A mathematical model of the evolution of individual differences in developmental plasticity arising through parental bet-hedging

Abstract

Children vary in the extent to which their development is shaped by particular experiences (e.g. maltreatment, social support). This variation raises a question: Is there no single level of plasticity that maximizes biological fitness? One influential hypothesis states that when different levels of plasticity are optimal in different environmental states and the environment fluctuates unpredictably, natural selection may favor parents producing offspring with varying levels of plasticity. The current article presents a mathematical model assessing the logic of this hypothesis - specifically, it examines what conditions are required for natural selection to favor parents to bet-hedge by varying their offspring's plasticity. Consistent with existing theory from biology, results show that between-individual variation in plasticity cannot evolve when the environment only varies across space. If, however, the environment varies across time, selection can favor differential plasticity, provided fitness effects are large (i.e. variation in individuals' plasticity is correlated with substantial variation in fitness). Our model also generates a novel restriction: Differential plasticity only evolves when the cost of being mismatched to the environment exceeds the benefits of being well matched. Based on mechanistic considerations, we argue that bet-hedging by varying offspring plasticity, if it were to evolve, would be more likely instantiated via epigenetic mechanisms (e.g. pre- or postnatal developmental programming) than genetic ones (e.g. mating with genetically diverse partners). Our model suggests novel avenues for testing the bet-hedging hypothesis of differential plasticity, including empirical predictions and relevant measures. We also discuss several ways in which future work might extend our model.