Predicting the purebred-crossbred genetic correlation from the genetic variance components in the parental lines

Abstract Background The genetic correlation between purebred and crossbred performance ( $${r}_{pc}$$ r pc ) is an important parameter in pig and poultry breeding, because response to selection in crossbred performance depends on the value of $${r}_{pc}$$ r pc when selection is based on purebred (PB) performance. The value of $${r}_{pc}$$ r pc can be substantially lower than 1, which is partly due to differences in allele frequencies between parental lines when non-additive genetic effects are present. This relationship between $${r}_{pc}$$ r pc and parental allele frequencies suggests that $${r}_{pc}$$ r pc can be expressed as a function of genetic parameters for the trait in the parental lines. In this study, we derived expressions for $${r}_{pc}$$ r pc based on genetic variances within, and the genetic covariance between parental lines. It is important to note that the variance components used in our expressions are not the components that are typically estimated in empirical data. The expressions were derived for a genetic model with additive and dominance effects (D), and additive and epistatic additive-by-additive effects (EAA). We validated our expressions using simulations of purebred parental lines and their crosses, where the parental lines were either selected or not. Finally, using these simulations, we investigated the value of $${r}_{pc}$$ r pc for genetic models with both dominance and epistasis or with other types of epistasis, for which expressions could not be derived. Results Our simulations show that when non-additive effects are present, $${r}_{pc}$$ r pc decreases with increasing differences in allele frequencies between the parental lines. Genetic models that involve dominance result in lower values of $${r}_{pc}$$ r pc than genetic models that involve epistasis only. Using information of parental lines only, our expressions provide exact estimates of $${r}_{pc}$$ r pc for models D and EAA, and accurate upper and lower bounds of $${r}_{pc}$$ r pc for two other genetic models. Conclusion This work lays the foundation to enable estimation of $${r}_{pc}$$ r pc from information collected in PB parental lines only.