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Understanding the Relationship Between the Inbreeding Coefficient

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Understanding the Relationship Between the Inbreeding Coefficient Heredity (2004) 93, 255–265 & 2004 Nature Publishing Group All rights reserved 0018-067X/04 $30.00 www.nature.com/hdy Understanding the relationship between the inbreeding coefficient and multilocus heterozygosity: theoretical expectations and empirical data J Slate1, P David2, KG Dodds1, BA Veenvliet1, BC Glass1, TE Broad1,3 and JC McEwan1 1AgResearch, Invermay Agricultural Centre, Mosgiel, Private Bag 50034, New Zealand; 2Centre d’Ecologie Fonctionelle et Evolutive, Centre National de la Recherche Scientifique, 34293, Montpellier Cedex 5, France Geneticists have been interested in inbreeding and inbreed- locus heterozygosity. Multilocus heterozygosity was only ing depression since the time of Darwin. Two alternative weakly correlated with inbreeding coefficient, and hetero- approaches that can be used to measure how inbred an zygosity was not positively correlated between markers more individual is involve the use of pedigree records to estimate often than expected by chance. Inbreeding coefficient, but inbreeding coefficients or molecular markers to measure not multilocus heterozygosity, detected evidence of inbreed- multilocus heterozygosity. However, the relationship be- ing depression for morphological traits. The relevance of tween inbreeding coefficient and heterozygosity has only these findings to the causes of heterozygosity–fitness rarely been investigated. In this paper, a framework to predict correlations is discussed and predictions for other wild and the relationship between the two variables is presented. In captive populations are presented. addition, microsatellite genotypes at 138 loci spanning all 26 Heredity (2004) 93, 255–265. doi:10.1038/sj.hdy.6800485 autosomes of the sheep genome were used to investigate Published online 14 July 2004 the relationship between inbreeding coefficient and multi- Keywords: inbreeding; heterosis; heterozygosity; overdominance; identity disequilibrium Introduction produce individuals of known f, which are then compared to outbred individuals from the same popula- When related individuals mate, their offspring are tion. A similar approach is to use pedigree records to generally less viable, less fertile or smaller than the calculate f for all of the individuals in the population. population mean – a phenomenon known as inbreeding Inbreeding depression is then inferred by regressing depression. Consequently, inbreeding has been the focus phenotype (or log-transformed phenotype) on the of considerable attention in a number of areas of biology inbreeding coefficient (Morton et al, 1956; Lynch and including animal and crop production, human medicine, Walsh, 1998). conservation biology and the evolution of mating If inbreeding coefficients are unavailable, an alterna- systems (Thornhill, 1993; Hedrick and Kalinowski, tive approach is to examine the association between 2000; Keller and Waller, 2002). Inbreeding depression marker heterozygosity (typically measured at 5–10 loci) arises because inbreeding increases the probability that and phenotypic value. This approach, sometimes termed an individual will be (a) homozygous for segregating heterozygosity–fitness correlations (HFCS), originated deleterious recessive alleles and (b) homozygous at loci with the advent of soluble allozyme markers (Allendorf exhibiting overdominance (Falconer, 1989; Lynch and and Leary, 1986; Mitton, 1993; David, 1998). Initial Walsh, 1998). Deleterious recessive alleles are thought to investigations with allozymes sought to address whether be the major cause of inbreeding depression (Charles- genetic variation was maintained by drift or selection; worth and Charlesworth, 1999). in other words, did genotype at individual loci have a Inbreeding depression can be inferred in a number direct effect on fitness? However, in recent years, a of ways (Keller and Waller, 2002). The most straight- number of studies have reported significant relationships forward approaches utilise the inbreeding coefficient between multilocus heterozygosity (hereafter MLH) in f (Wright, 1922) – defined as the probability that noncoding DNA and fitness-related traits in wild two alleles at a locus are identical by descent (ibd). populations, with inbreeding depression usually re- For example, relatives can be deliberately mated to garded as the most likely explanation for the relationship (Coltman et al, 1999; Marshall and Spalton, 2000; Slate Correspondence: J Slate, Current address: Department of Animal and et al, 2000; Amos et al, 2001; Acevedo-Whitehouse et al, Plant Sciences, University of Sheffield, Western Bank S10 3TN, UK. 2003). This explanation is intuitively appealing as inbred E-mail: j.slate@sheffield.ac.uk individuals are expected to be relatively homozygous 3Current address: Australian Equine Genetics Research Centre (AEGRC), University of Queensland, St Lucia, Brisbane, QLD 4072, Australia throughout the genome. However, the inbreeding coeffi- Received 27 September 2002; accepted 18 November 2003; cient and MLH do not measure the same quantity. When published online 14 July 2004 two alleles at a locus are ibd, the genotype is said to be Inbreeding coefficient and heterozygosity J Slate et al 256 autozygous, otherwise the genotype is allozygous. Allozy- (ii) test this theoretical prediction with an extensive gous genotypes may be homozygous (identical by state) data set (590 individuals of known f, typed at up or heterozygous, but in the absence of recent mutation an to 138 microsatellites) from a domestic sheep autozygous genotype is always homozygous (Hartl and population. Clark, 1997). (iii) provide some predictions on the relationship be- Unfortunately, there are (at least) three possible tween f and MLH in several intensively studied explanations for HFCs (David, 1998; Hansson and populations, in order to determine how effectively Westerberg, 2002), only one of which requires inbreed- microsatellites can be used to infer inbreeding ing. The first is that some or all of the marker loci have a depression in wild populations. direct effect on fitness with heterozygous genotypes conferring the greatest fitness (ie the locus exhibits overdominance). This explanation can generally be Methods excluded for studies using microsatellite loci as they are usually nonfunctional. The second explanation is that The model the markers are in physical linkage with either over- It is assumed that the inbreeding level of an individual is dominant or dominant loci that influence fitness. If a characterised by a single f value determined by its marker and trait locus are in linkage disequilibrium, then pedigree. All loci are assumed to be equally affected by individuals that are heterozygous at the marker locus inbreeding. Note that estimates of f based on known will also tend to be heterozygous at the trait locus. This pedigrees may slightly differ from the true value of f,as explanation is often termed a local effect. A third founders are assumed to have an f of zero. However, explanation is that the heterozygosity at marker loci provided the pedigrees are correct and several genera- reflects heterozygosity at unlinked trait loci. Such an tions (three or more) deep, they should enable good association is only expected to arise in populations that estimates of true f. The distribution of f has probability exhibit variance in inbreeding and is sometimes termed a density function p(f ). general effect or identity disequilibrium (Weir and Let hi be the heterozygosity (0 for a homozygote and 1 Cockerham, 1973). It is this explanation that is invoked for a heterozygote at marker locus i). The expected when it is claimed that an HFC indicates inbreeding heterozygosity E(h ) at locus i is h (1Àf ) for a given f, depression. Note that the first two explanations do not i 0,i where h0,i is the genetic diversity at locus i, or the require inbreeding. Spurious HFCs can also arise when expected heterozygosity in the absence of inbreeding. individuals are sampled from several populations that It is assumed that any correlation among hi at exhibit between-population variation in both heterozyg- different loci across individuals only arises due to osity and nongenetic (eg environmental) components of within-population variation in f. In other words, no trait variance. In other words, the HFC is an artefact of correlation will be expected in individuals that share population structure. the same value of f. This is usually true for unlinked Given that f and MLH are popular metrics for inferring loci. Note that 96% of locus pairs are unlinked in the inbreeding depression, it is surprising that the relation- Coopworth sheep data set presented in this study, with ship between the two has only rarely been investigated only 0.12% of locus pairs located within 10 cM of each theoretically (Bierne et al, 2000) or empirically (Hedrick other. et al, 2001; Curik et al, 2003). Further investigation of the The term H refers to standardised MLH, calculated as relationship would not only help determine when MLH the proportion of typed loci at which an individual was can be used as a reliable alternative to f, but would also heterozygous divided by the population mean hetero- help to ascertain the genetic basis of HFCs (Hansson and zygosity of those typed loci. This standardisation was Westerberg, 2002). Indeed, most of the available HFC initially used by Coltman et al (1999) in a study of Soay theory predicts that MLH and fitness, under the sheep, where individuals had been typed at different inbreeding hypothesis, should only correlate as a subsets of the same loci. The standardisation
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