Published May 6, 2016
Research
Models for Genome ´ Environment
Interaction: Examples in Livestock
Ben J. Hayes,* Hans D. Daetwyler, and Mike E. Goddard
Abstract
In livestock, genotype ´ environment interaction
(G ´ E) has been widely investigated, with genotype defined at the level of subspecies, breeds,
individual animals within a breed (for example
performance of offspring of elite sires across
environments), and genotypes at single-nucleotide polymorphisms (SNPs). Environments can
be described by category (e.g., tropical vs. temperate, high vs. low farm input levels, countries)
and by continuous variables such as temperature. To predict breeding values of genotypes in
environments described by categories, multitrait
models with each category a different trait are
used. The models are now being used to predict genomic estimated breeding values (GEBV)
for different environments such as the value of
a bull’s genetics for his daughter’s milk production in different countries. The multitrait genomic
model has also been used to enable reference
populations to be merged across environments
and across countries, leading to more accurate
GEBV. When the environment can be described
by a continuous variable, random regression
models have been used to predict response
of genotypes to the environment. For example,
these models have been used to determine if
there are SNP genotypes associated with less
sensitivity of milk production to increasing temperature. In both livestock and plant breeding,
methods that use genomic information can better cope with a reduced degree of replication of
individuals across environments, as it is actually the alleles that must be replicated across
environments. More accurate estimates of G ´
E with the genomic approach may therefore be
achievable than was possible in the past.
B.J. Hayes, and H.D. Daetwyler, AgriBio, Centre for AgriBioscience,
Biosciences Research, DEDJTR, Victoria, Australia and Biosciences
Research Centre, La Trobe Univ., Victoria, Australia; M.E. Goddard,
Melbourne School of Land and Environment, Univ. of Melbourne,
Victoria, Australia. Received 28 July 2015. Accepted 1 Dec. 2015.
*Corresponding author ([email protected]).
Abbreviations: BMSCC, bulk milk somatic cell count; G ´ E, genotype ´ environment interaction; GEBV, genomic estimated breeding
value; SNP, single-nucleotide polymorphism.
G
enotype ´ environment interactions in livestock have
been widely investigated. The genotypes compared have
included subspecies (Bos taurus vs. Bos indicus), breeds, individual
animals within a breed and genotypes at SNPs. The environments
have been described by category (e.g., tropical vs. temperate) and
by continuous variables such as temperature. A G ´ E is defined
to exist if the difference between genotypes depends on the
environment in which it is measured. As in plant breeding, this
includes two different situations: the genotypes can change ranking between environments, or they can retain the same ranking
but the differences can be larger in one environment than in the
other. These two different types of G ´ E have different implications for the breeding program with the former being more
important. Therefore, the G ´ E is commonly analyzed as a multiple-trait situation in which the trait measured in the different
environments are treated as different but correlated traits. Then,
the genetic correlation between the traits measures the degree of
reranking between the environments. The genetic correlations
(rg) reported are reviewed below but, in general, rg < 0.8 usually
only occur if the environments are very different, for example,
tropical vs. temperate. Genotype ´ environment interaction can
be incorporated into traditional calculation of estimated breeding
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.org1
values based on records of phenotype and pedigree. The
global analysis of dairy bulls, which is routinely performed
by Interbull (http://www.interbull.org), is an excellent
example, where phenotypes, such as milk yield in different countries, are treated as different traits. This is possible
because, for dairy cattle breeding, a small group of elite
sires are very widely used across the globe, and in contrast
to plant breeding programs, there is very little introgression to generate new genetic diversity, that is, essentially
the same genotypes are evaluated again and again.
In most other livestock species, however, G ´ E are
not routinely included in estimated breeding value calculations, that is, most analyses are based on phenotypic data
from a limited range of environments and few animals
have offspring in very different environments. The use
of SNP genotypes in the calculation of GEBV has the
potential to overcome this problem because GEBV could
be calculated for many different environments based only
on SNP genotype data. These analyses require that the
SNP alleles have been observed in different environments,
which is much more likely than individuals having offspring in multiple environments. Using GEBV for different environments could substantially increase selection
intensities in breeding programs; for example, dairy bulls
from anywhere in the world could be screened for the
performance of their daughters in Australia. Note that if
nonadditive effects are important, it is not just SNP allele
effects that must be observed in the different environments but the SNP genotype effects and SNP ´ SNP
genotypes in the case of epistasis. Genomic selection that
incorporates G ´ E could also accelerate genetic gains in
predicted future climates.
Properly accounting for G ´ E is important when reference populations (used to derive SNP prediction equations) are merged with the aim of increasing the accuracy
of the GEBV. This is of increasing interest, as very large
reference populations are required to calculate accurate G
´ E, and it may be difficult to assemble such large populations in multiple environments. If these reference populations have phenotypes measured in different environments, then not accounting for G ´ E can reduce the
accuracy of GEBV from the combined reference populations and cause bias (Haile-Mariam et al., 2015).
In this review, we discuss models of G ´ E including models used to derive GEBV for different environments. We then give some examples of G ´ E in livestock
including SNP by environment interactions. Finally,
inclusion of G ´ E to maximize progress from breeding
programs is discussed as well as similarities and contrasts
with accommodating G ´ E in plant breeding programs.
2
Modeling Genotype ´
Environment Interactions
To take account of G ´ E and to obtain GEBVs in different
environments, two models have been used: multitrait models
and reaction norm (also called random regression) models.
Multitrait Models
Multitrait models treat performance of a genotype for a
trait in different environments as different but potentially
correlated traits. The multitrait approach can handle a
wide variety of definitions of environment. Example trait
definitions include the following:
Countries: performance of a genotype in different
countries
Farming systems: performance in high- and low-input
systems
Environment descriptors such as heat stress measured by
temperature, humidity, and altitude (e.g., performance at
high and low levels of descriptor)
The multitrait approach is also relatively straightforward to extend to genomic predictions that capture G ´ E,
as described below.
For two environments (two traits), the multitrait model
is as follows (e.g., Hayes et al., 2003; Mulder et al., 2004):
é y1 ù é I1
ê ú =ê
ê y2 ú ê 0
ë û ë
0 ù é m1 ù éZ1 0 ù é g1 ù é e1 ù
úê ú+ê
úê ú+ê ú
I 2 úû êëm 2 úû êë 0 Z2 úû êë g2 úû êëe 2 ûú
where y1 and y2 are trait records for genotypes in Environment 1 and Environment 2, respectively, I1 and I 2 are
identity matrices, µ1 and µ 2 are the means for Environment
1 and Environment 2, Z1 and Z2 are the design matrices
that relate breeding values with the response variables, g1
and g 2 are the breeding values for genotypes for Environment 1 and Environment 2, and e1 and e2 are vectors
of random residuals for Environment 1 and Environment
ée ù
2. The random residuals are assumed êê 1 úú ~ N (0, I Ä R ) ,
ëe 2 û
é s2 s ù
e1
e12
ú , the residual variance–covariance
where R = êê
2 ú
ëêse12
se2 ûú
matrix for Environment 1 and Environment 2, I is a genotype ´ genotype identity matrix, and ⊗ is the Kronecker
product. Extension to more than two environments is
straightforward.
When the multitrait approach to modeling G ´ E
is implemented in livestock, genotype is usually defined
as the individual animal. It is rare that animals have performance recorded in two or more different environments; 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
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crop science, vol. 56, september– october 2016
the genetic relationships between animals. For example, a
dairy bull may have daughters in two or more environments, and these daughters inherit half of the bull’s genes.
These relationships can be modeled though the A matrix
(Henderson 1984), which describes the expected proportion of the genome that each pair of individuals share so
that the distribution of breeding values is assumed to be
é s2
é g1 ù
ê ú  N (0, A Ä T) , where T = ê g1
ês
ê g2 ú
êë g12
ë û
sg12 ùú
, the genetic
s2g 2 úûú
variance–covariance matrix for Environment 1 and Environment 2. The estimate of breeding values for individuals for Environment 1 and Environment 2 are then
and , respectively. The estimate of the genetic correlation between performance in the two environments
is
s¢g12

2 
2
s
g1 s g 2
• Farm input levels. Herd average production level
is often used as a surrogate for the level of feeding. This approach has been used in beef cattle,
sheep, and dairy cattle (Calus et al., 2002; Fikse et
al., 2003; McLaren et al., 2015; Hayes et al., 2003;
Pegolo et al., 2011)
• Farm disease level, for example, herd average levels
of somatic cell count, an indicator of mastitis
(Calus et al., 2006; Streit et al., 2013a).
The response of each genotype to change in the environmental descriptor is modelled as a unique curve. For
instance, the breeding value of a single genotype (with
genotype either an individual SNP or individual animal
or a variety) in an environment with environmental
descriptor variable w, can be modelled as a polynomial:
(variance components can be estimated
by software such as ASReml [Gilmour et al., 2006]).
This model can be extended to include data on SNP
genotypes. The SNP information can be used to model
genomic relationships among animals to obtain GEBV. If the
genomic relationship approach is taken, all that is required is
to replace A (the pedigree derived relationship matrix) with
G, which are the relationships derived from the markers as
described by VanRaden (2008) or Yang et al. (2010):
é g1 ù
ê ú  N (0, G Ä T )
ê g2 ú
ë û
The assumptions underlying this formulation are
described in Appendix 1. Then ĝ1 and ĝ2 from fitting the
model are the GEBV for animals for Environment 1 and
Environment 2.
One interesting feature of the genomic implementation of the multitrait model is that it is not necessary to
have close relatives (for example daughters of the same
bull) in different environments, as even the small coefficients of genomic relationship contribute to the estimate
of an individual’s breeding value in each environment. For
example, in human genetics, this multiple-trait approach
has been used with individuals that only share small proportions of their genome (Maier et al., 2015).
Reaction Norm Models
If the environment is better described by a continuous
variable than by a series of categories, reaction norm
models are an alternative to multitrait models. Examples
of continuous environmental descriptors are as follows:
• Temperature humidity indices, as a measure of
heat stress (Ravagnolo and Misztal 2000; Hayes et
al., 2003; Haile-Mariam et al., 2008; Hammami et
al., 2015)
crop science, vol. 56, september– october 2016 g = S 0 + wS1 + w 2S 2 + …
where S¢ = (S 0 S1 S 2) are regression coefficients, specific
to this genotype, which are treated as random variables
with var(S) = C (for a model with intercept and slope,
the elements of the C matrix would be the variance of
the intercepts, the variance of the slopes, and the covariance between them). This can be done with random
regression, where each genotype has its own intercept,
slope, and potentially higher-order terms that describe the
trait response to increases in the environmental descriptor (for more details on random regression see Jamrozik,
and Schaeffer, 1997). In practice, only the intercept and
slope are usually considered (variance components associated with higher order terms such as quadratic and cubic
coefficients can be difficult to estimate). Reaction norm
models have been applied with animals as genotypes (e.g.,
Fikse et al., 2003; Ravagnolo and Misztal 2000) and also
to estimate SNP ´ environment interaction (e.g., Streit
et al., 2013a; Hayes et al., 2009). The random regression
implementation of the reaction norm model (with intercept and slope) is as follows.
For n individuals whose breeding value are stored in
(n1) a vector g, the model using pedigree becomes g = Ws,
where W = (W0, W1), a n ´ 2n matrix, where {wi} jk = w 2j
if j = k, and 0 otherwise, S ¢ = (S0¢S1¢ ) (a 1 ´ 2n) vector,
where Si is a n ´ 1 vector of breeding values for trait Si (I
= 0 is the intercept and i = 1 is the slope). The variance of
é s2
S is (S) = A Ä C , where C = êê
S0
êësS10
sS01 ùú
and A is the rela2 ú
sS1
úû
tionship matrix derived from pedigree as described above.
Thus the reaction norm model is a multitrait model
in which the traits are random regression coefficients (for
example for the intercept, and linear slope).
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Given some assumptions (Appendix 2), GEBV for the
slope and intercept can be predicted by replacing A with
.
G,
Examples of GENOTYPE ´
ENVIRONMENT INTERACTIONS
in Livestock
Multiple-Trait Models
A good example of implementation of the multiple-trait
approach to estimate breeding values in different environments was growth of Angus cattle at high and low
altitudes (Williams et al., 2012). At high altitudes, cattle
can suffer high mountain disease, also called brisket disease, which is heart failure as a result of hypoxic pulmonary hypertension. This can severely compromise growth.
Williams et al. (2012) assessed growth rate (weaning
weights) of more than 77,000 cattle on farms in Colorado
at a range of altitudes. Two traits were defined: growth at
high altitude and growth at low altitude. Relationships
between animals were derived from pedigree record. The
genetic correlation for growth at high and low altitudes
was 0.74. This indicates significant reranking between
sires will occur between high- and low-altitude farms,
and the genetic evaluation for growth should include the
genotype ´ altitude interaction.
The multitrait genomic approach to accommodate G
´ E was exemplified by Haile-Mariam et al. (2015). In this
study performance of dairy cattle in Australia were treated
as one trait and performance in the Netherlands and New
Zealand another trait. Milk yields, protein yields, fertility,
and longevity were investigated with this approach. The
aim of the study was actually to improve the accuracy of
the Australian GEBVs by increasing the size of the reference population by including information on genotype
performance from other countries. There were 5720 bulls
with daughter records in one, two, or all three countries,
and these bulls were genotyped for 36,000 SNP markers.
The genomic relationship matrix was constructed among
the bull from the SNP genotypes as described by Yang
et al. (2010). As a result of implementing the multitrait
model described above, GEBVs were produced for Australian and the other country environments. Including
information from the other countries improved the accuracy of genomic breeding values in Australia (as demonstrated in a validation population) by up to 10% for milk
yield. The genetic correlation between performance in
the different countries was as low as 0.72 for longevity
and 0.8 for protein yield. The fact that these correlations
are significantly <1 indicates that significant reranking
of sires occurs between the countries, and breeding programs specific to each country are justified.
4
Reaction Norm Models
A good example of the reaction norm approach to model
genotype ´ farm disease level interactions was presented by Calus et al. (2006). Those authors used bulk
milk somatic cell count (BMSCC) as the environmental
descriptor. Bulk milk somatic cell count is the number of
somatic cells that are present in milk samples pooled across
the cows in a herd: high levels of BMSCC indicate mastitis
is prevalent in the herd, and low levels of BMSCC indicate
low incidence of mastitis in the herd. The practical question is whether sires can be identified that have daughters with low somatic cell counts even when mastitis is
prevalent in the rest of the herd (high BMSCC). The data
set included 344,029 test-day records (somatic cell count
records) of 24,125 cows sired by 182 bulls in 461 herds.
The model included random regressions for each sire on
herd test-day BMSCC. The genetic correlation was 0.72
between somatic cell counts at low and at high BMSCC.
This is considerably <1, suggesting sires rerank considerably for their performance (in this case somatic cell counts
of their daughters) in low and high disease incidence herds.
The reaction norm approach has also been used to
derive GEBV for heat tolerance. Nguyen et al. (2015)
defined heat tolerance of a cow as the drop in milk production with increasing temperature and humidity (combined in a temperature and humidity index, which predicts
heat stress). Milk production data was recorded at least five
times during each cow’s lactation for 343,016 cows, and this
data was combined with daily temperature and humidity
measurements from weather stations closest to the tested
herds for 10 yr of data. Tolerance to heat stress was then
estimated for each cow using random regression (intercept
and slope) to model the rate of decline in production with
increasing temperature humidity index accumulated over
the 4 d before and the day of milking for milk yield, fat
yield, and protein yield. The slopes from this model were
used to define daughter averages (daughter trait deviations
[DTD] for their sires, of which, 2735 Holsteins and 710
Jersey had genotypes [either real or imputed]) for 632,003
SNP. Genomic best linear unbiased prediction was used to
calculate GEBV for heat tolerance. The reference population consisted of either genotyped sires only (2300 Holstein
and 575 Jersey sires) or genotyped sires and cows where the
cows had genotypes (2191 Holstein and 1190 Jersey). The
reminder of the sires (435 Holsteins and 135 Jerseys) were
used as a validation set, and accuracy of GEBV for heat
tolerance was calculated as the correlation of GEBV and
DTD divided by the accuracy of the DTD for these sires.
The accuracy of GEBV for heat tolerance was 0.46 for the
Holstein validation sires and 0.49 for the Jersey validation
sires. These accuracies are moderate to high, suggesting
genomic selection for heat tolerance could be included in
dairy cattle breeding programs to improve production in
environments where heat stress occurs.
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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 investigate individual SNP marker by temperature and humidity index interaction. In this case random regression was
used to model the response of each SNP allele to increasing temperature humidity index (Fig. 1). The model was
fitted for 39,048 SNPs one a time. The SNPs associated
with response of milk production to the temperature
humidity index were identified on chromosome 9 and 29,
and these were validated in two independent populations,
one a different breed of cattle.
Another interesting example of SNP by environment
interaction in livestock is the effect of myostatin genotype
on body temperature during heat and cold stress (Howard
et al., 2013). Mutations in the myostatin gene can result
in the double-muscling phenotype in Belgian Blue, Piedmontese, and other breeds of cattle. In this study, animals
that were homozygous wild-type, heterozygous, or homozygous for the Piedmontese-derived myostatin mutation
had rectal temperatures collected during periods of heat
and cold stress. The results indicated a G ´ E did exist for
the myostatin mutation; the additive effect was +0.10°C
during heat stress and the dominance estimate was −0.12°C
in rectal temperature. During winter stress events, the
additive estimate was 0.10°C and dominance estimate was
0.054°C. All these effects were significant (P < 0.05). The
study of Howard et al. (2013) illustrates a SNP G ´ E
exists for the myostatin mutation, and that heterozygous
animals were more robust to environmental extremes in
comparison with either homozygous genotype.
crop science, vol. 56, september– october 2016 Overall Extent of Genotype ´ Environment
Interaction in Livestock
The extent of G ´ E in livestock depends very much on
the genotypes involved, the classification of environment,
the trait, and the statistical method used to estimate G ´
E (Table 1). As might be expected, G ´ E is largest when
performance for very different environments is compared
(e.g., tropical vs. temperate performance) and very different genotypes are compared (Bos taurus vs. Bos indicus).
Within breeds and within countries, the magnitude of G ´
E is usually much smaller. These conclusions are similar to
those of Burrow (2012) in a review of the importance of G
´ E in tropical beef breeding systems. The extent of G ´ E
also appears to be larger for traits more closely related to fitness, for example, for fertility (Haile-Mariam et al., 2008).
Accounting for Genotype ´ Environment
Interactions in Livestock Breeding Programs
An obvious question that stems from Table 1 is what level
of G ´ E justifies different breeding programs or different genomic evaluations? Robertson (1959) proposed that
a correlation of performance between environments of
above 0.8 would indicate that there would be minimum
reranking of selection candidates in the two environments; correlations below 0.8 would indicate considerable
reranking and would justify separate breeding programs.
Mulder and Bijma (2005) reached a similar conclusion;
those authors considered two environments: a selection
environment and a commercial production environment,
with a genetic correlation between performance in the two
environments. They concluded that when this correlation
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Table 1. Some examples of genotype ´ environment (G ´ E) and genome ´ environment interaction in livestock.
Species
Environment
Trait
Dairy cattle
Farming system
(grazing vs. confinement)
Milk production
Beef cattle
Pasture or feedlot
Final weight,
average daily
gain and scrotal
circumference
Yearling
weight
Beef cattle
Dairy cattle
Dairy cattle
Pigs
Beef cattle
Dairy cattle
Dairy cattle
Dairy cattle
Dairy Cattle
Dairy cattle
Dairy cattle
Dairy cattle
Dairy cattle
Sheep
Sheep
Sheep
Sheep
Genotype
Body weight
Milk yield
Milk production
Milk yield, udder
health, and fatty
acid profile in milk
Fertility
Reference
0.89
Kearney et al. 2004
0.75, 0.49, 0.89
Raidan et al. 2015
Saavedra-Jiménez
et al., 2013
Multitrait
0.23 (wet tropic,
temperate) to 0.99
(dry tropic, temperate)
0.93, 0.79
Mulder et al., 2004
Multitrait
0.78 to 0.90
Fikse et al., 2003
Statistical
model
Animal, Holstein
Correlation of
breed
estimated breeding
value from two
environments
Animal, Nellore
Multitrait
breed
Climatic zone: dry tropic,
Animal, Braunvieh
wet tropic, temperate
cattle
climates in Mexico
Robotic milking vs.
Milk yield, somatic Animal, Holstein
conventional milking
cell score
breed
Country (Australia, Canada,
Milk yield
Animal, Guernsey
United States, South Africa)
Conventional vs.
Growth,
Breed
organic farming system
carcass quality
Farm input (herd
weight gain)
Temperature and
humidity
Country (Luxembourg,
Tunisia)
Temperature and
humidity
Extent of G ´ E and
genetic correlation
between extreme
environments†
Animal, Nellore
breed
Animal, Holstein
breed
Animal, Holstein
breed
Animal, Holstein
breed
Multitrait
Multitrait
Random
regression
Random
regression
Random
regression
Random
regression
Temperature and
Animal, Holstein
Random
humidity
regression
Farm input level (herd
Milk yield
SNP‡ genotype
Random
production level as a proxy
regression
for level of feeding)
Farm disease level (bulk
Milk yield
SNP genotype
Random
milk somatic cell count
regression
Farm input level (herd
Milk yield
SNP genotype
Random
production level as a proxy
regression
for level of feeding)
Temperature and
Milk yield
SNP genotype
Random
humidity
regression
Farm environment,
Weight, ultrasound
Animal,
Random
expressed as principal
back-fat, muscle
Texel breed
regression
component loadings
depths
after clustering on farm
characteristics
Farm environment
Lamb weaning Animal, Norwegian
Multitrait
weight
white and Spel
breeds
Farm environment
Fecal egg count and Animal, Merino Multitrait, random
production
breed
regression
Farm environment
Growth
Animal, Santa
Multitrait, random
Ines breed
regression
Except weight gain,
Brandt et al., 2010
no major shift of the ranking
order within environment
between genotypes.
0.09–0.74
Pegolo et al., 2011
>0.90
0.50
0.80, 0.64, 0.67
(depending on fatty acid)
0.79
28 SNP validated
for slope
11 SNP validated
for slope
27 significant SNP
for slope
SNP on chromosome 29
validated for slope
Brügemann et al.,
2011
Hammami et al.,
2009
Hammami et al.,
2015
Haile-Mariam et al.,
2008
Streit et al., 2013b
Streit et al., 2013a
Lillehammer et al.,
2009
Hayes et al., 2009
McLaren et al.,
2015
0.82
Steinheim et al.,
2008
Significant but
small G ´ E
>0.70
Pollott and Greeff,
2004
Santana et al., 2013
† 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
the commercial production environment resulted in more
gain than selection based on sibs of selection candidates
measured in the selection environment. Within a country, particularly countries with temperate environments,
the genetic correlation between environmental extremes
rarely falls below 0.8 (Table 1). This is in contrast to
6
between countries and between tropical and temperate
zones within a country where correlations of performance
can be considerably below 0.8. For example, milk production in Luxemburg and Tunisia has a genetic correlation of 0.5 (Hammami et al., 2009). For a tropical dairy
system in Kenya, Okeno et al. (2010) compared genetic
progress from a local progeny testing with importation of
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crop science, vol. 56, september– october 2016
semen from temperate countries and concluded importation was the superior strategy only if the genetic correlation between milk production in Kenya and the temperate
counties was greater than 0.7 despite the fact that progeny
test schemes were much larger in the temperate countries.
Between Australia and North America, genetic correlations for performance of Holstein cattle are 0.8 or below
(http://www.interbull.org). The opportunity cost of not
accounting for G ´ E can be quite large. It has been estimated that if breeding programs for Australian dairy cattle
were based purely on breeding values calculated using North
American information, $12 million yr−1 in genetic progress
could be lost (J.E. Pryce, personal communication, 2015).
One option for using genotypes that are genetically
superior in one environment but are not well adapted to
the target environment, would be to introgress alleles for
adaptation in the target environment. This already occurs
for tropical dairy production in Brazil, where high-performance Holstein cattle are crossed to adapted Bos indicus
cattle to form a composite called Girolando. Most of the
milk production in Brazil is now from Girolando cows
(da Costa et al., 2015). More targeted introgression has
also been demonstrated; Dikmen et al. (2014) introgressed
an allele at SLICK hair locus (a mutation that changes
the hair follicle and thermotolerance) from Senepol cattle
into Holsteins. There are relatively few examples of this
in livestock; however, as long generation time means that
introgression is very slow. Genome editing for adaption
alleles would be a potentially more rapid alternative.
There is increasing interest in livestock in breeding for
“robustness”. While this is a vague term, one interpretation is breeding for animals that produce well across a range
of environments. Reaction norm models directly identify
“robust” genotypes– these are the genotypes with low slope
values in response to the environmental indicator, whereas
sensitive genotypes have steep slopes. Note that in plant
breeding the equivalent term for robustness would be stability across environments. Lillehammer et al. (2009) identified SNP genotypes associated with improved milk production in dairy cows that were robust to the herd average
level of production, that is, animals with these genotypes
had improved production at low and high levels of feeding (high intercept and low slope). Streit et al. (2013a) used
a similar approach to identify SNPs that could be used to
select for robustness of milk production to the average level
of disease (mastitis) for the farm (e.g., animals with these
SNP genotypes produced well regardless of whether the
farm had a high disease load or a low disease load).
As another example of using genotype ´ environment models to enable breeding for robustness was Rose
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 approach. The heritability of body weight loss in harsh
nutritional conditions was 0.05 to 0.16, and the genetic
correlation between body weight gain in good conditions
and body weight loss in poor conditions was negative but
low. This led the authors to conclude that sheep can be
bred to be more tolerant to variation in feed supply.
Parallels and Differences Between
Genotype ´ Environment Interactions
in Livestock and Plants
One reason why G ´ E is potentially more crucial for
plants is that livestock can, to some extent, move to avoid
or mitigate stressors (and in some cases are kept in controlled environments, such as barns, where temperatures
can be to some extent increased or increased to avoid
stress), whereas plants are obviously less able to do so. A
further point of differentiation is that in livestock, the
focus in estimation of G ´ E has been largely on additive
effects to generate selection gains, whereas in plants G ´
E for dominance and espistatic effects can be exploited
more easily through hybrids or clonal propagation. In
terms of modeling G ´ E , the approaches outlined above
can and have also been applied in plants (e.g., Burgueño et
al., 2011; Jarquín et al., 2014). One key point is that in the
past, quantification of G ´ E without pedigrees required
each genotype to be grown in all environments. Provided
genomic markers (or pedigree) are available, the relatedness among lines can be modelled using matrices G or A,
and as in animal studies, G ´ E methods that use genomic
information can better cope with a reduced degree of
replication of individuals across environments (in the
genomic approach it is actually the alleles that must be
replicated across environments). More accurate estimates
of G ´ E with the genomic approach may therefore be
achievable than was possible in the past.
Conclusion
In livestock, G ´ E is considerable when genotype is
defined at the level of subspecies (Bos taurus vs. Bos indicus) and environments are described by different climatic
zones (tropical vs. temperate) but less for individuals within
a breed and within (most) countries. Models that include G
´ E, particularly the multitrait model, are now being used
to enable the reference populations used for genomic selection to be merged across environments and across countries,
leading to higher accuracy of GEBV. In either multitrait or
reaction norm models, using genomic information can lead
to more accurate estimates of G ´ E, as it is more likely
that SNP genotypes are well replicated across environments
than individual animals or their close relatives.
www.crops.org7
Appendix 1. Prediction of
MultiTrait Genomic Estimated
Breeding Values
References
Define breeding values as g = Uq, where U is a matrix containing the genotypes of animals at all the SNPs (n animals
´ m, where m is the number of SNP coded as the number
of copies of the second allele), and q is the effect of each
SNP on the trait, is a linear model for the breeding value g.
The SNP effects (q) are treated as random effects sampled
from a distribution; for instance, a normal distribution q
~N(0,D). The D matrix is usually diagonal, implying that
the effect of different SNPs are independent of each other,
,
for example, for the ith SNP in Environment 1,
is the variance associated with the ith SNP in
where
Environment 1. The covariance of the SNP effects in Environment 1 and 2 is Dij = sij,12. Then for the multitrait model
described in the text, the variance of breeding values are as
follows:
é g ù é UD11 U ' UD12 U ' ù
ú.
var ê 1 ú = ê
ê g2 ú ê UD12 U ' UD22 U 'ú
ë û ë
û
If we assume that all SNP effects for each trait are
drawn from the same normal distribution (q ~ N(0, Is12 ),
ég ù
then var êê 1 úú can be written as
. That is, the
ë g2 û
expected relationship matrix A is replaced by G, the realized relationship among individuals calculated from the
markers (G = UU¢/m) is calculated for example.
é g1 ù
ê ú  N (0, G Ä T ) .
ê g2 ú
ë û
Appendix 2. Prediction of Genomic
Estimated Breeding Values for
Reaction Norms
If there are SNP genotypes U (an n ´ m matrix, where
m is the number of SNP, and genotypes are coded as the
number of copies of the second allele), then the breeding values for animals for trait 0 (the intercept) are S0 =
Uq 0, where q 0 is the effect of the SNP on the intercept,
and var(q 0) = D0, a m ´ m diagonal matrix, and likewise
for the other traits. For the case with intercept and slope,
cov(q 0,q1) = D01, a diagonal matrix (m ´ m) of covariances
among the SNP effects on the intercept and slope, and
é UD00 U ' UD01U 'ù
ú.
var (S) = ê
ê UD10 U ' UD11U ' ú
ë
û
2
If Dii = Isi and Dij = Isi2 then var (S) = G Ä C , where
é s2
C = êê S 0
êësS10
sS 01 ùú
, as above, and G = UU¢/m, or versions of
sS21 úúû
the genomic relationship matrix described for example by
VanRaden (2008) or Yang et al. (2010).
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