Cannibalistic Egg-Larva Interactions in Tribolium: An Explanation for the Oscillations in Population Numbers

Abstract

We develop a model of larval cannibalism of Tribolium eggs that is both analytically and numerically tractable and that is consistent with available data on Tribolium dynamics. The model consists of a system of nonlinear integral equations amenable to a bifurcation analysis. We are thus able to predict the presence of multiple attractors for the same parameter values in the model. Our model lets us determine the effect of varying cannibalism rates, fecundity, survival, and lengths of egg and larval stages on stability. In particular, intermediate lengths for larval stages are least stable, and increasing the length of the egg stage is always destabilizing. The model thus provides a conceptual framework for further studies of Tribolium dynamics.