Oscillations in Population Numbers: Age-Dependent Cannibalism

(1) Interactions among different age-classes or life stages within single species animal populations are quite common. As an example of this type of interaction, we focus attention on larval cannibalism of eggs in the flour beetle Tribolium. As we do not consider any benefit of cannibalism for larvae, the dynamics of this interaction are the same as those of competition where a later life stage preempts resources used by an earlier life stage. (2) A mathematical model of the egg-larval interaction allows for the evaluation of the impact of the duration of the egg and larval intervals, fecundity, survival and cannibalism rates on the stability of the equilibrium number of larvae. (3) The local stability boundary, which separates the region of parameter space leading only to unstable equilibria and oscillations from that region yielding the possibility of stable equilibria, is dramatically modified by the inclusion of age-dependence in the cannibalism by larvae. In contrast to a model ignoring this age-dependence, the model which includes age-dependence predicts that all flour beetle cultures should display oscillations in larval numbers. (4) Review of over a half-century of Tribolium experiments is consistent with the model's forecast: egg and larval numbers oscillate in all reported data sets.