MATING DESIGNS FOR ESTIMATING DIRECT AND MATERNAL GENETIC VARIANCES AND DIRECT-MATERNAL GENETIC COVARIANCES

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Abstract
The problem of obtaining unbiased estimates of direct and maternal genetic variances and direct-maternal genetic covariances often is encountered when studying quantitative traits of mammalian and other dioecious diploid populations. Direct genetic variance is used in the classical sense as defined originally by Sir Ronald Fisher. Three mating designs are proposed which permit simultaneous estimation of 6 genetic and 2 environmental parameters. The 3 designs yield 13, 10 and 12 different types of relatives, respectively. Expected genetic covariances between relatives are derived assuming no epistasis. The genetic parameters that can be estimated include direct additive and dominance variances, maternal additive and dominance variances and direct-maternal additive and dominance covariances. The non-genetic parameters are random and maternal environmental variances. A least squares'' procedure is employed in order to obtain unbiased estimates of the 8 parameters. The vector of observed covariances between relatives is the set of dependent variables, while the matrix of expected coefficients for each of the 8 parameters is the set of independent variables. The 8 unknown causal components of variance and covariance then are solved as partial regression coefficients. The matrices of simple correlations among the various coefficients are very similar for the 3 mating designs, since 8 of the 16 different types of relatives are common to all 3 designs. A criterion is presented for determining the most appropriate of the 3 designs to use under certain conditions.