Published May 6, 2016

Research

Models for Genome ´ Environment Interaction: Examples in Livestock

Ben J. Hayes,* Hans D. Daetwyler, and Mike E. Goddard

B.J. Hayes, and H.D. Daetwyler, AgriBio, Centre for AgriBioscience, Abstract Biosciences Research, DEDJTR, Victoria, Australia and Biosciences In livestock, ´ environment interaction Research Centre, La Trobe Univ., Victoria, Australia; M.E. Goddard, (G ´ E) has been widely investigated, with geno- Melbourne School of Land and Environment, Univ. of Melbourne, type defined at the level of subspecies, breeds, Victoria, Australia. Received 28 July 2015. Accepted 1 Dec. 2015. individual animals within a breed (for example *Corresponding author ([email protected]). performance of offspring of elite sires across Abbreviations: BMSCC, bulk milk somatic cell count; G ´ E, geno- environments), and at single-nucle- type ´ environment interaction; GEBV, genomic estimated breeding otide polymorphisms (SNPs). Environments can value; SNP, single-nucleotide polymorphism. be described by category (e.g., tropical vs. tem- perate, high vs. low farm input levels, countries) and by continuous variables such as tempera- ture. To predict breeding values of genotypes in enotype ´ environment interactions in livestock have environments described by categories, multitrait Gbeen widely investigated. The genotypes compared have models with each category a different trait are included subspecies (Bos taurus vs. Bos indicus), breeds, individual used. The models are now being used to pre- animals within a breed and genotypes at SNPs. The environments dict genomic estimated breeding values (GEBV) have been described by category (e.g., tropical vs. temperate) and for different environments such as the value of by continuous variables such as temperature. A G ´ E is defined a bull’s genetics for his daughter’s milk produc- tion in different countries. The multitrait genomic to exist if the difference between genotypes depends on the model has also been used to enable reference environment in which it is measured. As in plant breeding, this populations to be merged across environments includes two different situations: the genotypes can change rank- and across countries, leading to more accurate ing between environments, or they can retain the same ranking GEBV. When the environment can be described but the differences can be larger in one environment than in the by a continuous variable, random regression other. These two different types of G ´ E have different impli- models have been used to predict response cations for the breeding program with the former being more of genotypes to the environment. For example, important. Therefore, the G ´ E is commonly analyzed as a mul- these models have been used to determine if tiple-trait situation in which the trait measured in the different there are SNP genotypes associated with less environments are treated as different but correlated traits. Then, sensitivity of milk production to increasing tem- the genetic correlation between the traits measures the degree of perature. In both livestock and plant breeding, reranking between the environments. The genetic correlations methods that use genomic information can bet- (r ) reported are reviewed below but, in general, r < 0.8 usually ter cope with a reduced degree of replication of g g individuals across environments, as it is actu- only occur if the environments are very different, for example, ally the that must be replicated across tropical vs. temperate. Genotype ´ environment interaction can environments. More accurate estimates of G ´ be incorporated into traditional calculation of estimated breeding E with the genomic approach may therefore be achievable than was possible in the past. Published in Crop Sci. 56:1–9 (2016). doi: 10.2135/cropsci2015.07.0451 © Crop Science Society of America | 5585 Guilford Rd., Madison, WI 53711 USA All rights reserved. crop science, vol. 56, september–october 2016 www.crops.org 1 values based on records of and pedigree. The Modeling Genotype ´ global analysis of dairy bulls, which is routinely performed Environment Interactions by Interbull (http://www.interbull.org), is an excellent To take account of G ´ E and to obtain GEBVs in different example, where , such as milk yield in differ- environments, two models have been used: multitrait models ent countries, are treated as different traits. This is possible and reaction norm (also called random regression) models. because, for dairy cattle breeding, a small group of elite sires are very widely used across the globe, and in contrast Multitrait Models to plant breeding programs, there is very little introgres- Multitrait models treat performance of a genotype for a sion to generate new genetic diversity, that is, essentially trait in different environments as different but potentially the same genotypes are evaluated again and again. correlated traits. The multitrait approach can handle a In most other livestock species, however, G ´ E are wide variety of definitions of environment. Example trait not routinely included in estimated breeding value calcu- definitions include the following: lations, that is, most analyses are based on phenotypic data from a limited range of environments and few animals Countries: performance of a genotype in different have offspring in very different environments. The use countries of SNP genotypes in the calculation of GEBV has the Farming systems: performance in high- and low-input potential to overcome this problem because GEBV could systems be calculated for many different environments based only on SNP genotype data. These analyses require that the Environment descriptors such as heat stress measured by SNP alleles have been observed in different environments, temperature, humidity, and altitude (e.g., performance at which is much more likely than individuals having off- high and low levels of descriptor) spring in multiple environments. Using GEBV for dif- The multitrait approach is also relatively straightfor- ferent environments could substantially increase selection ward to extend to genomic predictions that capture G ´ E, intensities in breeding programs; for example, dairy bulls as described below. from anywhere in the world could be screened for the For two environments (two traits), the multitrait model performance of their daughters in Australia. Note that if is as follows (e.g., Hayes et al., 2003; Mulder et al., 2004): nonadditive effects are important, it is not just SNP effects that must be observed in the different environ- éyg ù éI0 ùém ù é Z 0 ùé ù é e ù ê11 ú= ê úê 1 ú++ ê 1 úê 1 ú ê 1 ú ments but the SNP genotype effects and SNP´ SNP ê ú ê úê ú ê úê ú ê ú ëyg2 û ë0I 22 ûëm û ë 0 Z22 ûëû ëû e 2 genotypes in the case of . Genomic selection that incorporates G ´ E could also accelerate genetic gains in where y1 and y2 are trait records for genotypes in Envi- predicted future climates. ronment 1 and Environment 2, respectively, I1 and I2 are Properly accounting for G ´ E is important when ref- identity matrices, µ1 and µ2 are the means for Environment erence populations (used to derive SNP prediction equa- 1 and Environment 2, Z1 and Z2 are the design matrices tions) are merged with the aim of increasing the accuracy that relate breeding values with the response variables, g1 of the GEBV. This is of increasing interest, as very large and g2 are the breeding values for genotypes for Envi- reference populations are required to calculate accurate G ronment 1 and Environment 2, and e1 and e2 are vectors ´ E, and it may be difficult to assemble such large popula- of random residuals for Environment 1 and Environment tions in multiple environments. If these reference popu- éùe lations have phenotypes measured in different environ- 2. The random residuals are assumed êú1 ~ N ( 0,IRÄ ) , êúe ments, then not accounting for G ´ E can reduce the ëû2 éùss2 accuracy of GEBV from the combined reference popula- where R = êúe1 e12 , the residual variance–covariance êúss2 tions and cause bias (Haile-Mariam et al., 2015). ëûêúe12 e2 In this review, we discuss models of G ´ E includ- matrix for Environment 1 and Environment 2, I is a geno- ing models used to derive GEBV for different environ- type ´ genotype identity matrix, and ⊗ is the Kronecker ments. We then give some examples of G ´ E in livestock product. Extension to more than two environments is including SNP by environment interactions. Finally, straightforward. inclusion of G ´ E to maximize progress from breeding When the multitrait approach to modeling G ´ E programs is discussed as well as similarities and contrasts is implemented in livestock, genotype is usually defined with accommodating G ´ E in plant breeding programs. as the individual animal. It is rare that animals have per- formance recorded in two or more different environ- ments; they may remain on the one farm throughout their life. The performance of an animal’s genetics can still be evaluated in multiple environments by modeling

2 www.crops.org crop science, vol. 56, september–october 2016 the genetic relationships between animals. For example, a • Farm input levels. Herd average production level dairy bull may have daughters in two or more environ- is often used as a surrogate for the level of feed- ments, and these daughters inherit half of the bull’s . ing. This approach has been used in beef cattle, These relationships can be modeled though the A matrix sheep, and dairy cattle (Calus et al., 2002; Fikse et (Henderson 1984), which describes the expected propor- al., 2003; McLaren et al., 2015; Hayes et al., 2003; tion of the genome that each pair of individuals share so Pegolo et al., 2011) that the distribution of breeding values is assumed to be • Farm disease level, for example, herd average levels éù2 of somatic cell count, an indicator of mastitis éùg1 ssg1 g12 êú N (0,ATÄ ), where T = êú, the genetic (Calus et al., 2006; Streit et al., 2013a). êúg êúss2 ëû2 ëûêúg12 g2 variance–covariance matrix for Environment 1 and Envi- The response of each genotype to change in the envi- ronment 2. The estimate of breeding values for individu- ronmental descriptor is modelled as a unique curve. For als for Environment 1 and Environment 2 are then instance, the breeding value of a single genotype (with and , respectively. The estimate of the genetic corre- genotype either an individual SNP or individual animal lation between performance in the two environments or a variety) in an environment with environmental

s¢g12 descriptor variable w, can be modelled as a polynomial: is (variance components can be estimated 22 ssgg12 2 g = S0 + wS1 + w S2 + … by software such as ASReml [Gilmour et al., 2006]).

This model can be extended to include data on SNP where S¢ = (S0 S1 S2) are regression coefficients, specific genotypes. The SNP information can be used to model to this genotype, which are treated as random variables genomic relationships among animals to obtain GEBV. If the with var(S) = C (for a model with intercept and slope, genomic relationship approach is taken, all that is required is the elements of the C matrix would be the variance of to replace A (the pedigree derived relationship matrix) with the intercepts, the variance of the slopes, and the cova- G, which are the relationships derived from the markers as riance between them). This can be done with random described by VanRaden (2008) or Yang et al. (2010): regression, where each genotype has its own intercept, slope, and potentially higher-order terms that describe the éùg trait response to increases in the environmental descrip- êú1 N(0,GTÄ ) êú tor (for more details on random regression see Jamrozik, ëûg2 and Schaeffer, 1997). In practice, only the intercept and The assumptions underlying this formulation are slope are usually considered (variance components associ- described in Appendix 1. Then gˆ1 and gˆ2 from fitting the ated with higher order terms such as quadratic and cubic model are the GEBV for animals for Environment 1 and coefficients can be difficult to estimate). Reaction norm Environment 2. models have been applied with animals as genotypes (e.g., One interesting feature of the genomic implementa- Fikse et al., 2003; Ravagnolo and Misztal 2000) and also tion of the multitrait model is that it is not necessary to to estimate SNP ´ environment interaction (e.g., Streit have close relatives (for example daughters of the same et al., 2013a; Hayes et al., 2009). The random regression bull) in different environments, as even the small coef- implementation of the reaction norm model (with inter- ficients of genomic relationship contribute to the estimate cept and slope) is as follows. of an individual’s breeding value in each environment. For For n individuals whose breeding value are stored in example, in human genetics, this multiple-trait approach (n1) a vector g, the model using pedigree becomes g = Ws, 2 has been used with individuals that only share small pro- where W = (W0, W1), a n ´ 2n matrix, where {}wijk= w j portions of their genome (Maier et al., 2015). if j = k, and 0 otherwise, S¢= ()SS01 ¢¢ (a 1 ´ 2n) vector,

where Si is a n ´ 1 vector of breeding values for trait Si (I Reaction Norm Models = 0 is the intercept and i = 1 is the slope). The variance of If the environment is better described by a continuous éùss2 variable than by a series of categories, reaction norm S is (S) =Ä AC, where C = êúS0 S01 and A is the rela- êúss2 models are an alternative to multitrait models. Examples ëûêúS10 S1 of continuous environmental descriptors are as follows: tionship matrix derived from pedigree as described above. Thus the reaction norm model is a multitrait model • Temperature humidity indices, as a measure of in which the traits are random regression coefficients (for heat stress (Ravagnolo and Misztal 2000; Hayes et example for the intercept, and linear slope). al., 2003; Haile-Mariam et al., 2008; Hammami et al., 2015)

crop science, vol. 56, september–october 2016 www.crops.org 3 Given some assumptions (Appendix 2), GEBV for the Reaction Norm Models slope and intercept can be predicted by replacing A with A good example of the reaction norm approach to model G, . genotype ´ farm disease level interactions was pre- sented by Calus et al. (2006). Those authors used bulk Examples of GENOTYPE ´ milk somatic cell count (BMSCC) as the environmental descriptor. Bulk milk somatic cell count is the number of ENVIRONMENT INTERACTIONS somatic cells that are present in milk samples pooled across in Livestock the cows in a herd: high levels of BMSCC indicate mastitis Multiple-Trait Models is prevalent in the herd, and low levels of BMSCC indicate A good example of implementation of the multiple-trait low incidence of mastitis in the herd. The practical ques- approach to estimate breeding values in different envi- tion is whether sires can be identified that have daugh- ronments was growth of Angus cattle at high and low ters with low somatic cell counts even when mastitis is altitudes (Williams et al., 2012). At high altitudes, cattle prevalent in the rest of the herd (high BMSCC). The data can suffer high mountain disease, also called brisket dis- set included 344,029 test-day records (somatic cell count ease, which is heart failure as a result of hypoxic pulmo- records) of 24,125 cows sired by 182 bulls in 461 herds. nary hypertension. This can severely compromise growth. The model included random regressions for each sire on Williams et al. (2012) assessed growth rate (weaning herd test-day BMSCC. The genetic correlation was 0.72 weights) of more than 77,000 cattle on farms in Colorado between somatic cell counts at low and at high BMSCC. at a range of altitudes. Two traits were defined: growth at This is considerably <1, suggesting sires rerank consider- high altitude and growth at low altitude. Relationships ably for their performance (in this case somatic cell counts between animals were derived from pedigree record. The of their daughters) in low and high disease incidence herds. genetic correlation for growth at high and low altitudes The reaction norm approach has also been used to was 0.74. This indicates significant reranking between derive GEBV for heat tolerance. Nguyen et al. (2015) sires will occur between high- and low-altitude farms, defined heat tolerance of a cow as the drop in milk pro- and the genetic evaluation for growth should include the duction with increasing temperature and humidity (com- genotype ´ altitude interaction. bined in a temperature and humidity index, which predicts The multitrait genomic approach to accommodate G heat stress). Milk production data was recorded at least five ´ E was exemplified by Haile-Mariam et al. (2015). In this times during each cow’s lactation for 343,016 cows, and this study performance of dairy cattle in Australia were treated data was combined with daily temperature and humidity as one trait and performance in the Netherlands and New measurements from weather stations closest to the tested Zealand another trait. Milk yields, protein yields, fertility, herds for 10 yr of data. Tolerance to heat stress was then and longevity were investigated with this approach. The estimated for each cow using random regression (intercept aim of the study was actually to improve the accuracy of and slope) to model the rate of decline in production with the Australian GEBVs by increasing the size of the refer- increasing temperature humidity index accumulated over ence population by including information on genotype the 4 d before and the day of milking for milk yield, fat performance from other countries. There were 5720 bulls yield, and protein yield. The slopes from this model were with daughter records in one, two, or all three countries, used to define daughter averages (daughter trait deviations and these bulls were genotyped for 36,000 SNP markers. [DTD] for their sires, of which, 2735 Holsteins and 710 The genomic relationship matrix was constructed among Jersey had genotypes [either real or imputed]) for 632,003 the bull from the SNP genotypes as described by Yang SNP. Genomic best linear unbiased prediction was used to et al. (2010). As a result of implementing the multitrait calculate GEBV for heat tolerance. The reference popula- model described above, GEBVs were produced for Aus- tion consisted of either genotyped sires only (2300 Holstein tralian and the other country environments. Including and 575 Jersey sires) or genotyped sires and cows where the information from the other countries improved the accu- cows had genotypes (2191 Holstein and 1190 Jersey). The racy of genomic breeding values in Australia (as demon- reminder of the sires (435 Holsteins and 135 Jerseys) were strated in a validation population) by up to 10% for milk used as a validation set, and accuracy of GEBV for heat yield. The genetic correlation between performance in tolerance was calculated as the correlation of GEBV and the different countries was as low as 0.72 for longevity DTD divided by the accuracy of the DTD for these sires. and 0.8 for protein yield. The fact that these correlations The accuracy of GEBV for heat tolerance was 0.46 for the are significantly <1 indicates that significant reranking Holstein validation sires and 0.49 for the Jersey validation of sires occurs between the countries, and breeding pro- sires. These accuracies are moderate to high, suggesting grams specific to each country are justified. genomic selection for heat tolerance could be included in dairy cattle breeding programs to improve production in environments where heat stress occurs.

4 www.crops.org crop science, vol. 56, september–october 2016 Fig. 1. Example of reaction norms for single-nucleotide polymorphism alleles. Allele A is associated with the highest milk production at low levels of temperature and humidity, while at very high levels of temperature and humidity, allele C performs better.

Hayes et al. (2009) used a similar approach to investi- Overall Extent of Genotype ´ Environment gate individual SNP marker by temperature and humid- Interaction in Livestock ity index interaction. In this case random regression was The extent of G ´ E in livestock depends very much on used to model the response of each SNP allele to increas- the genotypes involved, the classification of environment, ing temperature humidity index (Fig. 1). The model was the trait, and the statistical method used to estimate G ´ fitted for 39,048 SNPs one a time. The SNPs associated E (Table 1). As might be expected, G ´ E is largest when with response of milk production to the temperature performance for very different environments is compared humidity index were identified on chromosome 9 and 29, (e.g., tropical vs. temperate performance) and very dif- and these were validated in two independent populations, ferent genotypes are compared (Bos taurus vs. Bos indicus). one a different breed of cattle. Within breeds and within countries, the magnitude of G ´ Another interesting example of SNP by environment E is usually much smaller. These conclusions are similar to interaction in livestock is the effect of myostatin genotype those of Burrow (2012) in a review of the importance of G on body temperature during heat and cold stress (Howard ´ E in tropical beef breeding systems. The extent of G ´ E et al., 2013). Mutations in the myostatin can result also appears to be larger for traits more closely related to fit- in the double-muscling phenotype in Belgian Blue, Pied- ness, for example, for fertility (Haile-Mariam et al., 2008). montese, and other breeds of cattle. In this study, animals that were homozygous wild-type, heterozygous, or homo- Accounting for Genotype ´ Environment zygous for the Piedmontese-derived myostatin mutation Interactions in Livestock Breeding Programs had rectal temperatures collected during periods of heat An obvious question that stems from Table 1 is what level and cold stress. The results indicated a G ´ E did exist for of G ´ E justifies different breeding programs or differ- the myostatin mutation; the additive effect was +0.10°C ent genomic evaluations? Robertson (1959) proposed that during heat stress and the estimate was −0.12°C a correlation of performance between environments of in rectal temperature. During winter stress events, the above 0.8 would indicate that there would be minimum additive estimate was 0.10°C and dominance estimate was reranking of selection candidates in the two environ- 0.054°C. All these effects were significantP ( < 0.05). The ments; correlations below 0.8 would indicate considerable study of Howard et al. (2013) illustrates a SNP G ´ E reranking and would justify separate breeding programs. exists for the myostatin mutation, and that heterozygous Mulder and Bijma (2005) reached a similar conclusion; animals were more robust to environmental extremes in those authors considered two environments: a selection comparison with either homozygous genotype. environment and a commercial production environment, with a genetic correlation between performance in the two environments. They concluded that when this correlation

crop science, vol. 56, september–october 2016 www.crops.org 5 Table 1. Some examples of genotype ´ environment (G ´ E) and genome ´ environment interaction in livestock.

Extent of G ´ E and genetic correlation Statistical between extreme Species Environment Trait Genotype model environments† Reference Dairy cattle Farming system Milk production Animal, Holstein Correlation of 0.89 Kearney et al. 2004 (grazing vs. confinement) breed estimated breeding value from two environments Beef cattle Pasture or feedlot Final weight, Animal, Nellore Multitrait 0.75, 0.49, 0.89 Raidan et al. 2015 average daily breed gain and scrotal circumference Beef cattle Climatic zone: dry tropic, Yearling Animal, Braunvieh Multitrait 0.23 (wet tropic, Saavedra-Jiménez wet tropic, temperate weight cattle temperate) to 0.99 et al., 2013 climates in Mexico (dry tropic, temperate) Dairy cattle Robotic milking vs. Milk yield, somatic Animal, Holstein Multitrait 0.93, 0.79 Mulder et al., 2004 conventional milking cell score breed Dairy cattle Country (Australia, Canada, Milk yield Animal, Guernsey Multitrait 0.78 to 0.90 Fikse et al., 2003 United States, South Africa) Pigs Conventional vs. Growth, Breed Multitrait Except weight gain, Brandt et al., 2010 organic farming system carcass quality no major shift of the ranking order within environment between genotypes. Beef cattle Farm input (herd Body weight Animal, Nellore Random 0.09–0.74 Pegolo et al., 2011 weight gain) breed regression Dairy cattle Temperature and Milk yield Animal, Holstein Random >0.90 Brügemann et al., humidity breed regression 2011 Dairy cattle Country (Luxembourg, Milk production Animal, Holstein Random 0.50 Hammami et al., Tunisia) breed regression 2009 Dairy cattle Temperature and Milk yield, udder Animal, Holstein Random 0.80, 0.64, 0.67 Hammami et al., humidity health, and fatty breed regression (depending on fatty acid) 2015 acid profile in milk Dairy Cattle Temperature and Fertility Animal, Holstein Random 0.79 Haile-Mariam et al., humidity regression 2008 Dairy cattle Farm input level (herd Milk yield SNP‡ genotype Random 28 SNP validated Streit et al., 2013b production level as a proxy regression for slope for level of feeding) Dairy cattle Farm disease level (bulk Milk yield SNP genotype Random 11 SNP validated Streit et al., 2013a milk somatic cell count regression for slope Dairy cattle Farm input level (herd Milk yield SNP genotype Random 27 significant SNP Lillehammer et al., production level as a proxy regression for slope 2009 for level of feeding) Dairy cattle Temperature and Milk yield SNP genotype Random SNP on chromosome 29 Hayes et al., 2009 humidity regression validated for slope Sheep Farm environment, Weight, ultrasound Animal, Random McLaren et al., expressed as principal back-fat, muscle Texel breed regression 2015 component loadings depths after clustering on farm characteristics Sheep Farm environment Lamb weaning Animal, Norwegian Multitrait 0.82 Steinheim et al., weight white and Spel 2008 breeds Sheep Farm environment Fecal egg count and Animal, Merino Multitrait, random Significant but Pollott and Greeff, production breed regression small G ´ E 2004 Sheep Farm environment Growth Animal, Santa Multitrait, random >0.70 Santana et al., 2013 Ines breed regression † For random regression models, these correlations are typically between performance at the fifth and 95th percentile of the environment descriptor. ‡ SNP, single-nucleotide polymorphism. was lower than 0.8, selection based on progeny tested in between countries and between tropical and temperate the commercial production environment resulted in more zones within a country where correlations of performance gain than selection based on sibs of selection candidates can be considerably below 0.8. For example, milk pro- measured in the selection environment. Within a coun- duction in Luxemburg and Tunisia has a genetic correla- try, particularly countries with temperate environments, tion of 0.5 (Hammami et al., 2009). For a tropical dairy the genetic correlation between environmental extremes system in Kenya, Okeno et al. (2010) compared genetic rarely falls below 0.8 (Table 1). This is in contrast to progress from a local progeny testing with importation of

6 www.crops.org crop science, vol. 56, september–october 2016 semen from temperate countries and concluded importa- approach. The of body weight loss in harsh tion was the superior strategy only if the genetic correla- nutritional conditions was 0.05 to 0.16, and the genetic tion between milk production in Kenya and the temperate correlation between body weight gain in good conditions counties was greater than 0.7 despite the fact that progeny and body weight loss in poor conditions was negative but test schemes were much larger in the temperate countries. low. This led the authors to conclude that sheep can be Between Australia and North America, genetic corre- bred to be more tolerant to variation in feed supply. lations for performance of Holstein cattle are 0.8 or below (http://www.interbull.org). The opportunity cost of not Parallels and Differences Between accounting for G ´ E can be quite large. It has been esti- Genotype ´ Environment Interactions mated that if breeding programs for Australian dairy cattle in Livestock and Plants were based purely on breeding values calculated using North One reason why G ´ E is potentially more crucial for American information, $12 million yr−1 in genetic progress plants is that livestock can, to some extent, move to avoid could be lost (J.E. Pryce, personal communication, 2015). or mitigate stressors (and in some cases are kept in con- One option for using genotypes that are genetically trolled environments, such as barns, where temperatures superior in one environment but are not well adapted to can be to some extent increased or increased to avoid the target environment, would be to introgress alleles for stress), whereas plants are obviously less able to do so. A adaptation in the target environment. This already occurs further point of differentiation is that in livestock, the for tropical dairy production in Brazil, where high-per- focus in estimation of G ´ E has been largely on additive formance Holstein cattle are crossed to adapted Bos indicus effects to generate selection gains, whereas in plants G ´ cattle to form a composite called Girolando. Most of the E for dominance and espistatic effects can be exploited milk production in Brazil is now from Girolando cows more easily through hybrids or clonal propagation. In (da Costa et al., 2015). More targeted introgression has terms of modeling G ´ E , the approaches outlined above also been demonstrated; Dikmen et al. (2014) introgressed can and have also been applied in plants (e.g., Burgueño et an allele at SLICK hair locus (a mutation that changes al., 2011; Jarquín et al., 2014). One key point is that in the the hair follicle and thermotolerance) from Senepol cattle past, quantification of G ´ E without pedigrees required into Holsteins. There are relatively few examples of this each genotype to be grown in all environments. Provided in livestock; however, as long generation time means that genomic markers (or pedigree) are available, the related- introgression is very slow. Genome editing for adaption ness among lines can be modelled using matrices G or A, alleles would be a potentially more rapid alternative. and as in animal studies, G ´ E methods that use genomic There is increasing interest in livestock in breeding for information can better cope with a reduced degree of “”. While this is a vague term, one interpreta- replication of individuals across environments (in the tion is breeding for animals that produce well across a range genomic approach it is actually the alleles that must be of environments. Reaction norm models directly identify replicated across environments). More accurate estimates “robust” genotypes– these are the genotypes with low slope of G ´ E with the genomic approach may therefore be values in response to the environmental indicator, whereas achievable than was possible in the past. sensitive genotypes have steep slopes. Note that in plant breeding the equivalent term for robustness would be sta- Conclusion bility across environments. Lillehammer et al. (2009) iden- In livestock, G ´ E is considerable when genotype is tified SNP genotypes associated with improved milk pro- defined at the level of subspecies Bos( taurus vs. Bos indi- duction in dairy cows that were robust to the herd average cus) and environments are described by different climatic level of production, that is, animals with these genotypes zones (tropical vs. temperate) but less for individuals within had improved production at low and high levels of feed- a breed and within (most) countries. Models that include G ing (high intercept and low slope). Streit et al. (2013a) used ´ E, particularly the multitrait model, are now being used a similar approach to identify SNPs that could be used to to enable the reference populations used for genomic selec- select for robustness of milk production to the average level tion to be merged across environments and across countries, of disease (mastitis) for the farm (e.g., animals with these leading to higher accuracy of GEBV. In either multitrait or SNP genotypes produced well regardless of whether the reaction norm models, using genomic information can lead farm had a high disease load or a low disease load). to more accurate estimates of G ´ E, as it is more likely As another example of using genotype ´ environ- that SNP genotypes are well replicated across environments ment models to enable breeding for robustness was Rose than individual animals or their close relatives. et al. (2013), where the aim was to identify sheep that lost less body weight in harsh nutritional conditions. Rose et al. (2013) used both a multitrait approach (body weight loss defined as a phenotype) and the random regression

crop science, vol. 56, september–october 2016 www.crops.org 7 Appendix 1. Prediction of References MultiTrait Genomic Estimated Brandt, H., D.N. Werner, U. Baulain, W. Brade, and F. Weissmann. 2010. Genotype–environment interactions for growth and car- Breeding Values cass traits in different pig breeds kept under conventional and Define breeding values as g = Uq, where U is a matrix con- organic production systems. Animal 4:535–544. doi:10.1017/ taining the genotypes of animals at all the SNPs (n animals S1751731109991509 ´ m, where m is the number of SNP coded as the number Brügemann, K., E. Gernand, U.U. von Borstel, and S. König. 2011. of copies of the second allele), and q is the effect of each Genetic analyses of protein yield in dairy cows applying ran- SNP on the trait, is a linear model for the breeding value g. dom regression models with time-dependent and temperature humidity-dependent covariates. J. Dairy Sci. 94:4129–4139. The SNP effects q( ) are treated as random effects sampled ´ doi:10.3168/jds.2010-4063 from a distribution; for instance, a normal distribution q Burgueño, J., G. de los Campos, K. Weigel, and J. Crossa. 2011. ~N(0,D). The D matrix is usually diagonal, implying that Genomic prediction of breeding values when modeling gen- the effect of different SNPs are independent of each other, otype ´ environment interaction using pedigree and dense for example, for the ith SNP in Environment 1, , molecular markers. Crop Sci. 52:707–719. doi:10.2135/crop- where is the variance associated with the ith SNP in sci2011.06.0299 Environment 1. The covariance of the SNP effects in Envi- Burrow, H.M. 2012. Importance of adaptation and genotype ´ ronment 1 and 2 is D = s . Then for the multitrait model environment interactions in tropical beef breeding systems. ij ij,12 Animal 6:729–740. doi:10.1017/S175173111200002X described in the text, the variance of breeding values are as Calus, M.P., A.F. Groen and G. de Jong. 2002. Genotype ´ envi- follows: ronment interaction for protein yield in Dutch dairy cattle as quantified by different models. J. Dairy Sci. 85:3115–3123. éùg1 éUD11 U'' UD12 U ù doi:10.3168/jds.S0022-0302(02)74399-3 var êú= ê ú. êú ê ú Calus, M.P., L.L. Janss, and R.F. Veerkamp. 2006. Genotype by ëûg2 ëUD12 U'' UD22 U û environment interaction for somatic cell score across bulk milk If we assume that all SNP effects for each trait are somatic cell count and days in milk. J. Dairy Sci. 89:4846– 2 4857. doi:10.3168/jds.S0022-0302(06)72533-4 drawn from the same normal distribution (q ~ N(0, Is1 ), éùg da Costa, A.N., J.V. Feitosa, P.A. Montezuma, Jr., P.T. de Souza, then var êú1 can be written as . That is, the and A.A. de Araújo. 2015. Rectal temperatures, respiratory êúg ëû2 rates, production, and reproduction performances of crossbred expected relationship matrix A is replaced by G, the real- Girolando cows under heat stress in northeastern Brazil. Int. ized relationship among individuals calculated from the J. Biometeorol. 59:1647–1653. doi:10.1007/s00484-015-0971-4 markers (G = UU¢/m) is calculated for example. Dikmen, S., F.A. Khan, H.J. Huson, T.S. Sonstegard, J.I. Moss, G.E. Dahl, and P.J. Hansen. 2014. The SLICK hair locus derived éùg from Senepol cattle confers thermotolerance to intensively êú1 N(0,GTÄ ) . êú managed lactating Holstein cows. J. Dairy Sci. 97:5508–5520. ëûg2 doi:10.3168/jds.2014-8087 Fikse, W.F., R. Rekaya, and K.A. Weigel. 2003. Genotype ´ Appendix 2. Prediction of Genomic environment interaction for milk production in Guernsey Estimated Breeding Values for cattle. J. Dairy Sci. 86:1821–1827. doi:10.3168/jds.S0022- 0302(03)73768-0 Reaction Norms Gilmour, A.R., B.J. Gogel, B.R. Cullis, and R. Thompson. 2006. If there are SNP genotypes U (an n ´ m matrix, where ASReml User Guide 2.0. VSN International Ltd., Hemel m is the number of SNP, and genotypes are coded as the Hempsted, UK. number of copies of the second allele), then the breed- Haile-Mariam, M., M.J. Carrick, and M.E. Goddard. 2008. Gen- otype by environment interaction for fertility, survival, and ing values for animals for trait 0 (the intercept) are S0 = Uq , where q is the effect of the SNP on the intercept, milk production traits in Australian dairy cattle. J. Dairy Sci. 0 0 91:4840–4853. doi:10.3168/jds.2008-1084 and var(q ) = D , a m ´ m diagonal matrix, and likewise 0 0 Haile-Mariam, M., J.E. Pryce, C. Schrooten, and B.J. Hayes. 2015. for the other traits. For the case with intercept and slope, Including overseas performance information in genomic evalu- cov(q0,q1) = D01, a diagonal matrix (m ´ m) of covariances ations of Australian dairy cattle. J. Dairy Sci. 98:3443–3459. among the SNP effects on the intercept and slope, and doi:10.3168/jds.2014-8785 éùUD U'' UD U Hammami, H., B. Rekik, H. Soyeurt, C. Bastin, E. Bay, J. Stoll, var S = êú00 01 . and N. Gengler. 2009. Accessing genotype by environment ( ) êú ëûUD10 U'' UD11 U interaction using within- and across-country test-day random If DI=s2 and DI=s2 then var(S) =Ä GC, where regression sire models. J. Anim. Breed. Genet. 126:366–377. ii i ij i doi:10.1111/j.1439-0388.2008.00794.x éùss2 Hammami, H.B., J. Vandenplas, M.L. Vanrobays, B. Rekik, C. Bas- C = êúSS0 01 , as above, and G = UU¢/m, or versions of êú2 tin, and N. Gengler. 2015. Genetic analysis of heat stress effects ëûêússSS10 1 on yield traits, udder health, and fatty acids of Walloon Holstein the genomic relationship matrix described for example by cows. J. Dairy Sci. 98:4956–4968. doi:10.3168/jds.2014-9148 VanRaden (2008) or Yang et al. (2010).

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