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.