How to Account for Past Selection When Maternal Effects Are Cascading

Many forms of maternal effects are said to be 'cascading', in which an individual's phenotype is partially a function of its mother's phenotype. The mother's phenotype is also partially a function of the grandmother's phenotype, and so each individual phenotype depends on the phenotypes of all its previous maternal lineage ancestors. In previous work we developed quantitative genetics models to assess the evolutionary consequences of such cascading maternal effects under pragmatic modelling assumptions. Here we show that the theoretical framework underlying our previous studies should be extended to treat past maternal states as being under selection in the current generation to account more consistently for the cascading nature of phenotypic parental effects. While accommodating selection of past maternal states does not significantly change the qualitative results of our previous studies, we find typically small quantitative changes in the evolving genetic components, offspring phenotype and fitness. The extended framework offers a conceptually more consistent approach that can inform future quantitative genetics models of parental effects. In particular this new formulation captures the impact of genetic covariances between current and past states on the evolutionary dynamics, and provides a flexible framework that can be adapted to analyse transgenerational influences from any combination of ancestors.