Modeling Genome By Environment Interaction in Allohexaploid Wheat

A long term plant breeding objective has been to develop varieties that are stable across a defined set of environments. Genetic variation of stability implies that there is a heritable portion of environmental variance that can be explained by genetic differences between individuals. As an autogamous allohexaploid, wheat (Triticum aestivum) represents a unique opportunity to study the interaction of multiple genomes, A, B and D, and their interactions with the environment. To investigate the effect of genome by genome and genome by environment interactions, genome specific additive genetic covariance matrices can be calculated from markers belonging to each genome respectively. Using genome specific covariance matrices, estimates of genome specific variances and additive effects can be determined in a linear mixed model with separate kernels for each genome. Similarly additive by additive effects between genomes can be modeled using the Hadamard product of genome specific covariance matrices. Genome by environment effects, as well as higher order interactions can also be modeled using the Kronecker product of the genetic environmental covariance matrix with the genome specific additive covariance matrices. To examine the influence of each genome and their interactions on stability, double hierarchical generalized linear models can be used to estimate additive genetic variance of the variance as well as genotype specific additive effects of the variance to identify stable lines. This methodology is applied to two multi-environment trial data sets of wheat, and provides insights into genetic variation, heritability and predictability of genome by environment interactions and stability in allopolyploids.