Bias and precision of estimates of genotype-by-environment interaction: A simulation study

Re-ranking of genotypes across environments is a form of genotype-by-environment (G × E) interaction with serious consequences for breeding programmes. The degree of such G × E interaction can be estimated using the genetic correlation (rg) between measurements in two environments for a given trait. When rg is lower than 0.8, G × E interaction is commonly considered to be biologically significant. Here a stochastic simulation was used to study the impact of population structure on bias and precision of genetic correlation estimates between two environments. Simulated populations resulted from a nested mating design (1 sire to 2 dams). Simulated rg was 0.0, 0.5, or 0.8. A trait with heritability (h2) of either 0.3 or 0.1 in both environments was simulated. Simulation results show that genetic correlation estimates are biased downward especially when the simulated rg is 0.8, heritability is 0.1, and family size is less than 10. A downward biased genetic correlation estimate incorrectly suggests the existence of G × E interaction. This can lead to the erroneous conclusion that a multi-environment breeding programme is needed. The optimal design with the lowest mean square error for rg for a trait with low h2 requires a large family size (20–25) and a low number of families (100–80 or 50–40 for population size fixed to 2000 and 1000 animals, respectively). For traits with moderate h2, the optimal family size is 10 with 200 or 100 families for population size fixed to 2000 and 1000, respectively. We also studied the effect of selective mortality on G × E estimates. However, schemes with unequal family sizes due to differences between families in survival produced similar results for the optimum design as schemes with equal family sizes. Equal-family-size design can thus be used to determine the optimal design for estimating G × E interaction. Our study can be used as a guideline for estimating a genetic correlation for practical breeding programmes.