Estimation of Heritability from Experiments with Inbred and Related Individuals

Abstract

SUMMARY Assuming an arbitrary amount of inbreeding and certain types of relationships among individuals in the parent population, it is shown how for nested and diallel mating designs the genetic and environmental variance components can be estimated from the mean squares in the usual analyses of variance. The systems of equations are given explicitly for the case of equal numbers of offspring per mating. A method for dealing with unequal numbers of offspring is outlined. In a previous paper (Hinkelmann [1969]) modifications of the usual procedures for estimating heritability from nested and diallel mating designs were given for the case that the dams are related. It was shown how this relationship induces a certain covariance structure for some random effects in the underlying linear model. However, just as the variance components can be expressed in terms of genetic and environmental variance components, these covariance components are simply functions of the genetic variance components and the coefficients of relationship. Since the coefficients of relationship can be evaluated from the pedigree, it is then easy to estimate the genetic and environmental variance components from the mean squares in the usual analysis of variance, and hence estimate heritability. In the present paper this method is extended to allow for an arbitrary amount of inbreeding and certain types of relationships in the parental population. The most general situation would be to allow for all types of relationships, i.e., among sires, among dams, and among sires and dams. This, however, may lead to inbreeding in the offspring generation which in turn leads to problems in evaluatiing covariances between relatives, an approach on which the results in this paper are based. Harris [1964] has developed formulae for the covariance between inbred relatives which involve additional genetic parameters not present in the usual covariance formulae for non-inbred relatives (e.g. Kempthorne [1957]). These parameters are not estimable from the usual mating designs. Also, Cockerham [1963] and Harris [19641 give special conditions under which the covariance between inbred