Supplementary Mathematica Sheet from Evolution of epigenetic transmission when selection acts on fecundity versus viability

Existing theory on the evolution of parental effects and the inheritance of non-genetic factors has mostly focused on the role of environmental change. By contrast, how differences in population demography and life history affect parental effects is poorly understood. To fill this gap, we develop an analytical model to explore how parental effects evolve when selection acts on fecundity versus viability in spatio-temporally fluctuating environments. We find that regimes of viability selection, but not fecundity selection, are most likely to favour parental effects. In the case of viability selection, locally adapted phenotypes have a higher survival than maladapted phenotypes and hence become enriched in the local environment. Hence, simply by being alive, a parental phenotype becomes correlated to its environment (and hence informative to offspring) during its lifetime, favouring the evolution of parental effects. By contrast, in regimes of fecundity selection, correlations between phenotype and environment develop more slowly: this is because locally adapted and maladapted parents survive at equal rates (no survival selection), so that parental phenotypes, by themselves, are uninformative about the local environment. However, because locally adapted parents are more fecund, they contribute more offspring to the local patch than maladapted parents. In case these offspring are also likely to inherit the adapted parents’ phenotypes (requiring pre-existing inheritance), locally adapted offspring become enriched in the local environment, resulting in a correlation between phenotype and environment, but only in the offspring’s generation. Because of this slower build-up of a correlation between phenotype and environment essential to parental effects, fecundity selection is more sensitive to any distortions due to environmental change than viability selection. Hence, we conclude that viability selection is most conducive to the evolution of parental effects. This article is part of the theme issue ‘How does epigenetics influence the course of evolution?’.