. a. opo on o n o e phase a ke pa s w h e en e e s o p e e en a pa n b. e o p e e en a pa n on a u a o r es a es o oup n an epu s on phase s p e a ke pa s
70 ______Chapter 3
u n n ha he a e s a e on e s on a e be ween ene an ph s a s an e s essen a ons an ou s e he en o e e ons eno e w e e o b na on a e has shown ha he p ospe s o n e a n aps a oss ho o o ues an be ween pa en s a e oo an shou no pose un ue s ess on he un e n ho o o ue aps e a so oun e e en e o e o b na on “hot spots” or “cold spots” outside the en o e es as e en e b he h h a ues asso a e w h ou ene ph s a s an e e ess ons upp e en a ab e
Potato cytology n o a on on he pa n beha o o po p o s has a ona been ene a e o o o a s u es ne o he o e n uen a pub a ons on po a o o o has been he e ew o wa na han an owa who su a se he n n s o p e ous esea he s su h as a an a an a ns o he ean nu be o u a en s pe e a ak nes s an s e aphase n e ap o S. tuberosum an n o o wa na han an owa h s o o a e en e has been use o suppo he use o a s p e pa n o e n po a o app n an ana s s s n e hen a ke e a uo e a a ke e a a shaw e a a ke e a n ou s u we ha e use a ke a a o es a e he a e o oub e e u on an o h s o e apo a e he ke e uen o u a en s we on ons e ua a en s n o e a on o ua a en s ans a es o be ween an ua a en s pe e ons s en w h he o na o o a findings of Lamm performed on the cultivar ‘Deodara’ and the line ‘36/209’ from the oss e a s enk one n a
General polyploid model e p s ha e p e ous been a e o e e op a ene a heo o nka e app n n e ap o s wh h s u aneous ons e s he poss b o p e e en a pa n an u a en o a on u e a o n o he au ho s he p e e en a pa n a o s se o o he ase o an o pa n he o e p es ha he a on o ua a en s w e ua an ha o b a en s h s s ons s en w h he an o en pa n o e ha assu es pa n n a on o u s a one se o e o e es w h p obab o ha he pa n a he o he e o e es w esu n a sepa a on n o b a en s ohn an en e son u a a shows ha p e e en a pa n oes no o u n po a o e we ha e no oun a a on o ua a en s as h h as u n n s on ua a en pa n a e n ne w h a p e ous e ew o au opo p o e os s wh h oun a ean u a en e uen a en s an ua a en s o o e e en s u es a se an he ske has a so been shown ha ow nu be s o u a en s oes no ne essa su es ha p e e en a pa n beha o o u s ben a ben a
71 ______Double reduction landscape
Identification of double reduction e decided to ta e a more stringent approach than studies hich consider t o or even a single locus as sufficient evidence for dou le reduction Luo et al 2006 ac ett et al 20 3 his is li el to have led to an under estimation of D on our part o ever all uantification of D using mar er data are li el to under estimate the true rate of dou le reduction to some e tent or instance D segments can e hidden no segregating allele carried on the segment or due to limited num ers of mar ers one might onl recover part of a dou le reduction segment igher densit lin age maps here all homologue parts are covered segregating mar ers ill lead to more accurate estimates of the rate of dou le reduction unless a strong ias e ists in ho mar ers are distri uted or here D occurs n this stud ith over 3000 ell distri uted simple nulliple mar ers e feel e have sufficient mar er coverage for a detailed understanding of the dou le reduction landscape
imple nulliple mar ers give the most unam iguous information a out the presence of dou le reduction hen compared ith other mar er segregation t pes ther mar er classes could have een used as ell for e ample simple simple mar ers hich are e pected to sho triple scores in 0 of the cases of dou le reduction involving one of the simple alleles o ever no mar er class other than simple nulliple allo D scores to e distinguished directl as a dou le reduction product a imum li elihood approaches that estimate the rate of dou le reduction such as that descri ed in Luo et al 2006 ma e useful for the identification of dou le reduction in cases here it is not clear although e feel that flan ing simple nulliple mar er information hich supports the duple score should e used as e have done here
Double reduction increases towards the telomeres t has een idel reported that the rate of dou le reduction is e pected to increase to ards the telomeres ather 936 isher 9 utruille and oiteu 2000 tift et al 200 emorin et al 20 2 ielins i and cheid 20 2 given that the pro a ilit of a cross over occurring et een the centromere and a locus should increase as that locus is situated further from the centromere evertheless it has onl rarel een e perimentall verified he clearest evidence e found in the literature came from an anal sis of tetraploid potato using iso me mar ers although the num ers of mar ers used ere rather fe ith less than 0 loci considered a nes and Douches 993 n our stud e have clearl sho n using high densit mar er data of over 3000 mar ers that the rate of dou le reduction steadil increases ith distance from the centromere e have furthermore een a le to visualise this phenomenon hich has not previousl een reported
72 ______Chapter 3
he fact that the fre uenc of dou le reduction increases to ards the telomeres is perhaps cause for some concern as this could e considered a s stematic source of error in the mar er data evertheless ith dense mar er data it is no possi le to accuratel estimate the rate of dou le reduction in a mapping population n cases here the rate of dou le reduction is lo and mar er num er high it is uestiona le hether highl complicated models ith man parameters to e estimated are actuall useful particularl if the do not distinguish et een singleton dou le reduction scores and genot ping errors ur simulations have sho n that even ith full uadrivalent pairing pair ise estimators for recom ination fre uenc et een coupling phase simple nulliple mar ers under a ivalent pairing model are close to eing e act and as these are the most informative pairing scenario the are the most important estimates for lin age map construction e loo for ard to comparing our estimates for dou le reduction in tetraploid potato ith other pol ploid species and in gaining a deeper understanding of h these rates differ in hat are other ise classified collectivel as autopol ploids
Double reduction in mapping ome authors claim that dou le reduction should e included in map estimation and L anal sis to increase the po er and accurac of the anal sis Li et al 20 0 ur findings sho that uadrivalents have little effect on the mapping of simple mar ers in the highl informative coupling phase n potato at least our data sho s that the level of uadrivalent formation and preferential pairing is ver lo and is therefore not li el to e of serious orr for lin age mapping o ever confirmation of this finding for other mar er t pes is still needed
t is also orth pointing out that uadrivalent formation not onl leads to dou le reduction ut can also result in the formation of homologue com inations of more than t o parental homologues ved 96 hich can result from pairing partner s itches ones and incent 99 along the chromosome he fact that this is alread part of the simulation process in edigree im oorrips and aliepaard 20 2 increases the accurac of our approach not onl in terms of modelling dou le reduction ut also in our stud of the effect of uadrivalents on map estimation
Double reduction in breeding Dou le reduction has man implications for pol ploid reeding ne conse uence that has een descri ed is its potential to lead to a higher in reeding coefficient in dihaploids derived from tetraploid lines a nes and Douches 993 iven the efforts currentl under a to ards h rid potato reeding Lindhout et al 20 D ma have un anted impacts on genetic diversit at the diploid level if future diploid founder
73 ______Double reduction landscape material is derived from tetraploid lines n the other hand h rid reeding is dependent on the production of highl homo gous in red lines etraploid potato reeding might elcome greater levels of homo gosit in a crop that is often complicated high hetero gosit itde illigen et al 20 3 as ell as the potential purging effect that D can have e posing deleterious alleles to selection utruille and oiteu 2000 D could also speed up the accumulation of rare ut favora le alleles through mar er assisted selection ere e have developed the tools for the identification of D in a segregating population hich could e applied reeders in the selection of founder parents for su se uent crossings or for confirmation studies of L positions
Conclusions n this stud e constructed 96 separate homologue lin age maps of tetraploid potato using segregating simple mar ers e estimated the appro imate rate of dou le reduction 0 or more at the distal regions and predicted simulation that a fraction uadrivalents of 20 – 30 is re uired to account for this level of dou le reduction e found no evidence of preferential pairing in our data consistent ith previous reports on the mode of inheritance in potato imulation studies using simple nulliple mar ers revealed that mar er phasing and recom ination fre uenc estimation under a simplif ing ivalent pairing model are relativel ro ust even hen some level of multivalent pairing occurs
Acknowledgements he authors ould li e to ac no ledge eter os for assistance ith genot pe calling and and veris for providing potato varieties as ell as all partners involved in the TKI polyploids project “A genetic analysis pipeline for polyploid crops” (project num er 26 03 002 00 hich helped fund this research he authors ould also li e to than effre ndelman for helpful comments leading to a correction in the original manuscript he development of the ol arra as financiall supported a grant from the Dutch technolog foundation pro ect 926
Supplementary data is available online at: http // genetics org/content/20 /3/ 3 supplemental
74 ______Chapter 3
Supplementary Figure 1. istogra sho ing distri tion of lengths of strings of d ple scores in the dataset
75
Chapter 4
Integrating haplotype-specific linkage maps in tetraploid species using SNP markers
Peter M. Bourke1, Roeland E. Voorrips1, Twan Kranenburg1, Johannes Jansen2, Richard G. F. Visser1, Chris Maliepaard1
1 Plant Breeding, Wageningen University & Research, Droevendaalsesteeg 1, 6708 PB Wageningen, The Netherlands.
2 Biometris, Wageningen University & Research, Droevendaalsesteeg 1, 6708 PB, Wageningen, The Netherlands.
Published as Bourke, P.M., Voorrips, R.E., Kranenburg, T., Jansen, J., Visser, R.G., and Maliepaard, C. (2016). “Integrating haplotype-specific linkage maps in tetraploid species using SNP markers”, Theoretical and Applied Genetics 129 (11), 2211-2226
77 ______Integrating haplotype-specific maps
Abstract ,
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78 ______Chapter 4
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79 ______Integrating haplotype-specific maps
Here, ‘phase’ or ‘phasing’ means determining whether linked markers are physically on the same homologous chromosome within a parent n our approach, we first develop separate maps for every parental homologous chromosome (termed ‘homologue’ here) using all marker segregation types, integrating them afterwards into one chromosomal map for each set of eight homologues arker phasing is thus an essential aspect of our approach, which is of importance in the development of marker haplotypes consisting of more than a single marker
lthough methods to include dou le reduction in a linkage analysis have already een developed (either using two point estimation ( uo et al , ) or multi point estimation ( each et al , )), linkage analysis can e considera ly simplified in autopolyploid mapping populations if it is assumed that only random ivalent pairing occurs review of metaphase of autopolyploid meiosis found that ivalents accounted for appro imately of the pairing structures o served ( amsey and chemske, ) with uadrivalents accounting for appro imately (there were relatively few univalents or trivalents o served more comple multivalents were not recorded at higher ploidy levels) ompara le rates have also een reported for potato ( waminathan and Howard, ourke et al , ) n the computations of this study, we have assumed a complete a sence of preferential pairing and multivalent formation or e ample, in the case of markers, a duple score in the offspring would effectively e treated as a missing value, as it is not an e pected score according to our model However, we took care to e amine what effect oth preferential pairing and multivalents might have on the pairwise estimation of recom ination fre uency as well as the effects on the accuracy of marker phasing
lthough roadly similar, our mapping approach differs from that of Hackett et al ( ) in the following respects
he initial clustering of all marker segregation types into linkage groups is defined y their linkage to or ( segregating) markers, ena ling automatic marker phasing during mapping Homologue maps are first created (per parent) and then integrated into a single consensus map per chromosome using linear programming e include the results of a comparison study etween two different methods for deciding the most likely phase riteria are determined for inning markers together efore map ordering ll marker segregation types are included in the mapping (in particular, we also include and marker types)
80 ______Chapter 4
n this study, we descri e a method to perform linkage mapping in an autotetraploid species under the assumption of random ivalent pairing, and apply it to a genotyped mapping population of tetraploid potato e e plore some of the potential complications involved in polyploid mapping and discuss the implication of these for future mapping efforts
Materials and methods
Plant material and genotyping n population of individuals from the cross etween two out red tetraploid cultivars ‘Altus’ (parent 1 or P1) and ‘Columba’ (P2) was genotyped using the SolSTW nfinium array which assays , s ( os et al , ) arkers were assigned dosages using the fit etra package ( oorrips et al , ) as previously descri ed ( ourke et al , ) Highly skewed markers (using a χ² test with p ) as well as markers with more than missing values were removed from the dataset n a previous study, a pair of duplicate offspring individuals were identified in this population as well as an individual which showed unrealistic num ers of recom inations ( ourke et al , ) he suspect individual was removed as well as the duplicate with most missing values, leaving a mapping population si e of individuals
Marker dosage conversion small num er of markers for which one of the parental dosages was missing were e amined and the likely parental dosage imputed using the o served offspring segregation (if possi le), after which marker dosages were converted to their most fundamental form n a tetraploid species genotyped using i allelic markers, the possi le marker dosages classes are (nulliple ), (simple ), (duple ), (triple ) or 4 (quadruplex) depending on the number of copies of the ‘reference’ allele carried y that individual arker conversion simplifies the analysis y reducing the num er of marker types that need to e considered or e ample, simple nulliple , triple uadruple , triple nulliple and simple uadruple markers all segregate in a fashion and all carry a segregating allele inherited from parent ( ) hey can therefore e re coded as markers using suita le score conversions in the offspring ( upplementary a le ) ltimately, this results in nine fundamental marker segregation types as previously mentioned n determining linkage etween markers and other markers in , the set of markers were re coded y symmetry into to facilitate the calculations he physical distri ution of the segregating markers was
81 ______Integrating haplotype-specific maps visualised in ap hart 2 ( oorrips 2 2) using the previously published centromere boundaries (Sharma et al 2 1 )
Linkage analysis The maximum li elihood framewor for determining pairwise estimators for recombination frequency (r) and their significance ( ) scores under the assumption of random bivalent pairing has already been described in ac ett et al (2 1 ) We independently derived the li elihood functions for all possible mar er pairs and phases (of which we counted 2 possible combinations between the nine fundamental mar er types mentioned) using routines written in athematica 1 (Wolfram esearch nc 2 14) We describe the procedure through a wor ed example in ppendix 1 (Supplementary ile S1) The maximum li elihood functions (for each of these 2 cases) were coded in ( ore Team 2 1 ) for use in the lin age analysis
Marker phasing To explain the concept of phasing by way of example there are three possible phases between a DxN and a DxS marker: ‘coupling’, ‘mixed’ and ‘repulsion’, with ‘mixed’ implying only one pair of uplex alleles is in coupling phase in P1 (there is no phase consideration in P2 since one of the mar ers is ulliplex in that parent) or pairs of mar ers with segregating alleles from both parents such phases are combined (e.g. ‘coupling mixed’ refers to coupling phase in P1 and mixed phase in P2). One criterion for selecting the correct phase (and hence the correct estimator for r) is to use the maximum of the log li elihood function between phases for which r ≤ 0.5 ( ac ett et al 2 1 ) which we refer to as nother possibility is to choose the minimum estimate of r over all phases (which we term ) We performed a simulation study to determine which of these criteria was optimal across all possible mar er pair combinations using the simulation software PedigreeSim ( oorrips and aliepaard 2 12) ne hundred separate populations were generated for each of three population si es ( 1 1 2 and 4 ) ach simulated individual carried a single chromosome with 1 mar er positions spaced 1 c apart ll possible mar er types were assigned to each of these loci with a random assignment of the segregating alleles across homologues or each simulated population phasing accuracy was determined by recording the proportions of correctly phased pairs using both the and phasing strategies n a few cases it was not possible to distinguish between phases (e.g. SxS with DxD ‘coupling repulsion’ and ‘repulsion coupling’ phases produce precisely the same r estimates and scores) n diploid species an analogous situation can arise in cross pollinated species where certain mar er type combinations cannot be phased (e.g. x with x ) in which case other mar er segregation types are needed to complete the phasing ( aliepaard et al 1 ) We dealt with such instances
82 ______Chapter 4 by considering both phases to be e ually correct since we do not use these particular phase assignments themsel es, only their r and OD alues).
Linkage group identification and marker clustering Preliminary identification of linkage groups was performed by clustering the SxN and NxS) markers, based on the OD of the recombination fre uency estimate between marker pairs. routine for marker clustering was written in using a grouping algorithm analogous to that employed by the oin ap software Stam, 1 an Ooi en, 2 an Ooi en and ansen, 2 1 ). Of the 1 NxS markers able 1), three did not ha e any strong linkage to other NxS markers and were therefore remo ed at this stage we were later able to ‘rescue’ one of them when more markers were assigned to chromosomes).
Table 1. Tetraploid marker segregation types after filtering (adapted from Chapter 3) Parental dosage Segregation Amount a Simplex x nulliplex 1:1 1 Nulliplex x simplex 1:1 1 Duplex x nulliplex 1: :1 Nulliplex x duplex 1: :1 2 Simplex x simplex 1:2:1 2 Simplex x triplex 1:2:1 1 Duplex x simplex 1: : :1 Simplex x duplex 1: : :1 Duplex x duplex 1: :1 : :1 2 Total 6912 a Number of SNP markers after marker con ersions ha e been made
t a clustering threshold of OD , the NxS marker data di ided into 12 clusters. e isualised how clusters split across different OD alues for these 12 putati e chromosomes in , allowing the identification of tightly linked sub clusters putati e homologues or fragments thereof). n the ma ority of cases, these large clusters split into four sub clusters at higher OD alues as expected for a tetrasomic species). owe er, one cluster of 1 markers) could not be further subdi ided at higher OD alues. e therefore assumed that this cluster represented part of) one homologue and used the repulsion linkage information to assign it to one of the other clusters. nother cluster broke down into two clear sub clusters at OD i.e. it contained two chromosomal groups), which further sub di ided into sub clusters at OD . lustering in P1 was more straightforward, with 12 clear chromosomal clusters emerging at OD .
83 ______Integrating haplotype-specific maps
luster numbers were re laced with chromosome numbering for consistenc with the reference h sical ma using marker ositions gi en b os et al. ). n chromosomes and contained fi e sub clusters with the rest ha ing four. n chromosomes and were found to contain fi e sub clusters at this stage the rest ha ing four. n cases where more than four sub clusters are identified a isualisation of cross cluster hase assignments allowed us to uickl identif which sub clusters were albeit distantl ) linked in cou ling hase resol ing the and marker data into linkage grou s the e ected number of homologues. ollowing this the ast ma orit of markers within the com lete dataset were unambiguousl assigned to homologue clusters using cou ling hase linkage with markers a single linkage abo e a threshold of was used as e idence of linkage although in ractice there were often hundreds of such linkages identified). markers are e tremel useful for this ste as the unambiguousl tag a single homologue. here multi le assignments were ossible assignments with the greatest number of significant cou ling linkages ) were chosen as the most likel linkage grou s. or those markers which could not be com letel assigned to the e ected number of homologues in both arents due to oor linkage with markers linkage anal sis was erformed between these markers and all other marker segregation t es to identif their most likel chromosome and homologue assignment. inall the marker data was s lit into twel e subsets one for each chromosome) and a com lete airwise linkage anal sis was run between all markers within each chromosome.
Map construction
Homologue mapping er chromosome there are eight homologues that can be ma ed se aratel in an autotetra loid. arkers which a ear on these homologues are alread identified through their linkage with or ) markers. n addition to the cou ling hase linkages considered we also included some re ulsion hase linkages in our homologue ma s. arkers with at least one u le allele are com letel s mmetrical between the ‘reference’ and ‘alternative’ alleles in the Duplex parent. For example, DxN markers are initiall assigned to two homologues these being the homologues on which the reference allele can be found. owe er it is e uall informati e to consider the air of ‘alternative’ alleles from the same parent, as these carry the same linkage information as the reference alleles. e therefore used markers in the ma ing of four homologues and for the ma ing of fi e homologues and markers for
84 ______Chapter 4 all eight. ll of these marker types as ell as x and x are extremely useful as “bridging” markers for the integration of homologue maps.
here remained some linkages that e did not exploit, e.g. xN and xN in repulsion. he variance of these repulsion phase estimates is high and hence, D values are lo , and therefore the added computation time from including these estimates is not orth the marginal increase in linkage information that they yield a similar conclusion as arrived at in previous studies. e.g. ipol et al., .
Marker binning inkage information per homologue as first assem led into t o pair ise matrices one for r estimates and one for D scores , after hich the strength of linkage as tested to determine hether marker inning as possi le – i.e. markers ith a small recom ination fre uency estimate r of lo variance thus high D ere inned together. he minimum non ero num er of recom inations that can e o served in a mapping population of si e N and hence N gametes is one, in hich case the smallest non ero r estimate should e N ignoring the influence of errors . iven an average missing value rate of µ, a population si e ad usted for missing values is approximately and therefore . stimates of r that ere smaller than this value ere taken as eing elo the threshold of minimum resolution . 𝑁𝑁𝑎𝑎 = (1 − 𝜇𝜇)𝑁𝑁 𝑟𝑟𝑚𝑚𝑚𝑚𝑚𝑚 ≈ 1⁄ (2(1 − 𝜇𝜇)𝑁𝑁) 𝑚𝑚𝑚𝑚𝑚𝑚 Not all estimates of the recom ination fre uency are e ually accurate. e therefore𝑟𝑟 determined criteria for inning markers together ith a high degree of confidence. o achieve this, e ran simulations using edigree im oorrips and aliepaard, and recorded the D scores as ell as the range of true recom ination fre uencies for r estimates elo the threshold of minimum resolution over a ide range of population si es F to in steps of and rates of missing values to in steps of . e chose a maximum allo a le deviation et een the true and estimated r as . approximately c and determined the corresponding D score to ensure this over all possi le marker pair com inations hence e took the most stringent D threshold to cover all cases . For each population si e and rate of missing values, e examined the distri ution of D scores for those recom ination fre uency estimates for hich the deviation as less than . upplementary Figure . . From this e could determine a suita le D threshold for marker inning as a function of mapping population si e and rate of missing data.
iven a set of markers that have een inned together, e chose the xN marker ith the fe est num er of missing values for mapping xN recom ination fre uency estimates ith other marker types are exact as opposed to eing numerically
85 ______Integrating haplotype-specific maps appro imated in bins ith no markers the marker ith the fe est missing alues as sele ted.
Marker ordering he remaining marker data after binning ere on erted into pair ise data file format .p d for ea h homologue and imported into oin ap . an oi en for ordering. hree rounds of mapping using the eighted least s uares algorithm ere used (using the default settings with a “jump threshold” of 5), and with Haldane’s mapping fun tion used for distan e on ersion. ap files ere subse uentl e ported and all binned markers ere re added to the maps.
Map integration he homologue maps ere first re orientated if ne essar before integrating. ap re orientation as a hie ed b lo ating bridging markers bet een the maps and determining the orrelation bet een the positions of these markers. negati e orrelation suggests that maps are orientated in re erse order relati e to one another. in e not all homologues ne essaril share bridging markers the pa kage igraph sardi and epus as used to find an order of omparison through the eight homologue maps per hromosome to allo step ise orrelations to be al ulated for e ample might be one su h order . n e ample of this is sho n in igure for hromosome . n this e ample three separate re orientations ere re uired to ensure onsisten in orientation. hen all eight maps ere similarl orientated the pa kage merge ndelman and lomion as used to integrate them. merge eliminates the minimum number of onstraints in the marker order of the underl ing maps onfli ts in order bet een maps in order to generate hat is alled a “feasible system”, and then uses linear programming to find the solution with the minimum error bet een the underl ing maps and the integrated map ndelman and lomion .
Map quality checks e he ked the ualit of our linkage maps using three different approa hes
onsisten bet een the integrated maps and the underl ing homologue maps omparison ith the reported ph si al position of the mapped markers omparison to other published tetraploid potato maps
86 ______Chapter 4
Figure 1. Visualisation of map connections on chromosome 7. n this e ample, there were suffi ient bridging mar ers to pro ide onne tions between all homologues hree re ersals were needed in order to ensure all homologues were onsistently orientated before map integration
Consistency between the integrated maps and the underlying haplotype-specific homologue maps e ompared the mar er positions on the underlying homologue maps and the integrated maps in order to identify possible map distortion ap distortion is partly refle ted in the absolute error (δ) between the underlying maps and the integrated maps Howe er, in ases where the telomeres of all homologues are not e ually o ered by mar ers, shifting the position may o ur to align the maps, ontributing to an apparent in rease in δ without implying any map distortion e ran a simple linear regression between the integrated map positions ( ) and the underlying homologue positions ( ) and re orded the slope and adjusted alues of the fit as well as isually inspe ting ea h hromosome to identify potential distortion
Comparison with the physical position of the mapped markers he physi al positions of the mar ers were ta en as des ribed in os et al ( 5) lotting the geneti positions against the physi al positions allowed us to identify whether our maps were orre tly orientated (i.e. orresponding to the lowest bp alue) and we re orientated our maps if ne essary n ases where a dis repan y was found between the reported hromosome and that found through our lin age analysis, we ed the mar er se uen es (pro ided in the upplementary aterial of
87 ______Integrating haplotype-specific maps
os et al ( 5) and reprodu ed here) to the potato seudomole ules referen e genome ersion (Hirs h et al , ) to he the mar er positions (website http solana eae plantbiology msu edu blast shtml, a essed 5)
Comparison to other published tetraploid potato maps he ol nfinium array ( el her et al , ) has been used to genotype at least two other published tetraploid potato mapping populations (Ha ett et al , assa et al , 5) e ompared the geneti map positions of the ommon mar ers as a further he on the alidity of our maps
Simulation study to check mapping assumptions wo ru ial assumptions were made prior to mapping that there is no preferential pairing beha iour between any homologues and that all pairing is between bi alents (as opposed to tri alents or uadri alents), i.e. there is no double redu tion t had pre iously been established that the rate of uadri alent pairing in this population was between ( our e et al , 5) n ontrast to pre ious studies whi h also rely on these assumptions, we wanted to test what effe t de iations from these assumptions might ha e on our ability to produ e unbiased and a urate estimates for r between mar er pairs as well as the effe ts on phasing a ura y
e simulated mapping populations using different degrees of uadri alents and preferential pairing in edigree im ( oorrips and aliepaard, ) he simulation parameters we hose were population si es of , and offspring, le els of preferential pairing from (fully random pairing or tetrasomi beha iour) to (fully preferential pairing or disomi beha iour, asso iated with allopolyploidy) in steps of , or fra tion uadri alents from to in steps of or ea h population si e we generated separate populations a h simulated indi idual arried a single hromosome with mar er positions spa ed apart ll possible mar er types were assigned to ea h of these lo i, with a random assignment of the segregating alleles to homologues at all mar er positions n total, we simulated , populations to o er our hosen range of uadri alents and preferential pairing for these population si es and number of repetitions (( ) )
fter the populations were generated (i.e. their dosage genotypes nown), we ran our lin age analysis fun tions a ross all populations i en that the datasets were simulated, the true re ombination fre uen y and orre t phasing between all mar er positions was nown, allowing us to test whether our estimation of re ombination fre uen y and mar er phasing was robust against these de iations from the random bi alent model o generate a erage results from the repeat populations per setting, we ran a simple linear regression on the estimated r ersus true r alues, re ording the
88 ______Chapter 4 slope, inter ept, and residual standard de iation of the regression e also re orded the proportion of2 situations not estimated (e.g. due to undefined numbers in the 𝑅𝑅𝑎𝑎𝑎𝑎𝑎𝑎 li elihood e uation) and the proportion of pairing situations that were orre tly phased Results
Genotypes he numbers of mar ers that were a ailable for mapping after mar er filtering and uality he s was , as outlined in able he brea down of mar er segregation types after mar er on ersions were performed is pro ided in able
Figure 2. Distribution of 6836 of the 6912 segregating markers used in this study for which a physical assignment was available. istan es shown in bp haded regions indi ate entromeres, as pre iously defined ( harma et al )
ppro imately of the mar ers segregate in a fashion and these were mapped in a pre ious study ( our e et al , 5) he physi al distribution of all mar er types for whi h physi al positions were a ailable is gi en in igure , highlighting the differen e in mar er distribution between telo and entromeri regions
Table 2. Breakdown of SNP marker numbers after quality filtering (adapted from Chapter 3)
Steps in SNP filtering Amount % ol nfinium array total s osages assigned by fit etra a 5 b pattern a eptable onomorphi 55 5 olymorphi Polymorphic and ≤ 10% NA values 6912 a ar ers not s ored were monomorphi or not learly resol ed ar ers with a single missing parental dosage s ore whi h was imputed ha e been in luded b riteria for la of fit presen e of null alleles, in alid s ores, highly s ewed segregation (P )
89 ______Integrating haplotype-specific maps
Linkage analysis and marker clustering
Maximum likelihood pairwise estimates for r e ounted separate mar er type and phase ombinations for whi h we deri ed ma imum li elihood fun tions, although this may ontain s enarios that an be ounted together (pre iously, situations ha e been reported (Ha ett et al , )) or larity we pro ide a table of all the possible mar er type and phase ombinations we onsidered ( upplementary able ) n many ases, the ma imum li elihood e uation annot be solved analytically, in which case we used Brent’s algorithm ( rent, ) to numeri ally estimate the re ombination fre uen y with the highest li elihood, onstrained to the inter al , 5 t is also possible that a negati e estimate for r ould be the most li ely (this an o ur in low information situations, in ol ing repulsion phases) e e amined the true alues of r underlying su h ases using simulated data and found a wide range of true r alues were possible hene er r was found, we artifi ially set r = 0.499, LOD = 0 and phase “unknown”, thereby excluding these estimates from the map ordering step
Optimal phasing strategy ur simulations re ealed the optimum phasing strategy to use for different mar er ombinations ( upplementary igure ) he ma imum log li elihood strategy ( ) as proposed by Ha ett et al ( ) pro ed in general to be a ery good method of sele ting the orre t phase (and hen e the orre t estimate for r) n only one situation did we find to outperform , namely with mar ers he impro ement was, howe er, marginal at a population si e of indi iduals for e ample, ga e a ura y ersus a ura y using hene er phase was in orre tly assigned, we found that the s ore was also low (and the re ombination fre uen y estimates tended to be high) – in other words, in orre t phasing only o urred in poorly informati e situations whi h would ha e little or no impa t on the subse uent ordering step (espe ially sin e our mapping strategy fa ours oupling phase estimates whi h tend to be more informati e than those of repulsion phase) n all situations in ol ing at least one mar er there was no differen e between the two methods or the ase of paired with mar ers, the a ura y of appeared at first glan e to be higher Howe er, this parti ular ombination of mar ers ontains an essentially un estimable phase with e tremely high arian e (repulsion oupling phase see also esults se tion “Simplex x Triplex markers”). Removing this phase from the accuracy calculation, MLL was found to perform signifi antly better among the phases that a tually matter in this ombination inally, phasing a ura y was found to slightly in rease as a fun tion of population si e, with a ura y on a erage for a mapping population of si e
90 ______Chapter 4
compared with 9 accuracy for a population of 00, and 4 for a population of 00). breakdown of the phasing accuracy rates is provided in Supplementary ile S .
Map construction and integration
Simplex x Triplex markers SxT markers have previously been reported as problematic where they are termed SS markers ackett et al., 0 )). hen we examined the issue, we found that SxT in combination with SxS produce highly variable estimates for r in repulsion coupling phase, where the estimates for r are essentially random. They are the only marker combination and phase) that exhibit such behaviour. e therefore artificially set LOD = 0 in this phase it would be small but non ero otherwise) which automatically excludes these estimates from exerting any influence on map ordering.
Marker binning Once all linkages between markers had been estimated we were in a position to identify co segregating markers. The r and LOD estimates give a convenient measure of linkage which can be applied across all marker segregation types in a binning procedure. n example of the relationship between r and LOD for pairs of DxD markers is visualised in igure . s higher LOD values correspond to a lower standard error in r, we wanted to define thresholds for r and LOD which would identify markers which co segregate with a high degree of confidence.
Figure 3. Estimated recombination frequencies (r) versus associated LOD for duplex x duplex marker pairs on potato chromosome 1. Only of the 9 possible phases were identified for marker pairs on this chromosome.
e previously introduced the concept of the threshold of minimum resolution for recombination fre uency, iven our mapping population si e and missing error
𝑟𝑟𝑚𝑚𝑚𝑚𝑚𝑚. 91 ______Integrating haplotype-specific maps rate in the filtered dataset) we estimated to be approximately 0.00 , the smallest non ero recombination fre uency we should be able to observe. rom our simulation of 𝑟𝑟𝑚𝑚𝑚𝑚𝑚𝑚 different population si es and rates of missing data, we observed a clearly linear relationship between the mapping population si e and the LOD threshold needed to ensure a margin of error of less than 0.0 in the estimation of r Supplementary igure .c). By performing a linear regression between the LOD thresholds and the ad usted mapping population si es ), we were able to derive an empirical relationship between a binning LOD threshold and the ad usted population si e which ensures this margin of (𝑁𝑁𝑎𝑎 error in r is not exceeded
𝑎𝑎 iven our dataset, we binned 𝐿𝐿𝐿𝐿𝐿𝐿markers ≈ 23 together.43 + 0.1158𝑁𝑁if we found that the pairwise r estimate was less than 0.00 and the LOD for that estimate exceeded 0.4. n total, 0, 49 markers were used in the map ordering step across 9 separate homologue maps note that some markers were present multiple times because they are present on multiple homologues), after which 099 binned markers were re assigned a position to give a total of , 4 map positions Supplementary Table S ). s binning was performed using a nearest neighbour clustering, there is a danger that binned markers might have a non negligible distance between them. hen we examined this, we found that the maximum recombination fre uency estimate between binned markers was 0.0 , or approximately 3.3 cM using Haldane’s mapping function (Supplementary ile S ). owever, the mean inter marker distance within bins was only 0. cM, and almost 99 of binned markers were less than cM from each other. n other words, our binning strategy rarely appears to have falsely binned markers together. These , 4 map positions represented 9 0 uni ue marker loci, i.e. only two of the 9 markers available for mapping were not mapped. e suspect that the two unmapped markers which showed no linkage may have harboured abnormally high numbers of errors, although we cannot verify this. full list of all marker positions per chromosome is provided in Supplementary ile S .
Map integration L merge ndelman and lomion, 0 4) was run for all linkage groups to determine the integrated maps with lowest absolute error δ between the homologue maps and the integrated map per linkage group referred to as RMS by the authors). lthough the L merge algorithm is deterministic . ndelman, personal communiation), we found the resulting maps differed when the input maps were flipped. This suggests the current version of L merge should be run twice to identify the best integrated map. The maximum interval si e see ndelman and lomion 0 4) for a description) was set at default 4) and the map with the minimum error was saved for the final selection of the
92 ______Chapter 4
“globally” optimal integrated maps. LPmerge currently reports the error associated with each possible solution but does not save this information automatically. e therefore altered part of the source code to create an output file of the errors and map lengths per ma imum interval, allowing us to identify the best results. he altered source code of the LPmerge function is provided in upplementary File .
Map quality
Consistency between the integrated maps and the underlying haplotype-specific homologue maps e visualised the relationship between the homologue maps and the integrated map for each chromosome (Figure 4). Apart from a small number of ‘kinks’, there was a very high level of linearity observed between the component maps and the integrated maps as well as an acceptable correspondence in map lengths ( upplementary able ), demonstrating that the integration step did not create undue distortion. his linearity was also reflected in the high values associated with the regression analysis – with a minimum of . and a mean2 of . (i.e. essentially co linear). he slopes and ad usted 𝑅𝑅𝑎𝑎𝑎𝑎𝑎𝑎 correlation coefficients of the different maps are provided in upplementary able 4.
Comparison with the physical position of the mapped markers ne of the advantages of developing mapping theory and software using data from potato is the availability of physical maps which provide a reference marker position (Potato enome e uencing onsortium, Felcher et al., os et al., ). e orienting the integrated genetic maps if necessary, we found the e pected profiles for all chromosomes (Figure ) and could also clearly identify markers for which the chromosome assignment on the physical map appears to be incorrect. he physical location of other markers was previously unknown (recorded as b on chromosome ), for which we can now provide an appro imate physical position based on these plots ( upplementary File 4). hese plots also provided information on the location of the pericentromeric regions. e found differences between our identified pericentromeric boundaries and those previously reported for potato chromosomes , , and ( harma et al., ). n all these cases we noted that the published regions were too large i.e. some stretches of the pericentromeric regions of these chromosomes show little or no suppression of recombination. ne issue that did arise on chromosome was the mapping of what we suspect is a centromeric marker to a non centromeric position (Figure ). All markers binned with this marker were therefore also at a non centromeric position. hen we re ran the mapping without binning in this homologue, we saw essentially the same result – i.e. marker binning was not to blame. he integration of information from telocentric chromosomes may result in such minor ordering errors
93 ______Integrating haplotype-specific maps given that multi point estimates (from which the map is ultimately derived) are one sided at the telomeres.
Comparison to other published tetraploid potato maps A subset of the ol Ps came directly from the ol AP P array, with 4 of these having an acceptable F pattern after fitting, of which segregated. e mapped of these ol AP markers, allowing a direct comparison of our genetic maps with previously published tetraploid maps which use these markers ( ackett et al., assa et al., ). nly a single marker from this set was found to have been assigned to a different linkage group between the three studies (solcap snp c ), which was mapped on chromosome by ackett et al. and which both we and assa et al. mapped on chromosome 4. e double checked the physical position by LA ing the marker se uence against the potato genome ( irsch et al., 4) and found it produced a single hit on chromosome 4.
A comparison of the maps is shown in upplementary Figure . n general, our map positions correspond well with those of previous studies, apart from chromosome where we found that a group of markers most likely to be centromeric (based on a comparison with the physical map) were mapped at c by ackett et al. ( ) even though the pericentromeric region of chromosome is positioned at appro imately c in their map. here also appear to be several cases where markers were binned together by ackett et al. ( ) which we assigned to different genetic positions ( upplementary Figure , chromosomes , 4, and ). owever, the binning strategy employed by ackett et al. ( ) differs considerably from our approach, in that markers are not automatically binned before map ordering, but only end up in a “bin” if they fail to map after two rounds of JoinMap’s weighted regression ordering algorithm. espite these discrepancies, the mapping performed in previous studies is broadly consistent with our results.
94 ______Chapter 4
Figure 4. Comparison between marker positions on underlying homologue maps and integrated map positions for potato chromosomes 1-12. ifferent colours denote different homologues. δ denotes the absolute error between the eight homologue maps and the integrated map, as calculated by merge.
95 ______Integrating haplotype-specific maps
Effect of quadrivalents and preferential pairing on mapping
Quadrivalents ne notable effect of uadri alent pairing in meiosis is the phenomenon known as double reduction, where two copies of the same parental homologue segment are transmitted to an offspring. t has pre iously been shown that uadri alents ha e a relati ely minor impact on recombination fre uency estimates of pairs of markers ourke et al., . ere we e tend the analysis to all possible marker segregation types of a tetraploid cross. n general, we can confirm our pre ious finding that uadri alents ha e a minor impact on r estimates for most marker pairs and phases, but lead to an under estimation of r when the proportion of uadri alents approaches one e.g. and in coupling repulsion phase, upplementary igure . owe er, no obser ations of such high proportions of uadri alents ha e been reported yet as far as we know in an autopolyploid species waminathan and oward, amsey and chemske, ourke et al., . n upplementary ile .a, we pro ide full details of the results of this study.
Preferential pairing referential pairing constitutes a much greater de iation from the assumption of random bi alent pairing, and this was reflected in the results of the simulation study. e again saw a downward bias in r with greater le els of disomic beha iour, which was accompanied by a drop in the correlation between the true and estimated alues. higher population si e can help to mitigate these effects, but when the rate of preferential pairing p e ceeds . this makes little difference. orrect phase estimation was surprisingly robust against preferential pairing, although in a fully disomic situation p it was not possible to estimate r in certain cases specifically, the combination between a duple and simple allele in either parent when both alleles are present on the same bi alent, leads to on a erage inestimable alues . e ertheless, recombination fre uency estimates showed high le els of stability and robustness, e en when significant le els of preferential pairing occur. or identifying linkage groups, preferential pairing has almost no impact on the accuracy of coupling linkage estimates with markers which we use for marker clustering , with the possible e ception of markers. n e ample of the results for and markers in coupling coupling phase is gi en in upplementary igure . n upplementary ile .b, full details of the results of this study can be found.
96 ______Chapter 4
Figure 5. Comparison between physical and integrated genetic maps for 6872 mapped markers on potato chromosomes 1-12. ifferent colours denote different marker segregation types. entromeres as defined in harma et al. are shown with dashed lines. markers for which the chromosome assignment differed were remo ed before plotting. utlying markers positioned at Mb had no physical position – for which we suggest appro imate positions based on these plots c.f. upplementary ile .
97 ______Integrating haplotype-specific maps
Discussion
Homologue mapping r
e.g.
98 ______Chapter 4
The necessity of simplex x nulliplex markers –
Marker binning
99 ______Integrating haplotype-specific maps
Figure 6. Distribution of binned markers on eight homologue maps of potato chromosome 7.
100 ______Chapter 4
Map integration
Application to other tetraploid species various reports of “segmental allopolyploidy” e.g.
Conclusions
101 ______Integrating haplotype-specific maps of map omputation as ell as providing long range aplotype information it mar er p ase eing automati ally assigned prior to mapping it out t e need for manual intervention e time limiting step remains mar er ordering ut e ave found t at our inning approa offers a su stantial speed up in omputational time it out adversely affe ting map uality
Acknowledgements e aut ors ould li e to a no ledge eter os and erman van for s aring t eir e pertise aul rens for riti ally reading t e manus ript and o an van oi en ya ma for elpful suggestions e aut ors also is to a no ledge t e editor and t o anonymous revie ers ose omments elped improve t e manus ript unding for this research was provided through the TKI polyploids project “A genetic analysis pipeline for polyploid crops”, project number BO
Supplementary data is available online at: ttps lin springer om arti le s upplementary aterial
102 ______Chapter 4
Supplementary Figure 1. a. lot of true recombination fre uencies versus their O scores when the estimated r value fell below the threshold of minimum resolution rmin In this e ample, the simulated population si e was and there were missing values in the data thus the adjusted population si e a) was 595). The red line shows the “acceptable” deviation of adopted in this study b. istribution of O values for recombination fre uency estimates that fall below the threshold of minimum resolution rmin and have a deviation of less than from the true value The appro imate O threshold for this population si e is shown by the arrow c. elationship between O threshold and a to guarantee a ma imum deviation of between an estimate of ero recombination fre uency and its true value for all possible tetraploid mar er pair combinations derived using simulated data The fitted line was used to determine an appropriate binning threshold given the population si e and average rate of missing data used in this study
103 ______Integrating haplotype-specific maps
Supplementary Figure 2. eatplots showin res lts o the si lation to deter ine the overall phasin acc rac in all pairs o ar er t pes sin a i lo li elihood ) or ini r ) or vario s appin pop lation si es.
104 ______Chapter 4
Supplementary Figure 3. o parison between previo sl p blished tetraploid potato lin a e aps ac ett et al. assa et al. 5) and the inte rated ap described here.
105 ______Integrating haplotype-specific maps
Supplementary Figure 4. is alisation o the e ect o adrivalents on pairwise r esti ates or and ar ers in co plin rep lsion phase. q denotes rate o adrivalent pairin .
106 ______Chapter 4
Supplementary Figure 5. is alisation o the e ect o pre erential pairin on pairwise r esti ates or and ar ers in co plin co plin phase. p denotes stren th o pre erential pairin ro pol so ic) to diso ic).
107
Chapter 5
Partial preferential chromosome pairing is genotype dependent in tetraploid rose
Peter M. Bourke1, Paul Arens1, Roeland E. Voorrips1, G. Danny Esselink1, Carole F. S. Koning-Boucoiran1, Wendy P. C. van ‘t Westende1, Tiago Santos Leonardo1, Patrick Wissink1, Chaozhi Zheng2, Geert van Geest1,3, Richard G. F. Visser1, Frans. A. Krens1, Marinus J. M. Smulders1, Chris Maliepaard1
1 Plant Breeding, Wageningen University & Research, Droevendaalsesteeg 1, 6708 PB Wageningen, The Netherlands.
2 Biometris, Wageningen University & Research, Droevendaalsesteeg 1, 6708 PB Wageningen, The Netherlands.
3 Horticulture and Product Physiology, Dept. of Plant Sciences, Wageningen University & Research, Droevendaalsesteeg 1, 6708 PB Wageningen, The Netherlands.
Published as Bourke, P.M., Arens, P., Voorrips, R.E., Esselink, G.D., Koning- Boucoiran, C.F.S., Van ‘T Westende, W.P.C., et al. (2017), “Partial preferential chromosome pairing is genotype dependent in tetraploid rose”, The Plant Journal 90 (2), 330-343
109 ______Partial preferential chromosome pairing
Abstract t as on een reco nised t at o y oid s ecies do not a ays neat y a into t e cate ories o auto or allopolyploid, leading to the term “segmental allopolyploid” to descri e everyt in in et een. T e eiotic e aviour o suc inter ediate s ecies is not u y understood, nor is t ere consensus as to o to ode t eir in eritance atterns. n t is study, e used a tetra oid cut rose Rosa hybrida o u ation, enoty ed usin t e Wa S P array, to construct an u tra i density in a e a o a o o o ous c ro oso es, usin et ods revious y deve o ed or autotetra oids. sin t e redicted iva ent con i urations in t is o u ation, e uanti ied di erences in airin e aviour a on and a on o o o ous c ro oso es, eadin us to correct our reco ination re uency esti ates to account or t is e aviour. T is resu ted in t e re a in o , S P ar ers across a o o o ues o t e seven rose c ro oso es, tai ored to t e airin e aviour o eac c ro oso e in eac arent. We con ir ed t e in erred di erences in airin e aviour a on c ro oso es y e a inin re u sion ase in a e esti ates, ic a so carry in or ation a out re erentia airin and reco ination. Current y, t e c osest se uenced re ative to rose is Fragaria vesca. i nin t e inte rated u tra dense rose a it t e stra erry eno e se uence rovided a detai ed icture o t e synteny, con ir in overa co inearity ut a so revea in ne eno ic rearran e ents. ur resu ts su est t at airin a inities ay vary a on c ro oso e ar s, ic roadens our current understandin o se enta a o o y oidy.
Key words i density inte rated a , se enta a o o y oid, o y oid enetic in a e a , Rosa hybrida, eiotic c ro oso a airin e aviour.
110 ______Chapter 5
Introduction olyploids are generally di ided into t o types – a topolyploids and allopolyploids here ontin es to e de ate a o t the de inition o these ategories – namely, hether they sho ld e de ined y their pres med or no n mode o origin or their o ser ed mode o inheritan e amsey and hems e, , other ise des ri ed as the ta onomi or geneti de initions oyle and gan, ording to the ta onomi de inition, polyploids are disting ished y their n m er o o nder spe ies one in the ase o a topolyploids, t o or more in the ase o allopolyploids hereas the geneti de inition disting ishes polysomi inheritan e res lting rom random pairing o hromosomes d ring meiosis a topolyploid , rom disomi inheritan e res lting rom non random or pre erential pairing allopolyploid oyle and herman royles,
heoreti ally at least, it has long een re ognised that there may also ‐ e intermediate orms o polyploidy, ario sly termed segmental allopolyploidy te ins, , partial pre erential pairing et al , , in omplete polysomy imar es et al , , heterosomy o and annell, or mi osomy oltis et al , n these intermediate ategories, the geneti de inition i.e. pairing eha io r d ring meiosis ta es pre eden e ig re a his pairing eha io r is primarily important as it determines the e tent o re om ination et een homolog es or homoeolog es, pro iding a diagnosti o the type o polyploidy arisod et al , oyle and herman royles, rthermore, it may in l en e o r a ility to prod e lin age maps and s se ently per orm a rate antitati e trait lo s analysis, o ‐ importan e or oth ndamental and applied plant resear h nderstanding the pairing eha io r o polyploid spe ies is also rele ant or the st dy o genome e ol tion pon genome d pli ation
ario s ornamental rops, Rosa spe ies in parti lar, ha e a long history o hy ridisation and polyploid ormation et een and ithin spe ies to generate the di ersity o lti ars e ha e today m lders et al , his reeding and sele tion is li ely to ha e ontri ted to di eren es in homology et een ario s hromosomes, tho ght to play a role in meioti pairing eha io r ingham and illies, ent et al , airing in other spe ies has een sho n to e nder geneti ontrol or e ample, the Ph1 lo s o he aploid heat amoto, iley and hapman, or the PrBn lo s in Brassica napus en e s i et al , i olas et al , , t may also e in l en ed y en ironmental a tors om lies et al , espite some ad an es in
111 ______Partial preferential chromosome pairing
Figure 1. The meiotic pairing behaviour of tetraploid rose is not fully understood, yet exhibits many features of a segmental allopolyploid; mapping populations and high- resolution maps can shed light on such questions. a. b. c.
112 ______Chapter 5
Genetic mapping in rose Rosa Rosa Rosa Synstylae Gallicanae Indicae Pimpinellifoliae Rosa hybrida Rosa chinensis R. gallica R. alba R. x odorata Rosa hybrida Rosa Rosa chinensis
Identifying and quantifying preferential pairing
113 ______Partial preferential chromosome pairing
i.e.
(𝜌𝜌)
Experimental Procedures
Plant material, DNA isolation and genotyping The tetraploid “K5” cut rose mapping population, consisting of 172 individuals of the cross between “P540” (mother) and “P867” (father) was used in this study
114 ______Chapter 5
This population has previously been used in studies on powdery mildew (Podosphaera pannosa) resistance ( an et al , 2006), a range of morphological traits ( itonga et al , 2014 itonga et al , 2016), stomatal functioning ( arvalho et al , 2015), and lin age map construction using P and mar ers (Koning oucoiran et al , 2012) enomic was e tracted from free e dried young leaves, using the easy Plant ini Kit ( iagen, http www iagen com ) following the protocol of ( sselin et al , 200 ) amples were sent to ffymetri for genotyping using the ag h P 68 iom P array (Koning oucoiran et al , 2015) This array targets 68,8 Ps with every P targeted with two probes (which we refer to as the P and probes) oth parents were genotyped in triplicate (two biological replicates and one technical replicate)
Genotype calling and data preparation The P array data was converted into dosage scores using the fitTetra pac age ( oorrips et al , 2011) uality chec s were subse uently performed to ensure consistency between the parental scores and those of the offspring, and to chec for the possibility of “shifts” in dosage assignments which can occur when fewer than the five possible dosage classes occur s each P was targeted with two probes (P and ), the genotype calls for these probe pairs had to be compared and merged if they were found to be consistent ( 10 conflicts, where missing values were not considered conflicting), with conflicting scores made missing Probes with more than 10 conflicting scores (including parental scores) were kept as separate markers, by appending the letters “P” and “Q” to the marker names. Markers with more than 10% missing values were removed from the dataset, as well as those mar ers showing highly s ewed segregation patterns under either a tetrasomic or disomic model (P 0 001)
n a tetraploid genotyped using bi allelic P mar ers, the possible dosage classes range from nulliplex (0 copies of the alternative allele, coded ‘N’) to quadruple (4 copies, coded ‘Q’), with marker segregation types defined by their parental scores. Marker dosage scores were re coded as described in ( our e et al , 2016), resulting in mar er classes ( , , , , , T, , , ) uplicate individuals were identified by genotype pairs with an unusually high correlation ( 5 similar scores) these individuals were merged (if both scores were non missing and conflicting, the merged score was made missing) ndividuals with more than 10 missing values were also removed
Marker clustering and linkage group assignment nitially, the simple nulliple ( ) and nulliple simple ( ) mar ers were clustered using the for lin age value of 4 was found to split the data evenly, with clusters of fifteen or more mar ers selected as candidate homologue groups n P1
115 ______Partial preferential chromosome pairing this resulted in clusters, one more than the expected. ach cluster was then tested over a range of thresholds (from to 10) to ensure the markers remained clustered together. n P at a threshold of , clusters were identified. wo of these clusters split at , resulting in 0 P clusters. hese clusters were subsequently assigned to linkage groups using their linkage to xN (or Nx ) markers, which provide cross homologue linkage. here more than four putative homologues were present, the predicted phasing across clusters was used to merge these into single homologues. n total, P1 homologues across chromosomes were identified, and P homologues across chromosomes in P (i.e. we missed one P homologue). hromosomes were re numbered according to the M numbering previously introduced ( piller et al., 011), through linkage with markers from a previous study ( oning oucoiran et al., 01 ). ll other marker segregation types were subsequently assigned to both chromosomes and homologues based on their linkage to xN markers ( ).
Linkage analysis and map construction under a tetrasomic model Pairwise linkage analysis between all marker types was performed per chromosome and per parent. he maximum likelihood framework used to estimate the (phased) recombination frequency and score under the assumption of random bivalent pairing (i.e. no double reduction and no preferential pairing) is already described elsewhere ( ackett et al., 01 ourke et al., 01 ). Pairwise marker phase was primarily based on likelihood maximisation ( ackett et al., 01 ), although minimum recombination frequency was used to phase x marker pairs (as described in ourke et al. ( 01 )).
prototype version of the M Map software was kindly made available by its authors for map ordering (Preedy and ackett, 01 ). Maps were produced using unconstrained weighted metric multi dimensional scaling (with as weights and using Haldane’s mapping function) followed by principal curve fitting in two dimensions. Poorly mapping markers were identified either as outliers in the P plots ( udged by eye), or if their nearest neighbour fit exceeded . uch markers were removed, and up to three rounds of M Map were performed until stable maps free of outlying markers were produced. he final map positions of the 0 pairs of (unmerged) P and Q probes were compared. n cases, one of the probes was lost (either during the clustering stage or later when outliers were removed from the linkage maps) and the remaining probe was taken as the consensus marker. n cases where both probes were mapped, only 1 mapped less than 1 cM apart and had the same parental dosages these probes could be
116 ______Chapter 5
e ged hile the est e e dis a ded he a ing edu e as e eated using the a ended dataset
Estimation of a preferential pairing parameter e delled e e ential ai ing in the nte t i alent ai ing nside ing de iati ns ρ the e e ted a ilities unde a and del he e the a ilit ai ing et een h l gues and and et een and den ted is and that et een is e a ided si ultane usl esti ating 1 1 𝜌𝜌 a e e ential ai ing a t and a e inati n e uen hi h as und t lead t 3 + 𝜌𝜌 3 − 2 an e esti ati n the le el e e ential ai ing u et al in a u a t ste edu e that i st esti ates a a using t int tet as i lin age anal sis and then e ises th se esti ates hen a e e ential ai ing a t has een dete ined using a ulti int hidden a del H a a h heng et al
he a e data as si li ied unding a e siti ns t the nea est enti gan a te hi h ne ea h a e seg egati n t e as sele ted at ea h siti n he e e than ne a e a a ti ula t e as esent at a l us the a e ith the e est issing alues as h sen et a igin ides the st li el i alent ai ing in ea h indi idual lasses e e nu e ed h l gues su h that the ai ing n igu ati n ith the highest edi ted unt in et a igin as etc e then a lied a χ² test n the unts ea h lass t test de iati ns P the nu e st u tu es edi ted in ea h the th ee ai ing lasses 1 3a e and and assu ing and the li elih d un ti n gi en the se ed unts is 𝑛𝑛1 𝑛𝑛2 𝑛𝑛3 𝑛𝑛1 ≥ 𝑛𝑛2 𝑛𝑛1 ≥ 𝑛𝑛3
𝑛𝑛1 𝑛𝑛2+𝑛𝑛3 1 1 𝜌𝜌 ℒ(𝜌𝜌) ∝ ( + 𝜌𝜌) ( − ) l ing the li elih d e uati n leads3 t the a i u 3 2 li elih d esti ate
𝜌𝜌
2 1 𝑛𝑛1 − (𝑛𝑛2 + 𝑛𝑛3) 𝜌𝜌̂= 3 3 et a igin as e un all ing 𝑛𝑛the1 + ssi ilit 𝑛𝑛2 + 𝑛𝑛3 uad i alent ai ing in the s ing t in estigate the le el d u le edu ti n and t see hethe e e ential ai ing as still edi ted unde a del that in luded uad i alents he ate d u le edu ti n as dete ined e l us as the a e age the ha l t e a ilities that e eeded a ss the ulati n
117 ______Partial preferential chromosome pairing
Preferential pairing estimated from repulsion-phase linkages e esti ated the e ate in the gen t e data ai s du li ated indi iduals hi h nineteen ai s e e identi ied he a i ate e ate as ta en as the a e age n li t ate e all du li ate ai s e ll ed ust i et al in thei de initi n the es nden e et een the t ue and a a ent ates e inati n gi en an e ate s ust i et al Ha ett and ad t (𝜃𝜃0) (𝜑𝜑)
0 0 he ini u es luti n e inati n𝜑𝜑 =𝜃𝜃 (1 − 𝑠𝑠 e uen ) + (1 − 𝜃𝜃in)𝑠𝑠 a a ing ulati n si e N and issing alue ate is u e et al assu ing e ee data n the esen e e s the a e e uati n then i lies 𝜇𝜇 𝑟𝑟𝑚𝑚𝑚𝑚𝑚𝑚 ≈ 1/(2(1 − 𝜇𝜇)𝑁𝑁)
1 − 2𝜇𝜇𝜇𝜇𝜇𝜇 𝑟𝑟𝑚𝑚𝑚𝑚𝑚𝑚 ≈ e identi ied all ai s a e s2(1 − 𝜇𝜇that)𝑁𝑁 a ed ithin this distan e r n di e ent h l gues e ulsi n ai s nde a u el dis i del the e ulsi n hase a i u li elih d esti ate the e inati n e uen is gi en he e is the nu e s ing ith a d sage at 𝑛𝑛00+𝑛𝑛11 a e 𝑟𝑟𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑 =and𝑛𝑛00 a+ d sage𝑛𝑛01+𝑛𝑛10 + 𝑛𝑛 11 at a e 𝑛𝑛01 etc inhe itan e is tet as i this esti ate ne e alls el u and Han u e et al his s the asis 1 a in ial test H3 rdisom ≥ 1/3), corrected for multiple testing using FDR with α en a ini and H h e g his identi ied ss h l gue ai s that sh ed signi i ant de iati ns a tet as i del e then esti ated a e e ential ai ing a a ete the h l gue inati ns that sh ed signi i ant e iden e e e ential ai ing t e ulsi n hase a e s and l ated at the sa e geneti siti n the e inati n e uen esti ate et een the is a un ti n inde endent ass t ent ith n nt i uti n ss e s u and Han i en a e e ential ai ing a a ete the a ilities se ing ea h the lasses in the s ing a e es e ti el his 𝜌𝜌 1 𝜌𝜌 1 𝜌𝜌 1 𝜌𝜌 1 𝜌𝜌 leads t the ll ing e uati n 𝑛𝑛00, 𝑛𝑛01, 𝑛𝑛10, 𝑛𝑛11 6 − 4 , 3 + 4 , 3 + 4 , 6 − 4
𝜕𝜕 −(𝑛𝑛00 + 𝑛𝑛11) 𝑛𝑛01 + 𝑛𝑛01 (ln ℒ(𝜌𝜌)) ∝ + = 0 1 𝜌𝜌 1 𝜌𝜌 𝜕𝜕𝜕𝜕 4 − 4 + l ing ields the a i u li elih d(6 4) esti ate(3 4) the e e ential ai ing a a ete 𝜌𝜌
118 ______Chapter 5
2(𝑛𝑛00 + 𝑛𝑛11) − 4(𝑛𝑛01 + 𝑛𝑛01) 𝜌𝜌̂= 00 01 10 11 e e ded the ean and standa d3(𝑛𝑛 de iati n + 𝑛𝑛 + 𝑛𝑛 the+ n n 𝑛𝑛 negati e) esti ates t gene ate ai ing s e i i esti ates
Linkage analysis of a𝜌𝜌 segmental allopolyploid Ha ing esti ated the st ength e e ential ai ing all a e ted lin age g u s e e esti ated the ai ise e inati n e uen ies these ases he a i u li elih d esti ates e inati n e uen e e de i ed in athe ati a l a esea h n and e ted use in e ea des i ti n the li elih d del in luding e e ential ai ing is ided in u le enta eth ds a e s e e su se uentl e assigned t h s es and h l gues gi en the u dated in ati n and the a s e e e al ulated using a eed and Ha ett
Visualisation and quantification of haplotype diversity su set a e s hi h the e e e at least signi i ant lin ages t ea h the e e ted nu e h l gue luste s as used t de ine ha l t es hese all ed us t e a ine ai ise di e sit et een h l gues t in estigate the elati nshi et een h l gue si ila it and ai ing eha i u e de ined a si le dissi ila it easu e et een h l gues and ithin a ind ent ed at a e siti n j as
𝑁𝑁𝑗𝑗
𝐴𝐴−𝐵𝐵,𝑗𝑗 1 𝐴𝐴,𝑖𝑖 𝐵𝐵,𝑖𝑖 𝒟𝒟 = 𝑗𝑗 ∑|𝑑𝑑 − 𝑑𝑑 | 𝑁𝑁 𝑖𝑖=1 he e is the allele s e h l gue at a e siti n i (either ‘0’ or ‘1’) and is the nu e a e s ithin a sliding ind a und ea h a e 𝑑𝑑𝐴𝐴,𝑖𝑖 siti n j 𝑁𝑁𝑗𝑗 Integration with SSR and AFLP map e i usl a geneti lin age a the sa e ulati n using and a e s as u lished ning u i an et al e initiall atte ted t a all a e s t gethe ut und that the a e s tended t luste t gethe at the ends a lin age g u suggesting high tensi n et een the t a e datasets in age et een a e s and the set a e s as e aluated ith the th ee st signi i ant lin ages e ded gi ing these a e s a i ate siti ns n the a
119 ______Partial preferential chromosome pairing
Synteny analysis with Fragaria vesca he e re e e e e t ( ) ro hi h the h io rr r er ere eri e ere e i e r h i t the oo tr err e o e e (Fragaria vesca 0 1 e o o e e ( o o e o 19/09/2016 from http://www.rosaceae.org)) with ‘N’ used at the SNP position, as ro i e i e e t r e o o i o oir et ( 01 ) e 0 thre ho o 1 10 e to ret i o hi h ho o o o hit ith ti e hit i tere o t to oi t r eti ti e e i ie he ro e i e ere orie t te or i to the or er o the Fragaria e o e e e e ( i o e et ( 01 )) the re ti te i i e i the ir o o t re ( r i i et 00 ) he o t i e o itio o et o o e re ti r er ere o eter i e e o the o itio o their hit i the tr err e o e
ro i i itio i i tio or i o i e re tio Results
Marker filtering and dosage assignment o the h rr ere e t o ro e e i e to e to the i e e e t oth tr ( o i o oir et 01 ) ro e ere i e e e t ore i it etr ( oorri et 011) ere i tere or i to er o it riteri h o t i i t o t i i e (i ter i teri te ter er i ro e thi re e to 10 ) ei o e e (P 0 001) o t i i e er th i i or e e te ore ( e 1) i tere ro e ere er e here o i e ith o i ti ro e ei e t e r te i the i it he tho h re t ere e ot e i tri i te t o o the re t 1 ( 1) re i te ho e hi h er o i i e o o or e ith the o ri ( e e t o e e ot e ere i orre t e e ri re io ti i tio te ) here ore the re i te o 1 ith the e t o or e ith the o ri ore e e te here or t o o the three re i te ere o to h e e o i t (0 ) o e er e here ere 10 e re ti r er to e i i ith oo re o er the i e r er e ( e ) i etee ir o i te i i i ere i e ti ie ( ir i e e ot e orre tio 0 ) o i i i ith ore th 10 i i e ere o re o e re ti i i o tio i e o 1 1 i i i
Linkage map construction under a tetrasomic model e o o e the i ro e re e ri e or ot to i o r e et ( 01 ) tho h it ot o i e to o i te ho o o e ( i e i e or )
120 ______Chapter 5 c usters into chromosoma groups on the asis of repu sion phase in ages due to more noise in the data. nstead, coup ing in ages with dup e nu ip e N) mar ers were used to pro ide these associations. e used new mar er ordering software S ap Preed and ac ett, 2016) which great faci itated the creation of integrated chromosoma in age maps in this stud . ose is a predominant tetrasomic species and thus we can identif four homo ogous copies of each chromosome from each parent, assuming sufficient S N and N S mar ers e ist. er oth parents and se en in age groups there are therefore 2 6 homo ogue groups e pected. ift fi e of the e pected 6 homo ogues were identified, fo owing which we assigned e er other mar er t pe to oth its most pro a e in age group chromosomes, termed integrated consensus map ) groups 1 to , c.f. Spi er et a . 2011)) and homo ogue s) using a in age ogarithm of odds ) thresho d of .
Estimation of preferential pairing parameters i en an integrated in age map and a popu ation with dosage scores, etra rigin heng et a ., 2016) can e used to infer the identit descent ) pro a i ities for a offspring, usefu for su se uent ana ses ac ett et a ., 201 ). ere, we used it to estimate preferentia pairing etween chromosomes. sing the assumption of i a ent pairing, we app ied a χ² test to the predicted i a ent counts under the h pothesis of random pairing a e 1). t a significance e e of 0.001 three chromosomes e hi ited unusua eha iour 1 of P1 and and of P2), with an o er Table 1. Predicted pairing behaviour according to TetraOrigin, showing significance of the deviation from random pairing and the estimated preferential pairing parameter, ρ P1 a ICMb 12_34 c 13_24 14_23 χ² P-value d ρ 1 96 20 6 . 1.00E-14 0. 02 2 0 6 0. 0. 6 1.0 0.6 60 6 .2 0.0 6 0 12.2 0.002 6 61 6 .2 0.02 66 .1 0.02 P2 ICM 56_78 57_68 58_67 χ² P value ρ 1 6 1 6. 0.0 2 .6 0.1 1 22.6 0.00001 0.1 0 0 1 2 .0 1.3E-06 0.196 6 6 9. 0.01 6 2 2 0. 0.9 6 2 2 . 0.02 a P1 Parent 1, P2 Parent 2 integrated consensus map c he predicted num er of offspring with i a ent pairing etween homo ogues 1 and 2, and the second i a ent pairing etween and . d P value of the χ² test of the hypothesis of random pairing, significant values (P 0.001) in o d
121 ______Partial preferential chromosome pairing
representation of one i a ent configuration and an under representation of the other two, which was most e treme on chromosome 1 of P1 96 out of 1 1 counts were of the same pairing configuration). or in P1, there was a near significant departure from random pairing P 0.002) ut this arose from an under representation of one configuration, not two, which we ha e not attempted to mode .
Preferential pairing estimated from repulsion-phase linkages Preferentia pairing has pre ious een deduced from repu sion phase estimates between “nearby” SxN marker pairs in other studies. We estimated the minimum reso ution of recom ination fre uenc rmin) as appro imate 0.011 and found , 6 repu sion S N mar er pairs in P1 and 10 , 96 pairs in P2 mapped to within this distance on the integrated map a e S ). f these, 2 96 had significant e idence for non tetrasomic eha iour using a a se isco er ate ) corrected thresho d of 0.000 1, where α 0.0 ). Strong preferentia pairing was identified on 1 in P1, confirming our pre ious findings. he negati e og10 P) a ues of these tests in isua ised in igure 2. he strength of significance was not constant across the chromosome, part due to une en mar er distri ution. owe er, in the case of 1 of P1 this appears to a so e due to differences in pairing eha iour etween chromosome arms. possi e mode e p aining this eha iour is represented in igure 1. in which aria e pairing affinities are rea ised through a mi ture of i a ent and non random uadri a ent formation. ur estimated preferentia pairing parameters corresponded we with those from etra rigin a e 2), a though of P1 a so shows a region of preferentia pairing, which was not predicted etra rigin. he strongest e idence for preferentia pairing from repu sion phase in ages remains that of 1 in P1 and in P2.
Table 2. Significant preferential pairing identified using closely-mapping SxN marker pairs in repulsion
a c d Parent ICM h_a h_b ρ sd N Ns 1 1 1 0. 0.1 612 60 1 1 2 0.2 0.02 16 2 1 2 0.22 0.0 6 6 2 2 2 0.1 0.0 106 2 6 1 2 0.1 0.02 6 60 1 2 0.16 0.0 2 1 1 2 2 1 2 0.06 0.0 2 a integrated consensus map he standard de iation of the estimate for ρ, the preferentia pairing parameter etween homo ogues h a and h c he num er of non negati e estimates on which the estimate of ρ was ased d he num er of repu sion pairs that showed significant e idence for non tetrasomic eha iour
122 ______Chapter 5
Figure 2. Evidence for both disomic and tetrasomic behaviour from pairs of closely-mapped repulsion-phase SxN markers. he – o P a ues o a inomia test a ainst the hypothesis rr_d ≥ or SxN marker pairs in repu sion are p otted a ainst their approximate eneti position. 1 e ions3 o disomi beha iour hi h a ues o – o P are not uni orm y distributed su estin di eren es in pairin a inities a on hromosomes. he si ni i an e thresho d is shown as a dashed red ine. h h re ers to marker pairs rom homo o ues and . or simp i ity homo o ues in parent ha e been abe ed .
Ultra-high density Rosa hybrida linkage maps, tailored for segmental allopolyploidy We modi ied our pairwise re ombination re uen y ramework to in ude pre erentia pairin and re a u ated the re ombination re uen y s ore and phase or a a e ted inka e roups and then re mapped these hromosomes usin the amended estimates. or the ast ma ority o markers in the dataset there was no han e in the assi nment to hromosomes or homo o ues i.e. marker phasin was una e ted . We
123 ______Partial preferential chromosome pairing
ρ
Table 3. Numbers of markers mapped per linkage group on the ultra-high density Rosa hybrida map. Rosa ICM a length / cM N markers Max. gap (cM)
Prediction of quadrivalents and double reduction
124 ______Chapter 5
Figure 3. Comparison between the integrated genetic map (in centiMorgans) under a random bivalent model (x-axis) and a bivalent model that takes account of preferential pairing (y-axis) for rose chromosomes 1, 3 and 4. 𝑙𝑙𝑙𝑙𝑙𝑙 𝛿𝛿
Haplotype diversity and pairing behaviour
125 ______Partial preferential chromosome pairing
Synteny analysis with Fragaria vesca Rosa Fragaria c.f. –
Fragaria – –
126 ______Chapter 5
Figure 4. Overview of the synteny between Rosa hybrida and Fragaria vesca. a. Fragaria vesca . Fragaria vesca . b. Fragaria .
127 ______Partial preferential chromosome pairing
Discussion
Non-uniform distribution of preferential pairing . Indeed, in keeping with Stebbins’ description, Rosa chromosomal “mixosomy”; in rainbow trout it has been proposed that there may be “residual tetrasomy” Rosa e.g. Rosa
128 ______Chapter 5
runeau et al., ound the same chloroplast gene haplotypes in multiple species. more precise answer may there ore come rom genome se uences o arious diploid and polyploid accessions.
It is also worth noting here that pre erential pairing and marker skewness are di erent phenomena that may be con used. arker skewness can be caused by selection and can cause problems in linkage map construction an oi en and ansen, . or example, lethality or reduced itness is unlikely to be caused by a combination o alleles present in one o the parents since that parent is ali e and there ore, cross parental lethal combinations are more probable, which will not result in a pre erential pairing signal in one o the parents. Similarly, i selection is positi e e.g. at a resistance locus then the skewness is not in a our o a particular combination o parental homologues but rather o speci ic allele s ; in cases where there are two unctional copies in a single parent the e ect would appear as selection against a particular homologue combination i.e. “unpreferential” pairing). In any case, in this study we only mapped non skewed markers, so that all our e idence or pre erential pairing comes rom markers with no signi icant skewness. his is also isualised in igure S , showing that skewness le els among mapped markers were essentially uni orm across the rose genome.
Predicting pairing behaviour through homology e were interested to see whether pairing beha iour might be predicted rom the homology as de ined by our haplotype speci ic linkage maps. e chose a simple dissimilarity measure to analyse the di ersity between homologues in this study, similar to the most recent common ancestor measure used in population genetic studies oly et al., . e did not obser e any clear relationship between homology as estimated rom the mapped markers and pairing beha iour. owe er, as in all mapping studies, our data was biased towards higher di ersities since only segregating markers can be included on a genetic map. e should there ore treat these results with caution as they do not gi e a complete picture o homology, which only se uencing can ully re eal. elomeric homology, where pairing initiation is thought to occur S ed, ;Sybenga, ; i uentes et al., , might ha e more in luence than chromosome length homology and could be a target o uture se uencing e orts to clari y this.
Tailored genetic linkage maps In this study we generated genetic linkage maps tailored to the particular pairing beha iour o each chromosome. e could ha e urther re ined our maps by allowing the estimate or the rate o pre erential pairing to ary along the chromosome arms i this was deemed necessary. owe er, in this population the rate o pre erential pairing on
129 ______Partial preferential chromosome pairing the affected chromosomes was low enough that we could ha e ignored it in map construction. e can confirm our prediction that lin age mapping can e safely performed under the assumption of random pairing up to a le el of preferential pairing as high as ρ . ) after which estimates ecome seriously iased our e et al., ). his finding will li ely e welcomed y researchers in Rosa, for which the assumption of tetrasomic inheritance has generally een used. In this study, we used mar ers to pro ide lin s etween putati e homologue clusters of mar ers helping to identify chromosomal lin age groups). owe er, these may not always e informati e in cases of e treme preferential pairing, where simple simple ) mar ers may need to e used to pro ide cross homologue lin ages instead.
Synteny between Rosa and Fragaria In this study we used the close relationship etween Rosa and Fragaria to confirm the order and organisation of the lin age maps produced, as well as allowing us to position a set of non segregating mar ers which were indicati e of e treme preferential pairing in a distal region of maternal chromosome I . It also yielded a detailed picture of the high le el of genomic conser ation etween these species igure a, ). oth Rosa and Fragaria elong to the Rosoideae clade in the Potentilleae and Roseae tri es, respecti ely), whose di ergence is estimated to ha e occurred appro imately mya million years ago) iang et al., ). igh le els of gene conser ation ha e also een reported in the grass family, for e ample ennet en, ). n the other hand, despite an estimated di ergence time of mya, there is a much more stri ing difference in the genomic configuration of Brassica rapa and Arabidopsis thaliana urat et al., ), although this could e due to the fact that rassicaceae possess an e ceptionally high rate of iological radiation and di ersification ran e et al., ). It is tempting to speculate why rates of genomic di ergence differ etween plant families for e ample, the le el of acti ity of transposa le elements within the genome ennet en and ang, )), although such a meta analysis using data across multiple plant families has yet to appear in the literature. hat our study does ma e clear is that the pu lished reference se uence of Fragaria vesca continues to e a ery useful genomic resource for the ose research community, at least until such time as a ose se uence ecomes pu lically a aila le.
Concluding remarks In this study we ha e applied a no el approach for detecting and uantifying the le el of preferential pairing in a tetraploid iparental population of cut rose, and used this information to refine our estimates of recom ination to produce a tailored genetic map of this economically important species. e found conclusi e e idence for parent specific preferential pairing eha iour on three chromosomes whereas the other
130 ______Chapter 5 chromosomes showed tetrasomic eha iour. he picture that emerges is that the meiotic eha iour in polyploids may e difficult to predict without detailed analysis. e found that meiotic pairing eha iour can ary from chromosome to chromosome and from genotype to genotype, and perhaps e en along chromosome arms. ools which utilise chromosome wide inheritance information across all homologues are ery powerful in re ealing underlying meiotic mechanisms and confirm our findings using repulsion phase lin age information as well as information from syntenic mapping of non segregating duple mar ers to infer inheritance type. e unco ered a detailed picture of conser ed synteny with the closely related woodland straw erry, highlighting oth telomeric in ersions and reciprocal translocations which occurred somewhere in the lineages of one or oth of these species. ur ultra high density lin age map will facilitate down stream applications such as current efforts at genome assem ly as well as pro iding a asis for detailed analysis in the future.
Acknowledgements he authors would li e to than r. hristine ac ett and r. atherine reedy io ) for sharing a de elopmental ersion of ap, which was used in this study. he authors also wish to ac nowledge the two anonymous re iewers, whose comments helped impro e the manuscript. unding for this research was pro ided through the I polyploids project “A genetic analysis pipeline for polyploid crops”, project number BO . .
Supplementary data is available online at: http onlineli rary.wiley.com doi . tp . full
131 ______Partial preferential chromosome pairing
Supplementary Figure S1. A erage estimated probability of double reduction per parental meiosis o er t e se en rose c romosomes
132 ______Chapter 5
Supplementary Figure S2. isualisation of meiotically tailored ig density lin age maps, s o ing t e distribution of segregating mar er alleles across all eig t parental omologues for eac of t e se en rose lin age groups – , also listed in upplementary able using original mar er dosage coding
Supplementary Figure S3. A erage it in parent and bet een parent dissimilarity D for eac of t e se en rose c romosomes ultiple points correspond to eac set of omologue pairs it in t ese categories
133 ______Partial preferential chromosome pairing
Supplementary Figure S4. D
134 ______
Supplementary Figure S5. i.e. corrected for multiple testing using FDR with α = 0.05) assuming a χ
Chapter 5
135
Chapter 6 polymapR – linkage analysis and genetic map construction from F1 populations of outcrossing polyploids
Peter M. Bourke1, Geert van Geest1,2, Roeland E. Voorrips1*, Johannes Jansen3, Twan Kranenburg1, Arwa Shahin1,4, Richard G. F. Visser1, Paul Arens1, Marinus J. M. Smulders1, Chris Maliepaard1
1 Plant Breeding, Wageningen University & Research, Droevendaalsesteeg 1, 6708 PB Wageningen, The Netherlands.
2 Deliflor Chrysanten B.V., Korte Kruisweg 163, 2676 BS Maasdijk, The Netherlands.
3 Biometris, Wageningen University & Research, Droevendaalsesteeg 1, 6708 PB Wageningen, The Netherlands.
4 Van Zanten Breeding B. V., Lavendelweg 15, 1435 EW, Rijsenhout, The Netherlands.
Published (with modifications) as Bourke, P.M., van Geest, G., Voorrips, R.E., Jansen, J., Kranenburg, T., Shahin, A. et al. (2018). “polymapR – linkage analysis and genetic map construction from F1 populations of outcrossing polyploids”, Bioinformatics, doi: 10.1093/bioinformatics/bty371
137 ______polymapR - linkage mapping software
, many of the world’s most important crops. Genetic mapping in polyploids is more , . .
. , , , , , , . , , , , .
( ) . . .
, , , , ,
138 ______Chapter 6
n recent years there has een an acceleration of progress in the nderstanding of the genetics nderlying important traits in a topolyploid species. his has een to a large e tent d e to de elopments in high density genotyping platforms for single n cleotide polymorphism mar ers which ha e fo nd increasing application in polyploids. or e ample high density arrays ha e een de eloped in potato elcher et al. os et al. rose oning o coiran et al. alfalfa i et al. and chrysanthem m an Geest et al. c enhancing the scope for genetic st dies in these species.
n polyploid species as opposed to diploids co dominantly scored mar ers can possess multiple classes in the heterozygous condition, usually termed marker “dosage”. In a tetraploid there are fi e possi le dosage classes of a i allelic mar er namely n lliple with a dosage for one of the alleles simple with dosage d ple with dosage triple with dosage and adr ple with dosage . n a he aploid the n m er of dosage classes at a i allelic loc s rises to se en. ario s software ha e een de eloped to con ert the signal from e.g. arrays into these discrete dosage calls for polyploids s ch as fit etra oorrips et al. or l ster all chmit arley et al. .
Genetic lin age maps ha e traditionally een sed for oth e ploratory trait mapping often termed analysis and the s se ent fine mapping of traits as well as for assisting genome assem ly efforts y g iding the integration and orientation of contigs. igh density lin age maps may also impro e o r nderstanding of the chromosomal composition and genetics of polyploid species nco ering s ch phenomena as do le red ction or partially preferential chromosome pairing. n many polyploid species which lac reference genome se ences lin age maps are also a ital first genomic description of that species.
espite the importance of oth lin age maps and polyploid species there are still relati ely few software tools a aila le for polyploid lin age map constr ction. llopolyploid species showing disomic inheritance can e treated genetically spea ing as diploids with a wide range of software options a aila le. n the case of polysomic polyploids a topolyploids and segmental allopolyploids the options a aila le to the research comm nity are limited. ro a ly the most well nown a topolyploid mapping software is etraploid ap ac ett and o ac ett et al. which has een sed in st dies of ario s a totetraploid species s ch as potato alfalfa rose and l e erry e.g. radshaw et al. o ins et al. Gar et al. c all m et al. . ecently its s ccessor etraploid ap has een released to
139 ______polymapR - linkage mapping software accommodate high density marker data rom arrays ackett et al., . o e er, it can only handle autotetraploid datasets and pro ides a graphical user inter ace or the indo s plat orm only. inkage studies in species e hi iting strong pre erential chromosomal pairing or other ploidy le els are not currently possi le using this so t are. n alternati e polyploid mapping so t are is the package in
randke et al., . o e er, this so t are has een de eloped or use ith or ackcross populations rom homozygous parents only. In many cases, either due to in reeding depression or the di iculties imposed y polysomic inheritance, populations rom t o heterozygous parents are typically used instead.
In short, there is currently no so t are hich can per orm linkage mapping at arious ploidy le els under a ariety o inheritance models or outcrossing species using dosage scored marker data. ere e present polymap , an package ore eam, or linkage mapping in outcrossing polyploid species hich can generate linkage maps or polysomic triploids, tetraploids and he aploids, accommodating either ully tetrasomic or mi ed meiotic pairing eha iour segmental allopolyploidy at the tetraploid le el. Its modularity ill acilitate its adaption to other marker genotyping technologies or ploidy le els in the uture.
he polymap pipeline consists o our parts – data inspection, linkage analysis, linkage group assignment and marker ordering, hich are detailed elo . description o the unctions ithin polymap is descri ed in the ignette hich accompanies the package, going through all the steps in a typical mapping pro ect. or consistency and simplicity, all e amples mentioned here descri e a tetraploid cross.
he input data or polymap is dosage scored marker data, a aila le rom a num er o packages such as it etra oorrips et al., or luster all chmitz arley et al., . oth it etra and luster all are limited to tetraploid data e tensions to it etra to accommodate multiple ploidy le els are under ay. egardless o ho it is generated, the input dosage scored marker data should consist o a column o marker dosages or the mother, one or the ather ollo ed y a column or each o the o spring o the cross. hecks or marker ske ness and shi ted markers hen dosage scores are shi ted y a i ed amount are currently pro ided in polymap rom a suite o tools de eloped or the it etra package oorrips et al., .
140 ______Chapter 6
considered for a pair of 2x0 markers, from left to right, “coupling”, “mixed” and “repulsion”. could also be termed “subgenome specific” versus “subgenome straddling”.
– e.g.
141 ______polymapR - linkage mapping software
igh ualit data facilitates the generation of high ualit maps. ne indication of poor data ualit is a high proportion of missing values. he user ma choose to screen out markers or individuals ith more than a desired rate of missing values b default up to 0 is tolerated , or duplicate individuals. dentical markers, hich often occur in high densit marker datasets ith limited population si es and hence a limited number of recombination events, can be identified and reduced to one representative marker for the mapping steps, and reintegrated later. principal component anal sis can also be performed and visualised, hich ma highlight some un anted structure in the population for example due to pollination from an unkno n external pollen parent or from self pollination or outl ing individuals for example because of admixture .
2.1 Linkage analysis under a polysomic model n autopol ploid species ith pol somic inheritance, it is possible to model meiotic pairing structures as random bivalents or multivalents. n practice, both pairing structures tend to occur, ith a relativel lo fre uenc of multivalents in stable autopol ploids antos et al., 200 omblies et al., 20 . he main conse uence of multivalent formation from a genetic perspective is the phenomenon of double reduction, here t o segments of a particular homologue can end up in the same gamete and become transmitted together to offspring. t has been demonstrated that double reduction introduces some bias in recombination fre uenc estimates under a random bivalent model. his can be safel ignored if the rate of uadrivalent pairing is lo ourke et al., 20 ourke et al., 20 .
nder a random bivalent model, there are three possible bivalent pairing conformations in a tetraploid. n general, for an even ploid p 2n there are possible (2𝑛𝑛)! 𝑛𝑛 bivalent pairing conformations to be considered. iven an pair of𝑐𝑐 marker = (2 ).𝑛𝑛! loci ith unkno n recombination fre uenc r, e consider the contribution of recombinant homologues ith a ithin bivalent probabilit of and non recombinant homologues 1 ith a ithin bivalent probabilit of . n2 cases𝑟𝑟 here recombinants and non 1 recombinations cannot be distinguished,2 (1 both − 𝑟𝑟)are assigned a probabilit of . ssuming 1 random pairing, the probabilit of an particular pairing configuration is 2 in the case 1 of preferential pairing, e introduce a preferential pairing factor to model deviations 𝑐𝑐 from randomness here .
he expected fre uenc of each offspring class is first summed over all c bivalent conformations 𝑛𝑛𝑖𝑖𝑖𝑖 0 ≤ 𝑖𝑖, 𝑗𝑗 ≤2𝑛𝑛
142 ______Chapter 6
𝑐𝑐 1 𝐸𝐸(𝑛𝑛𝑖𝑖𝑖𝑖) = ∑ 𝑓𝑓𝑘𝑘(𝑟𝑟, 1 − 𝑟𝑟) 𝑘𝑘=1 𝑐𝑐 here denotes a function of and , dependant on the marker combination considered. iven these expected fre uencies, e relate them to the 𝑓𝑓𝑘𝑘(𝑟𝑟, 1 −𝑟𝑟) 𝑟𝑟 1 − 𝑟𝑟 observed counts of individuals in each class to ield the likelihood function
𝑂𝑂(𝑛𝑛𝑖𝑖𝑖𝑖) ℒ(𝑟𝑟) 2𝑛𝑛 𝑂𝑂(𝑛𝑛𝑖𝑖𝑖𝑖) ℒ(𝑟𝑟) ∝ ∏ 𝐸𝐸(𝑛𝑛𝑖𝑖𝑖𝑖) 𝑖𝑖,𝑗𝑗=0 he likelihood e uation results from e uating the first derivative of the log of the likelihood function ith ero
2𝑛𝑛 𝑐𝑐 1 𝑑𝑑 ∑ (𝑂𝑂(𝑛𝑛𝑖𝑖𝑖𝑖) . ∑ ln (𝑓𝑓(𝑟𝑟, 1−𝑟𝑟))) = 0 𝑖𝑖,𝑗𝑗=0 𝑘𝑘=1 𝑐𝑐 𝑑𝑑𝑑𝑑 n cases where no analytical solution exists, we use Brent’s algorithm rent, to numericall maximise the log likelihood function in the bounded interval . or an pair of markers there are a number of possible phases bet een these markers to 0 ≤ 𝑟𝑟 < 0.5 consider, hich describe the ph sical linkage bet een marker alleles. n the case of a pair of duplex x nulliplex (2x0) markers, these phases are termed “coupling”, “mixed” and “repulsion” (Figure 1.a). As the phase between markers is initially unknown, we must compute expressions for each of the possible phases, and select the most likel as the phase for hich and hich maximises the log of the likelihood ackett et al., 20 . 0 ≤ 𝑟𝑟 < 0.5 inall , e also compute the logarithm of odds score, hich provides a useful measure of the confidence in the estimate and is used for both marker clustering and marker ordering
ℒ(𝑟𝑟 =𝑟𝑟̂) 𝐿𝐿𝐿𝐿𝐿𝐿 =𝑙𝑙𝑙𝑙𝑙𝑙10 ( ) here is the maximum likelihood estimate ℒof( 𝑟𝑟r. = 0.5)
2.2 Linkage𝑟𝑟̂ analysis in the presence of preferential chromosomal pairing n certain pol ploid species the meiotic pairing is neither full random nor full partitioned into exclusivel pairing subgenomes, a situation described as segmental allopol ploid tebbins, . egardless of the underl ing mechanism, the result of
143 ______polymapR - linkage mapping software preferential pairing is that both the segregation ratios and the co inheritance of marker alleles are affected. n the example of a 2x0 marker introduced earlier, the expected segregation ratio in a polysomic autotetraploid is 1 1. ith increasing preferential pairing, this ratio will approach 1 2 1 in the case of subgenome straddling markers (Figure 1.b right), or approach non segregation in the case of subgenome specific markers (Figure 1.b left).
n order to model this beha iour, we introduce a preferential pairing parameter ρ, such that (in the case of a tetraploid) the probability of the chromosome pairing configuration 1 2 is and the probability of pairing configurations 1 2 and 1 2 is 1 . Attempting3 + 𝜌𝜌 to model preferential pairing at higher ploidy le els introduces further 1 𝜌𝜌 complications hu et al. (201 ) ha e proposed a solution for hexaploids by introducing 3 − 2 three preferential pairing parameters θ1, θ2 and θ3 to model de iations in bi alent configurations 1 2, and respecti ely, with all other configurations ha ing a probability of . n our software, we ha e not yet attempted to 1 1 model segmental allohexaploidy, and confine our attention to the tetraploid le el for 15 − 12 (𝜃𝜃1 + 𝜃𝜃2 + 𝜃𝜃3) now.
e do not simultaneously estimate ρ and r, which can lead to an o er estimation of the preferential pairing parameter ( u et al., 2002). nstead, we estimate the chromosome wide strength of preferential pairing after map construction and thereafter correct the pairwise recombination fre uency estimates to re ise the maps. A robust method of preferential pairing detection and estimation is to use inheritance probability estimates such as those pro ided by etra rigin ( heng et al., 201 ) in polymap we offer a simpler likelihood based approach which uses closely linked repulsion marker pairs to test for de iations from random pairing and simultaneously estimate the strength of this de iation
2(𝑛𝑛00 + 𝑛𝑛11) − 4(𝑛𝑛01 + 𝑛𝑛01) 𝜌𝜌 = 00 01 10 11 where is the number of offspring3(𝑛𝑛 with+ 𝑛𝑛a dosage+ 𝑛𝑛 0+ at 𝑛𝑛marker) A and 1 at marker B etc.
01 i en 𝑛𝑛a parent and chromosome specific estimate for the preferential pairing factor ρ, we modify the expression for the expected fre uency of indi iduals in marker class of a tetraploid as follows 𝑛𝑛𝑖𝑖𝑖𝑖
1 1 𝜌𝜌 1 𝜌𝜌 𝐸𝐸(𝑛𝑛𝑖𝑖𝑖𝑖) = ( + 𝜌𝜌)1 𝑓𝑓 (𝑟𝑟, 1−𝑟𝑟) + ( − ) 𝑓𝑓2(𝑟𝑟, 1−𝑟𝑟) + ( − ) 𝑓𝑓3(𝑟𝑟, 1−𝑟𝑟) 3 3 2 3 2
144 ______Chapter 6
ue to the lack of symmetry, we must consider all possible conformations within each phase, an example of which is shown in Figure 1.b. he procedure for estimating r and remain otherwise the same. he inclusion of preferential pairing imposes an extra computational burden as each phase can ha e up to four sub phase conformations, all of which are calculated prior to selection of the most likely phase and its associated r and score.
Finally, in both the case of random and preferential pairing, linkage calculations can be run in parallel (using do arallel ( icrosoft orporation and eston, 201 )) on any indows or nix like multi core desktop computer resulting in significant time sa ings. igh density marker datasets with tens of thousands of markers can be processed in a few hours.
n diploid studies, the term linkage group is loosely synonymous with the term chromosome. n autopolyploids two le els of linkage group exist – homologue groups and integrated chromosomal groups. he first step in linkage group assignment is to cluster the 1x0 linkage data into homologue groups, for which we currently use the package igraph ( sardi and epus , 200 ). lustering is performed using the pairwise linkage scores, although the for independence can be used if desired, which may be more robust with skewed marker data ( an oi en and ansen, 201 ).
A number of isual aids are pro ided to assist in clustering (Figure 2). n general, clustering should be performed o er a suitable range of thresholds (e.g. from to 10) in order to inform the choice of score to partition the data into both homologues and chromosomes (Figure 2.a, b). f chromosome and homologue clusters cannot be readily identified using 1x0 markers alone, coupling phase homologue clusters are first identified at a high and later re connected into chromosomal clusters using a higher dose marker type (Figure 1.c). isualisations help display the strength of associations between homologues (Figure 2.c). ccasionally homologues may split apart arious possibilities to merge these fragments are pro ided (Figure 2. d, e, f).
n the case of triploid populations, the phasing approach differs between the diploid and tetraploid parents for the diploid parent, phasing can be achie ed directly using the phase assignment from the linkage analysis. Following the definition of the chromosome and homologue structure using the 1x0 markers, all other marker segregation classes are assigned to both homologues and chromosomes using their linkage to these markers, generating the final phase assignment of all marker types.
145 ______polymapR - linkage mapping software
146 ______Chapter 6
r –
–
147 ______polymapR - linkage mapping software
Citrullus lanatus lanatus Vitis vinifera
– –
TetraploidSNPMap (TSNPM)
148 ______Chapter 6
PERGOLA
149 ______polymapR - linkage mapping software
n00 n44 labours under no such “generalist” difficulties. Phase considerations are trivial and – function to 400 cM using Haldane’s lengths of approximately 90 cM using Haldane’s and
–
work was supported through the TKI projects “A genetic analysis pipeline for polyploid crops” (project 001) and “Novel genetic and genomic tools for polyploid crops” (project number BO
150 ______Chapter 6
omparison of final linkage maps produced by polymap (y axis) and Tetraploid NPMap (x axis) using the sample dataset provided with the polymap package. or all linkage groups the marker order map length and the number of mapped markers were almost identical between both software.
151
Chapter 7
An ultra-dense integrated linkage map for hexaploid chrysanthemum enables multi- allelic QTL analysis
Geert van Geest1,2,3, Peter M. Bourke1, Roeland E. Voorrips1, Agnieszka Marasek- Ciolakowska4, Yanlin Liao1, Aike Post2, Uulke van Meeteren3, Richard G.F. Visser1, Chris Maliepaard1, Paul Arens1
1 Plant Breeding, Wageningen University & Research, Droevendaalsesteeg 1, 6708 PB Wageningen, The Netherlands.
2 Deliflor Chrysanten B.V., Korte Kruisweg 163, 2676 BS, Maasdijk, the Netherlands
3 Horticulture & Product Physiology, Department of Plant Sciences, Wageningen University & Research, Droevendaalsesteeg 1, 6708 PB Wageningen, the Netherlands 4 Research Institute of Horticulture, Konstytucji 3 Maja 1/3, 96-100 Skierniewice, Poland
Published (with modifications) as Van Geest, G., Bourke, P.M., Voorrips, R.E., Marasek-Ciolakowska, A., Liao, Y., Post, A., et al. (2017), “An ultra-dense integrated linkage map for hexaploid chrysanthemum enables multi-allelic QTL analysis”, Theoretical and Applied Genetics 130, 2527-2541
153 ______Ultra-dense chrysanthemum map
Abstract nstructi n an use lin a e a s is c allen in in e a l i s it lys ic in eritance ull a inte rati n re uires calculati ns rec inati n re uency et een ar ers it c le se re ati n ty es n a iti n, etecti n QTL in e a l i s re uires in r ati n n all si alleles at ne l cus r eac in i i ual e escri e a et t at e use t c nstruct a ully inte rate lin a e a r c rysant e u (Chrysanthemum x morifolium, 2n ) A i arental 1 ulati n 0 in i i uals as en ty e it an 1 ,000 en ty in array T e resultin lin a e a c nsiste 0, 12 se re atin ar ers all ssi le ar er sa e ty es, re resentin nine c r s al lin a e r u s an 107 ut 10 e ecte l ues ynteny it lettuce (Lactuca sativa) s e l cal c linearity erall, it as i en u t nu er t e c rysant e u c r s al lin a e r u s acc r in t t se in lettuce e use t e inte rate an ase lin a e a t rec nstruct in eritance arental a l ty es in t e 1 ulati n sti ate r a ilities r t e arental a l ty es ere use r ulti allelic QTL analyses n ur traits it i erent un erlyin enetic arc itectures T is resulte in t e i enti icati n a r QTL t at ere a ecte y ulti le alleles a in a i erential e ect n t e en ty e T e resente lin a e a sets a stan ar r uture enetic a in analyses in c rysant e u an cl sely relate s ecies re er, t e escri e et s are a a r ste r ar r lin a e a in an QTL analysis in e a l i s
Keywords aut e a l i , ar er sa e, i entity y escent, a l ty e, lys ic ly l i
154 ______Chapter 7
Introduction A lin a e a is a startin int r l calisati n en ic re i ns t at are ass ciate it a riculturally i rtant traits T is a es it an i rtant t l r A in r e ree in ( eace, 2017) r ly l i s, A in r e ree in as la e e in c are t i l i s, ecause en ty in c inant ar ers an lin a e a c nstructi n in ly l i s re uires s ecialise et s uc et s nee t e a le t an le i er se ar ers As se t i l i s, ly l i s a e ulti le c n r ati ns eter y us en ty es n a l cus it t alleles, a e a l i can a e i e i erent eter y us en ty es ran in r a sa e ne t a sa e i e T et er it t e t y us c n r ati ns, t is a s u t se en i erent sa e sc res
any lin a e a s ly l i s are c nstructe it sin le se ( resent a sent) ar ers usin et s e el e r i l i s T se in s a s are li ite t re resentin nly in i i ual l ues nte rati n se arate a s l us c r s es is nee e r trans era ility results et een a in stu ies an a in traits it a c le enetic arc itecture n an inte rate a , all ar ers are l cate relati e t eac t er, resultin in ne re resentati n t e siti ns all a e l ci, irres ecti e t e ase t eir alleles T is ena les c aris ns lin a e a s ase n i erent ulati ns a inte rati n re uires esti ati n lin a e et een sin le se ar ers in re ulsi n r lin a e et een i er se ar ers sti ati n lin a e ar ers in re ulsi n is i erent r i l i s an can nly e ne it ery l c n i ence, es ecially in a e a l i ( u et al , 1 2) e re ati n rati s i er se ar ers are airly c le , an calculati n rec inati n re uency nee s s eci ic statistical et s ( ac ett et al , 1 ) ecause t e c licate nature rec inati n re uency esti ati n et een i er se ar ers, e icate s t are is re uire
n an utcr ssin s ecies, t e nu er alleles t at can a ect a trait in a sin le in i i ual is t e sa e as t e l i y le el ( i ure 1 a) r QTL etecti n in an utcr ssin ull si ulati n it ut any ri r n le e n t e in l e alleles, all t el e ssi le alleles t at can e in erite r t e arents s ul t ere re e ta en int acc unt ( i ure 1 ) it use t e siti ns ar ers n a n n inte rate lin a e a l ues, nly in r ati n n t e resence r a sence ne ut t el e arental alleles is a aila le ( i ure 1 c) t e t er ele en alleles are i n re , any QTL t at es
155 ______Ultra-dense chrysanthemum map n t a e un erlyin alleles it a r e ect n t e trait ill e isse ulti allelic QTL a in t ere re nee s in r ati n all alleles er l cus
Figure 1. Marker allele considerations in an autohexaploid. a. a le a cr ss t arents it eac si i erent alleles b. An 1 r eny is c se t a etes it rec inati ns r t arents c. y c nsi erin a sin le 1 1 se re atin ar er, e can nly c aracterise a sence r resence ne allele in t e 1 s rin (c l ure an in icates ser e resence a ar er allele) e er, t e actual situati n is uc re c le n t at sa e l cus t ere are i e t er alleles t at all c ul a e s eci ic e ects n t e en ty e en ty e r a ility els try t rec nstruct t e actual situati n y esti atin a sence an resence r eac allele er l cus
st r ress in lin a e a in in an utcr ssin e a l i it lys ic in eritance as een re rte in s eet tat (Ipomoea batatas) n t is s ecies, se eral n n inte rate a s a e een u lis e ( s it an T s n, 1 7 rie ner et al , 200 er antes l res et al , 200 an et al , 200 n en et al , 201 irasa a et al , 2017), it t ree u licati ns re rtin in r ati n n l us c r s es it ut actually inte ratin t e a s n t u licati ns, t is in r ati n as ase n ar ers t at a a sa e t ( u le ) in ne arent an er (nulli le ) in t e t er (2 0 ar ers), an ar ers it a sa e t ree (tri le ) in ne arent an er in t e t er ( 0 ar ers ( s it an T s n, 1 7 er antes l res et al , 200 )) t ers a e i enti ie l us c r s es ase n ali n ent t a re erence en e ( irasa a et al , 2017) i ilar t s eet tat , c rysant e u is an utcr ssin e a l i it lys ic in eritance ( an eest et al , 2017c) airin at ei sis is ri arily t r u i alents, ut ulti alents ccur ( as et al ,
156 ______Chapter 7
1 en et al , 200 ) e rte et s r lin a e a c nstructi n ( an et al , 2010a an et al , 2011 ) an QTL analysis ( an et al , 2012a an et al , 2012 an et al , 201 a) r c rysant e u a e een li ite t et s e el e r i l i s, an c nstructe a s are t ere re n t inte rate
n a e a l i , an inte rate lin a e a is st re era ly c nstructe y esti ati n lin a e it i er se ar ers T se ulti se ar ers can c nnect l us c r s es it in arents an et een arents an can t ere re e use t inte rate t e r tetra l i s, et s t esti ate lin a e et een i er se inant ar ers a e een e el e ( ac ett et al , 1 ), an a lie t c nstruct inte rate lin a e a s ( eyer et al , 1 Lu et al , 2001 c allu et al , 201 ) Later, t ese et s a e een e ten e an a lie t i allelic ar ers ( ac ett et al , 201 ur e et al , 201 ur e et al , 2017) uc et s ul nee t e e ten e t e a l i s in r er t enerate inte rate lin a e a s it use i er se ar ers
An inte rate lin a e a can e use t rec nstruct in eritance arental a l ty es t a r ac a re resentati n as in t e e a le in i ure 1 T e t alleles i allelic s can e in lin a e ise uili riu it ulti le a l ty es, eac a in a i erent e ect n t e en ty e uc a l ty es can e i enti ie ase n t e c n i urati n nei urin alleles et s r rec nstructi n a l ty e in eritance y esti atin r a ilities i entity y escent ( ) in tetra l i i arental ulati ns a e een e el e ( ac ett et al , 201 ur e, 201 en et al , 201 ) Alt u all et s are t e retically e ten i le t e a l i s, t e et e el e y ( ur e, 201 ) is l i y le el in e en ent an is t ere re irectly a lica le t e a l i s
n t is a er, e escri e t e c nstructi n an inte rate lin a e a r all ssi le ar er sa e ty es in e a l i c rysant e u e are settin t e stan ar r trans era ility results y c r s al lin a e r u nu erin ase n synteny it lettuce (Lactuca sativa) an y eneratin a c re set ar ers t at can e use t anc r uture a s it t e inte rate lin a e a , e rec nstruct a l ty es ase n arental ri ins usin a relati ely si le r ce ure e e nstrate t e use ulness r QTL a in r ur traits r ic in r ati n all t el e se re atin alleles as ta en int acc unt
157 ______Ultra-dense chrysanthemum map
Materials and methods
Plant material and phenotyping e analyse t e se re ati n ar ers in a i arental ulati n t at c nsiste 0 in i i uals ri inatin r a cr ss et een 1 ( 1) an 2 7 ( 2), t aisy ty e, ite c rysant e u culti ars en ty in t lace in t e sa e e eri ent as escri e y ( an eest et al , 2017 ) n s rt, t e s rin an arents ere r n in t ree ran ise l c s in eac t ree seas ns su er ( ay t uly 201 ), late su er (Au ust t ct er 201 ), an autu n ( e te er t e er 201 ) A re licate c nsiste a iel c ntainin 10 t 0 lants lants ere r n in 12, 12 an 1 ays 1 , 21 an 21 t eri s r t e su er, late su er an autu n, res ecti ely T in uce l erin , t ey ere su se uently r n in 12 t eri s r t e lants r n in su er an late su er an in 11 t eri s r t e lants r n in autu n l er c l ur as rec r e ase n isual ser ati n l ers ere c letely ite, t ey ere sc re as 0, i t ey ere sli tly in as a 1, an in l ers ere sc re as 2 l erin ti e as rec r e as t e nu er ays (at s rt t eri ) nee e t reac c ercial aturity r at least 0 t e lants r n in a sin le iel T e nu er ray l rets as c unte r t e t ir l er ea r t e t ne l er ste r eac re licate T e en ty ic sc res taine r is l ret e reenin are escri e y ( an eest et al , 2017 ) erita ility as calculate y i i in t e esti ate en ty ic ariance y en ty ic ariance ariances ere esti ate usin an analysis ariance (A A) it trial an en ty e as i e e ects
Mitotic chromosome counting r it tic eta ase c r s e analysis, 1 c l n r ts ere c llecte r 1 ( 1) an 2 7 ( 2) an incu ate in e en r tu es in ice ater r 2 r an t en i e in et an l–acetic aci ( 1) s luti n r 12–2 r ts ere st re in i ati e at 20 until use r c r s e re arati ns, t e r t ti s ere as e ti es in in en y e u er (0 01 citric aci s iu citrate, ) an incu ate in an en y e i ture c ntainin 1 ( ) ect lyase 2 , 1 ( ) cellulase at 7 r a ut 1 uas re arati ns ere a e in a r acetic aci an r en in li ui nitr en T e c er sli s ere re e y usin a ra r la e T e sli es ere t en e y rate in a s lute et an l, air rie an staine it 1 l , ia i in 2 enylin le ( A , i a) in ectas iel ( ect r La rat ries) a es lu rescently staine c r s es ere ac uire usin a an n i ital ca era attac e t an A i t icr sc e it an a r riate ilter an t en r cesse usin
158 ______Chapter 7
Genotyping and marker quality filtering
p χ²
Linkage map construction r i.e. r i.e.
159 ______Ultra-dense chrysanthemum map
r in the range 0 ≤ r
suggested by the authors: we used Haldane’s mapping function, two
160 ______Chapter 7 with mar ers that formed the bac bone clustering f there were at least fi e coupling lin ages with mar ers at greater than , alleles were assigned to a homologue f the number of mar er alleles was not e ual to the number of assigned homologues, the mar er was not included in the phased map
s mar ers were disco ered from an se deri ed transcriptome assembly, each mar er is associated with a transcript contig se uence his information was used to in estigate the uality of the map ar ers of the type that originated from the same transcript contig should ha e a distance approaching c on the integrated map assuming the contig was assembled correctly or each homologue combination and for each lin age group, an o erall de iation was uantified by calculating the root mean s uare error of these differences on the integrated map for all mapped mar ers originating from the same transcript contig
o enable alignment of any future lin age maps in chrysanthemum by gene se uences, mar ers were identified that originated from contigs representing characterised genes or this, mapped mar ers were aligned to all proteins from the ni rot database from Chrysanthemum x morifolium ta onomy using ltschul et al , Hits were filtered for alignment lengths greater than and more than identity subset of mar ers originating from these filtered transcript contigs spread o er all lin age groups was selected to form a reference lin age map
Synteny with lettuce o in estigate the synteny of the integrated lin age map with lettuce Lactuca sativa , mapped transcript contigs were aligned to the mapped unigenes of lettuce as a ailable from the ettuce hip ro ect website ruco et al , using ltschul et al , ni ue hits with an e alue smaller than were used to assess synteny hrysanthemum were renumbered based on the number of alignment hits with the lettuce lin age groups
IBD probabilities n order to estimate presence of parental haplotypes in the offspring, we calculated probabilities as described by our e, schematic o er iew of the method is shown in igure ased on the phased map and lin age information, probabilities per mar er locus were calculated for each member of the population in two steps he information was stored in a three dimensional array for each chromosomal lin age group, with mar er, offspring indi iduals and homologue on the , y, and dimensions n the first step, only fully informati e dosage scores were used to fill the probability array his means that if a progeny has inherited all alleles of a mar er on specific homologues, this progeny will be assigned an probability of for these homologues
161 ______Ultra-dense chrysanthemum map at that mar er locus f none of the alleles are inherited, the probabilities for these homologues at the locus would be n general, any scores in the progeny that were larger than ero and smaller than the sum of the parental dosage scores were considered as non informati e e.g. for a mar er, progeny with a dosage of or a dosage of were considered informati e, and with a dosage of non informati e robabilities of loci at homologues of progeny that had non informati e mar er scores were gi en a starting probability of n the second step, inter mar er distance was used to estimate the probabilities of homologue loci with non informati e mar er scores or each mar er locus at each homologue in each progeny the closest informati e mar er was located, and probabilities were calculated based on this closest informati e mar er, where:
if Pj , and 𝑃𝑃𝑖𝑖 = 1 − 𝑟𝑟𝑖𝑖𝑖𝑖
𝑖𝑖 𝑖𝑖𝑖𝑖 if Pj 𝑃𝑃 = 𝑟𝑟 Here, P represents the probability, i indicates a mar er without full information and j indicates a fully informati e mar er, and r represents recombination fre uency between an informati e and non informative marker as calculated using Haldane’s mapping function from estimated distance on the integrated map fter assignment of probabilities, the sum of probabilities per parent was normalised to three as there are three homologous chromosomes in a gamete or each homologue in each indi idual, a cubic spline was fitted o er probabilities ersus position to calculate probability interpolations o er c inter als enotype information content for inter al k at homologue h for n indi iduals was calculated with the following formula:
𝑛𝑛 2 𝐺𝐺𝐺𝐺𝐺𝐺ℎ𝑘𝑘 = 1 − ∑ | 𝑃𝑃𝑖𝑖 − ⌊𝑃𝑃𝑖𝑖⌉ | where 𝑛𝑛 𝑖𝑖=1
⌊𝑃𝑃𝑖𝑖⌉ = 0, 0 ≤ 𝑃𝑃𝑖𝑖 ≤ 0.5, 𝑖𝑖 𝑖𝑖 his results in a score for ranging⌊𝑃𝑃 ⌉ = 1, from 0.5 to < , 𝑃𝑃 where≤ 1 represents a locus with little information, and with complete information
QTL mapping analysis was performed on bloc corrected mean phenotypic alues using an probability model, as described before for tetraploids our e, n additi e model modified from empthorne, as suggested by Hac ett et al , Hac ett et al , was modified to the he aploid le el:
162 ______Chapter 7
𝑌𝑌 = 𝜇𝜇 +𝛼𝛼2𝑋𝑋2 + 𝛼𝛼3𝑋𝑋3 + 𝛼𝛼4𝑋𝑋4 + 𝛼𝛼5𝑋𝑋5 + 𝛼𝛼6𝑋𝑋6 + 8 8 9 9 10 10 11 11 12 12 ere αi and Xi are t e𝛼𝛼 main𝑋𝑋 + effects 𝛼𝛼 𝑋𝑋 +and 𝛼𝛼 indicator𝑋𝑋 + 𝛼𝛼 varia les𝑋𝑋 + 𝛼𝛼for 𝑋𝑋allele i res ectivel e arameters re resenting omologue and omologue ere taken as t e reference classes and ere t erefore omitted from t e model as in all cases t ree alleles are in erited er arent o calculate t e significance t res old for detecting significant a t ousand ermutations ere run it randoml ermuted enot es urc ill and oerge taking t e t ercentile of t e ordered minimum values from eac genome scan anal sis as an a ro imate significance t res old o identif omologues affecting t e trait a sim le linear model as run for eac of t e t elve alleles se aratel
Figure 2. Visualisation of the estimation of IBD- probabilities. ot etical integrated linkage ma and t e se arate linkage ma s of t e si omologues of one arent are s o n in dark gre and ite res ectivel n t e u er anel of t e line gra ro a ilit t e calculation of ro a ilities for omologue are s o n for marker loci v ink tri le w ur le du le and y green sim le in a situation in ic all alleles of marker x lue sim le and z red du le are in erited ince all alleles of loci x and z are in erited t ese loci get an ro a ilit of for in eritance of omologue or marker loci v w and y none of t e marker alleles are resent on omologue t is t erefore not kno n et er is in erited at t ese loci e orange lines de ict t e relations i et een genetic distance and recom ination fre uenc r as a function of ma distance ecause distance et een all marker com inations is kno n from t e integrated ma e estimate t e ro a ilities of loci v w and y as r in case of in eritance of all alleles of x and z ere r is t e recom ination fre uenc et een t e locus and t e closest informative marker marker x in t e case of w and v and z in t e case of y e lo er anel of t e line gra s aded in gre ro a ilit de icts t e situation ere none of t e alleles of loci x and z are in erited Here ro a ilities for v w and y are estimated as r
163 ______Ultra-dense chrysanthemum map
Results
Linkage map fter removal of markers t at ere non segregating ad distorted segregation or ad more t an missing values markers remained in t e dataset f t ose ad uni ue dosage scores across t e rogen igure ecause markers it identical dosage scores in eac individual non uni ue markers ill ma to t e e act same osition t e ere reduced to a single uni ue marker for calculation of linkage and ordering e ot ers ere added to t e linkage ma after ma construction it onl uni ue markers
Figure 3. Distribution of 19 different marker types segregating in the bi-parental population. otal num er of markers of ic ere uni ue e non uni ue markers ad du licate dosage scores across t e o ulation e la els on t e a is re resent marker segregation types such as simples x nulliplex (1x0) etc. (“dosage parent 1” x “dosage parent 2”)
im le nulli le and nulli le sim le and markers ere used to construct ack one clusters t at re resent omologues is resulted in clusters for and clusters for eac containing five or more markers romosome counting s o ed t at ot arents ad n c romosomes t e e ected eu loid c romosome num er ur dataset as t erefore lacking markers identif ing one out of t e omologous c romosomes of dentification of c romosomal linkage grou s it sim le sim le markers resulted in a net ork of nine re resenting all omologue clusters of ot arents ll ot er marker t es ere su se uentl assigned to a ased on linkage it and markers n total uni ue markers could e assigned arkers ere ordered er ased on recom ination fre uenc it as eig ts resulting in ma lengt s ranging
164 ______Chapter 7
rom . to .0 c . ter ordering the groups o non uni ue mar ers ere added to the lin age map ased on the position o their uni ue representing mar er resulting in a lin age map containing 0 12 mar ers ( . o initial a le 1). the ordered mar ers the alleles o 2 ( . o initial) could e phased to an expected num er o homologues ased on parental dosages ith at least i e signi icant lin ages to 1x0 mar ers ( a le 1) resulting in a ully phased lin age map.
Table 1. Summary statistics of integrated linkage map CLG a Length (cM) N b Phased markers Contigsa Roundsb 1 2 2 2 2 1 1 2 2 . 1 110 1 11 3 . 2 0 2 1 2 4 .2 01 21 1 5 0. 2 1 0 6 1.1 1 1 2 7 1. 1 21 2 8 0 1 0 2 9 .1 10 0 1 sum 2.1 0 12 2 1 0 2 mean . 1 2 1 a chromosomal lin age group num er o mapped mar ers c um er o transcript contigs associated ith mapped mar ers. um er o rounds o pro lematic mar er remo al and re ordering a ter the irst ordering.
Synteny with lettuce and reference map e aligned mapped transcript contigs o chrysanthemum ith mapped lettuce unigenes ( igure ). e aligned the 1 0 2 mapped chrysanthemum transcript contigs to 12 1 mapped lettuce unigenes and o tained uni ue hits ith an e alue smaller than 1 100. his resulted in the identi ication o syntenic lin age groups et een lettuce and chrysanthemum. ll com inations o lin age groups o chrysanthemum and lettuce ith maximum num er o hits ere uni ue except or and . hese t o had oth most hits ith lettuce . he chrysanthemum ith least hits to lettuce as renum ered ased on the non assigned lin age group rom lettuce. his com ination still had 12 hits indicating partial similarity. yntenic analysis per resulted in identi ication o large regions ith linear correspondence et een locations o genes so the genomes appear to e partly co linear at local scale. his as not clear at a larger scale as syntenic regions ere scattered across the lin age map o lettuce hich can e
165 ______Ultra-dense chrysanthemum map interpreted as that each chromosome carries ma or in ersions and translocations. ith use o this data e ased the num ering o chrysanthemum on the num er o signi icant alignments o mapped transcripts. o mar these nine chrysanthemum lin age groups e present 2 de ining mar ers. hese are e enly spread o er all nine and originate rom contigs representing genes coding or protein entries o the ni rot data ase ( igure ). his should e a use ul tool or uture studies in chrysanthemum.
Figure 4. Synteny between the lettuce ultra-high density map (Truco et al. 2013) and chrysanthemum. ach dot represents a signi icant alignment et een lettuce unigenes and chrysanthemum transcript contigs
Linkage map quality e used t o analyses to e aluate the uality o the lin age map. irst to in estigate the concordance et een estimated pair ise r (rpair ise) and r ased on map distance (rmap) these t o estimators o r ere plotted against each other. ith high scores these t o estimators ere in concordance ith each other o er a ide range o r ( rom 0 to 0. ). econd to e aluate the position o near y 1x0 mar ers in coupling and repulsion e aligned the position on the integrated map o 1x0 mar ers that originated rom the same transcript contig rom the se assem ly. he positions o mar ers that originated rom the same contig and had the same phase ( mar ers in total) aligned nearly per ectly ( igure ) indicating lo error rates. he position o mar ers phased
166 ______Chapter 7 on di erent homologues ( 2 mar ers in total) as more spread. he residual mean s uared error ( ) as calculated or each lin age group ( igure ) and each com ination o homologues rom the same lin age group. as generally elo c ith some outliers on 2 and . hese outliers ere caused y one t o and t o mar ers respecti ely.
Figure 5. Integrated linkage map of phased markers with 1x0 markers (black), other marker types (grey) and CLG defining markers (red)
IBD probabilities he presence o each o the t el e segregating haplotypes per locus as estimated in all progeny indi iduals at 1 c map inter als hich as expressed in pro a ilities. n the middle o the the pro a ilities could e estimated ith high con idence. there ere no mar ers in large parts o one homologue the pro a ilities could still e close to 0 or 1 ecause in ormation rom the i e other homologues can complement the missing in ormation. en i no mar ers ere mapped on the entire homologue e.g. homologue 12 rom 2 on lin age group pro a ilities ere complemented ith in ormation rom the other i e homologues. enotype in ormation content as lo er to ards telomeres ecause in those regions mar ers ere o ten missing in a large range in at least t o homologues and in ormati e mar ers ere present on only one side.
167 ______Ultra-dense chrysanthemum map
Figure 6. Scatterplot of marker positions of 1x0 markers on the integrated map that originated from the same transcript contig. ach dot represents a com ination o mar ers that originated rom the same transcript contig. he red dots indicate mar ers phased on the same homologue grey dots on di erent homologues. he lac line represents y x
QTL mapping he population as phenotyped or our di erent traits lo er colour lo ering time dis loret degreening and num er o ray lorets. ll our traits had a moderately high herita ility ranging rom 0. to 0. 2. he phenotypes ere itted against the pro a ilities at 1 c inter als ith a main e ects model.
o regions ere highly signi icantly associated ith lo er colour at and and one region at as slightly associated ( igure ). he highly signi icant loci ere oth simplex ( igure .a). nalysis o ariance o the interaction et een the associated alleles sho ed a highly signi icant (p 1 1 ) interaction indicating that oth alleles need to e present to get a pin lo er colour. ogether the t o 1x0 mar ers that ere most closely lin ed to each o the explained . o the ariation indicating that the trait is mainly inherited y t o ma or alleles segregating rom t o loci rom each o the t o parents. here is a minor on ut some genotypic ariation is still to e explained y undetected .
168 ______Chapter 7
Figure 7. QTL analysis of flower colour (purple), flowering time (red), disk floret degreening (green) and number of ray florets (blue). igni icance thresholds ased on 1000 permutations are indicated y a dashed line
or lo ering time e ound three clear s on 2 and and one minor at ( igure ). or the simplex on presence or a sence o the allele at homologue 11 had a ma or e ect on the trait. n oth loci on 2 and presence o di erent alleles could ha e a positi e e ect a negati e e ect or no signi icant e ect on the phenotype ( igure . ). here ore at least three alleles underlie the s. or dis loret degreening three located on and ere detected ( igure ). or all three multiple alleles played a role ( igure .c). he on explained most phenotypic ariation and presence o the allele on homologue had the strongest e ect on the mean alue o dis loret degreening. or num er o ray lorets t o minor ere ound on and . he on as a ected y one allele rom the maternal parent. he on as a ected y alleles that originated rom only the maternal parent ith opposite e ects rom di erent homologues ( igure .d).
169 ______Ultra-dense chrysanthemum map
Figure 8. Analysis per homologue for four QTL. raits studied ere a. lo er colour at b. lo ering time at 2 c. dis loret degreening at d. num er o ray lorets at . he p alue or testing the signi icance o the explained ariation o pro a ilities o a single allele ersus phenotype ( ) is sho n as a heatmap. he estimated e ect o ull a sence or presence o an allele on the phenotypic alue is sho n in the black points. he plot 𝐺𝐺 𝐶𝐶 𝑖𝑖 𝑖𝑖 limits o the e ect is sho n𝑌𝑌 =in the 𝜇𝜇 +black 𝛼𝛼 𝑋𝑋 box meaning that the black points can range ithin the negati e and positi e alue et een the oundaries et een homologous indicated y grey lines. he dashed grey lines represent an e ect o ero
170 ______Chapter 7
Discussion n this paper e report the irst integrated lin age map in a hexaploid species ith polysomic inheritance. e ere a le to assign multi dose mar ers to their parental homologues. ith this phasing in ormation e could reconstruct inheritance o haplotype alleles in the i parental population and per orm analyses. e pro ide ma or steps to o ercome a num er o limitations to lin age map construction ased on mar ers in hexaploids including ull map integration and phasing.
An integrated and phased linkage map he ultra dense integrated map contained mar ers o all 1 possi le types in a hexaploid. ith our approach e irst de ined ac one mar er clusters that represented homologues ased on lin ages et een simplex x nulliplex (1x0) mar ers. ith 1x1 mar ers that contained in ormation a out homologous chromosomes e created net or s o 1x0 lin age groups that represented (chromosomal lin age groups). u se uently the other mar er types ere assigned to these ac one clusters. ecause e irst de ined ac one mar er clusters ased on 1x0 mar ers de inition o homologues relied on presence o 1x0 mar ers. ac o 1x0 mar ers on a homologue is possi le i there is a high degree o in reeding the population is rom a sel ing or i there is selection or a phenotype or hich alleles ha e an additi e e ect. o e er our experience in polyploid mapping to date has sho n that lo dosage mar ers tend to e the most a undant mar er type ( our e et al. 201 our e et al. 201 an eest et al. 201 c). e ertheless e ere not a le to de ine one homologue on lin age group e en though all others each had 1 mar ers or more. oo e mar ers there ore seems unli ely. reason could e that some com inations ith alleles on this homologue might ha e een lethal and 1x0 mar ers on this homologue might there ore ha e had highly distorted segregation. hese mar ers ould ha e een iltered out prior to lin age mapping.
he ap algorithm ( reedy and ac ett 201 ) has pro ed particularly use ul or the eighted ordering o our large num er o di erse mar er types. s the or lin age aries or the same alues o r or di erent mar er type com inations and phases a eighted ordering algorithm as re uired. he most re uently used algorithm or eighted ordering is ased on a eighted linear regression ( ) algorithm as deployed in oin ap ( an oi en 200 ). o e er current processor speed o des top computers limits the use o this algorithm to approximately a hundred mar ers per lin age group. ecause o this restriction ( our e et al. 201 ) used the algorithm to construct homologue maps separately hich ere later integrated. n a su se uent mapping study in tetraploid rose the ap algorithm as used to construct an integrated map containing o er 2 s ithout the need or inning or the separation o homologue
171 ______Ultra-dense chrysanthemum map maps e ore integration ( our e et al. 201 ). he ap algorithm also orms the core o the map ordering module ithin etraploid ap so t are ( ac ett et al. 201 ) although its release as a separate pac age opens up the possi ility o high density mapping at any concei a le ploidy le el gi en pair ise recom ination re uency in ormation. ith the ap algorithm e ere a le to order all mar ers rom a in one run (ranging rom 1 21 to 2 0 mar ers per ) resulting directly in an integrated map. his num er o mar ers ould pre iously ha e een completely intracta le using a . ith the ne algorithm such maps can e produced on an a erage des top computer ithin hours. s the ordering step is time and resource e icient running multiple rounds o mapping ith remo al o pro lematic mar ers is much more easi le.
in age map uality as assessed ased on t o analyses on the concordance et een rpair ise and rmap and on the relati e position et een 1x0 mar ers originating rom the same contig rom our transcriptome assem ly. ccording to the comparison o rpair ise and rmap the t o estimators ere in concordance i rpair ise could e estimated ith high con idence (high ). here ore there is little discrepancy et een the distance and ordering o di erent com inations o mar ers on the lin age map and their initial estimation o r. he second analysis resulted in in ormation on the uality o local integration o homologous chromosomes. his is ased on the assumption that recom inations are essentially a sent ithin a transcript contig. here ore e ould expect that mar ers originating rom the same contig ha e a distance ery close to 0 c . rom the position o mar ers originating rom the same contigs a di erence rom ero can e calculated and ith that a measure or error e used the . he o 1x0 mar ers mapped on the same homologue as generally ery lo indicating oth a high uality assem ly o transcripts containing mapped mar ers and high uality local ordering at the le el o the homologue. he o 1x0 mar ers phased on di erent homologues as higher. all mar er type com inations the estimation o genetic distance et een 1x0 mar ers in coupling is most accurate. stimation o distance et een 1x0 mar ers in repulsion relies on higher dose mar ers ecause high con idence estimation o recom ination re uency in repulsion o 1x0 mar ers as not possi le ith our population si e o 0 . he positions o 1x0 mar ers that are on di erent homologues relati e to each other are there ore estimated ith lo er certainty than i they ere in coupling phase. o e er errors in estimating distance et een these 1x0 mar ers in repulsion ere in general lo er than c . serious ordering issues occurred a much higher alue ould e anticipated. e ertheless there ere our homologue com inations ith alues higher than 10 c . nly one or t o mar ers per caused these high alues. s these mar ers ere not associated ith any nota le stress on the map it is li ely that these mar ers ere actually rom di erent
172 ______Chapter 7 loci in the genome and the contigs they originated may e the result o a chimeric contig assem ly rom t o ery similar transcripts originating rom the same chromosome.
arlier lin age maps o chrysanthemum are ased on ( hang et al. 2010a) and mar ers ( hang et al. 2011a). disad antage o these types o molecular mar ers is that they are di icult to trans er and di erent lin age maps there ore cannot e integrated. mar ers are se uence ased and executing single assays li e or a an are commonly applied la oratory procedures. hey can there ore e la lessly trans erred et een la oratories. o set a standard or chrysanthemum e present the se uences o a set o 2 ell distri uted mar ers originating rom conser ed coding se uences that can e used as a core set to align uture lin age maps to each o the chromosomal lin age groups presented here.
Estimating IBD probabilities e used a relati ely simple approach to estimate pro a ilities or a sence or presence o parental haplotypes in our segregating population ( our e 201 ). he method only uses in ormation o dosage scores i they are ully in ormati e. his means that in case o a 1x1 mar er or example a dosage o 0 and a dosage o 2 in the progeny is ully in ormati e ( hile assuming a sence o dou le reduction) ecause it represents inheritance o respecti ely none o the associated homologues or oth. dosage o 1 is not ully in ormati e as it is not no n rom hich parental homologue the allele originated. here ore higher dose mar ers carry relati ely e in ormati e dosage scores. conse uence o our method is that it is only accurate i mar ers ith a large raction o in ormati e dosage scores are e ually distri uted o er the homologues. n our data parts o homologues ere sometimes poorly endo ed ith in ormati e mar ers. his did not turn out to e pro lematic i at that position all other i e homologues or that parent carried enough in ormation. ore sophisticated methods ha e sho n that higher dose mar ers add more in ormation to the estimation o pro a ilities ( ac ett et al. 201 heng et al. 201 ). uch methods could result in more accurate estimates ut an ade uate mar er distri ution o er all homologues is ey to all methods.
he accuracy o genetic analysis ased on pro a ilities relies on the uality o the integrated map. the estimation o distance et een mar ers ith alleles on di erent homologues is poor estimation o pro a ilities o alleles on the presumed same locus ill e rong and ill there ore pro ide a poor representation. o e er the o the mar er positions on the integrated map as generally ell elo c . his ould not ha e a large e ect on the estimation o pro a ilities ecause according to Haldane’s mapping function a distance of 5 cM corresponds to a
173 ______Ultra-dense chrysanthemum map recom ination fre uenc of resulting in a relati el lo error of on t e estimation of pro a ilities
QTL mapping it t e integrated map and pro a ilities e ere a le to perform a multi allelic anal sis n a pol ploid t is t pe of anal sis as large ad antages o er t e use of met ods t at are de eloped for diploids ecause t at are regulated multiple different alleles can e detected and t eir genetic arc itecture in estigated Hac ett et al n a pol ploid more t an t o alleles can underlie a is means t at t e genot pe does not onl a e a dosage ut can also e multi allelic i.e. not onl different conformations of t e alleles and ut also com inations of e.g. and are possi le it in a locus o in estigate t e genetic arc itecture and it t at t e occurrence of multi allelic e performed a anal sis t at ma es use of using pro a ilities for four traits it different underl ing genetic arc itecture
e ma or loci associated it flo er colour ere i allelic oget er t e e plained a large part of t e p enot pic ariation and ere affected one allele for eac of t e t o loci e t o loci clearl s o ed an interaction suggesting t at presence of ot alleles is needed for pin colouration n c r sant emum pin colouration is caused ant oc anin accumulation tic land e interaction et een alleles could e caused t e re uirement of t o en me ariants needed for t e production or regulation of production of ant oc anin or t o gene copies t at are re uired for t e same limiting step needing t e additi e effect of ot to ecome isi le
e eral s associated it flo ering time dis floret degreening and num er of ra florets ere multi allelic ese s ad underl ing alleles it a positi e effect a negati e effect and no significant effect on t e p enot pe indicating presence of at least t ree alleles e e act num er of uni ue alleles t at affect t e p enot pe is difficult to determine o aplot pes t at a e t e same effect on t e p enot pe could a e t e same underl ing pol morp ism affecting t e p enot pe ic ould ma e t em t e same alleles n t e ot er and t e could contain different causati e pol morp isms t at a e a similar effect on t e p enot pe ased on our data it is not possi le to uni uel identif suc alleles ecause our anal sis is ased on genetic lin age and t e causati e alleles cannot e identified
ompared to flo er colour t e genetic arc itecture for flo ering time as more comple e at as i allelic meaning t at presence of one allele affected t e trait ereas t e ot er ele en alleles did not significantl affect t e p enot pe Ho e er in t o ot er ma or on and multiple alleles ere in ol ed t er studies on t e in eritance of flo ering time in c r sant emum also suggested
174 ______Chapter 7 in ol ement of multiple loci ang et al ang et al a lo ering time in s ort da plants is mainl t e result of an interaction et een gro t rate and signal transduction of en ironmental cues li e da lengt and temperature s t ese cues are strictl controlled in a green ouse t e role of t e en ironment ould e e pected to e relati el small is is supported t e relati el ig erita ilit ic as also found earlier e ong Ho e er genetic regulation of signal transduction and gro t rate is li el comple and it is t erefore not surprising t at multiple loci are in ol ed
is floret degreening is an important determinant of post ar est performance of c r sant emum after long storage an eest et al ree multi allelic ere identified ese e plained a relati el small fraction of t e p enot pic ariation is floret degreening is a p siologicall comple trait in t e in estigated population it is related to car o drate content of t e dis floret at ar est an eest et al Man su traits could affect car o drate content including genot pic ariation related to p otos nt etic rate and source sin relations ips urt ermore it as s o n t at car o drate content is not t e onl factor affecting degreening an eest et al t is t erefore not surprising t at e did not find ma or for dis floret degreening issecting t e trait furt er p enot ping for su traits suc as car o drate content or ac crossing progen ar ouring specific trait c aracteristics mig t elp to furt er identif specific loci underl ing t is comple trait
e num er of ra florets ad t e ig est erita ilit of t e in estigated traits ut least ariation could e e plained detected steraceae plants carr composite flo er eads t at are comprised of multiple florets ose florets can e categorised into dis florets and ra florets e num er of ra florets is affected t e num er of florets on a capitulum and organ identit of t ose florets egulation of floret identit is generall in erited t roug one or t o ma or loci in steraceae illies et al t is t erefore uite une pected e did not find an ma or associated it t e trait s ot parents ere of t e single flo er t pe it is possi le t at ot lac ed allelic ariation in t e ma or genes and e onl found ariation in more comple l regulated minor allelic effects
n t e anal ses possi le interactions et een alleles ere not ta en into account n alternati e model as descri ed Hac ett et al t at uses all possi le genot pe classes as parameters ould ena le detection of interactions Ho e er t e met od e used to estimate pro a ilities is not a le to estimate pro a ilities for t ese genot pe classes directl More importantl in a tetraploid t ere are possi le genot pe classes leading to a model it parameters t at is alread prone 4 4 (2) × (2))
175 ______Ultra-dense chrysanthemum map to o er fitting n a e aploid t is ould e genot pe classes leading to parameters o er fitting ould definitel ecome an issue 6 6 (3) × (3) ur results s o t at e aploid in c r sant emum complicates anal sis ecause multiple alleles it a differential effect can underlie an associated locus it t e integrated map and pro a ilities e ere a le to identif in eritance of parental aplot pes in t e progen ena ling us to identif effects of specific alleles t at affected t e p enot pe e indeed found clear e amples in ic different alleles from t e same locus and parent affected t e trait negati el or positi el it t ese findings e s o t at pol ploids it pol somic in eritance can ar our muc more di ersit on a single locus compared to a diploid and t is is er important to ta e into account during detection and reeding Conclusions e met ods descri ed in t is paper ena le construction of integrated lin age maps in e aploids it pol somic in eritance ur presented met ods can e used for future pro ects t at aim to construct integrated lin age maps and perform multi allelic anal ses in e aploids uccess of suc pro ects depends on se eral features of t e in estigated organism and t e o tained dataset irst it depends on t e predominance of random i alent pairing at meiosis econd sufficient and e enl distri uted mar ers are re uired t at can define eac omologous c romosome ast ig er dose co dominant mar ers ot uni parental and i parental e.g. and it alleles on eac omologous lin age group are needed t at pro ide information to integrate omologous lin age groups into c romosomal lin age groups it t e resulting integrated lin age maps it is possi le to perform anal sis t at ta es all possi le alleles into account at t e same locus is as ma or impact on t e possi ilities for localisation of genomic loci and t eir genetic arc itecture associated it traits in c r sant emum ut also for ot er agriculturall important e aploid species suc as s eet potato i i and persimmon Acknowledgements e aut ors ould li e to t an at erine reed and ristine Hac ett of io t e ames Hutton nstitute in undee for ma ing a de elopmental ersion of t e M Map soft are a aila le e aut ors ould also li e to t an en mulders for suggesting re isions to t e manuscript
Supplementary data is available online at: ttps lin springer com article s 5 upplementar Material
176 Chapter 8
Quantifying the power and precision of QTL analysis in autopolyploids under bivalent and multivalent genetic models
Peter M. Bourke1, Christine A. Hackett2, Roeland E. Voorrips1, Richard G. F. Visser1, Chris Maliepaard1
1 Plant Breeding, Wageningen University & Research, Droevendaalsesteeg 1, 6708 PB Wageningen, The Netherlands.
2 Biomathematics and Statistics Scotland, Invergowrie, Dundee DD2 5DA, UK.
Submitted
177 ______Power and precision of QTL analysis
Abstract New genotyping technologies, offering the possibility of high genetic resolution at low cost, have helped fuel a surge in interest in the genetic analysis of polyploid species. Nevertheless, autopolyploid species present extra challenges not encountered in diploids and allopolyploids, such as polysomic inheritance or double reduction. Here we investigate the power and precision of quantitative trait locus (QTL) analysis in outcrossing autotetraploids, comparing the results of a model that assumes random bivalent chromosomal pairing during meiosis to one that also allows for multivalents and double reduction. Through a series of simulation studies we found that marginal gains in QTL detection power are achieved using the double reduction model but at the cost of an impaired ability to determine the most likely QTL segregation type and mode of action. We also explored the effect of variable genotypic information across parental homologues and found that both QTL detection power and precision require high and uniform information contents. This suggests linkage analysis results for autopolyploids should be accompanied by marker coverage information across all parental homologues along with the per-homologue genotypic information coefficients (GIC). Visualising the GIC landscape of the homologues of interest around QTL peaks will help elucidate the limitations of QTL power and precision in further studies. Application of these methods to an autotetraploid potato (Solanum tuberosum L.) mapping population confirmed our ability to locate and dissect QTL in highly heterozygous outcrossing autotetraploid populations.
Key words Quantitative Trait Locus (QTL) analysis, autopolyploid, double reduction, QTL power, Bayesian Information Criterion (BIC), genotypic information coefficient (GIC).
178 ______Chapter 8
Introduction Autopolyploid species, characterised by having more than two homologous copies of each chromosome, present a number of challenges to genetic research not present in diploids or allopolyploids (which are essentially already diploidised, genetically- speaking). They have therefore been somewhat left behind when it comes to tools and methods for their genetic analysis. Among these challenges are the complexity of modelling polysomic inheritance and the occurrence of double reduction (the phenomenon whereby a particular segment of a parental chromatid and its recombinant “sister” copy migrate to the same gamete, which can only occur if multivalent pairing structures are formed and maintained through meiosis 1 (Haldane, 1930;Mather, 1935)). However, we are now at a stage where the availability and low cost of genotyping tools (based on single nucleotide polymorphisms, or SNP markers) are making the analysis of autopolyploids not just feasible, but of practical importance to crop breeders, increasing the need for both the methods and the tools to conduct these analyses, as well as knowledge on how best to apply these methods.
Breeders and researchers are often interested in knowing the genetic architecture of important traits, for example: 1. whether they are oligo- or polygenic; 2. where the quantitative trait loci (QTL) influencing the trait lie on the genome; 3. from which specific parental homologous chromosome (which we term “homologue”) the favourable alleles originate; 4. whether these alleles exhibit additive or dominant gene action; 5. whether they interact with alleles at other loci, or with the environment. Up to now, approaches such as QTL mapping in bi-parental populations or genome-wide association studies have been proposed, although not always addressing all of the above points. More recently, genomic selection has been advocated as a powerful method to increase genetic gain, without necessarily needing an understanding of the genetic architecture (Meuwissen et al., 2001;Slater et al., 2016). For quantitative traits with hundreds or thousands of causative genes, this is likely to be more appropriate in breeding programs. However, for traits with a few major causative loci, QTL mapping remains a viable option that additionally offers the promise of both understanding the genetics underlying the trait (including the possibility of finding the underlying genes) while also facilitating selection for it through marker-assisted selection.
QTL mapping in autopolyploids has evolved in the last 20 years to keep pace with changes in genotyping technologies. Approaches have been developed for both co- dominant and dominant marker systems, and range from simplified models that only consider bivalent pairing to more complex models that also include double reduction. However, there has been almost no investigation into the applicability or advantages of different models. Despite this, it is often asserted that models that ignore double
179 ______Power and precision of QTL analysis re uction are a priori inferior to those that inclu e it ( uo et al , ) ore complete mo els of polysomic inheritance that inclu e ou le re uction are often evelope un er the assumption of completely informative mar er systems (e.g. ( ie an u, i et al , u et al , )), there y avoi ing the statistical comple ities impose y partially informative mar ers (such as osage score mar ers) n fact, it is uite telling that the only pu lically availa le tools for analysis in autopolyploi s have a opte the simplifying assumption of ran om ivalent pairing (e.g. etraploi ap ( ac ett an uo, ac ett et al , ) an etraploi ap ( ac ett et al , )), whereas more complete mo el escriptions remain unimplemente
ecently, a metho to reconstruct inheritance pro a ilities (or i entity y escent ( ) pro a ilities) un er oth ivalent an multivalent pairing mo els has een evelope into a software pac age etra rigin ( heng et al , ) e use etra rigin an the simulation software e igree im ( oorrips an aliepaar , ) to investigate mapping in autopolyploi s, estimating etection power an precision, the effect of ou le re uction an multivalent pairing (while comparing mo els that oth ignore an inclu e it), the impact of population si e, trait herita ility an mar er istri ution, an the ifferences in etection an iagnostic power (i.e. correctly pre icting the position as well as the composition of the alleles) etween simple or more comple segregation types an ifferent mo es of action (a itive or ominant) e also e amine the well stu ie traits of plant maturity (earliness) an flesh colour in a i parental tetraploi potato population to further illustrate our fin ings, comparing the locations to the physical positions of can i ate genes un erlying these loci
ne important aspect of mapping that remains conspicuously a sent from most pu lishe stu ies in oth iploi an polyploi species is the topic of information content. Originally it was noted that “marker information content” could adversely affect the estimate position of a if mar ers of varia le informativeness were locate near a ( nott an aley, ) ncreasing information content was foun to lea to an increase test statistic, which coul ias the location of a pea ( nott an aley, nott et al , ) ther authors have propose alternative measures of information content than that of nott an aley, such as one ase on Shannon’s information content ( eyes al es an illiams, ) n autopolyploi species the issue of information content is argua ly even more important than in iploi s, as information content generally varies etween homologues e prefer to use the term “genotypic information coefficient” ( an oi en, an oi en, ) as it avoi s confusion when ealing with pro a ilities, which are multi point estimates of homologue transmission pro a ilities an not the mar er genotypes themselves n this article we e ten the efinition of the genotypic information coefficient ( ) to
180 ______Chapter 8 autopolyploids and e plore its usefulness in predicting detection power and precision. Our work will help to guide etter informed analyses in autopolyploids as well as deepening our understanding of the genetic architecture controlling important traits in these species.
Figure 1. Distribution of markers on potato chromosomes 1 and 12 from the integrated genetic maps of Hackett et al. (2013). hromosome shows poor marker coverage across most homologues in the region – c and was therefore chosen to investigate the genotypic information coefficient . hromosome has etter overall marker coverage. arental homologue h num ers are shown as h – h for parent and h – h for parent .
Materials and Methods Simulated tetraploid populations were the asis for much of the work presented here. e ased our simulated populations on previously pu lished genetic maps of tetraploid potato developed from dosage scored S markers ackett et al. . n polyploids marker dosages are generally understood to correspond to the allele counts of the “alternative” allele (as opposed to the “reference” allele of a bi allelic S marker . n hetero ygous autotetraploids the possi le dosages are and with a marker eing defined y its maternal and paternal dosages e.g. means a dosage of in parent the mother and a dosage of in parent the father . here are nine “fundamental” marker segregation types to consider in an autotetraploid cross, namely and to which all other marker types can e converted without loss or distortion of linkage information ourke et al. . or convenience, we often refer to simplex x nulliplex or “SxN” markers to indicate both or markers similarly duple nulliple markers imply either or . Simple simple S S refers to markers whose fundamental form is .
181 ______Power and precision of QTL analysis
Table 1. Details of parameter levels used in the simulation study. q N h2 QTL seg. QTL action QTL pos. QTL model Chm. 1 SxN additive random no xN dominant SxS Chm. 12 SxN additive c no xN dominant c SxS he phased genetic linkage maps of potato chromosomes and from ackett et al ( were used in the simulation of genotyped tetraploid populations with edigreeSim in this study Chm. chromosome q rate of uadrivalent formation (specified in edigreeSim chrom file N population 2 si e of population h (broad sense trait heritability QTL seg. segregation type, given as the maternal x paternal dosage of the (alternative marker allele he codes SxN refers to x and x markers, xN refers to x and x markers and SxS refers to x markers QTL pos. genetic position of the his was either random (chm or confined to a telomeric ( c versus centromeric ( c position on chm QTL model model used in analysis, either with double reduction ( or not (no
e limited our attention to potato chromosomes and as these displayed contrasting levels of marker coverage ( igure he range of parameters used in both simulation sets are outlined in able e used potato chromosome , with its uneven marker distribution, for the investigations into the genotypic information coefficient ( , while chromosome was used for the power analysis nless otherwise stated, all statistical analyses and visualisations were performed using the statistical computing environment version ( ore eam,
GIC study – potato chromosome 1 or each set of population parameters (all possible combinations of population si e ( op and rate of uadrivalent formation (q we simulated separate populations using edigreeSim and the phased linkage map of chromosome from ackett et al ( for the phased parental marker positions and dosages (visualised in igure , left hand side . ach simulated individual carried a single chromosome or each population, we generated phenotype sets for all possible combinations of the factors heritability (h2 , segregation type ( seg and action ( able he phenotype of the ith individual ( with dosage was randomly sampled from a Normal distribution according to 𝑃𝑃𝑖𝑖 𝑑𝑑𝑖𝑖
2 𝑃𝑃𝑖𝑖~𝒩𝒩(𝜇𝜇𝑖𝑖 +𝑄𝑄∗𝑑𝑑 , 𝜎𝜎𝑒𝑒 )
182 ______Chapter 8
where , he environmental variance 2 was determined by 2 1−ℎ 2 2 first calculating𝜇𝜇 𝑄𝑄 the genotypic variance across𝜎𝜎𝑒𝑒 the= (wholeℎ ) 𝜎𝜎 𝑔𝑔population given the individual dosages (in the case of a dominant2 these were taken as a dosage of 𝜎𝜎𝑔𝑔 and only ffspring genotypes were derived from the hsa and hsb output files of edigreeSim (which provide the exact location and origin of recombination points along offspring homologues oth the position and the configuration of the were randomised for each phenotype set (to c accuracy
etra rigin ( heng et al , was run on athematica version ( olfram esearch nc , with input files derived from the integrated linkage maps and dosage output of edigreeSim, using both bivalent decoding options ( alse rue to generate probabilities under both a model that allowed for double reduction ( and one that did not (no he other parameter settings used were parental dosage error probability (eps , offspring dosage error probability (eps , and parental bivalent hasing rue (i.e. assuming purely bivalent pairing predominates to determine parental marker phase, for computational efficiency ( heng et al , he probabilities at the marker positions were used to fit splines (using the smooth.spline function in ( ore eam, from which re normalised probabilities were interpolated at a c grid of positions (using the predict function in for subse uent analysis analysis was performed using a weighted regression of the homologue effects, weighted by the genotype probabilities ( ackett et al , he model described by ackett et al ( , , derived from the earlier work of empthorne ( empthorne, , can be written as
′ 2 2 3 3 4 4 6 6 7 7 8 8 having taken𝑌𝑌 the constraints =𝜇𝜇 + 𝛼𝛼 𝑋𝑋 + 𝛼𝛼 𝑋𝑋 + 𝛼𝛼 𝑋𝑋 + 𝛼𝛼 𝑋𝑋 +and 𝛼𝛼 𝑋𝑋 + 𝛼𝛼 𝑋𝑋 + 𝜀𝜀 into account ere, Y corresponds to the trait values, Xi the indicator variables for the presence 𝑋𝑋1 + 𝑋𝑋2 + 𝑋𝑋3 + 𝑋𝑋4 = 2 𝑋𝑋5 + 𝑋𝑋6 + 𝑋𝑋7 + 𝑋𝑋8 = 2 absence of a particular parental homologue ( for parent , for parent and the residual term. Hackett et al. (2014) describe this as the “additive” model, and used the 𝜀𝜀 probabilities of the possible genotypes as weights in a regression using the above model form. We firstly applied this approach (which we term the “no double reduction” or “noDR” model, where all or , subse uently extending it to use the set of genotype probabilities as weights (termed the “DR” model which includes the additional 𝑋𝑋𝑖𝑖 genotypes resulting from double reduction, i.e. are no longer constrained to e ual and , but rather = 0, 1 or 2). The “logarithm of odds ratio” (LOD) score for the 𝑋𝑋𝑖𝑖 regression was calculated using the formula 𝑋𝑋𝑖𝑖
183 ______Power and precision of QTL analysis
0 𝑁𝑁 10 𝑅𝑅𝑅𝑅𝑅𝑅 𝐿𝐿𝐿𝐿𝐿𝐿 = log ( 1) where N is the population si e, RSS0 is2 the residual𝑅𝑅𝑅𝑅𝑅𝑅 sum of s uares under the null hypothesis of no TL ( for trait values and overall trait mean ), and RSS1 is the residual sum of s uares from2 the regression model ( roman et al., 200 ). 𝑅𝑅𝑅𝑅𝑅𝑅0 = ∑𝑖𝑖(𝑦𝑦𝑖𝑖 − 𝑦𝑦̅) 𝑦𝑦𝑖𝑖 𝑦𝑦̅ chromosome wide scan was performed at 1 c intervals and the LOD score recorded at each position.
ignificance thresholds were determined through permutation tests ( hurchill and Doerge, 1 4), with each of the 1000 simulated phenotype sets per parameter set (10 populations 100 phenotypes) permuted once before recording the ma imum LOD score from the chromosome wide scan (i.e. recording 1000 ma ima). This generated appro imate e periment wise LOD thresholds by taking the 0. uantile of the sorted LOD values. TL was declared detected if the significance at the TL position e ceeded the significance threshold. ecause the true positions of most TL were not at the grid of 1 c positions tested, splines were fitted to the LOD profile to enable interpolation of the appro imate LOD score at the position of the TL itself (which was used to derive TL detection rates).
The values for homologue j at a particular locus were determined as follows
𝑁𝑁 4 𝐺𝐺𝐺𝐺𝐺𝐺𝑗𝑗 = 1 − ∑ 𝜋𝜋𝑟𝑟(1 − 𝜋𝜋𝑟𝑟) 𝑁𝑁 𝑛𝑛=1 using the noDR D probabilities, where is the probability of presence of homologue j in individual n at this locus ( ppendi 1). values were calculated at all 1 c 𝜋𝜋𝑟𝑟 splined positions used in the TL scan. We considered the e tension of the to include the case of double reduction, but found a homologue specific was no longer easily defined when an offspring can inherit more than one copy of part of a particular homologue.
To better understand the relative importance of on the power of TL detection, we re coded TL detection non detection as 1 0 and ran both a simple O as well as a L (using a inomial model with logit link) using the following model
2 where D is the TL𝐷𝐷 detection= 𝑞𝑞 indicator +𝑃𝑃𝑃𝑃𝑃𝑃 +ℎ variable,+ 𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄 and𝑄𝑄 + the𝑄𝑄𝑄𝑄 e planatory𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄 + 𝐺𝐺𝐺𝐺𝐺𝐺 variables are q (rate of multivalent formation), Pop ( opulation si e), h2 (heritability), QTLseg ( TL
184 ______Chapter 8 segregation type), QTLact (mode of TL action, either additive or dominant) and GIC (the product of per homologue values underlying the TL alleles).
To understand the influence of on the detection of more comple TL segregation types, we categorised the per homologue as either high (H) or low (L) using a threshold of both 0. and 0. for high (so for e ample in the former, Low 0.9 and High GIC ≥ 0.9). A DxN or SxS QTL could then be categorised as either LL, LH, HL or HH, depending on the underlying at each of the alleles with positive effect. or each parameter set we compared the power of detection of LL, LH HL (since both have one low and one high allele they were grouped together) and HH TLs.
– The simulations using chromosome 12 were similar to those of chromosome 1 with some differences (Table 1). i different rates of uadrivalent formation were tested (q = 0, 0.1, ..., 0. ) and for each set of population wise parameters, 0 separate populations were simulated. or each simulated population, 0 sets of phenotypes were generated as described above, e cept that the position of the TL was confined to two positions, namely 14 c (telomeric) and 4 c (centromeric). The choice of these positions was not arbitrary they were chosen to minimise the effect that differences in might have on the results, whilst noting that TL positioned at the telomere itself (0 c ) would be likely to suffer from lower detection rates due to lower information contents typically observed at the telomeric e tremes. The centromeric position (4 c ) was selected for study as it is known that the rate of double reduction typically falls to ero at the centromeres ( ourke et al., 201 ).
The TL analysis and setting of significance thresholds was performed as described above (although permutation tests were now based on 2 00 permutations, one of each phenotype set, with α = 0.05 as before). We also wished to investigate the rate at which the TL segregation type and mode of action was correctly reconstructed. Hackett et al. (2014) describe a TL model selection method by fitting the phenotype means at the TL peak and comparing the ayesian nformation riterion ( ) ( chwar , 1 ) for , D and models. This is given by the formula
where is the likelihood of the𝐵𝐵𝐵𝐵𝐵𝐵 TL= model −2 log being(𝐿𝐿) +tested, 𝑛𝑛 n ∗𝑝𝑝 is the number of observations (either or 100 for the noDR and DR models, respectively) and p is the number of 𝐿𝐿 parameters in the TL model.
185 ______Power and precision of QTL analysis
The (log) likelihood is a sum over the different genotype classes in the population, defined by their dosages in the case of an additive TL, or presence absence of the TL in the case of a dominant TL
𝑛𝑛 1 2 log(𝐿𝐿) = − (log(2𝜋𝜋) + 1 + log ( ∑ 𝜎𝜎𝑗𝑗 (𝑛𝑛𝑗𝑗 − 1))) 2 𝑛𝑛 𝑗𝑗 where is the variance associated with TL genotype class j, and is the number of observations2 within genotype class j (so that ). 𝜎𝜎𝑗𝑗 𝑛𝑛𝑗𝑗 𝑗𝑗 𝑗𝑗 s well as the , the kaike nformation∑ riterion𝑛𝑛 = 𝑛𝑛 ( ) ( kaike, 1 4) was also recorded for comparison, where
Whereas Hackett et al. (2014)𝐴𝐴𝐴𝐴𝐴𝐴 restricted= −2 log their(𝐿𝐿) + model 2 ∗ 𝑝𝑝 search to only three TL segregation types, we e panded the search to all possible bi allelic TL, comprising in total 240 different TL models (listed in upplementary Table 1). We compared the performance of the search of the full bi allelic model space to that of a restricted model space (the first models of upplementary Table 1, containing only , D and TL).
The Altus Colomba ( ) tetraploid potato mapping population was used to e plore both TL models and test the methods described earlier for simulated data. The genetic positions of 10 markers from the ol TW 20 array ( os et al., 201 ) were taken from a previously published high density linkage map developed using this population ( ourke et al., 201 ), distinct from the maps of Hackett et al. (201 ) used in the simulation study which were based on a different population. subset of these markers were selected as input data for TetraOrigin ( heng et al., 201 ). arkers were selected so that each consecutive 0. c window had (if possible) one marker of every segregation type (in total there are nine see beginning of ethods section), selecting markers randomly among those with fewest missing values. TetraOrigin D probabilities computed under the assumption of no double reduction (noDR) or allowing for the possibility of double reduction (DR) were saved for later TL analysis (after confirming that homologue numbering between the noDR and DR datasets was consistent).
186 ______Chapter 8
The two traits investigated were plant maturity and tuber flesh colour. oth were scored on an ordinal scale, with maturity scored from 1 (very late) to (very early) in increments of 1, and flesh colour scored from 4 to through varying shades (4 = white, = cream, = light yellow, = yellow, = dark yellow). aturity was scored visually in the field during the growing seasons 2012, 201 and 2014, with flesh colour scored post harvest for each of these years (three replicates). TL analysis was performed as described in the previous sections, using splined D probabilities as weights in both a noDR and DR model for comparison purposes. ndividual analyses per year were performed, as well as a general analysis using best linear unbiased estimates ( L s) generated using the lme function from the nlme R package ( inheiro et al., 201 ) with ear as random effect and genotype as fi ed effect. TLs were re mapped by saturating the LOD support intervals around the TL peaks (no marker binning performed) and re estimating D probabilities in TetraOrigin. TL analysis was subse uently performed at the marker positions themselves (rather than at splined positions) to better estimate the peak positions. The location of the L DO TOR 1 (StCDF1) locus on chromosome ( loosterman et al., 201 ) with gene annotation 000 D 40001 40 , and the T ROT H DRO L 2 (StChy2) locus on chromosome (Wolters et al., 2010) with gene annotation 000 D T40002 from the potato genome se uence version 4.0 ( pudD enome rowser S. tuberosum group hure a D 1 ( otato enome e uencing onsortium, 2011 Hirsch et al., 2014)) were used to compare the physical and genetic positions of the TL peaks. The most likely TL model at the peak positions was e plored by calculating the for all 240 bi allelic TL models (see previous section for details) and selecting the minimum as most likely. odels within 10 of the minima were also deemed plausible and recorded.
s e pected, there was a clear relationship found between the per homologue and the marker coverage of that particular homologue (an e ample is given in igure 2.a). Differences between coupling and repulsion marker information are detectable, for e ample where a single 1 0 ( ) marker tagging homologue 4 in parent 1 at 2 . c gave a large boost to the otherwise low values in that region on homologue 4, but also slightly increased the values on homologues 1, 2 and (there is no information about the meiosis of parent 2 from such a marker). The results of both the O and L analyses showed that the e plains a large proportion of the variance for TL
187 ______Power and precision of QTL analysis detection power, although not as much as the population si e or trait heritability ( upplementary ile 1).
part from the influence of on detection power, we were also interested in understanding the influence of on the accuracy of TL analysis. or this we e amined more closely the position of TL peaks in relation to their true position, for TL only (since these originate from a single homologue and are simpler to track). We noted a dramatic influence of on the TL peak position in regions of variable , even in situations with 100 detection power ( igure 2.b). Local ma ima in such as that observed in parent 1 homologue 4 at 28.5 cM serve as local “attractors” for TL peaks, an effect seen across all homologues. enerally speaking, there is a tapering of profiles at the telomeres, a conse uence of poorer marker information (coming from one side only).
Where is high, the true position and detected TL peak closely corresponded ( igure 2.b, 40 – 100 c region). visualisation of the homologue specific variation in TL detection power is given in igure 2.c. or more comple TL types such as D or TL, we were curious to know whether the presence of a single TL allele on a homologue with high would be enough to detect that TL, or whether high was needed on both homologues. s described in the ethods section, we categorised TLs as either LL, LH, HL or HH depending on the per homologue underlying the TL alleles with positive effect. s can be seen in Table 2, the detection power of LL type TL tended to be lower than that of LH or HL type TL, which themselves tended to be detected less often than HH type TL. n fact, the intermediate class (having only one positive TL allele residing on a high homologue) were detected at appro imately the midpoint of the LL type and HH type detection rates ( upplementary igure 1).
s noted in the previous section, population si e and trait heritability were found to have the most impact on TL detection power, followed by . On chromosome 12 we deliberately chose two TL locations to minimise the impact of and allow a comparison of centromeric versus telomeric effects (with average cross homologue s of 0. and 0. for 14 and 4 c respectively). The four most important factors in determining TL detection power (e cluding ) were population si e, trait heritability, TL segregation type and TL mode of action ( igure ). When we ran an O using all the available e planatory variables we found that neither the rate of multivalent formation (q) nor the form of the model used (DR or noDR) had any real impact on the TL detection power overall ( upplementary ile 2). However, there were
188 ______Chapter 8 some instances here the model could improve detection po er. or e ample hen the population si e or trait heritabilit is lo and rate of multivalent pairing is high the model does offer a slight advantage igure 4.a helping to maintain the same level of po er as that achieved hen there is strictl bivalent pairing q . he average distance from the pea to the true position is also adversel affected b double reduction igure 4.b . o ever in this instance no matter hat model is used the anal sis ill become slightl less accurate at higher values of q although there is some mitigation of the loss of accurac hen the model is used . ere e used distance as an absolute measure – the direction of this distance appeared to be biased to ards the side of the ith greater genetic length upplementar igure 2 .
High GIC threshold = 0.9 High GIC threshold = 0.95 2 .1 A 4 11 114 12 4 1 1 2 .2 A 2 1285 1 12 4 1 2 .1 D 41 121 12 124 1 2 2 .2 D 5 4 1228 15 11 1 22 2 .1 A 4 1 415 1 5 1 145 2 .2 A 4 2 4 1 1 5 1 4 2 .1 D 44 4 2 1 8 4 1 11 2 .2 D 85 8 1418 48 1 5 4 .1 A 54 1255 12 12 1 5 1 4 .2 A 12 1 4 124 8 8 4 .1 D 81 11 4 125 12 5 8 1 4 .2 D 84 11 8 1 2 1 12 52 2 4 .1 A 4 8 415 1 2 4 2 1 4 .2 A 5 4 421 1 5 2 14 4 .1 D 5 4 4 5 1 8 488 1 4 .2 D 11 1 1 44 148 QTL detection power was determined for two different definitions of “high GIC” – either e ceeding . or e ceeding . 5. esults for different levels of multivalent pairing and model used and no ere combined. umbers in brac ets refer to the numbers of separate on hich the estimates of po er are based. N opulation si e h2 heritabilit Seg. segregation t pe here denotes a duple so either 2 or 2 and implies a 1 1 mar er Act. mode of action either A additive or D dominant. and refer to ith alleles on homologues of both o of o and igh and of both igh respectivel . esults for and ere considered e uivalent and ere combined.
189 ______Power and precision of QTL analysis
Inf ence of mar er distri tion on GIC a es ca c ated sing no I pro a i ities on potato chromosome ac ett et a with parent a es in the ower pane and parent a es in the pper pane erage GIC a es o er the sim ated pop ations are shown as ines a o e the mar er distri tion and carr the same co o r n the a is h – h parent
190 ______Chapter 8
– – q –
191 ______Power and precision of QTL analysis
q
192 ______Chapter 8
– –
i.e. allelic QTL models (either a “restricted” search over 58 models or a “full” over 240 models (all possible bi – – –
193 ______Power and precision of QTL analysis
The mea ra of the correct QTL model amo those tested over a ra e of differe t rates of multivale t formatio (q The left pa el depicts results for the restricted model search (o l a d QTL co sidered i total 58 models hereas the ri ht pa el depicts the results he the full bi allelic QTL model space as searched (240 models olid li es ith circles i dicate the o results hile dashed li es ith tria les i dicate the results (i cludi double reductio mea ra of implies that o avera e the correct QTL model as al a s ra ed as most li el (i ori ties The avera e rates at hich the correctl ide tified the QTL co fi uratio (i.e. the fractio of cases here the of the correct model as ra ed as most li el The avera e differe ce (i u its of bet ee the selected model a d the true QTL model
194 ______Chapter 8
f e e ami e the cause of this poor performa ce e fi d that the has difficulties correctl predicti additive or QTL hereas domi a t QTL of these t pes cause o such issue ( uppleme tar i ure 4 The ai e formatio riterio ( as fou d to perform mar i all better tha the if the a al sis as co ducted usi the model (data ot sho althou h it ould still be u ise to use it i co u ctio ith the model
To help illustrate our fi di s e loo ed at t o ell studied traits for hich phe ot pic data as available from the tetraploid potato populatio is the result of a ide cross bet ee the late hite cream fleshed starch cultivar Altus a d the earl ello fleshed are cultivar Colomba avera e the rate of uadrivale t pairi as 0 24 (a d as similar bet ee pare ts pare t 0 2 0 0 a d pare t 2 0 25 0 05 ( uppleme tar i ure 5 co siste t ith a previous estimate of 0 2 – 0 from this populatio usi o l mar er i formatio ( our e et al 20 5 The phe ot pic traits themselves (pla t maturit a d flesh colour are alread e eticall ell characterised offeri the opportu it to compare QTL pea positio s ith the ph sical locatio of the u derl i ca didate e es as ell as a e ploratio of the most li el QTL models or both traits a si le ma or QTL as fou d ith both the o a d models ( i ure s ca be see from the bottom pa el of i ure the for some homolo ues as uite variable (e.g. chromosomes 4 or 2 but as overall relativel hi h across both pare tal maps
There as a si le QTL pea for pla t maturit o chromosome 5 arou d 8 – 20 c (Table si the model sli htl more of the varia ce as e plai ed tha ith the o model (44 versus 4 a d the idth of the L 2 i tervals as arro er ( c versus c he e saturated the QTL re io ith mar er i formatio a d re ra the calculatio s a d QTL a al sis e ere able to i crease the proportio of e plai ed varia ce at the pea QTL positio to 4 ith the pea occurri at appro imatel 20 c usi both models (Table 4 The most li el QTL model as a additive oooo x qqqQ with the early allele (‘Q’) coming from Colomba usi both the o a d models (Table 4). Here ‘o’ denotes an allele about which we have no information, which could be ‘q’, ‘Q’ or any other non se re ati allele ote that for a simple QTL a additive a d a domi a t model produce the same e pected se re atio a d therefore ca ot be disti uished ithi a populatio The mea maturity of offspring with the early ‘Q’ allele from Colomba as 0 8 a d ithout as 5 8 0 The e t most li el QTL model as the additive model QQ Q Q althou h this as far less likely (δ BIC = 18.1 or 16.8 for the noDR or DR models, respectivel t is possible that a multi allelic model ( ith differe t earli ess alleles of
195 ______Power and precision of QTL analysis different effect si es) may have fitted the data better (Hac ett et al., 4), although we did not see the need to model that here.
– aturity no . . . .4 no . . . . 4 no . .4 4 . .4 s no . .4 s . .44 lesh no . 4 .4 colour . .4 no . .4 . .4 4 no .4 4 . 4 . . s no . . s . . Chm. chromosome number Year year of phenotypic measurement, including best linear unbiased estimates ( s) over the years Model QT model used, either random bivalents (no ) or also allowing for double reduction ( ) Peak (cM) position of QT pea in centi organs N number of individuals with matching phenotypic and genotypic data LOD score at the pea LOD-2 (c ) range of QT support interval c positions (loci within of maximum ) |LOD-2| width of the support interval in centi organs Var. proportion of phenotypic variance explained by QT pea .
or flesh colour, the no and models resulted in the same rate of explained variance at the chromosome pea ( ), with the interval for the no narrower than that for the model ( c versus c ), in contrast to the results for plant maturity. hen we searched for the most li ely QT model we found in both cases (no and ) that a dominant model fit the data best, with segregation type oooo x QQqq (Table 4), while the additive version was not far behind (δ BIC = 3.4 in both cases). ndividuals who inherited either the allele from h or h had an average flesh colour of .4 . , whereas those without them had an average flesh colour of 4. . . nterestingly, the next most li ely model was . away using the no model, while only away using the model.
e were interested in comparing the position of the QT pea s with the physical location of the candidate genes StCDF1 (for maturity) and StChy2 (for tuber flesh colour). s described in the ethods section, we saturated the support interval
196 ______Chapter 8
c.f. esults using the no model (random bivalent) are shown above those of the model (allowing double reduction) for both traits. significance thresholds are shown as dashed red lines. The lowest panel shows the per homologue for the eight parental homologues (using the no probabilities), using the same colour scheme as igure .a. around the QT pea s with mar ers and re ran both the calculations and QT analysis, in a “re mapping” of both traits. or both chromosomes three and five, the expected sigmoid correspondence between the genetic and physical position of mar ers
197 ______Power and precision of QTL analysis
as obser e , ith an appro imately linear orrespon en e in the regions of interest ig re a an he pea positions ere omparable sing both the no an mo els ig re b an an able , hi h e ompare to the profiles for the homolog es in estion homolog e for StCDF1, an homolog es an for StChy2 n both ases, the gene position appeare to fall ithin the inter als of the pea s, altho gh there as no ifferen e in these inter als for plant mat rity for flesh olo r, the inter al as narro er sing the no mo el, an appeare to gi e a better in i ation of the position that the mo el ig re n both ases, there appeare to be s ffi ient mar er o erage on the important homolog es ithin the s pport inter als, as refle te by the relati ely high al es or plant mat rity, the StCDF1 region ha far more mappe mar ers than else here, s ggesting that this lo s as spe ifi ally targete in the e elopment of the ol array it e illigen et al , os et al , s an be seen from ig re a, e ere nable to separate these mar ers geneti ally e to the limite pop lation si e se for lin age map onstr tion , highlighting the ina e a y of this pop lation si e for fine mapping or
Peak Trait Chm. Model LOD Var. QTL seg. BIC (cM) at rity no A/D oooo A/D oooo lesh no D oooo olo r A oooo D oooo A oooo ploration of the ma or pea s sing all a ailable mar er information in the s pport regions Chm. hromosome n mber Peak (cM) position of pea in enti organs LOD s ore at the pea Var. arian e e plaine by pea QTL seg. segregation type an mo e of a tion, either A a iti e or D ominant A/D is se to in i ate that either an a iti e or ominant mo el is possible, as these annot be isting ishe in the ase of simple alleles with a positive effect are denoted ‘Q’, alleles with a negative effect are denoted ‘q’ and those with unknown effect ‘o’; BIC ayesian nformation riterion
ltho gh reporte as early as nott an aley, , the infl en e of a ariable in the i inity of has essentially been ignore in many s bse ent st ies both at the iploi an polyploi le el n this st y e hope to re emphasise its importan e by emonstrating the effe t of lo on ete tion po er, as ell as the effe t of ariable on pre ision
198 ______Chapter 8
enetic versus ph sical position of su set of arkers within the re apped Q region of chro oso e support intervals for the no and odels overlapped, shown here as hori ontal green purple lines he StCDF1 locus is highlighted a vertical arrow at p Inset: Genetic v’s physical position of markers used in initial etra rigin anal sis on chro oso e , with re apped region highlighted in red profiles of the re apping of the chro oso e Q for plant aturit no odel results are shown as a green solid line, with odel a purple solid line he s of ho ologue on which the Q earl allele was predicted to lie, highlighted underneath for each arker position used in the Q scan are also shown dotted red line axis labels “h5” – “h8” signify parent 2 ho ologues through enetic versus ph sical position of su set of arkers within the re apped Q region of chro oso e support intervals for the no and odels are shown here as hori ontal green purple lines he StChy2 locus is highlighted a vertical arrow at p Inset: Genetic v’s physical position of markers used in initial TetraOrigin analysis on chromosome , with support re apped region highlighted in red profiles of the re apping of the chro oso e Q for flesh colour no odel results are shown as a green solid line, with odel a purple solid line he product of s π(GIC) for ho ologue on which the Q alleles are predicted to lie highlighted underneath for each arker position used in the Q scan are also shown dotted red line
199 ______Power and precision of QTL analysis
ccording to our analysis the G is the third most important consideration in a T study after population si e and trait heritability suggesting that dense marker coverage across all homologous chromosomes is important for successful T mapping G values ere found to drop at the telomeres a conse uence of the one sided information available at these regions in the multi point estimation This has the un anted effect of biasing the T detection positions in ards making it unlikely for a telomeric T to be found at the correct position This could be cause for some concern given that telomeric regions tend to be more gene rich than more centromeric positions o ever as telomeric regions are also kno n to undergo more recombination Gaut et al 2 i et al 2 5 the extent of this effect is likely to be diminished by the genetic extension of telomeric regions
articularly in the case of autopolyploids kno ledge of homologue specific G values is crucial in predicting hether a T is likely to lie beneath a T peak since variable G profiles can lead to a significant bias in the estimated T position e ere unable to model homologue specific G in the context of double reduction as it as not obvious ho G should behave hen an offspring can inherit more than one copy of part of a particular homologue This could also be seen as an advantage of using the no model here a homologue specific G is a clearly defined concept ppendix
The G cannot be further increased by increasing mapping population si es hich is often thought to be the only ay to increase po er above the limitations imposed by marker density distribution and informativeness f G values are found to be lo on certain homologues it could be orth hile to develop more markers ithin that region on the affected homologues n scenarios here this is impossible e.g. due to long stretches of homo ygosity across homologues the investigator remains blind to any potential T ithin that region although it could be argued that such regions are unlikely to harbour segregating T either or complex T types ith more than one positive allele contributing to the trait our results sho that it is preferable to tag all T alleles through nearby informative markers rather than ust one or none
e initiated this study to determine hether it is orth hile to include double reduction in a T model Through a large simulation study e have demonstrated that the improvements to T analysis are at best marginal and sometimes counter productive e saw at most a 5% increase in detection power for “low power” situations (population si e 2 and trait heritability of hen a significant proportion of multivalents are formed q 5 n practice ho ever one is unlikely to encounter rates of multivalent
200 ______Chapter 8 formation t is i ( our e et al 5 e main disad anta e to usin t e dou le reduction ( model is t at it can efuddle later e ploration of pea s introducin a lar e de ree of uncertaint into t e most li el se re ation t pe and mode of action owe er t ere is no u e computational urden to runnin ot anal ses and comparin results e time limitin step in t e current pipeline was t e calculation of parental mar er p ase usin etra ri in (w ic is ar ua l a redundant step i en current lin a e mappin met odolo ies w ic also determine parental mar er p ase ( ac ett et al our e et al e su se uent estimation of ot no and pro a ilities can e er uic l enerated etra ri in followin w ic ot models can e fitted ermutation test results for ot models were found to e e tremel compara le and do not need to e run twice per trait anal sed lt ou ardl surprisin our results su est t at studies in autopol ploid species s ould focus more on e perimental set up and mar er distri ution t an on w et er dou le reduction s ould e included in t e model or not
re ious studies a e attempted to incorporate dou le reduction in t eir models wit out pro idin sufficient moti ation for suc models apart from t e completeness of t eir model ( ie and u i et al u et al s demonstrated ere and elsew ere ( our e et al 5 en et al estimation of t e rates of dou le reduction per parental c romosome as well as t e fre uenc of multi alent pairin are now relati el strai tforward i en modern i densit mar er datasets it t is stud we ope to a e pro ided a sufficientl alanced anal sis of ot t e no and models to allow an informed decision a out w ic model is most appropriate i en nowled e of t e specific meiotic e a iour of t e population in uestion
e compared a searc of t e full i allelic model space (under a purel additi e or dominant model onl wit one restricted to ust and i allelic and found t at a penalt was incurred includin more models in t e searc space
onsiderin all possi le multi allelic ( 5 and a more eneral formulation of inter allelic interactions would increase t e computation time of t is step wit out necessaril increasin predicti e accurac e ert eless for i er ploid le els t e li eli ood of a in more t an two distinct functional alleles at a sin le locus increases w ic also increases t e possi ilit of no el interactions etween t ese alleles (which cannot simply be termed “dominance effects” anymore). Extension of our current approac to include tri allelic or no el allelic interaction effects would e relati el strai tforward t is also interestin to speculate w et er mac ine learnin al orit ms mi t e applied to sol e t is pro lem rat er t an pro idin a fi ed num er of input models as potential candidates usin some form of cross alidation to c ec t e
201 ______Power and precision of QTL analysis results. e found that a nai e application of the was not suitable for the more complex model. his was because by usin the model we were enerally introducin extra classes unnecessarily so as it turned out. e elopin a model comparison framewor that wei hts offsprin enotype classes by their probability (since double reduction is a position dependent phenomenon occurrin with reater fre uency towards the telomeres) appears to be necessary althou h in esti ations in this direction fell outside the scope of the current study.
e ha e shown with this wor that sli ht ains in detection power in autopolyploids can be achie ed usin a model that incorporates double reduction althou h this comes at the cost of a diminished ability to correctly predict the se re ation type and mode of action usin current methods such as the ayesian nformation oefficient. his study also re instates the importance of hi h enotypic information content particularly when framed within the context of autopolyploids. e now live in the age of “high density” marker sets and linkage maps, even in polyploid species. owe er hi h mar er densities on an inte rated map do not necessarily translate to hi h mar er densities per homolo ue. herefore such terminolo y may offer a misleadin impression and fail to pro ide an accurate description of mar er density and distribution unless haplotype specific maps ha e also been examined and pro ided (e.g. i ure ). e ha e shown here that has an impact on detection power and accuracy. n extendin the definition of to autopolyploids we hope to encoura e future studies in polyploid species to include this important enetic description alon side any reported results. Funding for this research was provided through the TKI polyploids projects “A genetic analysis pipeline for polyploid crops” (project number BO . 001) and “Novel enetic and enomic tools for polyploid crops” (project number BO . ). recei ed an E short term fellowship to wor in the roup of at io undee cotland ( number – ) durin which this research was initiated. he wor of and the etraploid ap software de elopment were funded by the ural En ironment cience nalytical er ices i ision of the cottish o ernment. he authors wish to ac nowled e the potato breedin companies eris eeds . . and . . for pro idin the phenotypic data on the x population ichiel laassen for helpful comments and discussion and lenn arion for su estions on the final manuscript.
Supplementary data will accompany the online version of the published manuscript.
202 ______Chapter 8
an Ooijen ( 00 ) described a procedure to decompose the variance associated with a
T (VQ) into that which is e plained by the markers (VM) and a residual variance for which uncertainty remains (VR) The I is then defined as ( an Ooijen, 00 )
𝑉𝑉𝑀𝑀 𝑉𝑉𝑅𝑅 𝐺𝐺𝐺𝐺𝐺𝐺 = ⁄ 𝑄𝑄 = 1 − ⁄ 𝑄𝑄 e consider the case of the I for one𝑉𝑉 homologue𝑉𝑉 of a tetraploid, and limit our attention to the assumption of random bivalent pairing (no model) The derivation of the I per homologue when double reduction is admissible is less intuitive and has been omitted here
At a given locus, we assume we have already calculated the IB probability of inheritance of homologue j ( ) using TetraOrigin ( heng et al , 01 ) or some alternative method (e.g. ( ackett et al , 01 Bourke, 01 )) e can consider the IB 1 ≤ 𝑗𝑗 ≤8 probability of inheritance of a particular homologue to be the inheritance probability of the so called alternative allele ( ), with the corresponding probability of inheritance of the reference allele 𝜋𝜋𝑎𝑎 𝑟𝑟 𝑎𝑎 sing the definition𝜋𝜋 of= variance 1 − 𝜋𝜋 as ar( ) – ( ) , and using a mean of 1 for the reference allele and 1 for the alternative allele, the residual variance ( is given by 𝑉𝑉𝑅𝑅)
𝑁𝑁 1 2 2 2 𝑉𝑉𝑅𝑅 = ∑(𝜋𝜋𝑟𝑟(1) + 𝜋𝜋𝑎𝑎(−1) − (𝜋𝜋𝑟𝑟(1) + 𝜋𝜋𝑎𝑎(−1)) ) 𝑁𝑁 𝑛𝑛=1
𝑁𝑁 1 2 ⇒ 𝑉𝑉𝑅𝑅 = ∑((𝜋𝜋𝑟𝑟 + 𝜋𝜋𝑎𝑎) − (𝜋𝜋𝑟𝑟 − 𝜋𝜋𝑎𝑎) ) 𝑁𝑁 𝑛𝑛=1 and since ,
𝜋𝜋𝑟𝑟 + 𝜋𝜋𝑎𝑎 = 1 𝑁𝑁 1 2 𝑉𝑉𝑅𝑅 = ∑(1 − (2𝜋𝜋𝑟𝑟 − 1) ) 𝑁𝑁 𝑛𝑛=1
203 ______Power and precision of QTL analysis
𝑁𝑁 1 ⇒ 𝑉𝑉𝑅𝑅 = ∑ 2𝜋𝜋𝑟𝑟(2 − 2𝜋𝜋𝑟𝑟) 𝑁𝑁 𝑛𝑛=1
𝑁𝑁 4 ⇒ 𝑉𝑉𝑅𝑅 = ∑ 𝜋𝜋𝑟𝑟(1 − 𝜋𝜋𝑟𝑟) 𝑁𝑁 𝑛𝑛=1 N
j
𝑁𝑁 4 𝐺𝐺𝐺𝐺𝐺𝐺𝑗𝑗 = 1 − ∑ 𝜋𝜋𝑟𝑟(1 − 𝜋𝜋𝑟𝑟) 𝑁𝑁 𝑛𝑛=1 This is a quadratic function of the IBD probability π, taking a minimum when the IBD
π
204 ______Chapter 8
𝑞𝑞 → 0.5
205 ______Power and precision of QTL analysis
q
Codes: A B C D – additive
206 ______Chapter 8
–
207
Chapter 9
Multi-environment QTL analysis of plant and flower morphological traits in tetraploid rose
Peter M. Bourke1*, Virginia W. Gitonga1,2*, Roeland E. Voorrips1, Richard G. F. Visser1, Frans A. Krens1, Chris Maliepaard1
1 Plant Breeding, Wageningen University & Research, Droevendaalsesteeg 1, 6708 PB Wageningen, The Netherlands.
2 Current address: Selecta Kenya GmbH & Co. KG, P. O. Box 64132 – 00620, Nairobi, Kenya
* These authors contributed equally to this work.
Submitted
209 ______Multi-environment QTL analysis
Abstract Rose, one of the world’s most lo ed nd ommer ll m ort nt orn ment l l nts, s redom n ntl tetr lo d, ossess n fo r r ther th n two o es of e h hromosome h s ond t on om l tes enet n l s s nd so the m or t of re o s enet st d es n rose h e een erformed t the d lo d le el nste d owe er, there m e d nt es to erform n s h n l ses t the tetr lo d le el, not le st e se th s s the lo d le el of most reed n erm l sm ere, we l re entl de elo ed methods for nt t t e tr t lo dete t on n se re t n tetr lo d rose
o l t on to nr el the enet ontrol of n m er of e mor holo l tr ts hese tr ts were me s red oth n the etherl nds nd en n e orn ment l l nt reed n nd sele t on s n re s n l e n erformed t lo t ons other th n the rod t on s tes, en ronment ne tr l re re red to m m se the effe t eness of reed n ro r ms e dete ted n m er of ro st, m lt en ronment for s h tr ts s stem nd et ole r les, et l n m er nd stem w dth nd len th, th t were lo l sed on the re entl de elo ed h h dens t l n e m for rose r wor e lores the om le enet r h te t re of these m ort nt mor holo l tr ts t the tetr lo d le el, wh le hel n to d n e the methods for m r er tr t e lor t on n ol lo d s e es
Key words nt t t e r t o s n l s s, Rosa x hybrida , totetr lo d, mor holo l tr ts, m lt en ronment tr ls
210 ______Chapter 9
Introduction Rose Rosa x hybrida s w del ons dered to e one of the most m ort nt orn ment l l nt s e es rrentl lt ted he en s Rosa ont ns oth d lo d nd tetr lo d s e es w th se hromosome n m er of se en n ons stent hromosom l n m er n s heme h s een ro osed, sed on n nte r ted onsens s l n e m wh h n or or ted m r ers m ed n n m er of d fferent rose m n o l t ons ller et l , nd wh h we follow here lso h s ons sten n hromosom l n m er n h s f l t ted the om r son of res lts etween st d es, hel n to onf rm the os t on of m ort nt so r es of enet r t on for l r e n m er of tr ts of nterest
mon these tr ts, nderst nd n the enet s s of l nt nd flower mor holo n rose h s een m or rese r h m n the rose omm n t for m n e rs or holo l tr ts s h s l nt o r, resen e of r les on stem or et oles, the n m er of flower et ls etc. h e redom n ntl een n est ted t the d lo d le el e ener, res el et l , h ert et l , n et l , r nd nt nt et l , Rom n et l , r hett et l , w th f r fewer st d es ond ted t the tetr lo d le el R se et l , on n o o r n et l , h s s no do t d e to the om l t ons of enot e ll n , l n e m n nd nt t t e tr t lo n l s s n totetr lo ds, for wh h methods nd softw re o t ons rem n m h more l m ted th n for d lo ds owe er, there s n n re s n nterest n the enet n l s s of to ol lo d s e es oorr s et l , ett et l , o r e et l , o r e et l , ett et l , hm t rle et l , , s rred on e er de re s n enot n osts
he m or t of rose lt rs re tetr lo d m lders et l , nd most reed n wor s erformed t the tetr lo d le el r et l , ndeed, the de elo ment of l r e se re t n d lo d m n o l t ons s r l of l ttle or no ommer l m ort n e e ener nd nde, wh h m m ose onstr nts on the s e of s h o l t ons enet ns hts ned t the d lo d le el re often d re tl l ed to rel ted ol lo ds, t st d es re n re s n l dent f n enet nd e enet ontrol me h n sms t the ol lo d le el th t nnot e d re tl red ted ro en tor d lo d s e es ewl formed ol lo ds m e er en e homeolo e loss nd enome restr t r n , ltered tterns of ene e ress on s well s tr ns r t on l nd e enet h n es olt s et l , or e m le n totetr lo d ot to, o t of set of enes were fo nd to e d fferent ll e ressed n n e er ment l to ol lo d ser es t r et l , ore re entl , referent l llele e ress on for l r e set of enes w s dete ted mon nel of s totetr lo d ot to lt rs h m et l , s modern lt ted t rose s ro l est l ss f ed s se ment l
211 ______Multi-environment QTL analysis
llo ol lo d w th m nl tetr som nher t n e o r e et l , , t s l el to h e der ed from the h r d s t on of d st n t t losel rel ted ro en tor s e es s s h, ns hts nto oth llo nd to ol lo d s t on re otent ll rele nt n the well st d ed llotetr lo d otton Gossypium hirsutum , tetr lo ds were fo nd to h e h her elds nd rod ed h her l t f re th n the r d lo d ro en tors rown n the s me en ronment n et l , llohe lo d whe t Triticum aestivum w s fo nd to e s n f ntl more s lt toler nt th n e ther ts d lo d Aegiolops tauschii or tetr lo d T. turgidum ro en tors h s e rs to h e een onse en e of om n n f o r le tr ts from oth rents, t lso from ol lo d s e f henomen s h s the s lt nd ed e ress on of tr ns orter wh h w s tr ns r t on ll re ro r mmed follow n ol lo d s t on n et l , t d es l e these em h s se th t ol lo ds m ossess emer ent ro ert es nd tr ts not fo nd t the d lo d le el t therefore e rs refer le to n est te m ort nt reed n tr ts t the tetr lo d le el, oth to l d te re o s st d es n d lo d rose s well s to nderst nd the enet ontrol of these tr ts t the lo d le el t wh h the re s ll sele ted for
n th s st d we e m ned n m er of mor holo l tr ts s h s the n m er of et ls, the resen e of r les on stems nd et oles, the stem w dth nd len th, the hloro h ll ontent of le es nd the resen e of s de shoots hese tr ts were ssessed n d fferent lo t ons, en l n n n est t on of oss le enot e en ronment nter t ons ton et l , h s s of rt l r rele n e n modern d orn ment l reed n , where sele t on nd rod t on re often erformed n d fferent lo t ons for det ls see ton et l t l t of e ress on o er oth sele t on nd t r et en ronments s needed f m r er ss sted sele t on s to e effe t el l ed ere, we re n l se the d t of ton et l to erform n l s s s n the re entl l shed h h dens t tetr lo d rose l n e m ont n n o er s n le n leot de ol mor h sm m r ers o r e et l , r rrent st d hel s to n re se o r nderst nd n of the enet ontrol of these tr ts n tetr lo d rose, s well s test n nd e lor n the effe t eness of re entl de elo ed methods h ter for the enet n l s s of to ol lo ds
212 ______Chapter 9
Materials and Methods
Plant material and genotyping The tetraploid “K5” rose population, the result of a cross between contrasting lines “P540” and “P867” was used in this study. P540 (the maternal parent) possesses dark red flowers, has prickles on both stem and petiole and is susceptible to powdery mildew, whereas P867 (paternal) has pale salmon coloured flowers, few to no prickles and is more resistant to powdery mildew (Koning oucoiran et al., 0 itonga et al., 0 4).
The population resulting from this cross originally comprised of 8 indi iduals ( an et al., 006) but subse uently was found to consist of only 5 uni ue indi iduals ( ourke et al., 0 7) after genotyping with the 68K ag h P iom P array (Koning oucoiran et al., 0 5). The population segregates for uite a number of important traits (including flower colour, for which a T analysis has already been performed ( itonga et al., 0 6)), making it suitable for the current study into morphological traits (an e ample of the range of phenotypes obser ed for the number of flower petals is shown in igure ). iscrete dosage calls (ranging from nulliple condition (dosage 0) to uadruple condition (dosage 4)) were assigned using the fitTetra package in ( oorrips et al., 0 ) as pre iously described ( ourke et al., 0 7).
Figure 1. Example of the phenotypic diversity for petal number (and flower colour) in the tetraploid rose K5 population
213 ______Multi-environment QTL analysis
Phenotyping Plant trials were performed at three locations ageningen ( ) in The etherlands and at inchester farm, airobi ( ) and griflora farm, oro ( ), two production sites in Kenya. n the etherlands, obser ations were made during both the summer of 007 ( ) and the winter of 007 008 ( ) whereas in Kenya the obser ations were made during the period anuary – uly 00 . ull details of plant propagation and growth conditions are described in itonga et al. ( 0 4). description of the traits measured is pro ided in upplementary Table . Three u enile traits (date of bending, plant height and plant igour) were only recorded in the ageningen summer trial ( ). ll traits were measured with at least two replicates, with 4 indi idual plants per genotype constituting a replicate. There were two completely randomised blocks for both ageningen trials, and three completely randomised blocks for both Kenyan trials. est linear unbiased estimates ( s) for traits across en ironments were calculated using the nlme package (Pinheiro et al., 0 7) in ( ore Team, 0 6). Pearson correlations between single en ironment traits and multi en ironment s were calculated in , as well as the fre uency distributions of the traits in each of the en ironments (using the density function in ). Linkage map construction and QTL analysis The linkage map used in the current study has already been published, and was created using scripts de eloped using pre iously described methods ( ourke et al., 0 6 Preedy and ackett, 0 6 ourke et al., 0 7). ull details of map construction are described in ourke et al. ( 0 7). The final integrated linkage maps had 5,6 5 P markers (not all uni ue positions) and co ered 55 of the 56 e pected parental homologues (the base chromosome number in Rosa is 7 each tetraploid parent is e pected therefore to have 28 “homologue” maps, resulting in 56 maps across both parents).
subset of these markers was chosen for the estimation of inheritance probabilities in the population using the Tetra rigin software ( heng et al., 0 6). n an outcrossing autotetraploid there are nine distinct marker segregation types, namely 0, 0 , 0, 0 , , , , and , where the numbers represent the dosage of the marker in the mother and father, respecti ely. ll other marker types (e.g. 4 ) can be con erted to one of these types without loss or distortion of their linkage information ( ourke et al., 0 6). or each centi organ (c ) inter al, a single marker from each marker segregation type was selected (if possible) which had the lowest number of missing obser ations across the population. Tetra rigin ( heng et al., 0 6) was run on athematica ersion 0 ( olfram esearch nc., 0 4), allowing both bi alent decoding options ( alse True) in the ancestral inference stage. This generated
214 ______Chapter 9 i entit b escent probabilities or the population un er a ouble re uction model (which we subsequently refer to by “DR”) that allowed for both bivalents and multivalents in the parental meiosis i.e. bivalent eco ing alse , as ell as a purel bivalent mo el “noDR”) for which double reduction is ignored (i.e. bivalent eco ing rue n the latter case, une pecte scores are treate as genot ping errors b the so t are he ollo ing settings ere use parental osage error probabilit eps o spring osage error probabilit eps parental bivalent hasing rue hich assumes bivalent pairing pre ominates across the population in the etermination o parental mar er phase he probabilities at the mar er positions ere interpolate at c intervals using the e ault settings o the smooth.spline unction in ore eam, 2 6 an save or subse uent anal sis
scan as per orme using a eighte regression on the trait phenot pes ith probabilities rom the an no mo els as eights he orm o the mo el use has been escribe in etail else here empthorne, 5 ac ett et al , 2 ac ett et al , 2 , namel
′ 2 2 3 3 4 4 6 6 7 7 8 8 here each X𝑌𝑌i is an =𝜇𝜇in icator+ 𝛼𝛼 𝑋𝑋 +variable 𝛼𝛼 𝑋𝑋 + or 𝛼𝛼 one𝑋𝑋 +o 𝛼𝛼 the𝑋𝑋 eight+ 𝛼𝛼 parental𝑋𝑋 + 𝛼𝛼 homologues,𝑋𝑋 + 𝜀𝜀 having ta en the inheritance constraints an into account, an eighting b the probabilities as calculate 4 b etra rigin 8 ∑𝑖𝑖=1 𝑋𝑋𝑖𝑖 = 2 ∑𝑖𝑖=5 𝑋𝑋𝑖𝑖 = 2 o simpli the anal sis ue to une ual numbers o observations both ithin an across bloc s , e use the mean values per environment in the anal sis he mo el it environmental an e ects but not their interaction b irst itting environment e ects an saving the resi uals or the scan or the traits ben ing time, height an vigour that ere measure in the ageningen summer season alone , a single environment anal sis as per orme , using the phenot pe values rather than resi uals as the epen ent variable enome i e signi icance threshol s per trait ere etermine using permutation tests b recor ing the ma imum score rom each o genome i e scans using permute genot pes, ith the 5 uantile o the sorte scores ta en as the threshol ingle environment anal ses ere also per orme to assess the stabilit o across environments, ith signi icance threshol s per environment an per trait etermine using permutation tests as escribe o acilitate visualisation, threshol correcte pro iles ere etermine , assigning a value o to an score belo the threshol , an a value o – threshol or an score above
215 ______Multi-environment QTL analysis
Regions for which the D rofile of the multi environment analysis e ceeded the significance threshold were re ma ed by saturating the D intervals of the ea s with e tra mar ers before re running etra rigin to generate more recise D robabilities in the vicinity of hese e tra mar ers were selected as reviously described but with a binning window of c in the interval added to the already selected mar er set from the initial scan e followed the same a roach as before for detection (weighted regression with the D robabilities as weights) albeit limited to the lin age grou s where were originally detected
ea s from the (mar er saturated) multi environment analysis were also e lored to determine the most li ely segregation ty e and mode of action using the ayesian nformation riterion ( ) ( chwar ) as described by ac ett et al ( ) ll ossible bi allelic models (assuming additivity or dominance) were tested at each ea which meant com aring models for each detected or a oly loid various dominance models are ossible here we only tested for the sim lest case (i.e. aaa aa a versus aaaa) ny model within of the most li ely model (i.e. minimising the ) was recorded as a otential candidate model n cases where there were more than five ossible models the QTL segregation type and mode of action were classified as “unclear”.
single mar er analysis of variance ( ) was also conducted for each trait on the mar er dosage classes for all ma ed mar ers with the –log ( value) of the model fit used as a ro y for the D score ignificance thresholds were determined using permutation tests with N = 1000 and α = 0.05 as described above. ANOVA and IBD based results were visualised together to enable a com arison of the two a roaches
he genoty ic information coefficient ( ) er homologue was calculated using the following formula
𝑁𝑁 4 𝐺𝐺𝐺𝐺𝐺𝐺𝑗𝑗 = 1 − ∑ 𝜋𝜋(1 −𝜋𝜋) 𝑁𝑁 𝑛𝑛=1 where is the inheritance robability of homologue j in individual n at a articular locus estimated using the noDR model ( ha ter ) 𝜋𝜋
216 ______Chapter 9
Figure 2. LOD profiles of QTL scans for morphological traits across different growing environments in the K5 tetraploid rose population. T e results from single en ironment analyses are s own as coloured das ed lines wit t e multi en ironment analysis results as a solid black line (“Combine”). Environments tested were Njoro (“NJO”), Nairobi (“NAI”), Wageningen winter (“WAG_W”) and Wageningen summer (“WAG_S”). Significance thresholds for the multi en ironment analysis as determined y permutation tests are s own as red das ed lines. ote t at single en ironment L profiles das ed QTL lines e ceeding t e multi en ironment L t res olds are not necessarily significant.
217 ______Multi-environment QTL analysis
Results
Trait correlations across environments rait values were in general relativel consistent across environments (Su lementar igure ). owever for the traits chloro h ll content and side shoots, we observed a oor correlation across environments, with correlation coefficients as low as . in the case of the number of side shoots recorded in Nairobi when com ared to the multi environment Es. We also visualised the fre uenc distributions of the henot es across each environment, showing that some traits (like the number of etals) had a ver similar distribution of values across environments, whereas other (like chloro h ll content) did not (Su lementar igure ).
Detection of QTL using IBD probabilities We discovered a number of in this stud , although not all traits roduced significant eaks ( igure ). O significance thresholds for the multi environment anal ses were in the region of . – . as determined b ermutation tests. able summarises the main findings from the initial scan as well as those from the subse uent e loration of the eaks. or most traits, the osition, O score and e lained variances were relativel consistent between the initial scan and the subse uent re ma ing. We were unable to detect for the traits chloro h ll content or number of side shoots, either in the single or multi environment anal ses ( igure ). urthermore, some that were detected in single environment anal ses were not confirmed in the multi environment anal sis (e.g. s for stem length on linkage grou s and in Wageningen winter and summer, res ectivel ( igure )).
he rediction of segregation t e using the a esian Information Criterion ( IC) was not articularl clear, since man could be assigned multi le segregation t es and modes of action ( able ). Onl the eak for stem rickles on linkage grou IC had une uivocal su ort for a single model ( with additive action), with as man as otential models identified in the case of the IC eak for stem width ( able ). We com ared the results of the multi environment anal sis between a model incor orating double reduction ( model) with one that ignored it (no model). In general the results were ver com arable, although the model that included double reduction had slightl more detection ower in that the eaks rose slightl higher above the threshold (Su lementar igure ). revious simulation work has shown that the deci hering of configuration and mode of action is less accurate when the model is used (details in Cha ter ). herefore, given that the model did not alter the results significantl , we o ted to onl re ort results from the no model for sim licit (whilst still roviding a visual com arison in Su lementar igure
218 ______Chapter 9
Table 1. Summary of multi-environment QTL detected in this study using noDR IBD probabilities Trait N Thr. ICM cM LOD Expl. Var Model Act. BIC Stem A Length oooo x QQqq A 307.8 qqQq x QQqq D 308.1 QQqQ x QQQq D 309.0 QQqQ x QQqq A 309.1 Stem width Unclear: 14 models Prickles on D stem qqQQ x Qqqq A 248.9 Unclear: 6 models A Prickles on A petiole qQqq x Qqqq A 85.1 qQqq x Qqqq D 86.5 oooo x Qqqq A 88.9 Number of A petals qqQQ x QqQq A 343.9 oooo x qqQq A 345.7 qqQQ x QQQq A 348.2 A QQqQ x QQqQ A 346.6 QQqq x QQqQ A 346.8 QQqQ x QQqQ D 350.9 N Thr. N α ICM cM LOD Expl. Var. Model “Unclear” refers to situations wher i.e. there was no clearly best model(s) suggested). “Q” signifies a QTL allele with positive effect effect, “q” with a negative effect, and “o” a neutral effect (or more precisely, no Act. BIC
219 ______Multi-environment QTL analysis
Figure 3. Threshold-corrected LOD profiles for QTL scans of morphological traits in the K5 tetraploid rose population. or each trait and each environment (including the multi environment analysis), significance thresholds were determined using permutation tests, and subtracted from the L profiles shown in igure to show only significant results. The y a es therefore correspond to the L e cess above the significance thresholds. or traits hlorophyll content and ide shoots, no significant regions of the genome were identified and were therefore not plotted. The single environment analyses were conducted for trait data from oro ( ), airobi ( ), ageningen winter ( ) and ageningen summer ( ).
Single-marker ANOVA The single mar er analysis on the seven multi environment morphological traits in this study produced slightly different results to that using the probabilities (Table upplementary igure ). n some cases, the power of QTL detection was slightly higher using the ANOVA approach, for example a single marker “K5520_777” on lin age group was found to be significantly associated with chlorophyll content whereas no QTL were detected for this trait using the model. single QTL for stem width was identified on with the model, as opposed to
220 ______Chapter 9 using the mo el hich co localise ith the etecte for stem length on 2 or the other traits stem length, prickles on stem or petiole an num er of petals the same set of ere etecte , al eit ith some hat ifferent peak positions a les an 2
Table 2. Summary of multi-environment QTL detected in this study using the single-marker ANOVA additive effects model Trait N Thr. ICM cM -log10(p) Expl. Var Peak marker Marker phase tem ength 20 2 5 0 0 5 _ 2 x tem i th 20 7 7 7 5 0 0 5 K 7 7_275 x N rickles on stem 20 2 7 0 22 K7 2 _57 x 72 2 7 0 20 K 7 _ x 0 5 K 0 _ 2 x rickles on petiole 20 0 2 _7 0 x hlorophyll content 20 5 5 0 K5520_777 x Num petals 20 2 5 0 5_ 0 x 5 0 K5 _2 77 x N num er of offspring for hich genotype an phenotype ata ere a aila le for each trait Thr. experiment i e significance threshol , etermine y permutation test with N = 1000 and α = 0.05; ICM chromosomal linkage group, using the integrate consensus map num ering of piller et al 20 an ourke et al 20 7 cM centi organ position of peak log 0 p significance at peak, using the p alue from the mo el fit Expl. Var. fraction of phenotypic ariance explaine y the mo el at the peak position a uste 2 from the regression Peak marker marker ith the highest trait association a o e the threshol on that linkage group Marker phase parental marker phase consistent ith homologue num ering from a le n cases here the marker as not phase ue to insufficient linkage to x0 markers, the segregation type is gi en instea
Comparison with previously-reported QTL A comparison of our results ith those of pre ious stu ies sho e that some ha alrea y een i entifie in other populations on the same linkage groups as e i entifie , hile some iffere a le or example, an earlier stu y in the iploi population foun a for oth stem length an i th on 2 an et al , 2007 , although they also i entifie on an 5 for these traits hich e i not or the trait stem prickles e i entifie on , an , hereas pre iously stem prickle ha e een etecte on 2, an respel et al , 2002 in e et al , 200 Koning oucoiran et al , 20 2 he on 2 as reporte y Koning oucoiran et al 20 2 as foun using the same K5 mapping population an same phenotype ata as here although ith a ifferent type of analysis an ifferent genotypes here, the trait as foun to e associate ith linkage groups A2 2 an A2 , correspon ing to our 2 as ell as A , correspon ing to in parent n our stu y, there as a rise in O significance alues on 2 at the same position for this trait, although falling ust elo the significance threshol igure 2
221 ______Multi-environment QTL analysis
Table 3. Overview of previous QTL detected for the morphological traits in this study Trait Pop. N Ploidy LG Reference tem length 2x 2 5 an et al , 2007 tem i th 2x 2 5 an et al , 2007 tem prickles K5 x 2 Koning oucoiran et al , 20 2 2x respel et al , 2002 7 7 270 2x in e et al , 200 etiole 0 2 52 x a apakse et al , 200 prickles 0 2 52 x hang et al , 200 hlorophyll 2x 2 content 7 an et al , 2007 Num petals 0 2x e ener, 2x respel et al , 2002 7 7 270 2x in e et al , 200 2x i ran aint Oyant et al , 200 K5 x Koning oucoiran et al , 20 2 N mapping population si e use Ploidy of mapping population use , either iploi 2x or tetraploi x LG linkage group num ering accor ing to the integrate consensus map num ering of piller et al 20 0 n the case of the a apakse et al 200 an hang et al 200 stu ies, the num ering as impute through linkage ith microsatellite markers see main text for etails
Genotypic Information Coefficient (GIC) he genotypic information coefficient gi es a measure of the le el of information pro i e y marker ata on a scale from 0 to , ith 0 correspon ing to no information, an to full information an is homologue specific in our formulation hen ase on pro a ilities, can e thought of a measure of ho certain e are a out the inheritance of a parental homologue at a particular position, a erage across the population ost alues excee e 0 , reflecting the ense marker co erage across all parental homologues An example of the profile for linkage group is sho n in igure he telomeric region of homologue h7 of parent 2 ha a itional marker co erage hen compare to the other parental homologues ue to a 0 c stretch of simplex x nulliplex markers hich mappe there he content on all other se en homologues stea ily ecreases to ar s the telomere in this region, hile for homologue h7 it remains close to ips in the can also e seen to correspon to
222 ______Chapter 9 areas of lo er marker ensity along the chromosome igure he profiles for all se en rose linkage groups are pro i e in upplementary igure
Figure 4. Example of the distribution of marker alleles across the eight parental homologues on linkage group ICM 3, with the per-homologue genotypic information coefficient (GIC) plotted above. he lo er section sho s the four homologues of arent , the upper section those of arent 2 alues ere foun to e in the range 0 – approximately for oth parents, ith higher alues in icating greater amounts of genetic information for that homologue Discussion
Multi-environment QTL stu ies often report ithout necessarily consi ering hether these ill e useful in practice One of the more important consi erations is hether the reporte are ro ust across en ironments or are only expresse in a specific en ironment his is particularly rele ant for mo ern rose ree ing, for hich the selection an pro uction en ironments often iffer itonga et al , 20 n this stu y e analyse phenotypic ata from three locations, t o in Kenya an one in the Netherlan s, ith an extra set of phenotypes e aluate uring oth a summer an inter season in the Netherlan s e ere most intereste in i entifying that are effecti e across oth the selection an target en ironment e foun that a num er of ere en ironment specific, such as the for stem length present on linkage groups an , ut most ere i entifie in oth the Kenyan an utch trial ata igure he implication is that for the traits stu ie here, selection in a non target en ironment shoul
223 ______Multi-environment QTL analysis
heritable traits (according to the “breeder’s equation”); those
Consistency with previous studies
–
224 ______Chapter 9
oth a a a se et al. ( ) and hang et al ( ) re orted inding a or etiole
ric les in a tetra loid mapping population on their linkage group “B7” (Table 3). hang ( ) ro ided the ri er sequences o icrosatellite ar ers and hich ere re ortedl lin ed to this trait ( hang et al ) n o these ri er sequences on the Fragaria vesca geno e roduced hits on chro oso e Fv hich shares s nten ith rose ( our e et al ) ntriguingl the ar er as re iousl used in genot ing the a ing o ulation ( oning oucoiran et al ) and as a ed on hich ould be consistent ith our result o a single a or or etiole ric les on ( igure ) o e er this ar er ( ) sho ed greatest lin age to si le ar ers on ( our e et al ( ) able reco bination requenc r ≤ 0.09 and LOD ≥ 20.4), consistent ith the n results ndeed a ore detailed loo at the and a s o oning oucoiran et al ( ) ith the a s o our e et al ( ) sho s that lin age grou s and should robabl ha e been assigned to and to (in other ords the ho ologues o lin age grou do not a ear to or a single chro oso al lin age grou ) t is there ore unclear here the or etiole ric les o a a a se et al ( ) and hang et al ( ) should be laced on or hese sorts o e a les de onstrate the ressing need or a reliable h sical sequence in Rosa so that re orted ositions can be traced and quic l chec ed against the re erence h sical a to hel co are and integrate results ro di erent studies
es ite these hurdles e ere able to con ir an o the re iousl re orted in the resent stud as ell as ro iding robust e idence or so e re iousl unre orted or these i ortant or hological traits (e.g. the or ste ric les on and the or etal nu ber on ) n general the results ro di loid studies tall ell ith our results ro a tetra loid anal sis (e.g. inde et al ( ) or ebener and attiesch ( )) on ersel an o the re orted ro the di loid o ulation b an et al ( ) ere not detected in this stud (e.g. the or ste length and idth on lin age grou s and or the our se arate the detected or chloro h ll content ( able )) his a suggest that either large di erences in the genetic control o so e or hological traits could e ist bet een loid le els or ( ore li el ) that or these traits segregated in their o ulation hilst not in ours nother ossible cause is di erences in the ethodologies o detection and articularl signi icance threshold setting hich a ha e led to either in lated e or e errors bet een their stud and this one res ecti el
s long as rose breeding and roduction continues to be er or ed at the tetra loid le el studies at the tetra loid le el continue to ha e clear ad antages o er di loid studies
225 ______Multi-environment QTL analysis
or e ample marker a a that ha e been i enti ie at the iploi le el ma not ne e aril per orm ell at the tetraploi le el (e.g. ue to unkno n lanking o target h bri i ation etc.). Tetraploi o pring ith e irable ombination o trait an be ire tl u e in urther bree ing ork (or ma repre ent a ini he ariet ) herea there i le u e or o pring o a iploi ro . urthermore although there are more tool a ailable or iploi geneti anal i tho e or tetraploi tu ie are be oming in rea ingl ophi ti ate (e.g. Tetraploi ap ( a kett et al. 7) or the metho e ribe here). e there ore belie e that geneti anal e at the pol ploi le el ill be ome in rea ingl ommonpla e in the uture.
Phasing QTL ne o the prin ipal a antage o T anal e u ing B probabilitie in pol ploi i that T ete tion i per orme a ro all homologue imultaneou l . ingle marker approa he rel on oupling linkage bet een marker allele an T allele an ma be less powerful due to “genotypic noise” from other homologues if the marker is not in omplete oupling pha e ith the T allele . Thi be ome e en more important at higher ploi le el here there are e en more T on iguration po ible e rea ing the likelihoo o ull oupling linkage bet een a T an a nearb marker. n thi tu e per orme both an B ba e a ell a ingle marker T anal i . The re ult rom both approa he ere uite on i tent (a a ompari on o Table an ho ). o e er e i in a ingle igni i ant marker (“K5520_777” on linkage group ) hi h a a o iate ith hloroph ll ontent through the anal i ith no orre pon ing peak u ing the B ba e approa h. t i po ible that noi e in the B probabilitie near the T a er el a e te the ete tion po er (the at (marker “K5520_777” is located at 45.9 cM) for homologues h2, h4 and h5 were ≈ 0.858 , 0.843 and 0.895 respectively, below the chromosome ale a erage o . 33 . an . 3 although the o the other homologue ere all abo e . ). n the other han e ete te a T or tem i th on u ing the B mo el hi h a not pi ke up in the ingle marker anal i . Thi peak o lo ali e ith the T ete te or tem length on in rea ing the on i en e that an important gro th etermining a tor i lo ate in that region.
part rom ete tion po er B ba e anal e al o o er the po ibilit to etermine the mo t likel T egregation t pe an mo e o a tion hi h an onl be gue e at u ing ingle marker approa he (i.e. b looking at the egregation t pe o the mo t igni i ant marker Table ). The Ba e ian n ormation riterion ( h ar 7 ) ha pre iou l been ho n to orre tl i enti the T mo el in pol ploi T tu ie ith pre i tion a ura ie o up to or imple T ( etail in hapter ). e ere there ore ome hat i appointe ith the re ult obtaine in thi tu or T
226 ______Chapter 9 segregation type and mode of action able ). n only one case the on M for stem prickles) did we ha e a clear indication of the most likely phase, namely a simple triple additi e segregating as . hased information could help impro e the accuracy of marker assisted selection, where breeders would no longer select indi iduals based on single marker alleles, but on desirable combinations of parental haplotypes through a combination of specific alleles). aplotype assisted selection in polyploids has yet to be applied to our knowledge) but would re uire much clearer phasing than we were able to achie e in this study to be able to reliably construct a potential tagging haplotype marker. he possible causes for the uncertainty are many – conflicts in genotype information, inaccurate linkage maps, more comple or multi allelic rather than bi allelic) types, poorly scored or confused phenotype data etc. espite this, our approach of saturating regions with e tra markers tended in general to increase the significance and proportion of e plained ariances at positions able ), with a single e ception that may ha e been due to a sub optimal phasing solution returned by etra rigin which is a stochastic rather than deterministic procedure heng et al., 20 )). igh genotypic information coefficients around positions on the rele ant homologues ha e been shown to be necessary for the accurate and clear detection of as well as the precise estimation of their location and phase hapter ) and need to be taken into account if studies in polyploids are to deli er applicable results.
Concluding remarks n this study we applied recently de eloped methods to help unra el the genetic architecture underlying a number of important morphological traits in tetraploid rose. Most of the detected were found to be robust across en ironments, suggesting that selection for these traits can successfully be performed in locations other than the production site. owe er, traits displaying significant genotype en ironment interaction effects should probably not be selected for in another than the target location. part from identifying and confirming an important set of at the tetraploid le el, our work helps pa e the way towards haplotype assisted selection methods in the future. Acknowledgements unding for this research was pro ided through the TKI polyploids project “Novel genetic and genomic tools for polyploid crops” (project number BO 2 .0 009 004). he support of the companies participating in the polyploids pro ects is gratefully acknowledged. erra igra . . is acknowledged for generating the K5 mapping population and making it a ailable.
Supplementary data will accompany the online version of the published article.
227 ______Multi-environment QTL analysis
Supplementary Figure 1. omparison bet een single environment trait values and Best inear nbiased stimates (B s across environments for each of the seven morphological traits recorded in this study The four environments are sho n on the left hand margin namely Nairobi (N I Njoro (N O ageningen summer ( and ageningen inter ( The s uared earson correlation coefficients ( are printed for each comparison B s values ( a is are e ual across the four environmental comparisons
Supplementary Figure 2. istribution of rose morphological trait values over four different environments (Nairobi (N I Njoro (N O ageningen summer ( and ageningen inter ( ean parental values are sho n as either solid vertical arro s (maternal mean, ♀) or dashed vertical arrows (paternal mean, ♂).
228 ______Chapter 9
Supplementary Figure 3. omparison bet een multi environment T analysis for the seven multi environment morphological traits studied using a model that ignores double reduction (no versus one that includes it ( ignificance thresholds (as determined by permutation tests are sho n as dashed lines ith little difference found bet een thresholds for the no and models
229 ______Multi-environment QTL analysis
Supplementary Figure 4. ingle environment T analysis results for the traits bending time plant height and plant vigour assessed in ageningen ( only ignificance thresholds (as determined by permutation tests are sho n as dashed lines the analysis sho n used the no model hich assumes random bivalent pairing during meiosis only
230 ______Chapter 9
Supplementary Figure 5. omparison bet een IB based T analysis results (blac line ith a single mar er NO results (green dots for the seven multi environment morphological traits studied ignificance thresholds (as determined by permutation tests are sho n as dashed lines ith the red line corresponding to the IB based thresholds and light green line the NO based thresholds ignificance values for the IB based analysis are given on the left hand a es ( O scores ith the NO significance values on the right hand a es ( log (p values
231 ______Multi-environment QTL analysis
Supplementary Figure 6. enotypic Information oefficient ( I plots for rose lin age groups – visualising the information content per homologue of the IB probabilities used in the initial T scan ar er allele distributions for arent on homologues h – h are sho n in the lo er section ith mar er allele distributions for arent (homologues h – h sho n in the upper section I values ere found to be in the range – (appro imately for both parents ith higher I values indicating greater amounts of genetic information for that homologue The colouring scheme of the I per homologue and the mar er distribution on that homologue are identical
232 Chapter 10 polyqtlR – an R package to analyse quantitative trait loci in autopolyploid populations
Peter M. Bourke1, Roeland E. Voorrips1, Christine Hackett2, Geert van Geest1,3, Richard G. F. Visser1, Chris Maliepaard1
1 Plant Breeding, Wageningen University & Research, Droevendaalsesteeg 1, 6708 PB Wageningen, The Netherlands.
2 Biomathematics and Statistics Scotland, Invergowrie, Dundee DD2 5DA, UK.
3 Deliflor Chrysanten B.V., Korte Kruisweg 163, 2676 BS Maasdijk, The Netherlands.
233 ______polyqtlR: QTL analysis software
The investigation of quantitative trait loci (QTL) is an essential component in our understanding of how organisms develop and respond to their environment through the identification of genes and their alleles that contribute to trait variation. This knowledge can help guide and accelerate breeding programs aimed at developing superior genotypes through genomics-assisted breeding. Here we present polyqtlR, a new software tool to facilitate QTL analysis in autopolyploids that performs QTL interval mapping in F1 populations of outcrossing autopolyploids and segmental allopolyploids using identity- by-descent (IBD) probabilities. The allelic composition of discovered QTL can be explored, enabling favourable alleles to be identified and tracked in the population. Visualisation tools within the package facilitate this process, and options to include genetic co-factors (QTL positions or markers), covariates, randomised blocks or different environments are included.
Quantitative Trait Locus (QTL) analysis, polyploidy, identity-by-descent (IBD) probability, interval QTL mapping
234 ______Chapter 10
Polyploids, which carry more than the usual two copies of each chromosome, are an important group of organisms that occur widely among plants, particularly domesticated ones (Salman-Minkov et al., 2016). Many theories to explain their prevalence among crop species have been proposed, identifying features which may have appealed to early farmers in their domestication of wild species. Such features include their larger organs such as tubers, fruits or flowers (the so-called “gigas” effect) (Sattler et al., 2016), increased heterosis (Comai, 2005), their genomic plasticity (te Beest et al., 2011), phenotypic novelty (Udall and Wendel, 2006), their ability to be clonally propagated (Herben et al., 2017), increased seedling and juvenile vigour (Levin, 1983), the masking of deleterious alleles (Renny-Byfield and Wendel, 2014) or the possibility of seedlessness which accompanies aneuploidy (Bradshaw, 2016). It is currently believed that all flowering plants have experienced at least one whole genome duplication (WGD) during the course of their evolution, with many lineages undergoing multiple rounds of WGD followed by re-diploidisation (Vanneste et al., 2014). Polyploidy may also be induced deliberately (usually through the use of some chemical cell division inhibitor such as colchicine (Blakeslee and Avery, 1937)), often to combine properties of parents that could not otherwise be crossed (Van Tuyl and Lim, 2003), or to benefit from some of the other advantages listed above.
However, not all features of polyploids are necessarily advantageous. Perhaps one of the greatest difficulties in polyploid cultivation and breeding is the constant re-shuffling of alleles in each generation, a consequence of polysomic inheritance. We are currently witnessing a genomics revolution which could hold the key to understanding and tracking polyploid inheritance in detail. From a breeding perspective, we would like to be able to identify genomic regions that contribute favourable alleles to a particular trait of interest (quantitative trait loci (QTL)), and predict which offspring in a population carry favourable combinations of parental alleles. The software tools to perform such analysis at the polyploid level are still relatively rare – here, we introduce a novel R package, polyqtlR, for performing these analyses in outbreeding populations of autopolyploid and segmental allopolyploid species.
The analysis of QTL within polyqtlR can either be single marker-based, or identity-by- descent (IBD) probability-based. For single marker analyses, the dosage of each bi- allelic marker is used as the explanatory variable in a genome-wide scan. In polyploid species, marker dosage refers to the count of marker alleles (by convention the count of the “alternative” allele at a bi-allelic locus, as opposed to the “reference” allele). In an autotetraploid for example, the possible dosages range from nulliplex (0 copies of the alternative allele), simplex (1 copy), duplex (2 copies), triplex (3 copies) to quadruplex
235 ______polyqtlR: QTL analysis software
copies). he assign ent of ar er dosage in pol ploids is a non trivial proble in itself, but there are a nu ber possibilities for achieving this using dedicated soft are ids ehaug et al., oorrips et al., erang et al., ch it arle et al., ).
n the other hand, identit b descent I ) probabilities are the inheritance probabilities of parental alleles in a apping population. n algorith e plo ing idden ar ov odels as recentl proposed for tetraploids and i ple ented in the soft are progra etra rigin heng et al., ). pol tl can utilise the output of etra rigin for the anal sis of uantitative traits. lternativel , a ore si plistic algorith to appro i ate I probabilities as developed ithin our lab our e, ) and has also been i ple ented in pol tl . his algorith has the advantage of being applicable to all ploid levels as ell as being co putationall ver efficient, and as recentl used in the anal sis of several traits in he aploid chr santhe u van eest et al., a). pol tl offers the possibilit to e plore the possible allelic co position at positions and to trac the trans ission of such alleles ithin the apping population. ignificance thresholds can be deter ined using per utation tests, ith parallelised calculations to i prove perfor ance. he inclusion of genetic co factors, phenot pic co variates or co factors to specif e peri ental design e.g. bloc ing factors) can increase the po er of detection, as ell as allo ing for possible interactions bet een to be detected. s ith ost ne tools, pol tl ill continue to be developed to deal ith advances in genot ping technologies as ell as ethodologies for anal sis in pol ploid populations. hat said, the current i ple entation of pol tl should alread have a significant positive i pact on the breeding of pol ploid crops.
pol tl re uires dosage scored ar er infor ation ith an acco pan ing integrated lin age ap fro an population. in age aps can be generated for tetraploid populations using soft are such as etraploid ap ac ett et al., ) or pol ap hapter ). or triploid or he aploid populations pol ap is reco ended as etraploid ap does not currentl handle these ploid levels. In the case of tetraploids, lin age ap phase and I probabilities can be esti ated e ternall using the etra rigin soft are heng et al., ). urrentl , the onl public i ple entation of etra rigin is ritten in the proprietar soft are athe atica olfra esearch Inc., ), although an version ore ea , ) a also beco e available in
236 ______Chapter 10 future. ther ise, I probabilities can be esti ated ithin the pac age using a co putationall efficient internal algorith that uses the phased ap output of pol ap .
etails of the ethodolog behind the calculation of I probabilities in etra rigin can be found in heng et al. ). he internal algorith for esti ating I probabilities in pol tl currentl relies on a ethod originall described in our e et al. ) and re i ple ented b van eest et al. ). ne pre re uisite to calculating I probabilities ithin pol tl is a full phased lin age ap such as those produced b pol ap hapter ). In a he aploid species, for e a ple, such a ap ould be of the for sho n in able .
s I . . c I . . I . . p I . . I . . I . . I . . p I . s I . . t I . . As well as the marker position on an integrated map (columns “LG” for linkage group and “position” in centi organs), the configuration of ar er alleles across the t elve parental ho ologues is also sho n h – h for parent , h – h12 for parent 2). Generally a “1” corresponds to the presence of the segregating allele, although if the original marker coding is used, “1” corresponds to the alternative and “0” to the reference allele.
I probabilities of . are initiall assigned to the population for all parental ho ologues at all ar er positions co pletel uninfor ative priors). ull infor ative ar er scores are then used to assign probabilities of in the case of inheritance, or in the case of no inheritance. or e a ple, in a tetraploid population at a ar er single segregating allele originating fro parent ) hich as phased , offspring ith ar er dosage ould initiall be assigned probabilities of . , . , . , . , . , . , . ), and offspring ith ar er dosage ould initiall be assigned probabilities of . , . , . , . , . , . , . ) nor alisation of probabilities occurs later). artiall infor ative dosages in the offspring are not used e.g. an offspring dosage of fro a ar er – the origin of this allele could be fro either parent). nce all such probabilities have been assigned, probabilities at all other ar er positions are appro i ated b first locating the nearest lin ed ar er ith an infor ative
237 ______polyqtlR: QTL analysis software pro a ility (0 or 1). he pro a ility is then estimated as r in the case of a starting pro a ility of 0, or 1 – r in the case of a starting pro a ility of 1, where r is the recom ination fre uency etween the two markers, as derived from the map positions (for example, if Haldane’s mapping function ( aldane, 1 1 ) was used to generate the map, the inverse of this function is used to re calculate r). he pro a ilities are then normalised to ensure for each parent. inally, pro a ilities𝑃𝑃𝑖𝑖 are imputed at a grid of positions using𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 the function in ( y default, ∑𝑖𝑖 𝑃𝑃𝑖𝑖 = ⁄smooth.spline at 1 c spacings). 2
Single marker analysis or the single marker analysis, a genome wide scan is performed y fitting the following additive model at each marker position where is the vector of phenotypes, is the vector of marker dosage scores, is the 𝑌𝑌 = 𝑦𝑦̅ + 𝛼𝛼𝛼𝛼 + 𝜀𝜀 overall mean and the residuals. his model assumes additivity of L effects 𝑌𝑌 𝐷𝐷 𝑦𝑦̅ depending on the dosage, which may or may not hold. rom the A A ta le, the sum 𝜀𝜀 of s uared residuals (RSS1) is recorded and used to calculate the logarithm of odds (L ) score as follows ( roman et al., 200 )
0 𝑁𝑁 10 𝑅𝑅𝑅𝑅𝑅𝑅 where N is the population si e, 𝐿𝐿𝐿𝐿and𝐿𝐿 RSS= 0 islog the residual( ) sum of s uares under the ull 2 𝑅𝑅𝑅𝑅𝑅𝑅1 ypothesis of no L, i.e. . he amount of e plained variance at any tested position is also calculated using 2 𝑅𝑅𝑅𝑅𝑅𝑅0 = ∑𝑖𝑖(𝑦𝑦̅ − 𝑦𝑦𝑖𝑖)
𝑀𝑀𝑀𝑀𝑅𝑅 where is the mean s uared 𝑒𝑒𝑒𝑒residuals𝑒𝑒𝑒𝑒. 𝑣𝑣𝑣𝑣𝑣𝑣. from the =1− A A ta le, and is the total 𝑀𝑀𝑀𝑀𝑇𝑇 mean s uares,𝑀𝑀𝑀𝑀𝑅𝑅 (where are the total sum of s uares𝑀𝑀𝑀𝑀𝑇𝑇 terms from ∑ 𝑆𝑆𝑆𝑆 the A A ta le,𝑇𝑇 N the population si e and the num er of locks, taken to 𝑀𝑀𝑀𝑀 = 𝑁𝑁∗𝑛𝑛𝑛𝑛.𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏−1 𝑆𝑆𝑆𝑆 e one in the case of no e perimental locking). his is the same formula used to 2 𝑛𝑛𝑛𝑛. 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 generate the ad usted from the linear model fit (as returned y the summary.lm function in ).
IBD-based analysis he ased analysis has two different forms, depending on the origin of the pro a ilities. f the pro a ilities were estimated in etra rigin, then the pro a ilities of all possi le tetraploid genotype com inations are known, either possi ilities in the
238 ______Chapter 10 case of purel i alent pairing, or possi ilities in t e case ere uadri alent pairing is also allo ed ese genot pe pro a ilities are t en used as eig ts in a regression model originall proposed empt orne ( empt orne, , ut more recentl adopted in t e etraploid ap pipeline (Hac ett et al , Hac ett et al , Hac ett et al ,
ere t e constraints′ and a e alread 𝑌𝑌 =𝜇𝜇 + 𝛼𝛼2𝑋𝑋2 + 𝛼𝛼3𝑋𝑋3 + 𝛼𝛼4𝑋𝑋4 + 𝛼𝛼6𝑋𝑋6 + 𝛼𝛼7𝑋𝑋7 + 𝛼𝛼8𝑋𝑋8 + 𝜀𝜀 een applied Here, t e Xi are indicator aria les for eac parental omologue ( for 𝑋𝑋1 + 𝑋𝑋2 + 𝑋𝑋3 + 𝑋𝑋4 = 2 𝑋𝑋5 + 𝑋𝑋6 + 𝑋𝑋7 + 𝑋𝑋8 = 2 parent , for parent in a tetraploid and is t e residual term
or t e pro a ilities estimated internall ,𝜀𝜀 t e pro a ilities of combinations of parental alleles are un no n, ut t e in eritance pro a ilities of eac individual parental omologue is no n e form of t e model appears identical, i.e.
except no t e regression′ is un eig ted, and t e Xi are ectors of in eritance 𝑌𝑌 =𝜇𝜇 + 𝛼𝛼2𝑋𝑋2 + 𝛼𝛼3𝑋𝑋3 + 𝛼𝛼4𝑋𝑋4 + 𝛼𝛼6𝑋𝑋6 + 𝛼𝛼7𝑋𝑋7 + 𝛼𝛼8𝑋𝑋8 + 𝜀𝜀 pro a ilities of a specific parental omologue at a locus
or a exaploid, t e model is extended to include ten of t e t el e parental omologues, i.e.
′ 𝑌𝑌 =𝜇𝜇 + 𝛼𝛼2𝑋𝑋2 + 𝛼𝛼3𝑋𝑋3 + 𝛼𝛼4𝑋𝑋4 + 𝛼𝛼5𝑋𝑋5 + 𝛼𝛼6𝑋𝑋6 + etc. 𝛼𝛼8𝑋𝑋8 + 𝛼𝛼9𝑋𝑋9 + 𝛼𝛼10𝑋𝑋10 + 𝛼𝛼11𝑋𝑋11 + 𝛼𝛼12𝑋𝑋12 + 𝜀𝜀 pproximate significance t res olds are determined using ermutation ests ( urc ill and oerge, default, permutations of t e genot pes are generated, follo ing ic t e maximum genome ide scores are recorded from eac of t e anal ses, and t e t uantile of t e ordered score is ta en as an approximate significance t res old Ho e er, t ese num er are merel guidelines, and t e user as full control o er t e num er of permutations and t e selection of t e approximate Type I error rate α.
n cases ere a large effect is present and segregating in a population, it can e ad antageous to reduce t e le el of ac ground noise at ot er loci accounting first for t e ma or and running an anal sis on t e corrected p enot pes uc an approac as pre iousl een termed multiple mapping ( ansen, or composite inter al mapping ( eng, n pol tl , e offer a simple approac to correct for genetic co factors, eit er suppl ing t e name of a mar er closel lin ed to
239 ______polyqtlR: QTL analysis software t e ma or pea , or t e pea position from t e genome ide scan ( ic is usuall performed at a grid of splined positions ere is no limit to t e num er of co factors t at can e added, ut a parsimonious anal sis it onl significant, unlin ed as genetic co factors is recommended (as ell as anal ses including t ese co factors singl e model descri ed a o e for pro a ilities is initiall fitted at t e supplied position(s and t e residuals are sa ed to replace t e ector of p enot pe alues in t e scan
enot pic co ariates t at ma represent a source of confounding ariation can also e supplied, and t ese are also initiall fitted ( and t e residuals sa ed as a replacement for t e p enot pes under in estigation n cases ere incomplete 𝑌𝑌 ~𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 co ariates are supplied (i.e. containing missing alues t e missing alues are replaced it t e mean co ariate alue, ilst arning t e user of t e extent of t is pro lem f experimental design factors are included in t e anal sis, t e are also fitted ( after ic t e residuals are used to perform t e genome ide scan ote t at if 𝑌𝑌 ~𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 loc s are included, t e apparent dimension of t e model increase e genot pe matrix is erticall concatenated according to t e num er of loc s, ic also moti ated our decision to permute t e genotypes rat er t an t e phenotypes in t e ermutation est 𝑌𝑌 (t e association is ro en in ot cases, ut permuting genot pes and t en concatenating t em ensures t e correct le el of nesting of permutations is ac ie ed ot loc s, co ariates and co factors can e included (or an com ination of t ese t ree , in ic case loc s are first fit, follo ed co ariates and t en co factors ecause t e anal sis relies on simple linear models (using t e lm function in ( ore eam, , missing p enot pic alues can e pro lematic f loc s are used, t ere is t e possi ilit to impute missing p enot pes using t e fitted model for loc effects and t e non missing p enot pe scores for t at indi idual in t e ot er loc s default, at least o ser ations are re uired for imputation (e.g. minimum out of p enot pes non missing for t at indi idual in a loc situation
ne of t e main ad antages of an ased anal sis o er single mar er met ods is t e a ilit to explore pea positions to determine t e most li el configuration and mode of action (additi e dominant ese can e compared using a model selection procedure suc as t e a esian nformation riterion ( ( c ar , as pre iousl proposed (Hac ett et al , n addition, e can run a per omologue anal sis on lin age groups no n to possess segregating o ac ie e t is, e re run t e anal sis ile restricting t e genot pic matrix to a single column of aplot pe specific pro a ilities is ma assist in t e interpretation of t e most 𝑌𝑌 li el origin of fa oura le (or unfa oura le alleles (alt oug onl relia l so in
240 ______Chapter 10 cases of a simplex – for more complex, multi allelic t e output can e misleading n cases ere a loc ing factor(s is included in t e anal sis, est linear un iased estimates ( s s ould first e calculated using t e function pro ided ( ic uses t e lme function from t e pac age nlme ( in eiro et al , e enot pic nformation oefficient ( is a con enient measure of t e precision of our no ledge on t e composition of parental alleles at a particular position in eac offspring, a eraged across t e mapping population e of omologue j ( at eac position is calculated from t e pro a ilities using t e formula 1 ≤ 𝑗𝑗 ≤ ∑ 𝑞𝑞 𝑁𝑁 4 𝐺𝐺𝐺𝐺𝐺𝐺𝑗𝑗 = 1 − ∑ 𝑃𝑃𝑛𝑛,𝑗𝑗(1 − 𝑃𝑃𝑛𝑛,𝑗𝑗) ere is t e sum of parental ploid 𝑁𝑁 le els,𝑛𝑛=1 N is t e population si e and is t e pro a ilit of in eriting omologue j in indi idual n at t at position (t is is a ∑ 𝑞𝑞 𝑃𝑃𝑛𝑛,𝑗𝑗 generalisation of t e measure used in ap ( an oi en, an oi en,
e isualisation of results is an important aspect of an anal sis and is not neglected in pol tl profile plots across all c romosomes can e simpl generated, and can e o erlaid it pre ious anal ses if direct comparisons are re uired (suc as t e impact of including a cofactor (or multiple co factors in t e anal sis e profiles of eac parental omologue can also e plotted in a similar fas ion, facilitating a comparison et een t e position of pea s and t e landscape in t at region e results of omologue specific anal ses can also e plotted to elp interpret t e possi le configuration, and t e results of t e model selection procedure ( are also plotted to gi e an indication of t e li eli ood of competing models e aplot pe conformation of eac indi idual for an specified genomic region can e plotted, eit er for selected indi iduals or for t ose indi iduals it extreme p enot pes t is also possi le to automaticall screen for and identif recom inant indi iduals it in a specified region, or indi iduals carr ing dou le reduction products
241 ______polyqtlR: QTL analysis software
h2 † h2 h2 gene action, either “additive”, “dominant” or “epistatic additive” † “Broad sense” heritability of the simulated trait, as defined by 2 𝜎𝜎𝑔𝑔 2 2 2 ℎ = 𝜎𝜎𝑔𝑔+𝜎𝜎𝑒𝑒 i 𝑃𝑃𝑖𝑖 𝑑𝑑𝑖𝑖 2 𝑃𝑃𝑖𝑖~𝒩𝒩(𝑄𝑄𝑖𝑖 ∗𝑑𝑑 , 𝜎𝜎𝑒𝑒 ) + 𝒩𝒩(𝑌𝑌, 𝑠𝑠)
2 2 1−ℎ 2 2 𝜎𝜎 𝑒𝑒 = ( ℎ ) 𝜎𝜎𝑔𝑔 2 h2 𝜎𝜎𝑔𝑔 to the “broad sense” heritability
242 ______Chapter 10 inherited, dosage effects ere also included or traits and here multiple contributed, single locus phenotypes were added together to produce a “multi locus” phenotype sing the sample tetraploid dataset described, e estimated B probabilities using etra rigin heng et al , as ell as using our o n B estimation algorithm for comparison he etra rigin B s ere used to perform a analysis for the three simulated traits described in able , ith the results visualised in igure or rait , three significant pea s ere detected as listed in able , corresponding to the positions of the three simulated or rait , a single very sharp pea as observed at
ignificance thresholds are sho n as hori ontal dotted lines, as determined by permutation tests or rait , a co factor analysis using the ma or pea on lin age group yielded no e tra although the significance threshold reduced slightly, as sho n by the lo er blue dotted line or rait , the addition of the three pea s as co factors reduced the significance threshold also lo er purple dotted hori ontal line , although no ne ere detected purple profile line he distribution of mar ers on the integrated lin age map are sho n at the a is as vertical dashes rue positions are sho n by green triangles
243 ______polyqtlR: QTL analysis software
c although the support inter al did not include the true position which was at c co actor analysis using the pea position on lin age group did not result in any e tra eing detected igure second panel or rait three signi icant pea s were detected on lin age groups and with the remaining smaller on lin age groups and not detected ncluding either o the pea s on lin age groups and as a co actor increased the signi icance at the other pea ut had little e ect on the pro ile on lin age group igure ncluding all three pea s simultaneously as co actors in the analysis reduced the signi icance threshold slightly ut did not result in the detection o any new
he alues per homologue were calculated and ound to o ten e close to ull in ormation owe er some ma or dips in the pro ile can e seen or e ample on lin age group or homologues and corresponding to the region on the genetic lin age maps which har ours no segregating mar ers upplementary igure
rait A D A A D rait A rait D A D A Unclear : 10 models a in age roup o position osition o pea in centi organs c support inter al in centi organs d signi icance threshold as estimated rom permutation testing with N and α e d usted rom the model it at the pea the proportion o ariance e plained y the pea redicted con iguration using model selection procedure ased on BIC. “Unclear : 10 models” refers to situation when no clear minimum BI occurred here with competing models within units o the minimum g ode o action either additi e A or dominant D h ayesian n ormation riterion alues or models listed in column ‘Configuration’
he prediction o segregation type and mode o action y selecting the model which minimised the was accurate or rait and rait ut prediction o the con iguration o underlying rait pro ed more di icult a le t each pea oth additi e and dominant i allelic models are tested o which there are in total – c.f. hapter and any models within o the minimum are
244 ______Chapter 10 returne as ossi le mo els igure . or rait a i allelic mo el for the was not entirel a ro riate an the re icte t e Qqqq qQqq a le was not e actl that which was simulate Qooo oqoo where o is an allele which oes not contri ute to trait ariation while Q an q o . In some cases more than one mo el was suggeste igure .a while at times one clearl o timal mo el was foun igure . . he out ut of a single homologue anal sis was also isualise which ma hel in the inter retation of results an e am le of which is shown in igure .c . he re icte mo el can e erifie e amining the ha lot e structure of offs ring with e treme henot es which in theor shoul carr some or all of the “positive alleles” for the QTL igure .
he Ba esian Information Criterion BIC results for the lin age grou ea of rait . ach num er corres on s to a ifferent configuration for which there are in total u lementar a le . he a iti e mo el mo el minimises the BIC for this trait an mo el the ominant ersion of this mo el was secon most li el . BIC results for the ea of rait with the a iti e mo el suggeste mo el . ere there are no other mo els within BIC of the minimum. er homologue anal ses can also com lement the anal sis here the results of rait are shown. Colour scales are use to in icate significance of the single homologue mo el fit with the irection of the homologue effect shown lac lines a o e a is ositi e elow a is negati e . ere we see that ositi e allele effects originate from homologues an .
245 ______polyqtlR: QTL analysis software
the si late ataset provi e ith the pa a e e i ot i l e a rivale t pairi str t res or prefere tial hro oso al pairi ri the pop latio si latio i e i ree i o ever a ertai proportio of ltivale t pairi str t res are e pe te to for ri a topol ploi eiosis hi h a lea to the phe o e o of
o le re tio a al sis of the potato pop latio e ot pe si the ol T si le leoti e pol orphis arra os et al as es ri e i o r e et al reveale the prese e of o le re tio pro ts i a s set of i ivi als i the pop latio a sa ple for potato li a e ro p is sho i pple e tar i re
Three QTL ere ete te for Trait i re o li a e ro ps L a The QTL positio s are epi te otte re o e ith pl s alleles of positive effe t sho re stars a alleles of e ative effe t a ope s are ivi als a ha the hi hest trait val es L a resp pop latio ea e eral these i ivi als arrie the pre i te favo ra le alleles at these positio s h vis alisatio s a help o fir QTL a al sis res lts as ell as fa ilitate haplot pe assiste sele tio
o le re tio i e eral e erts o l a i or i fl e e o li a e a al ses o r e et al o r e et al or QTL a al ses hapter a a safel e i ore i ost ases pol tl QTL a al sis si a o el that i l es o le re tio is strai htfor ar provi e that pro a ilities fro a o el that allo e for o le re tio are availa le for e a ple si Tetra ri i he et al e a itio al feat re of pol tl that a e sef l for e e appi a sele tio is its a ilit to i e tif re o i a t i ivi als ithi a spe ifie re io of i terest a
246 ______Chapter 10 e a ple of hi h is sho i pple e tar i re here e i e tifie ei ht i ivi als ith a re o i atio et ee ho olo es a i the i terval – o li a e ro p
i all e also perfor e a si le ar er a al sis si the ar er osa es as a a itive pre i tor of phe ot pes hi hli hti so e iffere es et ee ase a si le ar er ase a al ses The ase a al sis as fo to e sli htl ore po erf l ith the L pea for Trait ei ete te si pro a ilities i re t isse e tirel si o l ar er osa es pple e tar i re i ifi a e threshol s varie et ee approa hes t ere ot o siste tl hi her or lo er i o e set or the other si le e tre el si ifi a t ar er as fo to e asso iate ith Trait o L as a e see i pple e tar i re This ar er (“DN_III35.6”) mapped to 19.3 cM (just 0.7 cM from the QTL) and was phased exactly as the QTL itself other or s it as a ear perfe t ar er for this parti lar QTL
this paper e have es ri e the possi ilities for perfor i QTL a al sis i i pare tal pop latio s of a topol ploi spe ies si the pol tl pa a e i e i this si si late tetraploi ar er osa e ata a three asso iate a titative traits ith o trasti e eti ar hite t re re or e over three ears e o fi e o r atte tio to a tetraploi ataset a have ot e o strate trait a al sis i triploi or he aploi pop latio s the other ost o o l e o tere ploi levels for e peri e tal pla t pop latio s a ree i pro ra s o ever all f tio s ithi pol tl have ee evelope to e a le to a al se these a pote tiall a other ploi levels a therefore the res lts o l e s sta tiall si ilar see for e a ple va eest et al for a es riptio of a QTL a al sis i the a tohe aploi or a e tal spe ies Chrysanthemum morifolium this is ssio e o si er a er of poi ts – the relative a va ta es or isa va ta es of ase a al ses over si le ar er approa hes the i porta e of a o pariso ith alter ative soft are a the s ope for f t re evelop e ts
pol tl offers the possi ilit to perfor QTL a al ses either si i e tit es e t pro a ilities or si the ar er osa e s ores ire tl ltho h e sho e that the ase a al sis ha so e hat ore po er ete ti a QTL that as isse the si le ar er a al sis e have ot perfor e a o prehe sive po er a al sis
247 ______polyqtlR: QTL analysis software to er fy th s. I D ased analyses allow us to pred ct the most pro a le QTL se re at on type and mode of ene act on as well as trac n the transm ss on of fa oura le or unfa oura le alleles n the populat on. They therefore offer a more comprehens e approach to QTL detect on than s n le mar er stud es. owe er there may also e s tuat ons n wh ch s n le mar er analyses may e prefera le to I D ased approaches. or example n cases where t s not poss le to rel a ly ass n d screte dosa e scores cont nuous mar er enotypes m ht e the only a a la le enotyp n data. These ha e already pro en to e useful n QTL assoc at on mapp n stud es n ar ous polyplo d spec es ( rand e et al. 016 Tum no et al. 016). The methods to determ ne I D pro a l t es us n cont nuous enotypes rather than d screte dosa e scores are not yet de eloped (nor ndeed are there methods to construct l n a e maps from such enotypes to the est of our nowled e). In such c rcumstances a s n le mar er analys s may e the only a a la le opt on. In the unl ely e ent that an nd dual mar er co se re ates nearly perfectly w th a QTL allele (as was the case here for Tra t_ ) then s n le mar er approaches w ll also e at least as powerful than I D ased analyses f not more so. In cases where the est mat on of I D pro a l t es s d ff cult due to ser ous errors n the enotypes l n a e map and or mar er phas n then (accurate) s n le mar ers may pro e more su ta le to detect QTL effects than an I D ased analys s. owe er on alance oth approaches ha e the r mer ts and t s enerally a ood dea to perform oth analyses and com ne results for a more comprehens e p cture.
It has pre ously een shown that a h h and un form I s needed for accurate QTL analyses ( hapter ). ere we descr e the calculat on of I and appl ed t to a s mulated tetraplo d dataset from the poly tl pac a e. owe er the usefulness of the I measure depends to a lar e extent on the ual ty of the al or thm to enerate I D pro a l t es upon wh ch t s ased. In cases where the I D pro a l t es are close to 0 or 1 ut are also ncorrect the I may e m slead n the I can only nd cate re ons where there s low nformat on content not incorrect nformat on. In what we present here we enjoyed unreal st cally fortunate c rcumstances w th error free s mulated data conta n n no m ss n alues. Th s was reflected n cons stently h h I s for most homolo ues and l n a e roups ( ure 1 ottom panel). In real ty we are unl ely to encounter such h h ual ty datasets. lthou h we ha e stud ed the I n deta l elsewhere ( hapter ) we ha e not yet attempted to uant fy what const tutes a “sufficiently high” GIC. However, we found that regions of variable GIC will tend to as the detect on of QTL to ne h our n loc w th h h I and that I s a stron pred ctor of QTL detect on power ( hapter ). Therefore t s prudent to exam ne the I prof les around QTL pea s part cularly on the homolo ues wh ch are nd cated to carry the QTL alleles.
248 ______Chapter 10
he only other software that is currently available to erfor si ilar analyses is etra loid a Hac ett et al., , available as free downloadable software with an advanced user friendly G I that can roduce integrated and hased lin age a s as well as erfor interval a ing in tetra loid o ulations. e transfor ed our si ulated ar er dosages, hased lin age a and henoty es into co atible in ut and re ran the analysis for the henoty es we used the s as henoty es as there is no facility for including bloc s in . n overview of the results is given in u le entary able . n the whole the results are very co arable. detected the sa e ea s in al ost recisely the sa e ositions, although the ea scores and esti ated e lained variances were not e actly the sa e tended to have slightly higher scores and greater e lained variances at the ea s, although both software e loy si ilar ethods . he a or difference in the results was in the redicted segregation ty e and ode of action. art fro additive and do inant odels, also tests “codominant factors”, where the QTL genotype classes are allowed to have independent eans. es ite this, the odel search s ace is currently li ited to , and ty es, whereas we currently consider all ossible segregation ty es there are bi allelic odels to consider in total Cha ter , u le entary able , albeit without the codo inant odel currently included. If we co are the redictions of oly tl able and u le entary able with the true configurations able , both erfor ed well, but there are so e s all differences. In general, returned ore ossible odels which we ta e as being within IC units of the ini u IC, which corres onds to between ositive and strong evidence of a eaningful difference between odels eath and Cavanaugh, . or the lin age grou of rait with configuration , found that was the best fitting, which is as far as it is able to go. oly tl also tests all possible 1x2 QTL types (what we term “simplex x duplex” QTL), and therefore found that the model Qqqq x QqqQ was the most likely. For Trait_2 (the “monogenic” trait both software correctly guessed that the segregated as with additive effect. However, also returned a second co eting odel, na ely QQqq x qqqq with codominant effect, with a ΔBIC of 1.9 (Supplementary Table 2). For oly tl there was no co eting odel within at least IC, i.e. it was a very clear front runner. Interestingly, both software had so e difficulties with rait – neither detected the inor s on G or , and oly tl in articular had roble s in correctly assigning the segregation ty e for the e istatic s of G , and . did better, correctly redicting the configuration of all three , but not always the ode of action which was difficult to define – an allele count of at least was needed at all three loci to roduce a subse uent additive effect . oth software use
249 ______polyqtlR: QTL analysis software the ayesian nformation riterion ( ) for model comparisons, and therefore discrepancies are most likely due to slight differences in the probabilities (which we were unable to compare as they are not part of the T output).
The statistical models behind the QTL analysis in polyqtl are simple yet powerful, with most of the complications of polyploid inheritance already dealt with in the earlier stages of phased linkage map construction and in the calculation of probabilities. There is however still scope to expand upon the developments already implemented. For example, we have not yet implemented any formal procedure for detecting epistasis. s we saw with Trait_ , polyqtl appears to have difficulties in correctly identifying the QTL configuration in such circumstances. n our treatment of genetic co factors we do not currently compare between models, but a model comparison framework such as the kaike or ayesian nformation riterion could be quite instructive here. There is also currently no provision for investigating genotype x environment ( x ) interactions, despite these interactions being relatively common (van euwi k et al., 2 1 ). ne reason we have not (yet) implemented x in polyqtl is the difficulty of including an interaction term for a polyploid population. hould this interaction effect be investigated homologue by homologue erhaps two at a time, or simultaneously n other words, capturing an interaction effect in a polyploid QTL model would likely require some simplifying assumptions which may or may not be appropriate. n time these will no doubt be investigated and implemented.
nother direction polyqtl could take in future is to integrate information across multiple populations in a single analysis either using pedigree or genomic relationship matrices, such as is done for example in FlexQTL ( ink et al., 2 ). The current dependence on bi parental F1 populations means that each analysis must be done separately, with perhaps some ad hoc integration of QTL results afterwards. n future, merging such analyses into a single study will improve not only detection power but also the robustness of results, but will require the development of novel approaches to estimate probabilities across populations and pedigrees.
Finally, we also expect that polyploid genotyping may soon differ from the single dosages that are currently the basis for much of the analysis in polyqtl . Time will tell how successful these new genotyping technologies will be at accurately capturing the full breadth of allelic diversity in polyploids and exploiting it for research and breeding purposes. polyqtl is flexible enough to allow adaption to deal with such multi allelic haplotype based markers, offering greater choice to users in future experiments and analyses.
250 ______Chapter 10
This work was supported through the TKI projects “A genetic analysis pipeline for polyploid crops” (project number BO 0 00 001) and “Novel genetic and genomic tools for polyploid crops” (project number BO 0 00 00 ) The authors would like to thank ric van de eg erman van ck en mulders ichiel Klaassen ( lant Breeding) and amillo Berenos ( mmen Orange B ) for their constructive feedback and discussions
isualisation of the marker coverage of the tetraploid linkage maps provided with the polyqtlR package arent 1 homologue maps are numbered h1 – h with parent homologue maps numbered h – h The integrated maps are shown in the centre for each linkage group ( 1 – corresponding to the five linkage groups) aps were generated and plotted using the polymapR package ( hapter ) ertain regions e.g. 0 – 0 c for linkage group 1 homologues 1 and contain no segregating marker information which is reflected in low I values for the affected homologues (c.f. igure 1)
251 ______polyqtlR: QTL analysis software
redicted haplotype conformation showing possible double reduction segments in red from selected individuals of the potato A 1 population chromosome 1 ighter shades of blue correspond to intermediate probabilities ertain individuals e.g A 001 or A 00 proved difficult to reconstruct with TetraOrigin and harbour double reduction segments of improbably short length
isualisation of the haplotypes of eight 1 individuals from the simulated dataset identified as having a recombination between homologues 1 and on linkage group between 1 c and c The user has the ability to select any set of homologues involved in recombination and any desired stretch of chromosome as well as any threshold probability with which a homologue (or segment thereof) is considered to be inherited (by default 0 )
252 ______Chapter 10
ingle marker analysis results (dark green points) using additive linear model on marker dosages to detect T reen hori ontal dotted lines correspond to O significance thresholds as determined by permutation tests (N 1000 α 0 0 ) Also shown are the results of interval T mapping using IB probabilities (reproduced from igure 1) with significance thresholds as hori ontal gold dotted lines The T peak on for Trait was not detected using the single marker approach but was found using the IB based approach
253
Chapter 11
General Discussion
255 ______General discussion
Foreword Working under the auspices of the department of plant breeding, one experiences a sense of responsibility that research findings should ultimately have a practical application in the plant breeding sector. This is particularly true of a project embedded within a public- private partnership, with a consortium of a dozen breeding companies providing matching funding for this work. That said, there was never the feeling that those enticing yet often time-consuming theoretical side-alleys should not be explored. In this discussion therefore, I address both aspects – how the findings of this thesis might be used to help in the breeding of polyploid crops, but also how this thesis has deepened our understanding of polyploids. Ultimately, both can help in the pursuit of better polyploid crops. As the saying goes, sometimes “there’s nothing more practical than a good theory” (Lewin, 1951). Or taken from a plant-breeding perspective, “the full potential and effectiveness of a plant-breeding program can be realised only when the reproductive, genetic and breeding behaviour of a species is known and understood” (Dewey, 1966). Can experimental populations yield unbiased information on meiosis? In this thesis I have tried to investigate real marker datasets beyond the traditional boundaries of genetic mapping, with a particular interest in polyploid meiotic phenomena. This began in Chapter 3 with a description of the “double-reduction landscape” in a tetraploid potato population. In Chapter 5 we reconstructed the pairing behaviour in a tetraploid rose population and from that inferred that homologue pairing and recombination was not random across all chromosomes. We took the further step of trying to relate homology at the level of SNP markers to the pairing behaviour, testing the theory that chromosomal homology is an important factor in pairing recognition and synapsis formation during meiosis (Naranjo and Corredor, 2008). Later in this discussion I also present some results on meiotic cross-over frequencies in polyploid meiosis using a tetraploid potato mapping population. In all of these cases, I am assuming that an experimental mapping population represents an unbiased record of parental meiosis. This is of course an unrealistic assumption, and like many experiments using living populations, suffers from what could be termed the survivors’ paradox. We only use plants that have survived in a mapping study, which often means that an initial selection has already occurred before the experiment has even started ( during gamete formation, post-fertilisation death of embryos, non-germination, pre- or post-emergence diseases ). One of the well-known consequences of such unknown selection is marker skewness (also called segregation distortion (Mangelsdorf and Jones, 1926)), where
256 ______Chapter 11 une pected or unbalanced proportions of marker alleles are observed. These markers are often removed prior to mapping to avoid the possible complication of false linkages, although in so doing, parts of entire linkage groups may unwittingly be removed an oi en and ansen, 3 .
ne of the uestions that arose during our work on rose meiosis Chapter 5 was whether segregation distortion and preferential homologue pairing could leave identical signatures in a mapping population and hence be confounded effects. e argued that the over abundance of certain pairing combinations was unlikely to have been caused by segregation distortion, unless for e ample a combination of alleles proved to be debilitating but non lethal to the spore in four of the si homologue pairings possible which is uite unlikely, but not impossible . In potato we estimated the average rate of double reduction at the centromeres and telomeres Chapter 3 , which could have been influenced by systematic bias if for e ample gametes resulting from multivalents were more fre uently infertile than those from bivalents loyd and omblies, . ith only genotyping data from a mapping population we cannot definitively resolve these ambiguities.
There are some complementary e perimental approaches that could help provide more conclusive answers to the precise nature of the biological phenomena involved. any of the earliest papers on polyploid meiosis were cytological – i physically observing the pairing behaviour of chromosomes during meiosis and for e ample counting the number of bivalents and multivalents that persisted into metaphase I estergaard, Cadman, 3 amm, 5 waminathan and oward, 53 . I luorescence i si u hybridisation or I enomic i si u hybridisation techni ues could be used to identify homologous and homoeologous pairing during meiosis, although till now these techni ues have mainly been used to establish base chromosomal number or identify sub genomes in polyploids (D’Hont, 2005;Eberhard et al., Chester et al., iu et al., . Another approach to investigate meiosis is tetrad analysis reuss et al., . In ra idopsis a ia a, mutant lines carrying mutations in the genes or produce con oined pollen tetrad cells which can help reveal the e act pairing and recombination behaviour at meiosis i nker et al., 3 . owever, being a recessive mutation reuss et al., it is uncertain how useful mutants would be in genetic studies of polyploids, assuming of course that homologues or genes of similar function e ist. Tetrad analyses also suffer from the survivors’ paradox, given that experimental results are based on surviving pollen cells the original study found that only half of all tetrads possessed four viable pollen grains reuss et al., . Therefore it seems that almost all e perimental approaches, no matter how elegant, rely on surviving germplasm with which to make inferences on
257 ______General discussion meiosis. he original tologi al studies ere arguabl the most unbiased regarding meiosis itsel , but the viabilit o the observed stru tures as inevitabl un no n. erhaps an exhaustive anal sis that tra s ever single spore and egg ell ould be imagined, but in pra ti e it seems hardl easible. or a breeder the issue o population indu ed bias is perhaps moot, as breeders onl or ith surviving germplasm. or a undamental resear her ho ever, su h biases need to be are ull onsidered and a ounted or. ur or sits some here bet een theoreti al and applied geneti s, and it is there ore hoped that highlighting su h issues here and in previous dis ussions is su i ient or no . he results e have obtained in this thesis regarding pol ploid meiosis using experimental populations are ertainl relevant or breeders, although orroborating data, ideall togeneti , ould be advantageous in uture studies to ull address the more undamental meioti uestions e have attempted to ans er. Cross-over rates in bivalent and multivalent meiosis ne o the e a tors that ensures the orderl division o homologues during meiosis is the ormation o hiasmata hi h helps generate me hani al tension at the entromeres and ineto hores during spindle ibre ormation. his tension is sensed b the ell, signalling that spindle ibres are orre tl atta hed and that homologues should segregate orre tl to opposite poles ( i las, ; ampson and heeseman, 20 . ivalent pairing in a pol ploid poses no additional hallenges to the me hanisms that have evolved to ensure balan ed hromosomal segregation in diploids (sin e all pairing in diploids occurs in bivalents). A multivalent on the other hand is a “novel” meiotic stru ture that potentiall disrupts these me hanisms. homologous pairing ere le t un he ed it ould lead to meioti haos, ith man unresolved entanglements bet een homologues leading to improper segregation. t has long been h pothesised that a redu tion in ross over re uen o urs in autopol ploid meiosis hi h ould have a stabilising e e t on meiosis ( osto , 0; ers, ; ollum, 5 ;Ha ari a and ees, . his h pothesis ollo s a ertain line o logi e er ross overs ould result in e er multivalents and hen e a more orderl meiosis, sin e at least three separate ross overs are re uired to generate an e e tive multivalent stru ture that an persist through to metaphase I (Chapter 1). Note that an “effective” multivalent in this ontext generall means a uadrivalent; a trivalent univalent ombination (in a tetraploid is not tolerated b the ell as it ould lead to unbalan ed segregation ( omblies et al., 20 . his has been borne out b a meta anal sis o autopol ploid meiosis, here ver e univalent or trivalent stru tures ere re orded ( amse and hems e, 2002 . n theor hexavalent stru tures are also possible at higher ploid levels, but these have onl rarel been reported in the literature ( amse and hems e,
258 ______Chapter 11
). Assuming that fe er cross overs do indeed occur in autopol ploids than ould be e pected from recombination rates in progenitor diploid species ( a ari a and ees 1 ) the uestion still remains ho this might be achieved b the cell. An interesting possible mechanism that as recentl proposed is that an increase in the effective distance of cross over interference could pla a significant role ( omblies et al. 1 ). As breeding ver often relies on recombinations to sort and shuffle favourable alleles into a single genot pe an limitation on the number of cross overs could have implications on the efficac of traditional breeding approaches.
Figure 1. Cross-over rates in bivalent and multivalent pairing structures. a. Average rate of o s rv d cross overs per meiosis in the A C tetraploid potato population either resulting from bivalent pairing (red s uares) or uadrivalent pairing (blue triangles). rror bars sho confidence intervals around the means for each chromosome. o sided t tests on the difference of means ere all highl significant ( 1 1 11). b. ample of possible discrepanc bet een the observed number of cross overs from I probabilities (above) and the actual cross overs that occurred during meiosis (belo ). Inherited chromosomal segments are highlighted in green and correspond to the I predictions. o ever the recombinant products from ivalent are not transmitted to the gamete and therefore the cross over is not observed. he data used to generate figure (a) onl consider observed recombinations. Cross overs ere identified from the output of etra rigin ( heng et al. 1 ) using a presence probabilit threshold of . (i an inheritance probabilities . ere discounted) and a minimum recombinant segment length of c .
259 ______General discussion
o ever there remains considerable uncertaint as to hether cross over rates (and hence uadrivalents) are activel suppressed in autopol ploids. In this thesis e have provided clear evidence for the e istence of uadrivalents in the meiosis of autopol ploids li e potato and rose (Chapter and Chapter respectivel ). herefore the assertion that uadrivalents are aberrant structures that cause a failure in the proper division of homologues ( arlington 1 ostoff 1 Carvalho et al. 1 lo d and omblies 1 ) does not hold across all species (and particularl not among established autopol ploids man of hich are domesticated crop species). ere e are once more plagued b the survivors’ paradox it could be that the – uadrivalent pairings that e estimated to have contributed to the potato A C population (Chapters ) might onl represent a fraction of the multivalent meioses that occurred the rest having perished. o ever even ere this to be true it still represents a large proportion of successful and balanced meioses that involved uadrivalents a fact that some of the literature mentioned above ould have ou doubt is even possible.
In fact e can actuall test the h pothesis that cross over rates influence the pairing behaviour using our population datasets. o demonstrate this point I re anal sed the identit b descent (I ) probabilities of the A C potato population reconstructing the cross over events that ere predicted for each of the 1 individuals ( igure 1). I chose a presence threshold probabilit of . ( hich meant that if the inheritance probabilit at a mar er for a homologue as less than . I did not consider that mar er to have been inherited) and ignored an recombinant sections less than c in length (to prevent over estimation of the number of recombinations in the case of nois results). After this initial filtering I counted the number of cross overs from bivalent or uadrivalent meioses (I treated double reduction products separatel and added them after ards). As can be seen in igure 1.a the rate of observed cross overs from bivalent pairing as significantl lo er than the number observed due to multivalent pairing across all 1 potato chromosomes ( 1 1 11). he rates for bivalents comprised of recombinations observed from t o bivalents the actual rates of cross over formation p r iva ould be e pected to be appro imatel the same if e consider that potentiall of all cross overs are unobserved ( igure 1.b). he findings here are consistent ith the previousl reported rates of cross overs per bivalent of appro imatel 1.1 in the autotetraploids saria vi u i ra . o us or i u a us . and ra idopsis ar osa . ( ulligan 1 avies et al. 1 ant et al. 1 ). here is also the possibilit of unobserved recombinations hen multivalents occur although an estimation of hat proportion this represents is less obvious than for bivalents. It ill be some hat less than depending on the total number of cross overs and ho the are arranged bet een chromatids. Cross overs from a uadrivalent structure can be hidden in the gamete if the
260 ______Chapter 11
(which seems a less parsimonious explanation). This phenomenon (“t mosaicism”) is it is considered of little practical relevance, but also because we didn’t have the tools to
Figure 2. Examples of offspring harbouring chromosomal mosaics of three parental homologues from potato chromosome 2 (AxC population).
261 ______General discussion
Opening the polysomic “black box” There are man challen es in breedin pol somic pol ploid crops. ne of the ma or difficulties encountered is that ever offsprin of a cross contains an un nown combination of parental homolo ue mosaics. n inbreedin diploid populations, parental lines are often full homo ous, in which case the transmission of parental homolo ues is essentiall nown. n outbreedin diploids this is not the case, but at an locus each individual carries one of possible allelic combinations. or tetraploids 2 2 this becomes ( ) ×combinations( ) = 4 (assumin no double reduction – it is 1 1 4 4 otherwise), while( ) for× ( hexaploids) = 36 this rises to combinations (or if 2 2 6 6 we include double reduction). hen we start( ) to× consider( ) = 400 multiple loci to ether (for example in the case of a trait influenced b a 3number3 of different enes) the number of possible allelic combinations explodes. ol somic inheritance, coupled with hi h hetero osit , leads to far more complex inheritance patterns than an thin encountered at the diploid level.
evelopin homo ous lines in pol ploids would simplif matters considerabl , both from a breedin and a enetics perspective. owever, aldane demonstrated the infeasibilit of reachin homo osit throu h repeated selfin ( aldane, ), a techni ue that is re ularl used in diploid breedin and research ( i ure of hapter ). part from the impracticalit of inbreedin , man pol ploids are also outbreedin species that poorl tolerate inbreedin (tetraploid lee ( iu a p oprasu .) is a ood example ( e lerc and an oc staele, )). This is enerall thou ht to be caused b lar e numbers of deleterious recessive alleles (also called the i oad, a point to which later return). ecause of these and related difficulties, the use of pol ploids in breedin pro rams is sometimes viewed as an unnecessar complication. fforts to convert potato from a hi hl hetero ous outbreedin pol ploid to an inbreedin , homo ous diploid are currentl underwa ( indhout et al., ans et al., ). n su ar beet ( a vu aris .) breedin , the use of tetraploid parental lines has been lar el abandoned ( ewe , ra cott, ) because of difficulties in autopol ploid breedin . reviousl , triploids and anisoploids (mixture of diploids, triploids and tetraploids from an open pollination) were developed for their superior ields, but these have lar el been replaced b diploids ( c rath and un , ).
evertheless, it is unli el that pol somic pol ploids will completel disappear from breedin pro rams. n ornamental breedin , it is routine to induce pol ploidisation while developin new varieties which has led to a preponderance of pol ploid in man ornamental breedin pro rams ( an Tu l and im, arase iola ows a et al.,
262 ______Chapter 11
usa i ru us a a us i is di a o sa iva ri o iu pra s which are helping to turn the key to open the polysomic “black box”.
ea of whether the polysomic “black box”
–
263 ______General discussion in estigate by simulation. i en that the costs of genotyping are continually falling the economics of such an exercise may start to make sense ery soon.
part from un erstan ing inheritance this thesis has been primarily moti ate by the e elopment of tools to fin sp i i markers to tag important traits. bree er might rightly won er why markers shoul be use if one or fi e might be use instea . n ee specific markers that tag important loci resistance genes or introgresse segments woul represent a more economical first use of marker technology. owe er the argument that polysomic inheritance is an insurmountable hur le to bree ing programs nee s to be put into its proper context gi en mo ern techni ues. bree er may not necessarily fully un erstan the mo e of inheritance of the bree ing material which such a marker set coul help re eal. s well as that knowle ge of genome wi e inheritance coul help facilitate so called “genomic selection”, which has been a ocate for polyploi bree ing later et al. but has yet to be shown to pro uce substantial gains in practice. enomic selection theory as currently implemente assumes that all markers are potentially in linkage ise uilibrium with genes that affect uantitati e traits of interest euwissen et al. euwissen et al. an therefore ery large marker atasets are often use . ore recently haplotype base approaches ha e been propose which may offer greater accuracy an power than single approaches ess et al. . herefore the selection of a set of highly informati e an well space markers for a range of applications is likely to become a regular feature of polyploi bree ing programs in the future.
264 ______Chapter 11
o c al a o al a k o ack o a a o a lo a t chosen ositions , and c a single ma e is de lo ed ma e s a e conside ed to o ide the most inhe itance in o mation in an a totet a loid o lation heng et al , b ecti eness o sing a minimal ma e set to t ac meiosis in an a totet a loid he and o genot e edictions associated with di e ent ma e n mbe s a e com a ed, sta ting with ma e at each o the th ee ositions and og essing th o gh to e loc s oth the and the genot ic in o mation coe icient a e a ected b ma e densit o lations we e sim lated in edig ee im oo i s and alie aa d, and obabilities we e estimated in et a igin heng et al ,
265 ______General discussion
o o bl c o a a o a al ne o the henomena loo ed at in some detail d ing this thesis was do ble ed ction , which it is claimed is the inci al so ce o s s a i ma e seg egation disto tion in ol loid genetic st dies o et al , he non andomness o this disto tion a ises om the act that the ate o inc eases towa ds the telome es athe , ishe , n that sense the bias is ositional, b t nli e t e seg egation disto tion that ma be associated with alleles o allelic combinations o a a tic la loc s, is combinato icall a andom ocess which occ s with e al e enc on all homolog es s mentioned in ha te , some a tho s li e to em hasise the im o tance o incl ding in thei models o com leteness o ten castigating those who do not , b t so a all ha e ailed to s bstantiate these claims with act al data o et al , et al , and a, o et al , i et al , et al , et al ,
n this thesis began b loo ing at the bias that int od ces in two oint lin age anal ses sing a andom bi alent ai ing model and sim le n lli le ma e data ha te s bse entl e anded this to incl de all ossible a totet a loid ma e seg egation t es ha te also com a ed the owe and ecision o a model that incl ded e s s one that did not ha te n the case o lin age ma ing, introduces a small bias in the estimation of recombination frequencies, although it’s negligible i the ate o adi alent ai ing is low a g ed that this bias co ld sa el be igno ed, a tic la l when we conside that lin age ma s a e ima il b ilt om highl in o mati e lin ages between nea b ma e s that a e nli el to be se e el a ected b a small n mbe o ne ected genot es s ch as int od ces ciall , gene ates a no el o s ing genot e class o sim le n lli le ma e s, namel d le o s ing, which a e not e ected in a andom bi alent setting n a ma ing a oach that igno es the e ecti el become missing al es in the initial ste s, which is ite a di e ent o osition than seg egation disto tion o genot ing e o s andoml missing al es will ed ce the e ecti e o lation si e on which ecombination e enc is estimated, the eb inc easing the a iance and dec easing the sco e t this noise is essentiall nbiased a a t om ositional conside ations it is ce tainl not s ewness im le n lli le ma e s o m the cent e iece o the theo etical amewo we ha e de elo ed o ol loid lin age ma ing ha te s , and a e also the ma e t e that a ea to occ in the g eatest ab ndance in o lations ha te s , , he e o e, no s stematic de iations a e int od ced b to the inci al st ct al elements o o lin age ma s
266 ______Chapter 11
egarding the re alence of , it has been re orted in a number of se arate studies that is a rare henomenon that occurs at lo frequencies radsha et al , tift et al , ac ett et al , heoreticians li e to argue o er the ma imum rate of , ith suggestions ranging from uo et al , radsha , heng et al , , ather, tift et al , ,1 oorri s and alie aard, and e en ⁄4 benga, radsha notes that the rate of de ends on hether a ring or chain 1⁄ 1⁄ 1⁄ quadri alent6 is in ol ed, hich com licates7 matters further radsha , n our8 or ith tetra loid otato e found that the rate of reached a ma imum of about – at the telomeres ha ter , hich is one of the fe studies that actuall quantifies the rate of in a o ulation as o osed to merel mentioning it theoretical ma imum rate of re resents the e ected rate at an infinite genetic distance from the centromere ften, such rates are used to moti ate more ad anced descri tions of ol loid meiosis, although it is questionable hether such rates ould e er occur in ractice urthermore, if bi alent airing is indeed someho romoted b the ol loid cell it is e en more unli el that high rates of ill occur a oint that is all but ignored b theoreticians he consistent re orts of lo rates of can therefore be seen as further ustification for the use of random bi alents to model ol somic inheritance
n e loring the effects of ignoring double reduction in ma ing e found that the gains in o er or recision ere d arfed b other considerations such as the trait heritabilit , the o ulation si e or the mar er distribution near regions ha ter ts inclusion as also found to ad ersel affect our abilit to correctl redict the segregation t e using either the ai e nformation riterion ai e, or the a esian nformation riterion ch ar , nce again e found that onl la ed a minor role and could safel be ignored o e er, a fle ible model of inheritance that allo s for the ossibilit of multi alents and can at times achie e much more accurate reconstructions of robabilities o er random bi alent models his is a arent hen one e amines some of the out ut of etra rigin heng et al , hen a lied to real datasets or e am le, e found that indi idual from the otato o ulation carried an e tensi e segment on chomosome hen e ran the anal sis using a bi alent model onl , the redicted ha lot es re eal a atch or of segments across both sets of arental homologues igure a t is unli el that such a high number of recombinations actuall occurred he indi idual highlighted earlier as carr ing a mosaic of three arental homologues igure as also oorl reconstructed hen onl bi alent airing structures ere allo ed igure b i en that the accurac and o er of our anal sis largel rests on the accurac of the robabilities, it is orr ing to see this sort of beha iour ere at last e ha e clear e idence that allo ing for multi alents including but not restricted to the henomenon
267 ______General discussion
xa l o a l al o l ca o o a b al o l c o c o o o co o o a b
a o o a c od o i ri a – disomic, polysomic (also termed “tetrasomic” for tetraploids and “hexasomic” for hexaploids) and mixosomic. Mixosomy can be interpreted as either a
268 ______Chapter 11 chromosome pairin , and is the mode of inheritance associated ith se mental allopolyploidy ( tebbins, oltis et al., ). n many important polyploid crop species the mode of inheritance is f lly a reed pon (examples incl de heat, oilseed rape (disomic) and potato (tetrasomic)), hile in other species it is not (examples incl de s arcane, lee and the ornamental species s ro ria). t may be that there is no fixed mode of inheritance for a species that, once dia nosed, ill predict all f t re meiotic beha io r of members of the same species. e ha e already enco ntered an example of this in rose the mode of inheritance aried bet een the parents of the mappin pop lation, ith both disomic and polysomic inheritance detected for different chromosomes in both parents ( hapter ).
ne may onder hether the mode of inheritance is merely of academic interest – do e need to orry abo t it as lon as crosses can be made and iable seeds prod ced f e o ld li e to employ mar ers in o r breedin pro ram the ans er is clearly yes, nderstandin the mode of inheritance is ital. enotypin polyploids is in eneral more complex and less reliable than enotypin diploids (Mason, ). his co ld be ca sed by off tar et amplification d e to d plication of mar er se ences at other loci ( imbor et al., ), b t is also d e in lar e part to the diffic lty in correctly estimatin the n mber of copies of a mar er allele, also no n as mar er dosa e assi nment ( hapter ). ne of the standard practices hen assi nin dosa e is to compare mar er scores bet een parents and offsprin . his acts as both a ality chec , by comparin the expected and obser ed allele fre encies, b t also acts as a means of determinin the correct ran e of dosa e al es ( oorrips et al., ac ett et al., chmit arley et al., ). n order to comp te the expected allele fre encies in a polyploid pop lation i en the parental dosa e scores, one needs to no the mode of inheritance i adva . his is potentially one of the reatest h rdles in the de elopment of enomic reso rces for no el polyploid research pro ects. hen additional iss es s ch as ane ploidy occ r (incl din the possibility of compensated ane ploidy ( sin , hester et al., )), it may be ery hard to interpret mar er data, ith no solid ro nd pon hich to b ild a hypothesis. o e er, all s ch iss es can potentially be resol ed if they are nderstood, b t re ire pioneerin enotypin (and possibly cytolo ical) st dies to pa e the ay for f t re breedin and research applications.
nderstandin the mode of inheritance is also re ired for the constr ction of phased, inte rated lin a e maps. e demonstrated this thro h sim lation st dies in hapters and , de elopin a flexible approach to lin a e analysis in hapter hich can accommodate fl ct ations in the mode of inheritance. o el mappin al orithms that do not require estimates of recombination frequency (“model free” approaches) might be more rob st. o e er, so far none ha e demonstrated the ability to enerate p as d
269 ______General discussion lin age maps of fundamental importance in polyploid genetics ( hapter ) herefore in order to use current mapping tools such as etraploid ap ( ac ett et al ) or polymap ( hapter ) the mode of inheritance of the population must be established etraploid ap is only suitable for tetrasomic species hereas polymap has been de eloped to accommodate all modes of inheritance from disomy through to tetrasomy (but at the tetraploid le el only) egarding mi osomic lin age mapping in non tetraploids it should be noted that e tending the lin age mapping frame or ithin polymap to include he asomic inheritance as itself a ma or underta ing necessitating lin age functions that required o er million characters of code ( ore eam ) n contrast tetrasomy required only lin age functions and ust o er characters ncluding the possibility of partial preferential pairing for tetraploids required almost million characters representing a fold increase o er the tetrasomic functions or he aploidy this fold increase can be e pected to be much greater than fi e gi en the increased comple ity herefore as currently implemented allo ing for mi osomy in he aploids ould be a gargantuan underta ing ne solution ould be to implement a fully general li elihood frame or rather than implementing each li elihood function separately similar to the approach used in etraploid ap ( ac ett personal communication) urrently ho e er implementing dynamic algebra in is cumbersome and that is hy pre programmed solutions generated in athematica ere used instead
e demonstrated ho important the mode of inheritance as for unbiased lin age analyses in hapter o the mode of inheritance affects detection models as not in estigated in this thesis although based approaches could be e pected to be quite robust against de iations from a polysomic model o e er this as not erified here therefore remains more or to do in properly accounting for the aried modes of inheritance in our polyploid genetic mapping pipeline o o a c o ne of the main preoccupations of diploid bio statisticians is to impro e their models to glean more predicti e po er from the data they are presented ith his hunger for bigger and better has yielded many fine de elopments o er the years or lin age mapping it is typical to consider t o point analyses as an initial step to ards more accurate three point or multi point analyses ( idout et al each et al ong et al ) or mapping more po erful approaches might include mi ed model methodologies ayesian mapping or machine learning algorithms ( ang et al a a ier et al ) or employing more comple or pedigreed populations ( in et al a anagh et al uang et al ) n this thesis e did not enture beyond t o point lin age analysis simple linear models or bi parental mapping
270 ______Chapter 11 populations here appears to be plenty of opportunities to e plore more comple (and potentially more po erful) approaches at detecting and deciphering effects in polyploid populations
o e er e are no li ing in a time hen the de elopments in genotyping technologies are dictating the de elopment of statistical methodologies in genetic mapping and not the other ay around erhaps this has al ays been the case but feel the pace of change has increased in recent decades o sooner ha e e established an effecti e pipeline to perform genetic mapping in autopolyploids using data than it becomes potentially redundant due to a shift to ards genotyping by sequencing ( ) data ( lshire et al ) optical mapping data ( ood in et al ) i data ( ieberman iden et al ) e are all guilty of technology chasing as nobody ants to be seen to be stuck working with yesteryears’ tools. On the other hand, by putting all our hope in a technological fi rather than a methodological fi to impro e po er or precision issues e ris becoming loc ed into a cycle of using sub optimal methods to eep pace
articularly in polysomic polyploids here the comple ity is already substantial for “basic” methods and models, it seems implausible to have sufficient time to replicate the hole suite of approaches that ha e been de eloped for diploid species in the time afforded by inter technological cool off periods ach ne genotyping technology carries ith it its o n set of challenges and characteristics from different ays to scoring mar er dosage ( oorrips et al an i et al lischa et al ) to differences in the amount and type of missing data or genotyping errors ( lshire et al a gain et al ) he later steps of lin age mapping analysis genome ide association mapping cannot be performed ithout the initial pre processing of genotype data the tools for hich can often appear many years after the first introduction of the technology (diploid tools tend to be de eloped sooner often by the genotyping pro ider but also by the much larger research community engaged in diploid genotyping e periments) nless a stable genotyping technology for polyploids comes along the polyploid genetics community is unli ely to ascend to the upper echelons of diploid biostatistics before building a ne ladder from scratch again urrently impro ements in po er and precision of genetic mapping e periments are being dri en by impro ements in genotyping approaches (although the production of robust and accurate phenotypic data remains a critical component as ell)
271 ______General discussion
x o ol o c ol lo b To the early agriculturalists, the polyploid nature of their crops probably wasn’t a major hindrance given the relatively simple techni ues that were employed in the selection and maintenance of germplasm. odern plant breeding as a science and art did not evolve until relatively recently, and therefore our ancestors were hardly troubled by issues such as polysomic inheritance, partial preferential chromosome pairing or double reduction indeed they were most li ely unaware of these issues in the first place . owadays, society is demanding the production of more with less, given the projected increase in the world’s population coupled with dwindling fossil fuel resources, increased climatic instability and the degradation of agricultural land radshaw, e et al., . These appear to be insurmountable challenges, yet we have at our disposal a much wider array of intellectual resources than ever before. The uestion is whether these can be translated into effective solutions uic ly enough, particularly given that many of our most important agricultural crops are polyploid.
erhaps the single most important trait within all breeding programs across all crops is yield, a trait that is notoriously comple even within diploids. It has been suggested that despite years of breeding for increased yield, phenotypic selection methods have done nothing to raise average potato yields in that time ans y, later et al., , in contrast to other major diploid crops li e mai e or rice. n the other hand, some authors remain convinced about the merit of polyploids and their potential to deliver higher yields through heterosis enny yfield and endel, . I don’t believe that polyploids lac the necessary ualities to rise to the challenges we are facing. owever, I do believe we need to carefully consider how polyploids are currently bred and what the implications are for future breeding material given our present selection decisions.
ne of the main difficulties in developing elite breeding material in polysomic polyploids is their i oad. ere, genetic load refers to lethal or debilitating recessive mutations that are mas ed in the hetero ygous condition but which carry a high fitness cost when present in homo ygous condition. lthough it is claimed that neo autopolyploids have a lower genetic load than their progenitor diploids tto and hitton, , in time it builds up to greater levels in established autopolyploids, leading to inbreeding depression onfort, tto, . This is not to be confused with self incompatibility which, if present, is usually under the control of one or more specific self incompatibility loci idout et al., ans y et al., . olyploids tolerate higher genetic loads than diploids, as for e ample elegantly demonstrated in a study of diploid and tetraploid pollen vigour usband, . ossibilities to select parents with a lower genetic load include evaluating derived haploids which may e press the deleterious alleles or by self pollinating parental lines and observing the
272 ______Chapter 11 proportion of non vigorous offspring ans y, . owever, it is unli ely that stringent selection against genetic load is routinely performed in polyploid breeding programs. ithout the benefits of purging selection, polysomic polyploids can be e pected to slowly accumulate deleterious mutations which may reduce the uality of breeding lines for many future generations.
ne solution would be to simply avoid the effects of genetic load by increasing the diversity of breeding material, thereby ensuring hetero ygosity at as many loci as possible. The development of different heterotic pools is one possibility to achieve this in. or e ample the tetraploid potato population hapters , , , a cross between a starch and a table variety, represents a population that normally would not be generated in a breeding program since these breeding pools are usually ept distinct os et al., . In we observed transgressive segregation for a number of important traits, demonstrating that wide crosses may generate une pected and favourable results. lternatively, genome wide mar er data could be used to predict heterotic effects, by crossing parents nown to carry different alleles across multiple loci.
n alternative to ma imising hetero ygosity is to try to reduce the genetic load. e have seen that inbreeding is not a practical proposition at the polyploid level aldane, it therefore seems we might have to “clean” polyploids at the haploid or diploid level by e posing deleterious mutations to selection. owever if we were to go that route, returning to the polyploid level might not be needed indhout et al., enny yfield and endel, ans y et al., . educing genetic load at the polyploid level might be aided by genomic tools but it would ta e a significant and perhaps unrealistic effort to pinpoint all such loci, over multiple traits, and e clude them from future breeding germplasm using mar er data. evertheless, the identification of some major lethality loci using the tools developed in this thesis could be a very useful research aim of breeding programs for e ample by identifying regions of s ewed segregation in selfed progenies and associating these with reconstructed parental haplotypes in these regions . y trac ing and purging such alleles from breeding material, breeders could enjoy slightly more freedom to mildly inbreed their parental lines, as well as improving the overall fitness of their breeding stoc . This may have direct implications to improve comple traits li e yield, but could more generally be seen as improving the elite germplasm within a crop, with positive noc on effects for a whole range of traits.
In considering the future of polysomic plant breeding it is important to distinguish between two categories, namely vegetatively propagated and seed propagated crops. amples of the former include potato and chrysanthemum, while e amples of the latter include alfalfa, red clover and leek. The potato cultivar Russett’s Burbank (introduced in 1902 as “Netted Gem” eth e et al., is an e ample of a single genotype that
273 ______General discussion possessed an above average combination of alleles for multiple traits that has led to it become North America’s most widely cultivated potato variety, despite all the competition from cultivars that have been bred in the intervening century ( ardigan et al., 201 . n the . , aris iper (introduced in 19 continues to be the most widely grown variety, while in the Netherlands Bint e (introduced in 1910 still holds this honour. egetative or clonal propagation immortalises favourable allelic combinations and heterotic effects which can lead to a single variety having a very long production life. owever, clonal propagation also comes with its own inherent disadvantages such as a slow rate of seed stock multiplication, increased risk of spreading soil borne diseases or endemic viral pathogens, more costly distribution and storage of propagation material and difficulties in maintaining germplasm in genebanks. espite these drawbacks, clonal propagation continues to dominate in crops like potato, chrysanthemum and rose.
The breeding of seed propagated polysomic crops is arguably much more challenging given the varietal registration re uirements of distinctness, uniformity and stability ( . btaining uniform progeny through seed can only be reliably predicted if parental lines are homo ygous at all loci affecting descriptor traits (these usually concern the morphology of the adult plant . or e ample, uniformity continues to be one of the main breeding goals for autotetraploid leek ( iu a p oprasu ( e lerc and an Bockstaele, 2002 . n recent years there has been a move from open pollinated varieties to 1 hybrids in leek breeding. lonally propagated male sterile plants as maternal lines restricts the amount of selfing that occurs, thought to account for up to 20 0 of open pollinations ( e lerc and an Bockstaele, 2002 . Given the e tremely high genetic load in leek, selfed progeny are likely to be the biggest contributor to lack of uniformity, with substantial loss of yield after only one or two rounds of self pollination ( e lerc and an Bockstaele, 2002 . Therefore, the use of specialised 1 hybrid breeding is another e ample of how breeders have devised strategies to overcome the high genetic load in polysomic polyploids.
nother e ample of a seed producing autopolyploid is the autotetraploid red clover ( ri o iu pra s . . Tetraploid clovers are often favoured over diploids due to their higher yields, greater persistence and higher levels of resistance to biotic and abiotic stresses (Taylor, 200 leugels et al., 201 . owever, the main drawback to tetraploid cultivars is their reduced seed yield ( leugels et al., 201 . The precise cause(s of this reduction remain unknown despite many years of investigation. The mechanism could be related to problems during meiosis or abnormal pollen tube growth (B y kkartal, 2002 200 , but it has also been proposed that flower morphology (particularly the length of the corolla may result in lower pollination levels in tetraploid clovers (Bender, 1999 uruya, 2001 . This trait represents one of the most important breeding aims in
274 ______Chapter 11 tetra loid clo er breedi which has til ow ro ed e tremely di ic lt to dersta d or im ro e ith the de loyme t o molec lar mar ers across tetra loid o latio s it co ld be ossible to determi e the e etic co trol i a y o seed mber i tetra loid clo er which co ld lead to more ro itable a d reliable seed yields
e o the more i teresti ossibilities or olysomic oly loid breedi that has bee s ested is the se o apo i i re rod ctio A omi is ca be de i ed as the rod ctio o seeds rom mater al tiss es by assi ormal se al re rod ctio omai ic ell a d ata ach here are mero s re orts o the associatio o ameto hytic a omi is with oly loidy et a d arla hitto et al with a mber o ossible theories ro osed both mecha istic a d e ol tio ary b t o co se s s o the recise reaso why this sho ld be ari et al omai ieli s i a d cheid hate er the co ectio the ote tial attracti e ess o ro rammable a omi is or breedi has widely bee ac owled ed illa e et al Abdi et al ic ell et al radshaw a d ot st at the oly loid le el st li e clo al ro a atio a omi is wo ld allow the i atio o heterosis a d has bee s ested as a s erior method to rod ce hybrids by immortalisi the rather tha recreati it each seaso thro h re eated crossi o i bred are tal li es his wo ld combi e the ad a ta es o tr e seed rod ctio while a oidi the mero s disad a ta es o e etati e clo es as already disc ssed A omi is has bee show to be der e etic co trol i m lti le s ecies re iewed i ic ell a d ata ach with a mber o rece t e etic ma i st dies i tro ical oly loid ora e rasses s ch as the tetra loid ra iaria d u s or the he a loid ro oa u idi o a re eali ma or derlyi the trait i a et al orthi to et al A ice e am le o where a omi is is acti ely sed i oly loid breedi is i e t c y bl e rass oa pra sis this s ecies a omi is is the orm whereas true outcrossings are termed “aberrants”. ech i es to i crease the rod ctio o aberra ts d ri the breedi cycle are sed radshaw ollowi which s erior li es are selected ost ro e y are o d to be a omictic o ce more res lti i immortal mater al li es which ca s bse e tly be mar eted as stable hybrids Altho h it mi ht seem li e a ideal sce ario the breedi o a omicts rese ts its ow set o challe es artic larly i the mber o aberra ts e erated is too low to allow crossi A e loidy may also accom a y a omi is as it is ot selected a ai st d ri meiosis which may lead to roblems i t re crosses i the a e loid is a ythi other tha the a omictic are t i di so rces o a omi is e es i related a d crossable s ecies is a rther challe e i tra s e ic a roaches to i trod ci the trait are ot easible or acce table this search the se o molec lar mar ers a d e omic reso rces thro h ca didate e e a roaches will be ital Altho h a omi is may o er ma y ad a ta es there has
275 ______General discussion
et to be an e am e o it being success u bred into a o oid cro and commercia e oited. ime wi te whether this orm o breeding wi be ado ted b the o oid communit or not.
eturning ina to the humb e otato the a arent ac o rogress in ie d o er the ast ears can erha s be best e ained in terms o o somic inheritance with each new ariet carr ing a reshu ed set o a e es as we as erha s some s eci ic disease resistance oci introgressed rom wi d s ecies . ha e ho e u demonstrated that o somic inheritance need no onger be considered a b ac bo . e are entering a time where auto o oid breeders wi ha e the choice to no onger ust acce t the shu ed hand the are dea t but to choose their own hand based on among other actors mar er data. n time wi te whether this wi become an intrinsic art o o oid breeding. conomics and the ease at which mar ers can be incor orated into the in rastructure o e isting breeding rograms wi u timate dictate the uture direction o o oid breeding.
o cl a k n this thesis ha e tried to stri e a ba ance between the de e o ment o too s to he unra e the com e ities o o oid genetics and what these too s can ro ide to breeders and researchers. do not consider these too s as ends in themse es but rather see them as a means to achie e certain goa s be it the identi ication o mar ers in ed to im ortant traits the creation o in age ma s re resenting the mo ecu ar ar ot e o a o u ation or the understanding o o oid meiosis inc uding how airing and recombination roceed. e ha e seen that such too s are e treme ower u at o ening u a window into o oid genetics which be ie e wi in time a ow or man more genomics in ormed breeding decisions to be made. e are ust at the beginning o a new era in o oid breeding with man e citing o ortunities ahead.
276 References Abdi, S., Dwivedi, A., and Bhat, V. (2016). "Harnessing apomixis for heterosis breeding in crop improvement," in Molecular Breeding for Sustainable Crop Improvement. (Springer), 79-99. Acquaah, G. (2012). Principles of Plant Genetics and Breeding. Wiley-Blackwell. Aguiar, D., and Istrail, S. (2013). Haplotype assembly in polyploid genomes and identical by descent shared tracts. Bioinformatics 29, i352-i360. Akaike, H. (1974). A new look at the statistical model identification. IEEE transactions on automatic control 19, 716-723. Akhunov, E., Nicolet, C., and Dvorak, J. (2009). Single nucleotide polymorphism genotyping in polyploid wheat with the Illumina GoldenGate assay. Theoretical and Applied Genetics 119, 507-517. Al-Janabi, S.M., Honeycutt, R.J., and Sobral, B.W.S. (1994). Chromosome assortment in Saccharum. Theoretical and Applied Genetics 89, 959-963. Albrechtsen, A., Nielsen, F.C., and Nielsen, R. (2010). Ascertainment Biases in SNP Chips Affect Measures of Population Divergence. Molecular Biology and Evolution 27, 2534-2547. Allendorf, F.W., Bassham, S., Cresko, W.A., Limborg, M.T., Seeb, L.W., and Seeb, J.E. (2015). Effects of crossovers between homeologs on inheritance and population genomics in polyploid-derived salmonid fishes. Journal of Heredity 106, 217-227. Allendorf, F.W., and Danzmann, R.G. (1997). Secondary tetrasomic segregation of MDH-B and preferential pairing of homeologues in rainbow trout. Genetics 145, 1083-1092. Altschul, S.F., Madden, T.L., Schaffer, A.A., Zhang, J., Zhang, Z., Miller, W., et al. (1997). Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. Nucleic Acids Res 25,3389-3402. Andrade, J., and Estévez-Pérez, M. (2014). Statistical comparison of the slopes of two regression lines: A tutorial. Analytica chimica acta 838, 1-12. Bajgain, P., Rouse, M.N., and Anderson, J.A. (2016). Comparing genotyping-by-sequencing and single nucleotide polymorphism chip genotyping for quantitative trait loci mapping in wheat. Crop science 56, 232-248. Baker, P. (2014). polySegratio: Simulate and test marker dosage for dominant markers in autopolyploids. R package version 0.2-4. Baker, P., Jackson, P., and Aitken, K. (2010). Bayesian estimation of marker dosage in sugarcane and other autopolyploids. Theoretical and applied genetics 120, 1653-1672. Balsalobre, T.W.A., Da Silva Pereira, G., Margarido, G.R.A., Gazaffi, R., Barreto, F.Z., Anoni, C.O., et al. (2017). GBS-based single dosage markers for linkage and QTL mapping allow gene mining for yield-related traits in sugarcane. BMC genomics 18, 72. Barker, M.S., Arrigo, N., Baniaga, A.E., Li, Z., and Levin, D.A. (2016). On the relative abundance of autopolyploids and allopolyploids. New Phytologist 210, 391-398. Barringer, B.C. (2007). Polyploidy and self-fertilization in flowering plants. American Journal of Botany 94, 1527-1533. Bartholomé, J., Mandrou, E., Mabiala, A., Jenkins, J., Nabihoudine, I., Klopp, C., et al. (2015). High- resolution genetic maps of Eucalyptus improve Eucalyptus grandis genome assembly. New Phytologist 206, 1283-1296. Bassil, N.V., Davis, T.M., Zhang, H., Ficklin, S., Mittmann, M., Webster, T., et al. (2015). Development and preliminary evaluation of a 90 K Axiom® SNP array for the allo-octoploid cultivated strawberry Fragaria × ananassa. BMC Genomics 16, 155. Beçak, M.L., Beçak, W., and Rabello, M.N. (1966). Cytological evidence of constant tetraploidy in the bisexual South American frog Odontophrynus americanus. Chromosoma 19, 188-193. Behrouzi, P., and Wit, E.C. (2017a). De novo construction of q-ploid linkage maps using discrete graphical models. arXiv preprint arXiv:1710.01063. Behrouzi, P., and Wit, E.C. (2017b). netgwas: An R Package for Network-Based Genome-Wide Association Studies. arXiv preprint arXiv:1710.01236. Benabdelmouna, A., and Ledu, C. (2015). Autotetraploid Pacific oysters (Crassostrea gigas) obtained using normal diploid eggs: induction and impact on cytogenetic stability. Genome 58, 333-348. Bendahmane, M., Just, J., Vergne, P., Raymond, O., Dubois, A., Szcesi, J., et al. (Year). "The Rose Genome Sequencing Initiative, Prospects and Perspectives. Abstract W659", in: Plant and Animal Genome XXIV Conference: https://pag.confex.com/pag/xxiv/webprogram/Paper19873.html).
277 ______References
Bender, A. (1999). An impact of morphological and physiological transformations of red clover flowers accompanying polyploidization on the pollinators' working speed and value as a guarantee for cross pollination. Agraarteadus, 4, 9-23. Benjamini, Y., and Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society. Series B (Methodological), 289-300. Bennetzen, J.L. (2007). Patterns in grass genome evolution. Current Opinion in Plant Biology 10, 176-181. Bennetzen, J.L., and Wang, H. (2014). The contributions of transposable elements to the structure, function, and evolution of plant genomes. Annual review of plant biology 65, 505-530. Berger, E., Yorukoglu, D., Peng, J., and Berger, B. (2014). Haptree: A novel Bayesian framework for single individual polyplotyping using NGS data. PLoS computational biology 10, e1003502. Bernardo, R. (2008). Molecular Markers and Selection for Complex Traits in Plants: Learning from the Last 20 Years. Crop Science 48, 1649-1664. Bernardo, R. (2016). Bandwagons I, too, have known. Theoretical and Applied Genetics 129, 2323-2332. Bertioli, D.J., Cannon, S.B., Froenicke, L., Huang, G., Farmer, A.D., Cannon, E.K., et al. (2016). The genome sequences of Arachis duranensis and Arachis ipaensis, the diploid ancestors of cultivated peanut. Nature Genetics 48, 438-446. Bertioli, D.J., Ozias-Akins, P., Chu, Y., Dantas, K.M., Santos, S.P., Gouvea, E., et al. (2014). The use of SNP markers for linkage mapping in diploid and tetraploid peanuts. G3: Genes| Genomes| Genetics 4, 89-96. Bethke, P.C., Nassar, A.M., Kubow, S., Leclerc, Y.N., Li, X.-Q., Haroon, M., et al. (2014). History and origin of Russet Burbank (Netted Gem) a sport of Burbank. American journal of potato research 91, 594- 609. Bicknell, R., and Catanach, A. (2015). "Apomixis: the asexual formation of seed," in Somatic Genome Manipulation. (Springer), 147-167. Bicknell, R., Catanach, A., Hand, M., and Koltunow, A. (2016). Seeds of doubt: Mendel’s choice of Hieracium to study inheritance, a case of right plant, wrong trait. Theoretical and Applied Genetics 129, 2253-2266. Bingham, E.T., and Gillies, C.B. (1971). Chromosome pairing, fertility, and crossing behavior of haploids of tetraploid alfalfa, Medicago sativa L. Canadian Journal of Genetics and Cytology 13, 195-202. Bink, M., Boer, M., Ter Braak, C., Jansen, J., Voorrips, R., and Van De Weg, W. (2008). Bayesian analysis of complex traits in pedigreed plant populations. Euphytica 161, 85-96. Blakeslee, A.F., and Avery, A.G. (1937). Methods of inducing doubling of chromosomes in plants: By treatment with colchicine. Journal of Heredity 28, 393-411. Blischak, P.D., Kubatko, L.S., and Wolfe, A.D. (2016). Accounting for genotype uncertainty in the estimation of allele frequencies in autopolyploids. Molecular ecology resources 16, 742-754. Bomblies, K., Higgins, J.D., and Yant, L. (2015). Meiosis evolves: adaptation to external and internal environments. New Phytologist 208, 306-323. Bomblies, K., Jones, G., Franklin, C., Zickler, D., and Kleckner, N. (2016). The challenge of evolving stable polyploidy: could an increase in “crossover interference distance” play a central role? Chromosoma 125, 287-300. Bourke, P.M. (2014). QTL analysis in polyploids. MSc thesis, Wageningen University, Wageningen. Bourke, P.M., Arens, P., Voorrips, R.E., Esselink, G.D., Koning-Boucoiran, C.F.S., Van ‘T Westende, W.P.C., et al. (2017). Partial preferential chromosome pairing is genotype dependent in tetraploid rose. The Plant Journal 90, 330-343. Bourke, P.M., Voorrips, R.E., Kranenburg, T., Jansen, J., Visser, R.G., and Maliepaard, C. (2016). Integrating haplotype-specific linkage maps in tetraploid species using SNP markers. Theoretical and Applied Genetics 129, 2211-2226. Bourke, P.M., Voorrips, R.E., Visser, R.G.F., and Maliepaard, C. (2015). The Double Reduction Landscape in Tetraploid Potato as Revealed by a High-Density Linkage Map. Genetics 201, 853-863. Bradbury, P.J., Zhang, Z., Kroon, D.E., Casstevens, T.M., Ramdoss, Y., and Buckler, E.S. (2007). TASSEL: software for association mapping of complex traits in diverse samples. Bioinformatics 23, 2633- 2635. Bradshaw, J. (2007). The canon of potato science: 4. Tetrasomic inheritance. Potato Research 50, 219-222. Bradshaw, J.E. (2016). Plant Breeding: Past, Present and Future. New York: Springer. Bradshaw, J.E., Hackett, C.A., Pande, B., Waugh, R., and Bryan, G.J. (2008). QTL mapping of yield, agronomic and quality traits in tetraploid potato (Solanum tuberosum subsp. tuberosum). Theoretical and Applied Genetics 116, 193-211.
278 ______References
Bradshaw, . ., ande, B., Bryan, . ., Hackett, C.A., Mclean, K., Stewart, H. ., et al. (200 ). nterval appin of uantitative trait loci for resistance to late bli ht Phytophthora infestans (Mont.) de Bary , hei ht and aturity in a tetraploid population of potato (Solanum tuberosum subsp. tuberosum). Genetics 16 , . Brent, R. (1 ). Al orith s for ini i in without derivatives . rentice Hall, n lewood Cliffs ( .). Broman, K.W., Wu, H., Sen, Ś., and Churchill, G.A. (2003). R/qtl: QTL mapping in e peri ental crosses. Bioinformatics 1 , 0. Brouwer, ., and sborn, T. (1 ). A olecular arker linka e ap of tetraploid alfalfa (Medicago sativa .). Theoretical and Applied Genetics , 11 1200. Bruneau, A., Starr, .R., and oly, S. (200 ). hylo enetic relationships in the enus Rosa: new evidence fro chloroplast A se uences and an appraisal of current knowled e. Systematic Botany 2, 66 . Br ustowic , ., Merette, C., ie, ., Townsend, ., illia , T., and tt, . (1 ). Molecular and statistical approaches to the detection and correction of errors in enotype databases. American Journal of human Genetics , 11 11 . Buitendi k, .H., Boon, . ., and Ra anna, M.S. (1 ). uclear A Content in Twelve Species of Alstroemeria . and So e of their Hybrids. Annals of Botany , . Bush an, B., Robbins, M., arson, S., and Staub, . (2016). enotypin by Se uencin in Autotetraploid Cocksfoot (Dactylis glomerata) without a Reference eno e, in Breeding in a World of Scarcity. (Sprin er), 1 1 . Butruille, ., and Boiteu , . (2000). Selection– utation balance in polyso ic tetraploids: i pact of double reduction and a etophytic selection on the fre uency and subchro oso al locali ation of deleterious utations. Proceedings of the National Academy of Sciences , 660 661 . B y kkartal, H. .B. (2002). n Vitro ollen er ination and ollen Tube Characteristics in Tetraploid Red Clover (Trifolium pratense .). Turkish Journal of Botany 2 , 61. B y kkartal, H. .B. (200 ). Causes of low seed set in the natural tetraploid Trifolium pratense . (Fabaceae). African Journal of Biotechnology , 12 0. Cad an, C. (1 ). ature of tetraploidy in cultivated uropean potatoes. Nature 1 2, 10 10 . Cao, ., sborn, T.C., and oer e, R.W. (200 ). Correct esti ation of preferential chro oso e pairin in autotetraploids. Genome Research 1 , 62. Carvalho, A., el ado, M., Bar o, A., Frescatada, M., Ribeiro, ., ikaard, C.S., et al. (2010). Chro oso e and A ethylation dyna ics durin eiosis in the autotetraploid Arabidopsis arenosa. Sexual plant reproduction 2 , 2 . Carvalho, .R., Konin Boucoiran, C.F., Fanourakis, ., Vasconcelos, M.W., Carvalho, S.M., Heuvelink, ., et al. (201 ). T analysis for sto atal functionin in tetraploid Rosa× hybrida rown at hi h relative air hu idity and its i plications on postharvest lon evity. Molecular Breeding , 1 11. Cavana h, C., Morell, M., Mackay, ., and owell, W. (200 ). Fro utations to MA C: resources for ene discovery, validation and delivery in crop plants. Current opinion in plant biology 11, 21 221. Cavana h, C.R., Chao, S., Wan , S., Huan , B. ., Stephen, S., Kiani, S., et al. (201 ). eno e wide co parative diversity uncovers ultiple tar ets of selection for i prove ent in he aploid wheat landraces and cultivars. Proceedings of the National Academy of Sciences 110, 0 062. Cervantes Flores, .C., encho, .C., Krie ner, A., ecota, K.V., Faulk, M.A., Mwan a, R. ., et al. (200 ). evelop ent of a enetic linka e ap and identification of ho olo ous linka e roups in sweetpotato usin ultiple dose AF arkers. Molecular Breeding 21, 11 2. Chaffin, A.S., Huan , . F., S ith, S., Bekele, W.A., Babiker, ., nanesh, B. ., et al. (2016). A consensus ap in cultivated he aploid oat reveals conserved rass synteny with substantial sub eno e rearran e ent. The plant genome . Chakravarti, A. (1 1). A raphical representation of enetic and physical aps: the Marey ap. Genomics 11, 21 222. Chalhoub, B., enoeud, F., iu, S., arkin, .A., Tan , H., Wan , ., et al. (201 ). arly allopolyploid evolution in the post eolithic Brassica napus oilseed eno e. Science , 0 . Chan , K. ., o, H.F., ai, .C., ao, . ., in, K.H., and Hwan , S. . (200 ). dentification of uantitative trait loci associated with yield related traits in sweet potato (Ipomoea batatas). Botanical studies 0, . Chee a, ., and icks, . (200 ). Co putational approaches and software tools for enetic linka e ap esti ation in plants. Briefings in bioinformatics 10, 60 .
279 ______References
Plant systematics and evolution , Tragopogon miscellus Proceedings of the National Academy of Sciences , Genetics , New Phytologist , Brassica napus Theoretical and Applied Genetics , Philosophical Transactions of the Royal Society of London B: Biological Sciences , Nature Reviews Genetics , Capsella bursa pastoris Molecular ecology , Spartina pectinata‐ Molecular breeding : Rosa Theoretical and Applied Genetics , InterJournal, Complex Systems , D’hont, A. ( Cytogenetic and genome research , D’hont, A., Denoeud, F., Aury, J. Musa acuminata Nature , Molecular plant , Saccharum spontaneum Genome , Brassica napus Functional & Integrative Genomics , Recent advances in cytology. BMC genomics : Lotus corniculatus Chromosoma , Nature genetics , Allium crop science: recent advances, Chrysanthemum morifolium Euphytica , Plant, cell & environment , Gartenbauwissenschaft , Critical reviews in plant sciences ,
280 ______References
Denoeud, F., rretero u et, ., Deree er, A., Dro , ., uyot, ., etre , ., et . ( . he o ee eno e ro de n ht nto the on er ent e o ut on o e ne o ynthe . Science , . De ey, D. . ( . n reed n de re on n d o d, tetr o d, nd he o d re ted he t r . Crop Science , . De ey, D. . ( . o e A t on nd t on o ndu ed o y o dy to nt reed n , n Polyploidy: Biological Relevance, ed. . . e . ( o ton, A r n er , . D d on, J. ., n , ., he rd, ., Fu, . ., n, ., De en , F. . ., et . ( . D o ery o no e r nt n enoty n rr y ro e enoty e retent on nd redu e ert n ent . BMC genomics : . Doy e, J.J., nd n, A. . ( . D t n the or n o o y o dy e ent . New Phytologist , . Doy e, J.J., nd her n roy e , . ( . Dou e trou e t ono y nd de n t on o o y o dy. New Phytologist, , . Dr y ott, A. . ( . Sugar‐ beet. John ey on . Dre e h u , ., nd John on, .A. ( . e rodu t on nt rent e ro . Current Biology , . erh rd, F. ., h n , ., eh en e , A., re, .A., endor er, ., nd uther nd, . . ( . hro o o e o o t on o n F Triticum aestivum T. turgidum . duru ro n y ed y DAr r er nd F . Crop and Pasture Science , . d e, .A., o den, . ., nd o nd, J. ( . A t on o o u t on e uen n ( or order n nd ut n enoty n y e uen n r er n he o d he t. G3: Genes, Genomes, Genetics , . h re, .J., u t , J. ., un, ., o nd, J.A., oto, ., u er, . ., et . ( . A ro u t, e enoty n y e uen n ( ro h or h h d er ty e e . PloS one , e . nde n, J. . ( . e or th ro e ne tru ture o the r ey on en u . BMC Genomics : . nde n, J. ., nd o on, . ( . er e n e or er n enet y ne r ro r n . Bioinformatics , . e n , ., u der , ., nd o n, . ( . dent t on o ut ro e (Rosa hybrida nd root to r et e u n ro u t e uen e t ed ro te te te r er . Theoretical and Applied Genetics , . n , .J., h , . ., o d n , . ., ed , .A., nd ed , A.A. ( . o ut on o the r e t n eno e. Genome Biology and Evolution , . Fe her, .J., oo , J.J., , A. ., n ey, . ., ton, J. ., e eu , . ., et . ( . nte r t on o t o d o d ot to n e th the ot to eno e e uen e. PLoS One , e . F er t, J. . ( . n n e to orre t nd o d de no o eno e e e ethod , h en e , nd o ut t on too . Frontiers in Genetics . F her, .A. ( . he theory o n e n o y o nher t n e. Philosophical Transactions of the Royal Society B: Biological Sciences , . F e tro , ., eu e n , ., nd te ner, J. ( . F r er n y u ort tetr on nher t n e n Lotus corniculatus . Theoretical and Applied Genetics , . F nt r , .A., horn erry, J. ., nd u er , . . ( . tru ture o n e d e u r u n nt . Annual review of plant biology , . Fou re D ne n, ., Jo y, ., rune u, A., o, . F., nd h n , . . ( . hy o eny nd o eo r hy o d ro e th e ttent on to o y o d . Annals of Botany , . Fr n e, A., y , .A., A heh , .A., o h, .A., nd u enho , . ( . e y r the e o ut on ry h tory o Brassicaceae. Trends in plant science , . Furuy , . ( . Comparisons of seed weight and seedling characteristics of diploid and autotetraploid red clover. D on o o e e n er t e , F or d o rd o du t on. rdo, .A., tt o , ., oto erd , ., n , . ., r n, . . ., no don, .J., et . ( . A o t on n o eed u ty tr t n Brassica napus . u n A nd nd d te ro he . Molecular Breeding : . rdo, . ., h , J., oney utt, ., ed , ., nd h er, . ( . D o ery o tetr o dy n . Nature , . o y, .F., nd tter on, J. . ( . n reed n de re on n n utotetr o d her three ohort e d tudy. New Phytologist , .
281 ______References
o y, .F., tter on, J. ., nd r , J. . ( . ut ro n r te nd n reed n de re on n the her eou utotetr o d, Campanula americana. Heredity, , . r, ., r ent, D.J., , . J., e n, ., h e , ., yrne, D. ., et . ( . An utotetr o d n e o ro e (Rosa hybrida d ted u n the tr erry (Fragaria vesca eno e e uen e. PLoS One , e . ut, . ., r ht, . ., on, ., D or , J., nd Ander on, . . ( . e o n t on n under re ted tor n the e o ut on o nt eno e . Nature Reviews Genetics , . e der nn, . ( . n e t t on on nher t n e o u nt t t e h r ter n n y ene r er . ethod . Theoretical and Applied Genetics , . d eh u , ., ent, ., ye , .J., nd en, . ( . enoty e n nd n o u t te r nt u n n At nt on e e t rr y. Bioinformatics , . e , A. ., u , ., oen, . ., nd A ott, .J. ( . n r y n the A ter e e enet nd e o ut on o r d te er u d o d o er he d , n Developmental genetics and plant evolution, (ed . . ron , . te n J. n . y or nd Fr n , ondon , . ton , . ., on n ou o r n, .F., er nden, ., Do tr , ., er, . ., e rd, ., et . ( . enet r t on, her t ty nd enoty e y en ron ent nter t on o or ho o tr t n tetr o d ro e o u t on. BMC Genetics : . ton , . ., to er, ., on n ou o r n, .F. ., Ae e , ., er, . .F., e rd, ., et . ( . nher t n e nd n y o the deter n nt o o er o or n tetr o d ut ro e . Molecular Breeding : . o er, . ., ede t , ., nd De o , . ( . o oeo o h t re they nd ho do e n er the Trends in plant science , . o d h dt, . ( . o e e t o e o ut on. Science , . ood n, ., her on, J.D., nd o e, . . ( . o n o e ten ye r o ne t ener t on e uen n te hno o e . Nature Reviews Genetics , . r nd e, F., n n th n, ., n er , ., De n, J. ., nd et er, D. ( . A t nd deter n t n e n o o y o d . BMC Bioinformatics : . r nd e, F., n h, ., eu en, . . ., De n, J. ., nd et er, D. ( . Ad nt e o ont nuou enoty e ue o er enoty e e or A n h her o y o d o r t e tudy n he o d hry nthe u . BMC Genomics : . r ndont, ., Jen e , ., nd oyd, A. ( . e o nd t de t on n o y o d nt . Cytogenetic and genome research , . r th , A.J., e er, . ., rro , . ., nd Doe ey, J. ( . An introduction to genetic analysis (10th edition). n. r et, ., nd Arrud , . ( . u r ne eno de t n the o e eno e o n ort nt tro ro . Current Opinion in Plant Biology , . r et, ., D hont, A., o ue , D., Fe d nn, ., n ud, ., nd nn, J. . ( . F n n u t ted u r ne (Saccharum . eno e r n t on n h y o y o d nd Aneu o d nter e y r d. Genetics , . u r e , . ., , . ., nd o r , . . . ( . o r t e n o Andropogoneae Saccharum L. (sugarcane) and its relation to sorghum and maize. Proceedings of the National Academy of Sciences , . ett, .A., r d h , J., nd o , J. ( . nter n o u nt t t e tr t o n utotetr o d e e . Genetics , . ett, .A., r d h , J., eyer, ., o , J., ourne, D., nd u h, . ( . n e n y n tetr o d e e u t on tudy. Genetics Research , . ett, .A., nd uo, . ( . etr o d on tru t on o n e n utotetr o d e e . Journal of Heredity , . ett, .A., nde, ., nd ry n, . ( . on tru t n n e n utotetr o d e e u n u ted nne n . Theoretical and Applied Genetics , . ett, .A., o , ., o o , A., reedy, .F., nd ne, . ( . etr o d o t re or n e An y nd n n Autotetr o d o u t on n Do e D t . Journal of Heredity , . ett, .A., r d h , J. ., nd ry n, .J. ( . n n utotetr o d u n do e n or t on. Theoretical and Applied Genetics , . ett, .A., nd ro d oot, . . ( . e t o enoty n error , n ue nd e re t on d tort on n o e u r r er d t on the on tru t on o n e . Heredity , .
282 ______References
ett, .A., e n, ., nd ry n, .J. ( . n e An y nd n n Do e D t n etr o d ot to n o u t on. PLoS One , e . ett, .A., ne, ., r d h , J. ., nd uo, . ( . etr o d or ndo n e on tru t on nd n n utotetr o d e e . Journal of Heredity , . d ne, J. ( . he o n t on o n e ue nd the u t on o d t n e et een the o o n ed tor . Journal of Genetics , . d ne, J. . ( . heoret enet o uto o y o d . Journal of Genetics , . ton, J. ., n ey, . ., h tty, . ., to e , ., , A. ., n Deyn e, A., et . ( . n e nu eot de o y or h d o ery n e te north er n ot to er . BMC Genomics , . ton, . ., nd err, .J. ( . o ut t on o the n er e dd t e re t on h tr or uto o y o d nd u t e o dy o u t on . Theoretical and Applied Genetics , . rd n, .A., eer, F. . ., e ton, ., r o n, ., ton, J. ., n ourt, ., et . ( . eno e d er ty o tu er e r n o nu un o er o e e o ut on ry h tory nd t r et o do e t t on n the u t ted ot to. Proceedings of the National Academy of Sciences . r n, J. ., nd De et, J. .J. ( . n . n e nd r yer the or n o o y o dy. The botanical review , . rr on, .J., A ey, ., nd ender on, . . ( . e o n o er n nt nd other reen or n . Journal of experimental botany , . yne , ., nd Dou he , D. ( . t t on o the oe ent o dou e redu t on n the u t ted tetr o d ot to. Theoretical and applied genetics , . r , ., nd ee , . ( . enoty ontro o hro o o e eh our n rye. . hro o o e r n nd ert ty n utotetr o d . Heredity , . e, ., u, ., o utt, . ., nd dout, . . ( . o y n to u ort t o o nt n e n y n utotetr o d . Bioinformatics , . ender on, .A., nd eeney, . ( . y n yn tone o e n t t on to the or t on nd ro r ed re r o D A dou e tr nd re . Proceedings of the National Academy of Sciences of the United States of America , . Herben, T., Suda, J., and Klimešová, J. (2017). Polyploid species rely on vegetative reproduction more than d o d re e n t on o the o d hy othe . Annals of Botany , . er ot , ., nd t , . ( . u t e nd y etr or n o o y o d do ro e hy r d (Rosa . e t. Caninae (D . er. n o n unredu ed ete . Annals of Botany , . e , ., Druet, ., e , A., nd rr , D. ( . F ed en th h oty e n ro e eno red t on ur y n n d ed d ry tt e o u t on. Genetics Selection Evolution : . r nd nt y nt, ., re e , ., e, ., h n , ., nd Fou her, F. ( . enet n e o ro e on tru ted th ne ro te te r er nd o t n ontro n o er n tr t . Tree Genetics & Genomes , . r h, .D., ton, J. ., h d , . ., e e , J., r o n, ., n ourt, ., et . ( . ud D A re our e or n n e uen e , enoty e , nd henoty e to e er te ot to reed n . The Plant Genome . o t , F. ( . h en e or e e t e r er ted e e t on n nt . Genetica , . u n , . ., er y , . ., er y , A. ., h n, ., n h, . ., ur, ., et . ( . A o u t on n ro urrent t tu nd uture ro e t . Theoretical and Applied Genetics , . u n , ., D n , J., Den , D., n , ., un, ., u, D., et . ( . Dr t eno e o the ru t Actinidia chinensis. Nature communications : . u , D. . ( . ue r e , n Fodder crops and amenity grasses, (ed . . o er, . . o e t F. erone . r n er, e or , . u e e , A. ., e , J., e e, J., A hr , ., uyy r u, ., F n , D.D., et . ( . De e o ent o Arr y or otton nd h Den ty n o ntr nd nter e o u t on o Gossypium . G3: Genes|Genomes|Genetics , . unter, . ( . e ot re o n t on the e en e o hered ty. Cold Spring Harbor perspectives in biology , . u nd, . . ( . on tr nt on o y o d e o ut on te t o the nor ty ytoty e e u on r n e. Proceedings of the Royal Society of London. Series B: Biological Sciences , . u nd, . . ( . e t o n reed n on o en tu e ro th n d o d nd tetr o d Chamerion angustifolium Do o y o d ut t on o d n o en American journal of botany , .
283 ______References
nternational heat enome Se uencing onsortium (201 ). chromosome based dra t se uence o the he aploid bread heat (Triticum aestivum) genome. Science 1 . sing, . (1 ). ytogenetic studies in Cyrtanthus . Segregation in an allotetraploid. Hereditas , 27 . slam, .S., Thyssen, . ., Jen ins, J. ., and ang, . . (201 ). etection, validation, and application o genotyping by se uencing based single nucleotide polymorphisms in pland cotton. The Plant Genome . Jannoo, ., rivet, ., avid, J., hont, ., and las mann, J. (200 ). i erential chromosome pairing a inities at meiosis in polyploid sugarcane revealed by molecular mar ers. Heredity , 0 7. Jannoo, N., Grivet, L., Dookun, A., D’hont, A., and Glaszmann, J.C. (1999). Linkage disequilibrium among modern sugarcane cultivars. Theoretical and Applied Genetics , 10 10 0. Jansen, . . (1 ). nterval mapping o multiple uantitative trait loci. Genetics 1 , 20 211. Jans y, S. (200 ). hapter 2 reeding, enetics, and ultivar evelopment, in Advances in Potato Chemistry and Technology. (San iego cademic Press), 27 2. Jans y, S.H., har o s i, . ., ouches, .S., usmini, ., ichael, ., eth e, P. ., et al. (201 ). einventing potato as a diploid inbred line–based crop. Crop Science , 1 12 1 22. Jarvis, . ., Ho, .S., ight oot, .J., Schm c el, S. ., i, ., orm, T.J. ., et al. (2017). The genome o Chenopodium quinoa. Nature 2: 07. Jenc e s i, ., ber, ., rimaud, ., Huet, S., ucas, . ., onod, H., et al. (200 ). PrBn, a ma or gene controlling homeologous pairing in oilseed rape (Brassica napus) haploids. Genetics 1 , . Je , J. ., ee, S. ., and Sherp, . . (201 ). The ne t green movement plant biology or the environment and sustainability. Science , 12 1 12 . Jiang, . ., right, .J., l i , K. ., and Paterson, .H. (1 ). Polyploid ormation created uni ue avenues or response to selection in Gossypium (cotton). Proceedings of the National Academy of Sciences , 1 2 . Jiao, ., ic ett, .J., yyampalayam, S., handerbali, .S., andherr, ., alph, P. ., et al. (2011). ncestral polyploidy in seed plants and angiosperms. Nature 7 , 7 100. John, ., and Henderson, S. (1 2). synapsis and polyploidy in Schistocerca paranensis. Chromosoma 1 , 111 1 7. Joly, S., ryant, ., and oc hart, P.J. (201 ). le ible methods or estimating genetic distances rom single nucleotide polymorphisms. Methods in Ecology and Evolution , . Joly, S., Starr, J. ., e is, .H., and runeau, . (200 ). Polyploid and hybrid evolution in roses east o the oc y ountains. American Journal of Botany , 12 2 . Jones, . ., Jerry, . ., Khat ar, .S., aadsma, H. ., an er Steen, H., Prochas a, J., et al. (2017). comparative integrated gene based lin age and locus ordering by lin age dise uilibrium map or the Paci ic hite shrimp, Litopenaeus vannamei. Scientific Reports 7. Jones, ., and incent, J. (1 ). eiosis in autopolyploid Crepis capillaris. . utotetraploids. Genome 7, 7 0 . Ka itani, ., Toshimoto, K., oguchi, H., Toyoda, ., gura, ., uno, ., et al. (201 ). icient de novo assembly o highly hetero ygous genomes rom hole genome shotgun short reads. Genome Research 2 , 1 1 . Kantars i, T., arson, S., hang, ., ehaan, ., orevit , J., nderson, J., et al. (2017). evelopment o the irst consensus genetic map o intermediate heatgrass (Thinopyrum intermedium) using genotyping by se uencing. Theoretical and Applied Genetics 1 0, 1 7 1 0. Kaur, S., ranc i, . ., and orster, J. . (2012). denti ication, characteri ation and interpretation o single nucleotide se uence variation in allopolyploid crop species. Plant biotechnology journal 10, 12 1 . ‐ Kempthorne, . (1 7). An introduction to genetic statistics. John iley Sons, e or . Kerr, .J., i, ., Tier, ., ut o s i, . ., and crae, T. . (2012). se o the numerator relationship matri in genetic analysis o autopolyploid species. Theoretical and applied genetics 12 , 1271 12 2. Kha a a, H. .T., Sybenga, J., and llis, J. . (1 7). hromosome pairing and chiasma ormation in autopolyploids o di erent Lathyrus species. Genome 0, 7 . Kihara, H., and no, T. (1 2 ). hromosomen ahlen und systematische ruppierung der ume rten. Zeitschrift für Zellforschung und mikroskopische Anatomie , 7 1.
284 ______References
im, C., Guo, ., ong, ., Chandnani, ., huang, L. ., and aterson, A. . ( 1 ). A li ation o genot ing b sequen ing te hnolog to a variet o ro breeding rograms. Plant Science , 1 . im, ., lagnol, ., u, . ., ooma ian, C., Clark, . ., sso ski, ., et al. ( ). e ombination and linkage disequilibrium in Arabidopsis thaliana. Nature genetics 9, 11 1 11 . irov, ., an Laere, ., De iek, J., De e ser, ., an o , N., and hrustaleva, L. ( 1 ). An horing linkage grou s o the Rosa geneti ma to h si al hromosomes ith ramide and N markers. PloS one 9, e9 9 . loosterman, ., Abelenda, J.A., Gomez, .D. .C., ort i n, ., De oer, J. ., o it ani h, ., et al. ( 1 ). Naturall o urring allele diversit allo s otato ultivation in northern latitudes. Nature 9 : . nott, ., Neale, D., e ell, ., and ale , C. (199 ). ulti le marker ma ing o quantitative trait lo i in an outbred edigree o lobloll ine. Theoretical and Applied Genetics 9 , 1 . nott, .A., and ale , C. . (199 ). a imum likelihood ma ing o quantitative trait lo i using ull sib amilies. Genetics 1 , 1 11 1 . oning ou oiran, C. . ., sselink, G.D., ukosavl ev, ., an t estende, . .C., Gitonga, . ., rens, .A., et al. ( 1 ). sing NA eq to assemble a rose trans ri tome ith more than 1 , ull length e ressed genes and to develo the ag h N k A iom N arra or rose (Rosa L.). Frontiers in Plant Science : 9. oning ou oiran, C. . ., Gitonga, . ., an, ., Dolstra, ., an Der Linden, C.G., an Der hoot, J., et al. ( 1 ). he mode o inheritan e in tetra loid ut roses. Theoretical and Applied Genetics 1 , 91 . oo man, .J., osman, ., abatino, G.J., isser, D., an u lenbroe k, J., De iek, J., et al. ( ). A L markers as a tool to re onstru t om le relationshi s in the genus Rosa (Rosaceae). American Journal of Botany 9 , . orte, A., and arlo , A. ( 1 ). he advantages and limitations o trait anal sis ith G A a revie . Plant methods 9: 9. osto , D. (19 ). ertilit and hromosome length. Correlations bet een hromosome length and viabilit o gametes in auto ol loid lants. Journal of Heredity 1, . rebs, .L., and an o k, J. . (199 ). arl a ting inbreeding de ression and re rodu tive su ess in the highbush blueberr , Vaccinium corymbosum L. Theoretical and Applied Genetics 9, . riegner, A., Cervantes, J.C., urg, ., anga, . ., and hang, D. ( ). A geneti linkage ma o s eet otato Ipomoea batatas (L.) Lam. based on A L markers. Molecular Breeding 11, 1 9 1 . rz inski, . ., hein, J. ., irol, ., Connors, J., Gas o ne, ., orsman, D., et al. ( 9). Cir os An in ormation aestheti or om arative genomi s. Genome Research 19, 1 9 1 . La han e, J., and ishko , .A. ( 1 ). N as ertainment bias in o ulation geneti anal ses h it is im ortant, and ho to orre t it. Bioessays , . Lamm, . (19 ). C togeneti studies in Solanum, se t. uberarium. Hereditas 1, 1 1 . Lam son, .A., and Cheeseman, . . ( 11). ensing entromere tension Aurora and the regulation o kineto hore un tion. Trends in cell biology 1, 1 1 . Le Comber, ., Ainou he, ., ovarik, A., and Leit h, A. ( 1 ). aking a un tional di loid rom ol somi to disomi inheritan e. New Phytologist 1 , 11 1 . Lea h, L.J., ang, L., earse , .J., and Luo, . ( 1 ). ultilo us tetrasomi linkage anal sis using hidden arkov hain model. Proceedings of the National Academy of Sciences 1 , . Leal ertioli, ., hirasa a, ., Abernath , ., oretzsohn, ., Chavarro, C., Clevenger, J., et al. ( 1 ). etrasomi re ombination is sur risingl requent in allotetra loid Arachis. Genetics 199, 1 9 11 . Lentz, ., Crane, C., le er, D., and Loegering, . (19 ). An assessment o re erential hromosome airing at meiosis in Dactylis glomerata. Canadian Journal of Genetics and Cytology , . Levin, D.A. (19 ). inorit tot e e lusion in lo al lant o ulations. Taxon, . Levin, D.A. (19 ). ol loid and Novelt in lo ering lants. The American Naturalist 1 , 1 . Le in, . (19 1). Field theory in social science: selected theoretical papers. London avisto k. Li ar hetti, C., Le ras, C., Chastellier, A., elion, D., orel, ., akr, ., et al. ( 1 ). D henot ing and L anal sis o a om le hara ter rose bush ar hite ture. Tree Genetics & Genomes 1 :11 . Li, ., an, G., ang, ., un, ., uan, ., ong, G., et al. ( 1 a). Genome sequen e o the ultivated otton Gossypium arboreum. Nature genetics , .
285 ______References
Li, J., Das, ., u, G., ong, C., Li, ., obias, C., et al. ( 1 ). algorithm or ma ing quantitative trait lo i in multivalent tetra loids. International Journal of Plant Genomics 1 , 1 1 . Li, ., an, ., ei, ., A har a, A., armer, A.D., o, J., et al. ( 1 b). Develo ment o an al al a N arra and its use to evaluate atterns o o ulation stru ture and linkage disequilibrium. PLoS One 9, e 9. Li, ., Li, L., and an, J. ( 1 ). Disse ting meioti re ombination based on tetrad anal sis b single mi ros ore sequen ing in maize. Nature Communications : . Lieberman Aiden, ., an erkum, N.L., illiams, L., makaev, ., ago z , ., elling, A., et al. ( 9). Com rehensive ma ing o long range intera tions reveals olding rin i les o the human genome. Science , 9 9 . Limborg, . ., eeb, L. ., and eeb, J. . ( 1 ). orting du li ated lo i disentangles om le ities o ol loid genomes masked b genot ing b sequen ing. Molecular ecology , 11 1 9. Linde, ., attendor , A., au mann, ., and Debener, . ( ). o der milde resistan e in roses L ma ing in di erent environments using sele tive genot ing. Theoretical and applied genetics 11 , 1 1 1 9 . Lindhout, ., ei er, D., hotte, ., utten, .C., isser, .G., and an k, .J. ( 11). o ards 1 h brid seed otato breeding. Potato Research , 1 1 . Liorzou, ., ernet, A., Li, ., Chastellier, A., houroude, ., i hel, G., et al. ( 1 ). Nineteenth entur ren h rose (Rosa s .) germ lasm sho s a shi t over time rom a uro ean to an Asian geneti ba kground. Journal of experimental botany , 11 . Liu, ., oulsen, .G., and Davis, . . ( 1 ). nsight into o to loid stra berr (Fragaria) subgenome om osition revealed b G anal sis o enta loid h brids. Genome 9, 9 . Llo d, A., and omblies, . ( 1 ). eiosis in auto ol loid and allo ol loid Arabidopsis. Current opinion in plant biology , 11 1 . Lu, ., ang, ., ong, C., Li, ., eng, ., ang, ., et al. ( 1 ). A multivalent three oint linkage anal sis model o autotetra loids. Briefings in bioinformatics 1 , . Luo, ., a kett, C., radsha , J., ni ol, J., and ilbourne, D. ( 1). Constru tion o a geneti linkage ma in tetra loid s e ies using mole ular markers. Genetics 1 , 1 9 1 . Luo, ., hang, ., and earse , . ( ). heoreti al basis or geneti linkage anal sis in autotetra loid s e ies. Proceedings of the National Academy of Sciences of the United States of America 1 1, . Luo, . ., hang, ., Lea h, L., hang, . ., radsha , J. ., and earse , .J. ( ). Constru ting Geneti Linkage a s nder a etrasomi odel. Genetics 1 , . able, ., Ale androu, ., and a lor, . ( 11). Genome du li ation in am hibians and ish an e tended s nthesis. Journal of Zoology , 1 1 1 . aenhout, . ( 1 ). rogeno . (Ghent niversit , elgium). alie aard, C., Jansen, J., and an oi en, J. (199 ). Linkage anal sis in a ull sib amil o an outbreeding lant s e ies overvie and onsequen es or a li ations. Genetical Research , . amanova, L., Co e , A.J., ott, C. ., ozare a, ., urner, . ., umar, A., et al. ( 1 ). arget enri hment strategies or ne t generation sequen ing. Nature Methods , 111 11 . and kov , ., Jol , ., rz inski, ., ummenho , ., and L sak, .A. ( 1 ). ast di loidization in lose meso ol loid relatives o Arabidopsis. The Plant Cell , 9 . angelsdor , .C., and Jones, D. . (19 ). he e ression o endelian a tors in the gameto h te o maize. Genetics 11: . arasek Ciolako ska, A., Arens, ., and an u l, J. ( 1 ). he ole o ol loidization and nters e i i bridization in the reeding o rnamental Cro s, in Polyploidy and Hybridization for Crop Improvement. C C ress), 1 9 1 1. ason, A. . ( 1 ). Challenges o Genot ing ol loid e ies, in Plant Genotyping: Methods and Protocols, ed. J. atle . (Ne ork, N ringer Ne ork), 1 1 1 . ason, A. ., iggins, . ., no don, .J., atle , J., tein, A., erner, C., et al. ( 1 ). A user guide to the Brassica 60K Illumina Infinium™ SNP genotyping array. Theoretical and Applied Genetics 1 , 1 . assa, A.N., anrique Car intero, N.C., Coombs, J.J., arka, D.G., oone, A. ., irk, . ., et al. ( 1 ). Geneti linkage ma ing o e onomi all im ortant traits in ultivated tetra loid otato (Solanum tuberosum L.). G3: Genes| Genomes| Genetics , . ather, . (19 ). edu tional and equational se aration o the hromosomes in bivalents and multivalents. Journal of Genetics , . ather, . (19 ). egregation and linkage in autotetra loids. Journal of Genetics , 1 .
286 ______References
c llister . . an iller . . 0 6 . Single nucleoti e polymorphism isco ery ia genotyping y se uencing to assess population genetic structure an recurrent polyploi i ation in Andropogon gerardii. American journal of botany 0 , . c allum S. raham . orgensen . o lan . . Bassil N. . ancoc . . et al. 0 6 . onstruction of a SNP an SS lin age map in autotetraploi lue erry using genotyping y se uencing. Molecular Breeding 6: . c amy P. ollo ay . u . unne . . Sch art B. . Patton . . et al. 0 . SNP ase high ensity lin age map of oysiagrass Zoysia japonica Steu . an its use for the i entification of associate ith inter har iness. Molecular Breeding 0. c lintoc B. . he significance of responses of the genome to challenge. Science 6, 0 . c ollum . . . omparati e stu ies of chromosome pairing in natural an in uce tetraploi Dactylis. Chromosoma , 60 . c onal . . ice .P. an esai . . 0 6 . Se spee s a aptation y altering the ynamics of molecular e olution. Nature , 6. c rath . . an ung . 0 6 . se of polyploi s. interspecific an intergeneric i e hy ri s in sugar eet impro ement in Polyploidy and Hybridization for Crop Improvement. Press 0 0. en el . . 66 . ersuche er Pflan enhy ri en. Verhandlungen des naturforschenden Vereines in Brünn B . I han lungen, – . ercier . ar . enc e s i . acaisne N. an relon . 0 . he molecular iology of meiosis in plants. Annual review of plant biology 66, . eu issen . ayes B. an o ar . 0 6 . enomic selection para igm shift in animal ree ing. Animal frontiers 6, 6 . eu issen . . . ayes B. . an o ar . . 00 . Pre iction of otal enetic alue sing enome i e ense ar er aps. Genetics , . eyer . il ourne . ac ett . Bra sha . cnichol . an augh . . in age analysis in tetraploi potato an association of mar ers ith uantitati e resistance to late light Phytophthora infestans . Molecular and General Genetics , 0 60. icrosoft orporation an eston S. 0 . oParallel oreach parallel a aptor for the parallel pac age. R package version .0. . il ourne . Bra sha . . an ac ett . . 00 . olecular apping an Bree ing in Polyploi rop Plants in Principles and Practices of Plant Genomics (Vol. 2: Molecular Breeding), e s. . Kole . . ott. Science Pu lishers . onca a . .P. o ar . ontoya . . on le . Spin el . an ccouch S. 0 6 . genetic lin age map of coffee Coffea arabica . an for yiel plant height an ean si e. Tree genetics & genomes : . on en . ara . a a . ahana . Ko ayashi . a uchi . et al. 0 . onstruction of a lin age map ase on retrotransposon insertion polymorphisms in s eetpotato ia high throughput se uencing. Breeding science 6 , . onroe . . llen . . anger P. ullen . . o ell . . oyers B. . et al. 0 . SPmap a tool ma ing use of tra eling salesperson pro lem sol ers in the efficient an accurate construction of high ensity genetic lin age maps. BioData mining 0: . oore . 0 . eiosis in polyploi s in Polyploid and hybrid genomics, e s. . . hen . . Birchler. ohn iley Sons Inc. . oragues . oma ran . augh . ilne I. la ell . an ussell . . 0 0 . ffects of ascertainment ias an mar er num er on estimations of arley i ersity from high throughput SNP genotype ata. Theoretical and applied genetics 0, . organ . . . an om segregation ersus coupling in en elian inheritance. Science , . orrison . an a hathy . 60 . re uency of ua ri alents in autotetraploi plants. Nature : . ota e i . e i er . in ers . an aliepaar . 0 a . riPoly a haplotype estimation approach for polyploi s using se uencing ata of relate in i i uals. bioRxiv, doi 10.1101/163162. ota e i . in ers . aliepaar . an e i er . 0 . ploiting ne t generation se uencing to sol e the haplotyping pu le in polyploi s a simulation stu y. Briefings in bioinformatics, 0 . uller . . hy polyploi y is rarer in animals than in plants. The American Naturalist , 6 . ulligan . . 6 . iploi an autotetraploi Physaria vitulifera ruciferae . Canadian Journal of Botany , .
287 ______References
Genome biology : Dactylis glomerata Botanical Gazette , Cytogenetic and genome research , Wiley Interdisciplinary Reviews: Computational Statistics , BMC genomics , Dioscorea alata Molecular Breeding , Nature , Frontiers in Plant Science Science , Brassica napus Plant Cell , Evolution by gene duplication. Wheat Inf Serv The American Naturalist , Nature Reviews Genetics , Cell , Annual review of genetics , and Evaluation of a High Density Genotyping ‘Axiom_Arachis’ Array with 58 K SNPs for Scientific Reports New Phytologist , PLoS One , Horticulture research : Rosa Journal of experimental botany , ‐ The Plant Journal ‐ Genetics , https://CRAN.R-project.org/package=nlme Proceedings of the 3rd international workshop on distributed statistical computing PloS one ,
288 ______References
Nature Genetic Reviews : Nature , Theoretical and Applied Genetics , Arabidopsis QUARTET QRT Science , Hyla versicolor Evolution , Nature , Theoretical and Applied Genetics , Paspalum notatum Sexual Plant Reproduction , Theoretical and Applied Genetics , Annual Review of Ecology and Systematics, Annual review of ecology and systematics, Bombyx Carlsberg Research Communications , Gossypium hirsutum Gossypium barbadense Scientific Reports Science , American journal of botany , Genetics Research , Genetics Research , Journal of heredity , Nature , Gene , Crop Science , Tree genetics & genomes : Genetics Research , The Plant Genome New Phytologist , ‐ ‐
289 ______References
Molecular Ecology , ‐ Higo chrysanthemum Dendranthema grandiflorum Journal of the Japanese Society for Horticultural Science , Nature plants : Arabidopsis thaliana Genetics , Planta , Phaseolus vulgaris Genetics : The Plant Genome Ranunculus kuepferi Ranunculaceae Plant Systematics and Evolution , Theoretical and Applied Genetics, Current opinion in plant biology , H1 Solanum tuberosum Plant Breeding , Frontiers in Plant Science The annals of statistics , Molecular Ecology Resources , ‐ PLoS One , Xenopus laevis Nature : G3: Genes| Genomes| Genetics , Scientific Reports Ipomoea batatas Scientific Reports Fragaria vesca Nature genetics , Acta Hort , Molecular breeding , The Plant Genome
290 ______References
Theoretical and applied genetics , Rosa Wild Crop Relatives: Genomic and Breeding Resources Plantation and Ornamental Crops American Journal of Botany , Current opinion in genetics & development , Proceedings of the National Academy of Sciences , Annual review of plant biology , — Nature biotechnology , Theoretical and Applied Genetics , Theoretical and Applied Genetics , The Plant Journal , Stebbins, G.L. (1947). Types of polyploids: their classification and significance. Advances in Genetics , Annals of Botany , Genetics , Journal of evolutionary biology , Urticaceen Jahrb Wiss Bot , American Journal of Human Genetics , Genetics , Drosophila Journal of Experimental Zoology Part A: Ecological Genetics and Physiology , ‐ BMC bioinformatics : Theoretical and Applied Genetics , Genomics , Genetics : Heredity , Theoretical and Applied Genetics ,
291 ______References
Solanum tuberosum Bibliographia Genetica , – General Cytogenetics. Chromosoma , Genome , Genome , Medicago truncatula BMC genomics : Crop Science , Beest, M., Le Roux, J.J., Richardson, D.M., Brysting, A.K., Suda, J., Kubešová, M., et al. (2011). The Annals of Botany , Streptococcus agalactiae “pan genome”. Proceedings of the National Academy of Sciences of the United States of America , G3: Genes, Genomes, Genetics , The Plant Genome Tree genetics & genomes , G3: Genes, Genomes, Genetics , Euphytica : Theoretical and Applied Genetics , Crop Science , PLoS One , Journal of the American Society for Horticultural Science , Ambystoma jeffersonianum Copeia , Nature Reviews Genetics , BMC Plant Biology : Current opinion in plant biology , Theoretical and Applied Genetics , Postharvest Biology and Technology ,
292 ______References
an eest, ., ost, A., Arens, ., isser, R. ., and an Meeteren, . (201 b). Breeding or postharvest per ormance in chrysanthemum by selection against storage induced degreening o dis lorets. Postharvest Biology and Technology 12 , . an eest, ., oorrips, R. ., sselin , D., ost, A., isser, R. ., and Arens, . (201 c). onclusive evidence or hexasomic inheritance in chrysanthemum based on analysis o a 1 S array. BMC genomics 1 : . an oi en, J. (200 ). Map TL , So t are or the mapping o uantitative trait loci in experimental populations o diploid species. Kya ma B. ., ageningen, etherlands. an oi en, J. . (1 2). Accuracy o mapping uantitative trait loci in autogamous species. Theoretical and Applied Genetics , 0 11. an oi en, J. . (200 ). JoinMap , So t are or the calculation o genetic lin age maps in experimental populations. Kyazma B.V., Wageningen, The Netherlands. an oi en, J. ., and Jansen, J. (201 ). Genetic mapping in experimental populations. ambridge niversity ress. an s, ., Andr e e s i, S., Ba er, ., Barrena, ., Bryan, .J., aromel, B., et al. (200 ). onstruction o a 10,000 mar er ultradense genetic recombination map o potato providing a rame or or accelerated gene isolation and a genome ide physical map. Genetics 1 , 10 10 . an Tuyl, J.M., and Lim, K.B. (200 ). nterspeci ic hybridisation and polyploidisation as tools in ornamental plant breeding. Acta Horticulturae 12, 1 22. anneste, K., Baele, ., Maere, S., and an De eer, . (201 ). Analysis o 1 plant genomes supports a ave o success ul genome duplications in association ith the retaceous– aleogene boundary. Genome research 2 , 1 1 . anraden, .M. (200 ). icient Methods to ompute enomic redictions. Journal of Dairy Science 1, 1 2 . igna, B.B., Santos, J. ., Jungmann, L., Do alle, .B., Mollinari, M., astina, M.M., et al. (201 ). vidence o allopolyploidy in Urochloa humidicola based on cytological analysis and genetic lin age mapping. PloS one 11, e01 . leugels, T., euppens, B., nops, ., Lootens, ., an ari s, .R., Smagghe, ., et al. (201 ). Models ith only t o predictor variables can accurately predict seed yield in diploid and tetraploid red clover. Euphytica 20 , 0 2 . oorrips, R. (2002). Map hart so t are or the graphical presentation o lin age maps and TLs. Journal of Heredity , . oorrips, R. ., ort, ., and osman, B. (2011). enotype calling in tetraploid species rom bi allelic mar er data using mixture models. BMC Bioinformatics 12 1 2. oorrips, R. ., and Maliepaard, .A. (2012). The simulation o meiosis in diploid and tetraploid organisms using various genetic models. BMC Bioinformatics 1 :2 . os, . ., aulo, M.J., oorrips, R. ., isser, R. ., an c , .J., and an eu i , .A. (201 ). valuation o LD decay and various LD decay estimators in simulated and S array data o tetraploid potato. Theoretical and Applied Genetics 1 0, 12 1 . os, . ., itde illigen, J. .a.M.L., oorrips, R. ., isser, R. . ., and an c , .J. (201 ). Development and analysis o a 20K S array or potato (Solanum tuberosum) an insight into the breeding history. Theoretical and Applied Genetics 12 , 2 2 01. u osavl ev, M., Arens, ., oorrips, R., an T estende, ., sselin , .D., Bour e, .M., et al. (201 ). igh density S based genetic maps or the parents o an outcrossed and a sel ed tetraploid garden rose cross, in erred rom admixed progeny using the rose S array. Horticulture Research 1 0 2. ang, ., hang, ., Rose, S., and an Der Laan, M. (201 a). A ovel Targeted Learning Method or uantitative Trait Loci Mapping. Genetics 1 , 1 1 . ang, K., ang, ., Li, ., e, ., ang, J., Song, ., et al. (2012). The dra t genome o a diploid cotton Gossypium raimondii. Nature genetics , 10 110 . ang, S., ong, D., orrest, K., Allen, A., hao, S., uang, B. ., et al. (201 b). haracteri ation o polyploid heat genomic diversity using a high density 0 000 single nucleotide polymorphism array. Plant biotechnology journal 12, . estergaard, M. (1 0). Studies on cytology and sex determination‐ in polyploid orms o Melandrium album. Dansk Botanisk Arkiv 10, 1 1 1. et, J.D., and arlan, J. (1 0). Apomixis, polyploidy, and speciation in Dichanthium. Evolution 2 , 2 0 2 .
293 ______References
International Journal of Plant Sciences , Arabidopsis thaliana Elife , Plant biotechnology journal , ‐ Rosa Botanical Journal of the Linnean Society , ‐ ‐ Plant Molecular Biology , Brachiaria decumbens Genetics , Theoretical and Applied Genetics , Genetics , Theoretical Population Biology , Journal of Computational Biology , Theoretical and applied genetics , Molecular Biology and Evolution Genetical Research , Briefings in Bioinformatics , Euphytica , Podosphaera pannosa European journal of plant pathology , Euphytica : Proceedings of the National Academy of Sciences , Nature Plants : Saccharum Molecular Breeding : Arabidopsis arenosa Current Biology , Medicago Nature , Frontiers in Plant Science
294 ______References
, Medicago sativa Molecular plant pathology , ‐ ‐ ‐ ‐ Proceedings of the National Academy of Sciences , Dendranthema morifolium Molecular breeding , Chrysanthemum morifolium Euphytica , Chrysanthemum morifolium Scientia Horticulturae , Chrysanthemum morifolium PLoS one , The Journal of Horticultural Science and Biotechnology , Molecular breeding , The Journal of Horticultural Science and Biotechnology , The American Journal of Human Genetics , Journal of the American Society for Horticultural Science , Medicago sativa PloS one , Nature Genetics , Genetics , bioRxiv, doi 10.1101/119271 Cold Spring Harbor perspectives in biology , Polyploidy and genome evolution
295
Summary Almost all higher organisms are diploid i.e. they carry two copies of each chromosome, one inherited from each parent. Although diploidy appears to be the norm in higher organisms, it is certainly not the rule. A small but significant proportion of higher organisms possess more than two copies of each chromosome. These are collectively termed “polyploids” and make up the central subject matter for this thesis.
We are now living in a time of unprecedented development in scientific tools, particularly for the life sciences. For many years diploid species have been the subject of genetic investigations, often with the aim of understanding the inheritance of specific traits. For polyploid species, many of which are important agricultural crops, this has often remained infeasible due to the increased complexity of polyploid genomics. This thesis represents part of the ongoing development of methods and software tools required to make polyploid genomics a reality, enabling genomics-assisted breeding decisions to be made for polyploid crops.
We begin in Chapter 2 with a review of the tools currently available to analyse polyploid populations. These tools encompass activities such as genotype assignment and marker dosage calling, haplotype assembly, linkage analysis and genetic map construction, genome-wide association analysis, genomic selection, the creation of reference sequence assemblies and the simulation of polyploid populations. Although introductory to the thesis, this review represents the current state of the art in polyploid software tools (and was compiled after the tools described in this thesis were developed).
Linkage maps represent a molecular karyotype of a species and its recombination landscape and have numerous applications such as in quantitative trait loci (QTL) analysis, synteny analysis, reference sequence assembly, fine mapping studies etc. They can also provide insights into meiosis and for polyploids, can be used to uncover some of the more curious features of polyploid meiosis. In Chapter 3 we generated a high- density linkage map from single nucleotide polymorphism (SNP) genotype data of a tetraploid potato population. This map allowed us to study the phenomenon of double reduction, where both copies of (part of) a chromatid end up being transmitted to an offspring. This was achieved using simplex x nulliplex markers only, which give unambiguous information about double reduction. We broadened our mapping approach to include all other SNP marker types in Chapter 4, while also investigating the effects of double reduction and non-random chromosomal pairing on the estimation of recombination frequency in autotetraploids. The topic of non-random, or preferential, chromosome pairing returns in Chapter 5, where we again used high-density linkage mapping to understand the patterns of meiosis in a tetraploid rose population. We
297 ______Summary disco ered that pairin a inities aried bet een parents chromosomes and e en chromosomal position in our population ith e idence or stron ly pre erential pairin localised to certain parts o a number o parental chromosomes s ell as dia nosin this beha iour e corrected or it in our linka e analysis leadin to the creation o a tailored hi h density enetic map or this important ornamental species his map allo ed us to unco er interestin enomic rearran ements bet een rose and its closest se uenced relati e the oodland stra berry Fragaria vesca and has since been used in e orts to create a re erence se uence assembly in rose n Chapter 6 e describe a ne so t are tool polymapR hich is reely a ailable as an packa e distributed throu h polymapR is currently able to enerate inte rated and phased linka e maps usin dosa e scored marker data in triploid tetraploid and he aploid populations that e hibit random chromosomal pairin polysomic inheritance as ell as se mental allotetraploids sho in pre erential chromosome pairin and represents a timely addition to the suite o tools a ailable to polyploid eneticists
n Chapter 7 e used polymapR to analyse a marker dataset rom a lar e population o he aploid Chrysanthemum morifolium eneratin the irst hi h density inte rated linka e map in this important ornamental species e used the phased map and marker dosa e scores to enerate identity by descent probabilities hich ormed the basis o a analysis or a number o important ornamental traits e return to the topic o double reduction in Chapter 8 uanti yin the e ect o double reduction on the po er and precision o studies in autotetraploids s ell as ainin insi ht into the mechanics o based analysis at the polyploid le el e e plored the e ect o ariable marker densities on enetic mappin usin the enotypic in ormation coe icient and ound that this measure has important implications or the results o polyploid studies e applied these methods in Chapter 9 to per orm a multi en ironment analysis or some important morpholo ical traits in rose his allo ed us not only to describe the enetic architecture o these traits but to test hether the en ironment has a stron in luence on the phenotypic e pression o reat rele ance to breeders and researchers per ormin studies a ay rom the tar et en ironment n Chapter 10 these de elopments orm the basis o polyqtlR an packa e to per orm inter al mappin in autopolyploid populations inally in Chapter 11 take a step back rom the technical inno ations presented in this thesis considerin the impact that these tools can ha e on our understandin o and our ability to breed polyploid crops
t is hoped that the methods and tools described in this thesis ill simpli y enetic mappin in polyploids and acilitate enomics assisted breedin decisions in the uture or these ascinatin species
298 Acknowledgements Being one of the most-read sections of a thesis, I am aware of the responsibility to properly thank all the people who in some way or another contributed to the work described within these covers. Given that the list is long and space is short, I will do my best, but please accept my apologies if you came here looking for your name and failed to find it! I had planned a special dedication to you further down in white ink, but the printers were unable to render it legibly...
But back to the serious topic of thanking people, first of all to my daily supervisors Chris Maliepaard and Roeland Voorrips, I wish to thank you both for your time, enthusiasm and expertise, and for inviting me to do this PhD in the first place. Our fortnightly supervision meetings were both friendly and focused, and we always seemed to end up laughing at some stage. Both of you contributed much to the content of the thesis, but also to the quality of the written output. Roeland, I hadn’t fully appreciated what the term “scrupulous” meant until I received feedback from you. Your attention to detail and command of the English language are impressive, indeed I am often left with the feeling that your English is more English than mine. Thank you both for enduring the editorial demands of this somewhat frenetic writer. Chris, thanks also for giving me the room to follow my own research goals during this work. Together with Roeland you helped define the work to be done, but you allowed me the space to develop many of the details. I think this is one of the strengths of a good supervisor and I’m very aware of how lucky I’ve been with the supervision team I’ve had here.
To my promoter Richard Visser, you provided not only the opportunity to do the PhD within the department of plant breeding, but also very valuable feedback on my project, particularly the written output. After 2.5 years you told me I could finish up whenever I liked (you were probably getting worried that you would have no free weekends left if I kept writing) – this really spurred me on to “opschiet een beetje” and encouraged me to finish writing the thesis in 3.5 years instead of the usual 4 (or 5!). You have always been approachable and friendly, and your dedication to the department is second to none. Thanks to my external supervisor Duur Aanen for making time for our annual meetings which I enjoyed. Thankfully you weren’t required to mediate at any stage! Within the department there are also a large number of individuals that have helped in many ways. I would like to thank René Smulders for the many interesting conversations and collaborations we’ve had, particularly on rose genetics but also more generally on quantitative genetics in polyploids. To Herman van Eck, like René you are also one of the people that helped me think more deeply and consider alternative ways to look at things. You have also given me a fuller appreciation of the power of a good question,
299 ______Acknowledgements and I must admit I am slightly relieved that you are not eligible to sit on the opponents’ ben h for my defen e han s to Paul Arens for the help and feedba during my pro e t as well as being su h a friendly olleague with whom I ould have a hat about “gewoon dinges” as well. You have helped me feel more at home in the Netherlands. han s also to Eric van de Weg you possess both a deep nowledge on geneti mapping as well as a meti ulousness that has helped separate the signal from the noise in a way no omputer ould. Your ideas and uestions helped broaden the boundaries of the wor in this thesis. I also appre iated your enthusiasm for my presenting style parti ularly when it led to my presenting hapter of this thesis to the polyploids session of the lant and nimal enome onferen e in . han s to Gerard van der Linden and Christian Bachem my thesis supervisors. hristian you managed to onvin e me to stay and do a h in plant breeding despite my advan ing years. I probably wouldn’t still be here otherwise here are also many other people that deserve a mention who have been involved in my pro e t be it inspirational or otherwise su h as Arwa Shahin Carole Koning-Boucoiran Chaozhi Zheng Danny Esselink Ehsan Motazedi Frans Krens Giorgio Tumino Herma Koehorst-van Putten who along with Michela Appiano helped fly the flag at my wedding Johan Willemsen Katherine Preedy Konrad Zych Linda Kodde, Marco Bink Peter Vos Richard Finkers Robert van Loo Ronald Hutten and Thijs van Dijk. han s also to everyone who ept the ournal lub going over the years hopefully it will ontinue into the future
spe ial than s to Christine Hackett for a epting my re uest to oin io for a month in . hris you have been one of the leading lights in polyploid geneti mapping for many years and it was a great e perien e to wor together with you. ur ollaboration led dire tly to hapter of this thesis but also helped greatly in developing hapters and . I would li e to than Hans Jansen for helping to define the goals in polyploid lin age mapping early on in the pro e t and for your infe tious enthusiasm for mapping and geneti s. I also want to than Johan van Ooijen for being so generous with your time and advi e in helping us understand some of the mapping steps in oin ap and trying to translate these ideas into polymapR. han you to Geert van Geest for all the wor in improving polymapR you too a set of fun tions and helped turn them into a great pa age. I learned a lot about programming from you and our ollaboration really helped push forward the progress in both of our pro e ts.
I also want to a nowledge the ontribution of the students I o supervised - Twan Kranenburg Patrick Wissink Yanlin Liao and Jitpanu Yamjabok. ll of you helped my pro e t by e ploring new ideas and I learnt a lot from the e perien e of supervision. han s to my paranymphs Jordi Petit-Pedro and Michiel Klaassen for your meditative pose and perfe t enun iation of any and all propositions during my
300 ______Acknowledgements defen e as well as being all round great guys. han s to my present and former offi e mates Anne Giesbers Charlie Chen Deniz Gol Ehsan Motazedi Mas Muniroh Michela Appiano Myluska Caro-Rios Narges Sedaghat Telgerd Yi Wu and Ying Liu and everyone from my short stay in . for putting up with a olleague that never goes away to the lab or the greenhouse – the offi e was my greenhouse the computer was my lab! To the many other friends and acquaintances I’ve made along the way than s for ma ing my time at plant breeding so enjoyable. I won’t list you all by name as that would involve literally listing everyone at and uite a few people at the other side of adi as well so you now who you are I should li e to parti ularly mention Anne Giesbers Jeroen Berg and Tim van der Weijde with whom I travelled to Nan ing hina for the international graduate onferen e in . part from being a great bunch of adventurous spirits, you also put up with my “wat vervelend Nederlands” and I thin the wee and a half I spent in hina really paid dividends for my ability to communicate using your “ingewikkeld taal”. o the se retaries past and present in the department of plant breeding Nicole Trefflich Letty Dijker Daniëlle van der Wee and Janneke van Deursen than you all for being su h a friendly and effi ient team eeping the wheels in motion within the department. You have always been very helpful with any problems or uestions that I had and always did it with a smile. spe ial than s to Ni ole for boo ing my thesis defen e first thing on a riday morning on your day off I also want to than all the polyploid pro e t partners who were there throughout my pro e t during presentations and wor shops as well as the o asional off site visit whi h I really en oyed. Your feedba was essential and I thin the involvement of so many partners with so many diverse polyploid rops has really helped broaden the hori ons of polyploid geneti s here in ageningen. o my fellow members of the h oun il – Amalia Francesca Jarst Jesse Jordi Kiki Kim Malaika Manos Martina Sandeep Sara Shanice Tieme and Tom I thin we a hieved a lot together on the oun il and had some fun along the way han s also to Douwe Zuidema Ingrid Vleghels and Ria Fonteyn from for all the help. I also want to than the reading committee (my “opponents”) for agreeing to read this thesis – without fore nowledge about its length. hey say brevity is the soul of wit – apologies for not writing a wittier thesis then
inally I would li e to a nowledge my family and in parti ular my parents who have always en ouraged and supported me despite the many twists and turns I have ta en along the way. han you for trusting that it will all wor out one day as indeed I hope someday it shall. final word of than s to my lovely wife lena who has been a onstant sour e of support and en ouragement throughout. y the time these words are in print we will already be nee deep in nappies and I loo forward to ontinue sharing all the happiness in the world together with you.
301 About the author
Peter Michael Bourke was born on 28th July 1982 in Cork, Ireland. In 2001 he represented his country twice – at the World Schools’ Debating Championship in Johannesburg, South Africa and the International Mathematical Olympiad in Washington DC, USA. He continued speaking and doing maths during his bachelors studies, graduating with joint first class honours in mathematics and physics from University College Cork. Having completed his studies, he bought a bicycle and headed overland and sea for China, with an English-language teaching qualification in his bag. Unfortunately, Russian immigration regulations and its winter intervened, forcing him to about-turn and return to western Europe, eventually pedalling 2300m above sea level to look for work in a ski resort in the French Alps. Having survived the winter (and learnt how to ski), he enrolled the following spring in a course on practical sustainability in Kinsale F.E.C., Cork. This led to a job with the Irish Seed Savers Association, an organisation dedicated to conserving open-pollinated landrace varieties of vegetables, grains and fruit trees in Ireland. After four years working as the garden co-ordinator he again took to his bicycle, visiting and working with organic breeding companies and seedbanks across Europe on a 10,000 km cycling tour. A love of cycling and a desire to learn more about plant breeding brought him to the Netherlands in 2012 where he enrolled in the MSc plant sciences program at Wageningen University (specialisation plant breeding and genetic resources). During his masters he was fortunate to do a minor thesis with Chris Maliepaard and Roeland Voorrips in the department of plant breeding, who offered him the possibility to continue this research as part of a PhD. In 2016 he was awarded an EMBO short-term fellowship to spend one month working in the group of Dr. Christine Hackett at BioSS, Dundee, Scotland. The results of his PhD project, started in September 2014, are described in this thesis.
302 List of publications
Bourke, P.M. an eest oorrips ansen ranenb rg Shahin et al.
pol map – lin age anal sis and genetic map constr ction rom pop lations o o tcrossing pol ploids Bioinformatics (in press) doi bioin ormatics bt
ibrand Saint ant ttin Bourke, P.M. et al. high alit genome se ence o Rosa chinensis to el cidate ornamental traits Nature Plants (accepted)
Bourke, P.M. oorrips isser and aliepaard C ools or genetic st dies in e perimental pop lations o pol ploids Frontiers in Plant Science doi pls
an eest Bourke, P.M. et al. n ltra dense integrated lin age map or he aploid chr santhem m enables m lti allelic anal sis Theoretical & Applied Genetics
Bourke, P.M. rens oorrips sselin D oning o coiran C S et al. artial pre erential chromosome pairing is genot pe dependent in tetraploid rose The Plant Journal
osa l e rens Bourke, P.M. et al. igh densit S based genetic maps or the parents o an o tcrossed and a sel ed tetraploid garden rose cross in erred rom admi ed progen sing the rose S arra Horticulture Research
Bourke, P.M. oorrips ranenb rg ansen isser aliepaard C ntegrating haplot pe speci ic lin age maps in a tetraploid species sing S mar ers Theoretical & Applied Genetics
Bourke, P.M. oorrips isser and aliepaard C he do ble red ction landscape in tetraploid potato as re ealed b a high densit lin age map Genetics
303 Education Statement of the Graduate School Experimental Plant Sciences
Issued to: Peter M. Bourke Date: 15 June 2018 Group: Laboratory of Plant Breeding University: Wageningen University & Research, Wageningen, The Netherlands
1) Start-up phase date ► First presentation of your project Title: QTL analysis in polyploids - models and methods 23 Jan 2015 ► Writing or rewriting a project proposal Title: Models and Methods for QTL analysis in polyploid crops 09 Dec 2014 ► Writing a review or book chapter "Tools for genetic studies in experimental populations of polyploids", Front. Plant Sci (2018), 9:513. doi: 10.3389/fpls.2018.00513 28 Dec 2017 ► MSc courses Programming in Python (INF-22306) Oct-Dec 2014 ► Laboratory use of isotopes Subtotal Start-up Phase 13.5 credits*
2) Scientific Exposure date ► EPS PhD student days EPS PhD student day 'Get2Gether', Soest, NL 29-30 Jan 2015 EPS PhD student day 'Get2Gether', Soest, NL 28-29 Jan 2016 EPS PhD student day 'Get2Gether', Soest, NL 09-10 Feb 2017 EPS PhD student day 'Get2Gether', Soest, NL 15-16 Feb 2018 ► EPS theme symposia EPS Theme 4 symposium 'Genome Biology', Amsterdam, NL 15 Dec 2015 EPS Theme 4 symposium 'Genome Biology', Wageningen, NL 16 Dec 2016 ► National meetings (e.g. Lunteren days) and other National Platforms Annual meeting 'Experimental Plant Sciences', Lunteren, NL 14-15 Apr 2014 Annual meeting 'Experimental Plant Sciences', Lunteren, NL 13-14 Apr 2015 Annual meeting 'Experimental Plant Sciences', Lunteren, NL 10-11 Apr 2017 ► Seminars (series), workshops and symposia EPS symposium: Omics advances for academia and industry 11 Dec 2014 EPS flying seminar: Whole-genome duplications, Yves van de Peer 02 Feb 2015 EPS flying seminar: Comparative & functional genomics of polyploidy, Jeff J. Doyle 12 May 2015 Biometris Symposium: From big data to biological solutions 18 Jun 2015 EPS flying seminar: Perianth evolution in Ranunculaceae, Sophie Nadot 20 May 2016 EPS seminar: Alternative splicing of a heat stress transcription factor, Sotirios Fragkostefanakis 02 Nov 2016 Seminar: Automated tetraploid genotype calling and its application to pedigree reconstruction in potato, Jeffrey Endelman 16 Nov 2016 Seminar: From QTLs to routine DNA-informed breeding: prospects, advances and needs, Cameron Peace 16 Nov 2016 Seminar: Genome-wide association analysis and prediction in tetraploid potato, Jeffrey Endelman 18 Nov 2016 EPS symposium 'WURomics-Technology-driven innovations for plant breeding', Wageningen, NL 15 Dec 2016 Seminar: Impact of ploidy level & genome evolution on the control of the frequency & distribution of recombination events in Brassicas, Alexander Pele 04 Jul 2017 Seminar: Breeding differently - The digital revolution: high-throughput phenotyping and genotyping, Tony Slater 17 Jul 2017 WEES seminar: From sex chromosomes to sex determination in Ledidoptera, Frantisek Marec 25 Oct 2017 ► Seminar plus ► International symposia and congresses EUCARPIA section Biometrics in Plant Breeding, Wageningen NL 09-11 Sep 2015 2nd International graduate conference Nanjing, China 27-30 Oct 2015 Plant and Animal Genome XXIV, San Diego CA. 09-13 Jan 2016 ► Presentations
304 Talks: Polyploids consortium meeting, Wageningen, NL 22 Jan 2015 B-WISE bioinformatics seminar, Wageningen, NL 07 Apr 2015 Polyploids consortium meeting, Wageningen, NL 25 Jun 2015 EUCARPIA Biometrics section in Plant Breeding 2015, Wageningen, NL 11 Sep 2015 2nd International graduate conference Nanjing, China (invited speaker) 27 Oct 2015 Plant and Animal Genome XXIV, San Diego CA, USA 10 Jan 2016 Polyploids consortium meeting, Wageningen, NL 04 Feb 2016 BioSS General Meeting, James Hutton Institute, Dundee, Scotland 26 Apr 2016 Plant meets Animal, Wageningen, NL 22 Jun 2016 EPS Theme 4 symposium, Wageningen, NL 16 Dec 2016 AWL Lunteren 2017 11 Apr 2017 Ernst van der Ende visits Plant Breeding, Wageningen, NL (flash presentation) 08 May 2017 Dümmen Orange B.V., De Lier, Netherlands (invited speaker) 01 Jun 2017 Polyploids consortium meeting, Wageningen, NL 27 Jun 2017 Polyploids consortium meeting, Wageningen, NL 29 Nov 2017 Poster: AWL Lunteren 2015 13-14 Apr 2015 ► IAB interview ► Excursions Visit to Enza Zaden (EPS trip) 12 Jun 2015 Subtotal Scientific Exposure 24.4 credits*
3) In-Depth Studies date ► EPS courses or other PhD courses Introduction to theory and implementation of genomic selection 13-17 Oct 2014 Bayesian statistics 20-21 Oct 2014 ► Journal club Member of literature discussion group Quantitative Genetics 2015-2018 ► Individual research training BioSS, James Hutton Institute, Invergowrie, Dundee, Scotland. 04 Apr-04 May 2016 Subtotal In-Depth Studies 6.5 credits*
4) Personal development date ► Skill training courses Competence Assessment (CA) 04 Nov 2014 EPS Introduction course 20 Jan 2015 Scientific Publishing 15 Oct 2015 Brain Training 20 Sep 2016 Reviewing a scientific paper (RSP) 22 Sep 2016 Teaching Outside of Academia Sep-Dec 2017 ► Organisation of PhD students day, course or conference EPS Get2Gether 2017 (Sponsorship, Abstract book, Company stalls) 2016-2017 EPS Get2Gether 2018 (Speakers, Poster) 2017-2018 ► Membership of Board, Committee or PhD council Mar 2016-Mar EPS Council member 2018 Subtotal Personal Development 9.6 credits*
TOTAL NUMBER OF CREDIT POINTS* 54.0
Herewith the Graduate School declares that the PhD candidate has complied with the educational requirements set by the Educational Committee of EPS which comprises of a minimum total of 30 ECTS credits
* A credit represents a normative study load of 28 hours of study.
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