Estimation of macro- and micro-genetic environmental sensitivity in unbalanced datasets

Genotype-by-environment interaction is caused by variation in genetic environmental sensitivity (GES), which can be subdivided into macro- and micro-GES. Macro-GES is genetic sensitivity to macro-environments (definable environments often shared by groups of animals), while micro-GES is genetic sensitivity to micro-environments (individual environments). A combined reaction norm and double hierarchical generalised linear model (RN-DHGLM) allows for simultaneous estimation of base genetic, macro- and micro-GES effects. The accuracy of variance components estimated using a RN-DHGLM has been explicitly studied for balanced data and recommendation of a data size with a minimum of 100 sires with at least 100 offspring each have been made. In the current study, the data size (numbers of sires and progeny) and structure requirements of the RN-DHGLM were investigated for two types of unbalanced datasets. Both datasets had a variable number of offspring per sire, but one dataset also had a variable number of offspring within macro-environments. The accuracy and bias of the estimated macro- and micro-GES effects and the estimated breeding values (EBVs) obtained using the RN-DHGLM depended on the data size. Reasonably accurate and unbiased estimates were obtained with data containing 500 sires with 20 offspring or 100 sires with 50 offspring, regardless of the data structure. Variable progeny group sizes, alone or in combination with an unequal number of offspring within macro-environments, had little impact on the dispersion of the EBVs or the bias and accuracy of variance component estimation, but resulted in lower accuracies of the EBVs. Compared to genetic correlations of zero, a genetic correlation of 0.5 between base genetic, macro- and micro-GES components resulted in a slight decrease in the percentage of replicates that converged out of 100 replicates, but had no effect on the dispersion and accuracy of variance component estimation or the dispersion of the EBVs. The results show that it is possible to apply the RN-DHGLM to unbalanced datasets to obtain estimates of variance due to macro- and micro-GES. Furthermore, the levels of accuracy and bias of variance estimates when analysing macro- and micro-GES simultaneously are determined by average family size, with limited impact from variability in family size and/or cohort size. This creates opportunities for the use of field data from populations with unbalanced data structures when estimating macro- and micro-GES.