The use of the relationship matrix to account for genetic drift variance in the analysis of genetic experiments

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Abstract
Selection experiments can provide information on genetic parameters such as realized heritability and response to selection. Often, due to lack of adequate replication, empirical sampling variances of estimated response cannot be computed and therefore use must be made of theoretical formulae. Most of the variance between a conceptually large number of selected lines drawn from the same base population is contributed by genetic drift, which depends on the population structure and can therefore be predicted before the experiment is carried out. The theory of variation of response to selection has been developed mainly by Hill, who produced formulae to adjust the variance of estimators to take account of genetic drift. In this paper, we draw attention to properties of the additive genetic relationship matrix that lead to well established results in population genetics theory. We show how inclusion of the additive genetic relationship matrix among the observations leads to sampling variances of estimators of genetic means that account for the variance due to genetic drift.