Heterogeneous variances and genetics by environment interactions in genetic evaluation of crossbred lambs

Accounting for environmental heteroscedasticity and genetics by environment interaction (G×E) in genetic evaluation is important because animals may not perform predictably across environments. The objectives of this study were to evaluate the presence and consequences of heteroscedasticity and G ×E on genetic evaluation. The population considered was crossbred lambs sired by terminal sires and reared under commercial conditions in the UK. Data on 6325 lambs sired by Charollais, Suffolk and Texel rams were obtained. The experiment was conducted between 1999 and 2002 on three farms located in England, Scotland and Wales. There were 2322, 2137 and 1866 lambs in England, Scotland and Wales, respectively. A total of 89 sires were mated to 1984 ewes of two types (Welsh and Scottish Mules). Most rams were used for two breeding seasons with some rotated among farms to create genetic links. Lambs were reared on pasture and had their parentage, birth, 5 week, 10 week, and slaughter weights recorded. Lambs were slaughtered at a constant fatness, at which they were ultrasonically scanned for fat and muscle depth. Heteroscedasticity was evaluated in two ways. First, data were separated into three subsets by farm. Within-farm variance component estimates were then compared with those derived from the complete data (Model 1). Second, the combined data were fitted, but with a heterogeneous (by farm) environmental variance structure (Model 2). To investigate G ×E, a model with a random farm by sire (F ×S) interaction was used (Model 3). The ratio of the F ×S variance to total variance was a measure of the level of G ×E in the population. Heterogeneity in environmental variability across farm was identified for all traits ( P<0.01). Rank correlations of sire estimated breeding value between farms differed for Model 1 for all traits. However, sires ranked similarly (rank correlation of 0.99) for weight traits with Model 2, but less so for ultrasonic measures. Including the F ×S interaction (Model 3) improved model fit for all traits. However, the F ×S term explained a small proportion of variation in weights (<2%) although more in ultrasonic traits (at least 10%). In conclusion, heteroscedasticity and G ×E were not large for these data, and can be ignored in genetic evaluation of weight but, perhaps, not ultrasonic traits. Still, before incorporating heteroscedasticity and G×E into routine evaluations of even ultrasonic traits, their consequences on selection response in the breeding goal should be evaluated.