Potential biases of incomplete linear models in heritability estimation and breeding value prediction

Potential biases associated with incomplete linear models in the estimation of heritability and the prediction of breeding values have been investigated. Results indicate that estimates of additive genetic variance and heritability as well as predicted parental breeding values from incomplete models will inevitably be biased as long as the true variance components of ignored effects are not zero. While models ignoring the interaction effect of males and females (SCA) × environment (E) interaction downwardly biased the estimates of additive genetic variance and heritability, models ignoring SCA and (or) the additive genetic effect (GCA) × E interaction yielded upward biases. The magnitudes of biases are functions of population genetic architecture, mating design, and field experimental design and can be precisely assessed with formulae derived for balanced data. Numerical simulations using unbalanced data of different mating and field experimental designs suggest that the formulae from balanced data can be used to approximate the minimum biases associated with unbalanced data. Because of the magnitudes of biases for some typical forest genetic scenarios, it is suggested that models ignoring SCA and (or) GCA × E should be avoided when the numbers of test sites and crosses per parent are small. However, incomplete model ignoring SCA × E interaction may be used to reduce computational demand with only negligible consequences.