Effects of competition on means, variances and covariances in quantitative genetics with an application to general combining ability selection

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Abstract
General expressions are established for means, variances and covariances, taking into account the effect of interactions between individuals. For simplicity, only groups of size two are considered so that interactions are restricted to pairs of individuals; genetic effects are reduced to additivity and to additive × additive interaction between the direct effect of an allele and the associate effect of another. The effect of family structure is studied, and some consequences of interest to plant breeding are discussed by an application to general combining ability selection. From a population genetic point of view, this approach reveals a new application of coefficients of kinship.