Abstract

Experiments with the flour beetle Tribolium revealed that animal numbers were higher in cultures grown in a periodically fluctuating volume of medium than in cultures grown in a constant volume of the same average size. Habitat volume is incorporated into a discrete stage-structured model of population growth by allowing all rates of cannibalism (larve on eggs, adults on eggs and pupae) to be inversely proportional to the volume of the culture medium. For parameter estimates derived statistically from the experimental data, this model predicts a larger (cycle-average) total population abundance when the habitat volume periodically fluctuates (with an amplitude as used in the experiment) than when the habitat volume is held constant (at the average size). This model prediction is consistent with the experimental observations. For habitat fluctuations of smaller amplitude than those used in the experiments, a region of multiple attractors is predicted by the model. One attracting cycle displays reduced population abundance, due to the habitat fluctuations, while the other "resonates" with the periodic habitat and displays larger population adundance. The analyses involve a thorough integration of mathematics, statistical methods, and biological detail.