Selection response in traits with maternal inheritance.

Maternal inheritance is the non-Mendelian transmission of traits from mothers to their offspring. Despite its presence in virtually all organisms, acting through a variety of mechanisms, the evolutionary consequences of maternal inheritance are not well understood. Here we review and extend a model of the inheritance and evolution of multiple quantitative characters with complex pathways of maternal effects. Extensions of the earlier model include common family environmental effects not associated with maternal phenotype, sexual dimorphism, and paternal effects (non-Mendelian influence of the father on offspring traits). We find that, in contrast to simple Mendelian inheritance, maternal inheritance produces qualitatively different evolutionary dynamics for two reasons: (1) the response to selection on a set of characters depends not only on their additive genetic variances and covariances, but also on maternal characters that influence them, and (2) time lags in the response to selection create a form of evolutionary momentum. These results have important implications for evolution in natural populations and practical applications in the economic improvement of domesticated species. We derive selection indices that maximize either the economic improvement in a single generation of artificial selection or the asymptotic rate of improvement in long-term selection programmes, based on individual merit or a combination of individual and family merit. Numerical examples show that accounting for maternal inheritance can lead to considerable increases in the efficiency of artificial selection.