Bayesian Estimation of Genetic Parameters

Abstract

A bayesian approach for estimating genetic parameters of quantitative traits, such as heritability and genetic correlation coefficient, was evaluated. In this estimation procedure, prior information on genetic parameters to be estimated (such as the proper ranges e.g.[0, 1] for heritability and [-1, l] for genetic correlation coefiicient) was used in the construction of prior distributions of the bayesian procedure, where the joint posterior distribution of the parameters was obtained by replacing the other parameters as the phenotypic mean, variance and covariance with their classical estimators. Processing the expectation of each of the genetic parameters in relation to the joint posterior distribution by numerical integration gave the bayesian estimators. We call this bayesian method 'hybrid bayesian estimation' and its estimator 'hybrid bayesian estimator' as a combination of 'bayesian' and 'classical' method was used. Statistical properties of hybrid bayesian estimators with classical and modified ones, which are obtained by setting the classical estimates beyond the proper ranges to the nearest bound values, were investigated in the case of one trait and two traits using Monte-Calor sirnulations. In the case of one trait, where only the heritability is of interest, simulations were carried out for two values of the heritability 0.2 and 0.8, while the phenotypic mean and variance were fixed at 0 and 1, respectively. It was shown that hybrid bayesian estimators have smaller m.s.e.'s (mean square errors) than classical and modified ones. In the case of two traits, where two heritabilities and a genetic correlation coefficient of two traits were jointly estimated, simulations were carried for two cases, first two heritabilities and a genetic correlation coefncient of 0.8, 0.2 and 0.0 and secondly 0.8, 0.2 and 0.5, respectively. The phenotypic mean vector and variance-covariance matrix were set at 0 and I₂ (2×2 identity matrix), respectively. Simulation results showed that for heritabilities, as in the case of one trait, hybrid bayesian estimators were superior to classical and modified ones while for the genetic correlation coefficient, the superiority of hybrid bayesian estimators was even more conspicuous. Therefore it is concluded that hybrid bayesian estimators of genetic parameters are superior to classical and modified ones and can be very useful in practice.