Parental effects and the evolution of phenotypic memory

Despite growing evidence for nongenetic inheritance, the ecological conditions that favour the evolution of heritable parental or grandparental effects remain poorly understood. Here, we systematically explore the evolution of parental effects in a patch‐structured population with locally changing environments. When selection favours the production of a mix of offspring types, this mix differs according to the parental phenotype, implying that parental effects are favoured over selection for bet‐hedging in which the mixture of offspring phenotypes produced does not depend on the parental phenotype. Positive parental effects (generating a positive correlation between parental and offspring phenotype) are favoured in relatively stable habitats and when different types of local environment are roughly equally abundant, and can give rise to long‐term parental inheritance of phenotypes. By contrast, unstable habitats can favour negative parental effects (generating a negative correlation between parental and offspring phenotype), and under these circumstances, even slight asymmetries in the abundance of local environmental states select for marked asymmetries in transmission fidelity.