AN APPROXIMATION OF THE MINIMUM-VARIANCE ESTIMATOR OF HERITABILITY BASED ON VARIANCE COMPONENT ANALYSIS

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Abstract
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.