Stochastic growth reduces population fluctuations in Daphnia-algal systems

Deterministic, size-structured models are widely used to describe consumer-resource interactions. Such models typically ignore potentially large random variability in juvenile development rates. We present simple representations of this variability and show five approaches to calculating the model parameters for Daphnia pulex interacting with its algal food. Using our parameterized models of growth variability, we investigate the robustness of a recently proposed stabilizing mechanism for Daphnia populations. Growth rate variability increases the range of enrichments over which small-amplitude cycles or quasi-cycles occur, thus increasing the plausibility that the underlying mechanism contributes to the prevalence of small-amplitude cycles in the field and in experiments. More generally, our approach allows us to relate commonly available information on variance of development times to population stability.