Genetic evaluation by BLUP in two-breed terminal crossbreeding systems under dominance

To obtain estimates of breeding values by BLUP using Henderson's mixed-model equations, it is necessary to invert the covariance matrix for each random effect in the model. In a model in which the genotypic value is included as a random effect (genotypic model), it is necessary to invert the genotypic covariance matrix. Under additive inheritance, the inverse of the genotypic covariance matrix can be computed efficiently. Under dominance inheritance, however, an efficient method to invert the genotypic covariance matrix has not yet been developed, especially for crossbred populations. Thus, the use of a genotypic model for BLUP is not suitable for genetic evaluation in large, crossbred populations. We present an equivalent model in which the genotypic effect is partitioned into additive and dominance effects. With this equivalent model, methods used for within-breed genetic evaluation by BLUP can be used for a two-breed terminal cross under dominance.