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ANIMAL GENETICS |
Great Southern Agricultural Research Institute, Katanning, Western Australia 6317, Australia
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Abstract |
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 Top Abstract IntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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Key Words: Fecal Egg Count • Gastrointestinal Parasites • Genetic Parameters • Genotype x Environment Interaction • Reaction Norm • Sheep
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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). The most commonly described situation is where two breeds are kept in two environments and change their ranking for a given trait in those two environments. However, several studies have extended this concept to consider how a group of genotypes varies in several environments. The estimation of a variance component to describe the additional variance in the population due to the genotype x environment effect is one approach (Hickman and Henderson, 1955; Meyer, 1987). Recent developments in the use of random regression models have led to the suggestion that the genotype x environment effect can be systematically investigated by regressing sire breeding values on some measure of the environments in which their offspring are found (Kolmodin et al., 2002). This paper describes an investigation of the genotype x environment effect for fecal egg count (FEC) and production traits in Australian Merino sheep using a range of methods. The use of the random regression approach to estimate genotype x environment effects also facilitated the calculation of both heritabilities and genetic correlations as they varied across a range of environments. |
Materials and Methods |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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The data were collected between 1988 and 2002 from 55 commercial Merino flocks located in the four main sheep producing states of Australia: Western Australia, New South Wales, Victoria, and South Australia. They were derived by combining databases from four major sources of records: Merino Genetic Services (Meat and Livestock Australia); Merino Benchmark (New South Wales Agriculture); and Sire Evaluation Test data from New England and Yardstick (Western Australia). Flocks were selected from all four sources on the basis of having a high proportion of their animals recorded for FEC over recent years. All available animal records were used from these "FEC flocks" regardless of whether the individual animal had a FEC record or not. The final amalgamated database comprised records from over 250,000 animals, of which 127,723 had recorded sire information.
The distribution of gastrointestinal worm species is commonly described with reference to the annual rainfall pattern in different parts of Australia. In the winter rainfall regions (Western Australia, South Australia, and parts of Victoria), the dominant species are Trichostrongylus spp. and Ostertagia spp., with Nematodirus spp., Oesophagostomum venulosum, and Chabertia ovina of lesser importance. In the summer rainfall regions (Queensland and New South Wales), Haemonchus contortus (in summer) and Trichostrongylus spp. (in winter) are the main species found, with Oesophagostomum and Nematodirus of secondary importance (Cole, 1986). In uniform rainfall areas, species prevalence varies on an annual basis (parts of Victoria, Tasmania). The exact parasite status of the contemporary groups used in this study was largely unknown, apart from the mean FEC level calculated from the data.
The traits analyzed in this study are described in Table 1. Fecal egg count was adjusted using the cube-root transformation (Woolaston and Piper, 1996). Standardized values for all traits were used in these analyses. There were two reasons for transforming the data in this way. First, heterogeneous variances in contemporary groups have resulted in spurious genotype x environment interactions (Maniatis and Pollott, 2002). This possibility was removed by standardizing the data in such a way as to make within-contemporary group variances have a value of one. Second, the use of random regression methods to model the way sire variance changed across different environments was found to give unrealistic values for heritability with untransformed data. Standardized values were calculated for each trait by adjusting the phenotypic value using the relevant contemporary group (CG) mean and standard deviation for that trait. For example, FECstd = (FEC –MeanFEC–CG)/SDFEC –CG, where MeanFEC –CG and SDFEC –CG refer to the mean and standard deviation of the CG of the individual animal whose data is being standardized for FEC (Hill, 1984). This was repeated for each trait using its own CG means and standard deviations to standardize that trait.
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It was possible to explore the data for genotype xenvironment effects because the use of reference sires linked flocks by common sires, and so the offspring of certain sires were born in a wide range of flocks. Table 2 shows the distribution of sires across flocks. Of the 2,186 sires in the dataset, 2,004 were only used in one flock and the remaining 182 were used in several flocks. Two rams were used very widely and 35 rams were used in more than three flocks. However, CG (flock, year, sex, age class, paddock) was the main grouping of animals used in these analyses. Linkage between CG varied according to the trait being analyzed. Of the 291 CG in the FEC dataset, all used at least two rams to mate their ewes and only 28 sires were used in a single CG. Thus, there would be a reasonable data structure with which to estimate any genotype xenvironment effect if all traits were recorded on all animals. However, this was clearly not the case (Table 3), and so the data structure for each trait varied. The number of CG for each trait is shown in Table 3 and ranged from 43 (staple strength) to 593 (fiber diameter). Mean CG size ranged between 78 animals for loin muscle depth to 185 for staple strength.
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A sire model (Model 1) was fitted to all standardized traits using ASREML (VSN Int., Hemel Hempstead, U.K.), and variances were considered to have been estimated when the log likelihood in successive iterations differed by less than 0.002x the current iteration number.
 | [Model 1] |
In Model 1, Yijkl was a record from one of the 12 standarized traits analyzed for the lth animal, in the ith birth type, the jth rearing type, and from the kth sire. Age and Age2 were fitted as covariates. The sire and residual effects were fitted as random variables. The number of animals, CG, and sires varied for each trait, depending on the level of recording of the trait, fixed effects, and covariates.
Genotype xEnvironment Effect
Random Effects for Sire xContemporary Group.
The first approach to estimating the genotype x environment effect for FEC was to extend Model 1 by fitting sire x CG as an additional random effect. Mixed models were run for all standardized traits using the final fixed effect structure derived from fitting Model 1 (Table 3
), with sire, residual and sire x contemporary group as random effects. The likelihood ratio test was used to test for significant additions/subtractions to the model against a 
2 value, the number of degrees of freedom being the difference in the number of sets of effects in the two models being compared. A genotype x environment variance ratio (ge2) was calculated from the sire x CG variance as a proportion of the total phenotypic variance.
Reaction Norm Approach.
The second approach to estimating genotype x environment effects used the so-called "reaction norm" approach (Kolmodin et al., 2002) by fitting random regression terms for each sire (Model 2). The CG average for the trait was used as the independent variable in all random regression models. This created an environmental gradient across the range of environments in the dataset, in this case each contemporary group being defined as a different environment. The environmental gradient was redefined for each trait according to the CG mean for the trait being analyzed. An example random regression model, for FEC, is shown in Model 2.
 | [Model 2] |
In Model 2 Yij = the jth animal’s recorded standardized FEC value, Sai = the additive effect of the ith sire and Sbi the regression coefficient of the ith sire’s breeding value on Xk, the kth CG mean FEC value. The variance of the sire "intercept" (Sai), slope of a linear regression of sire CG values on CG mean (Sbi), and the covariance between them (covSab) were estimated as random effects. For other traits a different set of fixed effects were used, depending on which effects were found to significantly affect the trait from previous analyses, and the Xk variable was the CG mean for the trait being analyzed from the kth CG.
Model 2 estimated the sire variance as the linear regression of sire breeding value in a specific environment on the mean CG value for that environment. Further analyses were carried out using a quadratic polynomial in place of the linear random regression for FEC (Model 3) to allow some flexibility in the sire terms. This was achieved by adding the term Sci(
2) to the model, plus its covariances with the other two random regression terms. The sire x CG term was added to the random part of Model 3 to allow an estimate of how much of the Sx CG variation was accounted for by the systematic effects described by the random regressions (Model 4).
 | [Model 3] |
 | [Model 4] |
Analyses using these models were repeated for each trait using standardized data with the appropriate fixed effect model for the trait.
Heritability of a Trait in Different Environments
The use of reaction norm models, using random regression across a range of environments, allows the estimation of the way in which the heritability of a trait varies with the environment. As described above, for each trait, the CG mean for that trait was used as the environmental variable. The method described by Kolmodin et al. (2002) was used to estimate the sire variance (
2s) of a trait at different values of the environmental variable. In a general matrix form this was:
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where V was a 1 x n vector of the environmental variable value (X) at which the sire variance was being estimated (1, X, X2, ..., Xn), n was the order of polynomial being fitted, and G was the n x n variance/covariance matrix of the random regression terms being fitted in the model. The additive genetic variance, at any given X value, was calculated as four times the sire variance and the phenotypic variance (2p) calculated as the residual plus the sire variance. Standard errors of the heritability were calculated as described by Gilmour et al. (2002) for each value of X.
Genetic Correlations across Contemporary Groups with Different Mean Fecal Egg Count Values
Genetic correlations between standardized FEC and six standardized production traits were calculated across the range of FEC environments using the reaction norm approach described by Kolmodin et al. (2002). The six traits were chosen for a number of reasons. Fiber diameter and greasy fleece weight are widely recorded and important traits in Merino flocks but had a zero genetic correlation with FEC. Body weight was a widely recorded trait, whereas fat depth, loin muscle depth, and staple strength all had point estimate genetic correlations different from zero. The sire covariance between FEC and each production trait was calculated using VGV', as described above, but in this case the G matrix was the variance/covariance matrix of all possible combinations of the polynomial terms fitted to both traits. Standard errors were calculated as described by Gilmour et al. (2002). In all cases standardized data were used for both traits and a quadratic polynomial was fitted for each trait.
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Results |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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A summary of the analyses adding sire x CG to the basic model (Table 3) for each trait is shown in Table 4. The likelihood ratio test showed that in all traits, except staple length and fiber curvature, the addition of sire x CG resulted in a better fit of the model to the data (P < 0.01). The proportion of phenotypic variance accounted for by this additional term ranged from 0.6 (fiber curvature) to 4% (grease fleece weight and loin muscle depth). The genotype x environment effect for FEC was 3%.
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. The linear random regression model reduced the log likelihood (P < 0.001) compared with the sire model (Model 1) and the polynomial random regression improved the fit of the model further (P < 0.001). There was little difference between the fit of the models containing either the sire x CG or the linear random regression effects.
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. Staple strength was the only trait where the use of the random regression model did not significantly decrease the log likelihood from the use of the sire model alone. Greasy fleece weight, clean fleece weight, and fiber diameter coefficient of variation showed a very high correlation between the slope of the sire random regression lines and the level of the sire breeding values. The slope of the individual sire regression lines accounted for more than 1% of the phenotypic variation in clean fleece weight, fiber diameter, fiber curvature, BW, fat depth, and loin muscle depth.
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from the quadratic polynomial random regression model. The rams demonstrating the greatest range of breeding values over the different environments were Ram 386 (–1.03 epg0.33) and Ram 925 (+1.08 epg0.33). Another indication of a genotype x environment effect would be a change in relative ranking of sires in different environments. This is difficult to summarize in a single statistic, but inspection of Figure 1 clearly demonstrates that the 10 sires ranked differently over the range of the environmental variable shown. Rams 925 and 536 are good examples of this; they had identical values of FEC in CG with a mean FEC value of 5 epg0.33, but were two units of FEC different in environments with a mean FEC level of 13 epg0.33.
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The calculation of the heritability of FEC from the use of quadratic random regression model to model the way the sires’ breeding values changed across the range of FEC environments is shown in Figure 2. In low- and high-FEC environments heritability was higher than in the middle of the range of environments. Because of the use of standardized data, this variation in heritability was almost entirely due to the change in sire variance across the environmental range.
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Heritability of Production Traits in Different Environments
The heritability results for the production traits are presented as a series of graphs (Figures 3 and 4) derived from using the polynomial random regression. In Figures 3 and 4, the environmental variable was the CG mean for the original data of each trait but expressed as a standard deviation of the CG means. This allowed a much easier comparison between traits on a common scale. The range ± 2 SD was used since this encompasses 95% of environments and represents the range of environments over which the heritability was most accurately estimated. Figures 2 to 4 also show the heritability standard errors and the distribution of CG means across the range of environments.
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to 4. Greasy and clean fleece weight (Figure 3) had a similar pattern to body weight (Figure 4) and fiber curvature (Figure 3). In environments characterized by a low environmental variable, those four traits had a high heritability, which fell rapidly as the environment improved and leveled off by ± 1 SD on either side of the mean. In the best environments, their heritability declined further. The fleece weight traits and BW were estimated from a large number of CG across the range of environments, as shown by the small standard errors at all but the lowest environmental values (–2 SD). The CG means were skewed slightly toward the lower end of the scale and there were no groups with a mean less than –2 SD from the overall mean, but there were groups with up to 3 SD above the mean. Some other traits showed very little variation in heritability in different environments (fiber diameter, fiber diameter CV, staple length). Because the phenotypic variance is about unity across the range of environments with standardized data, these results reflect a stable additive variance across the range as well. All three traits showed a normal distribution of CG means.
The remaining traits all had different patterns of heritability depending on a range of factors. The heritability of comfort factor (Figure 3) decreased from 0.62 (–2 SD) to 0.24 (0.5 SD). Because of the way comfort factor is calculated, it has a truncated normal distribution; no value can be higher than 100%. This is reflected in the distribution of CG means shown in Figure 3.
Staple strength (Figure 4) was recorded on the smallest number of CG, and its heritability was low (approximately 0.2) at both extremes of the environmental scale (+2 and –2 SD) and highest in the middle (0.43). The standard errors were large and indicate that this trait may have a constant heritability across the range of environments.
The distribution of fat depth CG means (Figure 4) was also skewed toward the lower end of the scale, and fat depth was not widely recorded. Its heritability was effectively the same across the range of values shown.
The distribution of loin muscle depth CG means (Figure 4) was skewed toward the lower end of the scale and ranged between –1.7 and 2.5 SD. It was not widely recorded, and the distribution of CG means above 0.25 SD was very low. This may account for the irregular pattern of loin muscle depth heritability shown in Figure 4, with low values at either end of the scale and a rise on the positive side of the scale.
Genetic Correlations
The pattern of genetic correlations between FEC and six production traits are summarized in Figure 5. In all cases, the environmental variable used was the mean CG FEC value. The two widely recorded wool traits, fiber diameter and FEC, showed very little correlation with FEC across the range of FEC environments studied; the highest correlation was < 0.1 at the highest level of FEC (fiber diameter). The two body measurements (fat depth and loin muscle depth) were found to vary with changing FEC environments; as the environment declined, the genetic correlation became more negative. This implies that under high levels of parasite challenge, genetically resistant animals will have a greater breeding value for fat and loin muscle depth than less resistant animals. Staple strength appeared to have a zero correlation with FEC across the range of environments, but this may have been due to it being recorded on a relatively small number of animals. Body weight also seemed to have a low and constant genetic correlation with FEC.
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also shows the point estimates of the genetic correlations estimated from these standardized data. All these point estimates could be found on their respective random regression lines, with the exception of staple strength, but there was no consistency about where on the environmental scale they were located. Most were below or at the mean FEC value of 8.85 epg0.33 |
Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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There was clear evidence of a genotype xenvironment interaction for FEC in this Australian Merino data. This was shown in a number of ways: by the ge2 value being different from zero, and by the slope variance of the random regression model being different from zero—the ram breeding values changing in different environments and the better fit of the models, including a genotype xenvironment effect (or random regression term), compared with those without.
The general level of the effect was rather low. On the basis of the results from the current dataset, the level of the genotype xenvironment effect for FEC would seem to be of little practical value. However, there were clearly some rams that did change their breeding values in different environments, and some rams appeared to have a negative random regression slope (i.e., they had a higher breeding value in a low-FEC environment than in a high-FEC environment).
The low level of genotype xenvironment effect may have been due to a range of factors. Firstly, parasite resistance, as measured by FEC, may be due to a general immunity to gastrointestinal parasites rather than a resistance to specific parasites. Thus, rams with a high level of genetic resistance to gastrointestinal parasites, used in a range of FEC environments with a different mix of parasites or environmental factors, may confer the same level of a general immunity to their offspring in all environments. This would result in no genotype xenvironment effect being found.
Secondly, FEC measurements do not indicate which parasites are present, and so the offspring of a particular ram may have immunity to different parasites in different environments. In Australia, internal parasite species vary between regions and seasons (Cole, 1986). This variation was not measured in this study, but would be useful information to collect to help the interpretation of this type of data.
There is very little evidence from other studies to help interpret these results. Morris et al. (1993) and our own unpublished results failed to detect a genotype xenvironment effect in trials designed to investigate the use of two contrasting FEC genotypes in two distinct FEC environments. More recent studies in New Zealand, looking at the genetic correlation of FEC for Trichostrongylus and Nematodirus spp. (Morris et al., 2004), found the genetic correlation to be approximately 0.43. This indicates that different genes are controlling the resistance to the two types of parasites and that a genotype xenvironment effect may exist.
Genotype xEnvironment Interactions in Production Traits
The results for the wool traits indicate that fleece weight is subjected to the highest level of genotype xenvironment interaction, with fiber diameter traits having a lower level of effect and the other fiber traits generally unaffected by genotype xenvironment influences. Very few reports of genotype xenvironment effects on wool traits are available. Dominik et al. (1999) quoted genetic correlations between related animals kept in two specific environments and concluded that there was no genotype xenvironment effect present for a range of production traits, despite some correlations being 0.62 ± 0.20 (clean fleece weight), 0.77 ±0.11 (fiber diameter), and 0.80 ±0.13 (staple strength).
Genotype xenvironment interactions of body traits in sheep have been reported by Hagger (1998) and Maniatis and Pollott (2002). Hagger (1998) analyzed pre-weaning growth rate in Swiss Black-Brown Mountain sheep and found ge2 values ranging from 4 to 6%. The results of Maniatis and Pollott (2002) were slightly lower at 2 to 3% for pre- and postweaning weights of Suffolk sheep in a U.K. sire-referencing scheme. The value of 2.6% reported in the current study for BW was very similar. Maniatis and Pollott (2002) also reported values of 2% for ultrasonically measured loin muscle depth and 2 to 4% for fat depth, which were similar to the values of 4 and 3.2% found in this study. From this limited amount of evidence, there appears to be a real but low level of genotype xenvironment effect for fleece and body traits in sheep, with less evidence for an effect on fiber characteristics.
Heritability of Traits in Different Environments
One by-product from the use of random regression models to investigate genotype xenvironment effects is that they allow the heritability of a trait to be estimated in a wide range of environments. The traditional way of estimating heritability, a point estimate for any given dataset, has become the norm, and authors tend to look for similarities between their estimates as a means of "verifying" their results. However, heritability was originally defined to relate only to the population under study in the environment in which it was found (Falconer 1981), and a range of values is to be expected. The use of reaction norm models makes it possible to revisit the idea of the heritability of a trait being related to a particular flock environment in a more systematic and comparable way than has been possible previously.
The heritability of FEC for this dataset was 0.23 ± 0.016. From Figure 2, it is apparent that this value is not that calculated by random regression at the mean FEC value (8.85 epg0.33), but may represent heritability calculated at an average weighted mean environmental value. Inspection of Figures 3 and 4 confirms this. In some cases, the point estimate heritability was at the mean environmental value (clean fleece weight, fiber diameter CV, staple length, fat depth), or within the standard error shown (comfort factor, staple strength, fiber curvature, BW, loin muscle depth). In other traits, this is clearly not the case (FEC, fiber diameter), but heritability tends toward the middle of the range of values found.
Figures 2 to 4 show how the heritabilities of the different traits vary in the range of environments analyzed in this study. These fall into several distinct patterns. Fleece and BW characteristics have a high heritability in environments characterized by a low value of the environmental variable, a stable heritability in the middle range of environments, and then a decreasing heritability as the environment improves at the upper extreme. The standard errors of the estimates at the extremes of the environmental range suggest that these are real differences. It is not surprising that these traits have a similar pattern because they are all related to size of the animal in some way. At low values of the environmental variable, the genetic variability of the traits was high, implying that some animals have the genetic ability to cope with poor conditions better than others. Under a range of relatively benign environments, the variability of breeding variables is stable and less than in the poor environments. Under good regimes, the genetic variability of growth and fleece traits is low and most genotypes respond similarly to the environmental conditions. It is impossible to tell from the current dataset how many, and which, genes are influencing these traits. However, it does seem logical to assume that different genes contribute to body and fleece weight under different environmental conditions.
A number of traits showed no difference in heritability across the range of environments in which they were recorded (fiber diameter CV, staple length, fat depth), or their standard errors were large at the environmental extremes and so no difference could be detected across the range, despite a nonlinear pattern (staple strength, fiber curvature, loin muscle depth). In these traits, the genetic variability remained stable in all environments, implying that the breeding values for the animals were invariant to the environmental conditions.
The remaining traits (FEC, fiber diameter, and comfort factor) demonstrated a variety of patterns for the way heritability varied across environments. Fiber diameter heritability was well estimated and only varied a small amount over the environmental range, and so it can be considered to be almost similar across the range. Comfort factor was a trait with a very skewed distribution and, because of the way it was calculated, higher variance is expected at lower trait values. Fecal egg count (Figure 2) was found to have a high heritability at the extremes of the environmental range, but a moderate level in the middle. This implies that in low-FEC environments, the genetic variation for FEC was high and therefore some rams have the genetic predisposition to have high egg counts even when the challenge is relatively low (i.e., they have no resistance to the parasites at all). Under a moderate challenge regimen, animals are more similar in their genetic control of FEC; presumably the animals with lower resistance in good environments increase their FEC values toward the animals with no resistance. At high challenges, some animals have the ability to resist the parasites more than others. Inspection of the small number of rams shown in Figure 1 adds weight to this interpretation. Some rams appear to have a reducing breeding value for FEC as the environment declines.
Several authors have reported the heritability of Merino production traits in two environments using common rams as the link between environments. Lewer and Ritchie (1992) compared two groups of ewes kept in simulated commercial (harsh environment) and stud (less harsh environment) environments and linked by common rams. The heritability of clean fleece weight, staple strength, and fiber diameter were lower in the commercial environment, although the standard errors were large. Dominik et al. (1999) analyzed a dataset that included that of Lewer and Ritchie (1992) and found no significant difference between heritabilities for FEC, clean fleece weight, fiber diameter, staple strength, fiber diameter CV, staple strength, and BW. Similar conclusions were reached by Erasmus (1988), who also compared the heritabilities of Merino production traits in two different environments. These results represent differences in heritabilities between the two environments over a very narrow range of environments compared with the ranges shown in Figures 2 to 4. Thus, the results reported in this article and those of Dominik et al. (1999) and Erasmus (1988) are in agreement.
The variety of patterns for the way heritability varies across the range of trait environments may have some implications for selection programs. For example, selection schemes could be designed to select against the animals that have high FEC in poor environments, as well as selecting those that have a low FEC in all environments.
Genetic Correlations
The pattern of the way that genetic correlations between FEC and some production traits change as the FEC environment changes suggest that in low-FEC environments, there will be no effect on most other traits of selection for low-FEC animals, fat depth being the only exception. However, in medium- to high-FEC environments, some increase in fat depth and muscle depth can be expected.
Heritability and the Genotype x Evironment Effect
Using the reaction norm approach to describe the systematic way that a genotype may vary in different environments has also allowed for a description of the way that the heritability of a trait varies across those same environments. The results were explored to investigate the relationship between the pattern of heritability across environments and any genotype xenvironment effect.
Using Figure 1 as an example, if no genotype xenvironment effect existed, then the regression lines of sire EBV on environmental value would be parallel. This would result in a heritability of the same value in all environments (i.e., the heritability line would be parallel to the x-axis on graphs such as Figure 2). Any deviation from the situation of parallel regression lines implies that a genotype xenvironment effect is present and would be reflected in a changing additive variance across the environmental range. Thus, a genotype xenvironment effect is expected for any standardized trait that does not have a constant heritability across the range of environmental variables.
Looking at Figures 2 to 4, some traits have a constant heritability across the environmental range (fiber diameter CV, staple length) and some traits may be considered to have constant heritability due to large standard errors (fiber diameter, fiber curvature, staple strength, fat depth, loin muscle depth). The other traits have a variable heritability (fecal egg count, clean fleece weight, comfort factor, BW). If we ignore comfort factor, because it is a trait with a truncated normal distribution, then the four traits with the most variable heritability patterns have the highest ge2 values; FEC (0.030), FEC (0.039), clean fleece weight (0.031), and body weight (0.024). The traits with either a flat heritability or large standard errors, indicating the possibility of a flat heritability line, all had ge2 values 
0.01 and were mostly not different from 0. The only exception to this was fiber diameter (ge2 = 0.024) which was well estimated and shows a small rise in heritability in the middle of the environmental range.
Relationship between Different Measures of the Genotype xEnvironment Effect
In this article, a range of measures of the genotype xenvironment effect has been used to investigate its presence in a number of Merino traits. These different measures were compared to see if any relationship between them existed. The use of ge2 estimates the variance in the trait due to deviations from the sire plus CG main effects. Thus, if a particular sire-CG combination has a value that differs from the sum of the two main effects, it will contribute to the s2 value. The variance due to the slope of the sire’s breeding value, calculated from the random regression model, shows how similarly all sires respond in the range of environments. If all sires responded in the same way to each environment, then the variance of slopes would be zero (i.e., they would all have the same slope). Thus, ge2 gives an insight into the existence of a genotype xenvironment effect, and the slope variance tells us how consistent that effect is across the environmental range; a low slope variance indicating a consistent systematic effect across all sires.
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Footnotes |
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2 Correspondence: Dept. of Anim. Sci., Imperial College London, Wye Campus, Ashford, Kent, TN25 5AH, U.K. (phone: +44 (0)20 759 42707; fax: +44 (0)20 759 42919; e-mail: g.pollott{at}imperial.ac.uk).
Received for publication December 23, 2003. Accepted for publication June 1, 2004.
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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