The contribution of dominance to the understanding of quantitative genetic variation.

Knowledge of the genetic architecture of a quantitative trait is useful to adjust methods for the prediction of genomic breeding values and to discover the extent to which common assumptions in quantitative trait locus (QTL) mapping experiments and breeding value estimation are violated. It also affects our ability to predict the long-term response of selection. In this paper, we focus on additive and dominance effects of QTL. We derive formulae that can be used to estimate the number of QTLs that affect a quantitative trait and parameters of the distribution of their additive and dominance effects from variance components, inbreeding depression and results from QTL mapping experiments. It is shown that a lower bound for the number of QTLs depends on the ratio of squared inbreeding depression to dominance variance. That is, high inbreeding depression must be due to a sufficient number of QTLs because otherwise the dominance variance would exceed the true value. Moreover, the second moment of the dominance coefficient depends only on the ratio of dominance variance to additive variance and on the dependency between additive effects and dominance coefficients. This has implications on the relative frequency of overdominant alleles. It is also demonstrated how the expected number of large QTLs determines the shape of the distribution of additive effects. The formulae are applied to milk yield and productive life in Holstein cattle. Possible sources for a potential bias of the results are discussed.