An approximation of the minimum-variance estimator of heritability based on variance component analysis.

An approximate minimum-variance estimate of heritability (h(2)) is proposed, using the sire and dam components of variance from a hierarchical analysis of variance. The minimum sampling variance is derived for unbalanced data. Optimum structures for the estimation of h(2) are given for the balanced case. The degree to which ĥ(2) is more precise than the equally weighted estimate ĥ(2) (S+D) is a function of the size and structure of the sample used. However, computer simulation reveals that ĥ(2) has less desirable behavior than ĥ(2) (S+D). An iterative procedure improved the estimation of h(2), especially in small populations, when those values of ĥ(2) (S) or ĥ(2) (D) outside the range of the parameter were constrained to zero or unity.