Maternal effects and the stability of population dynamics in noisy environments

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Abstract
Summary: It is widely appreciated that complex population dynamics are more likely in systems where there is a lag in the density dependence. The transmission of maternal environmental conditions to offspring phenotype is a potential cause of such a lag. Maternal effects are increasingly found to be common in a wide range of organisms, and might thus be a frequent cause of nonequilibrium population dynamics. We show that a maternal effects’ lag generally increases population variability. This may result from the lag inducing cycles (or more complex dynamics) in a deterministic environment or, in a stochastic environment, from the lag interacting with environmental noise to produce more variable dynamics than would otherwise occur. This may happen whether the underlying dynamics are equilibrium, periodic or more complex. Although maternal effects may generally destabilize dynamics there are a clear set of exceptions to this. For example, including a maternal lag may convert cycles to equilibrium dynamics, which may revert to cycles when external noise is added. The influence of the maternal effect depends importantly on the details of the model, whether it is structured or unstructured, the life‐history traits which are maternally affected, and the type of density dependence. Our results indicate that, if maternal effects are possible, failure to include them in models used predictively may result in quantitatively, and perhaps qualitatively, poor predictions.