A Proposed Framework for Establishing Optimal Genetic Designs for Estimating Narrow-sense Heritability

We develop a framework for establishing sample sizes in breeding plans, so that one is able to estimate narrow-sense heritability with smallest possible variance, for a given amount of effort. We call this an optimal genetic design. The framework allows one to compare the variances of estimators of narrow-sense heritability, when estimated from each one of the alternative plans under consideration, and does not require data simulation, but does require computer programming. We apply it to the study of a peanut (Arachis hypogaea) breading example, in order to determine the ideal number of plants to be selected at each generation. We also propose a methodology that allows one to estimate the additive genetic variance for the estimation of the narrow-sense heritability using MINQUE and REML, without an analysis of variance model. It requires that one can build the matrix of genetic variances and covariances among the subjects on which observations are taken. This methodology can be easily adapted to ANOVA-based methods, and we exemplify by using Henderson's Method III. We compare Henderson's Method III, MINQUE, and REML under the proposed methodology, with an emphasis on comparing these estimation methods with non-normally distributed data and unbalanced designs. A location-scale transformation of the beta density is proposed for simulation of non-normal data.