Point Estimators of Heritability Based on Confidence Intervals: a Closed-form Approximation to the Reml Estimator

95 Estimating heritability, the proportion of variation in phenotypic values due to (additive) genetic effects, is an important subject matter to plant and animal breeders alike. In most applications there is not an analytic expression for the restricted maximum likelihood (REML) estimator of heritability since it is obtained via an iterative procedure. The focus of this paper is to find a closed-form approximation to the REML estimator of heritability for those scenarios in which mixed linear models having two variance components are appropriate. This procedure is equivalent to constructing approximate pivotal quantities and thus confidence intervals for heritability. See Burch and Iyer (1997) and Harris and Burch (2000) for more details concerning this approach. The closed-form estimator is compared to the REML estimator by evaluating their asymptotic standard errors. An application involving yearling bulls from a Red Angus seed stock herd suggests that the closed-form estimator mimics the REML estimator and is a viable candidate for investigators seeking a non-iterative method to estimate heritability.