Computing heritability and selection response from unbalanced plant breeding trials

Heritability is often used by plant breeders and geneticists as a measure of precision of a trial or a series of trials. Its main use is for computing the response to selection. Most formulas proposed for calculating heritability implicitly assume balanced data and independent genotypic effects. Both of these assumptions are often violated in plant breeding trials. This article proposes a simulation-based approach to tackle the problem. The key idea is to directly simulate the quantity of interest, e.g., response to selection, rather than trying to approximate it using some ad hoc measure of heritability. The approach is illustrated by three examples.