Genotype ✕ Environment Interaction Bias to Parent‐Offspring Regression Heritability Estimates1

Parent‐offspring regression is a commonly‐used technique for estimating narrow sense herltability of quantitative characters in crop species. However, regression of progeny means on parent values evaluated in the same or similar environments may lead to biased heritabillty estimates. This bias arises from genotype ✕ environment interaction and error covarlances between parents and progenies. This paper deals with the theoretical effects of these covariances on parent‐offspring regression heritability estimates and emphasizes some considerations necessary in estimating heritability. Covariance analysis is recommended as a method of obtaining more meaningful narrow sense heritabillty estimates than simple parent‐offspring regression for a set of parents and their offspring evaluated in a set of environments.