How to Behave Around Cannibals: A Density-Dependent Dynamic Game

Abstract

The fate of a cannibalistic cohort developing in a seasonal environment hinges on a complex array of interacting features, prominently including a size-specific, density-dependent trade-off between growth and survival, mediated by activity and constrained by a seasonal time horizon. The dynamic size structure of such a cohort is partly self-imposed and partly determined by alternative prey availability, noncannibalistic sources of mortality, and other factors. In the work reported here, we derive a new model of cannibalism that incorporates these features and requires us to obtain numerical solutions of a density-dependent dynamic game between stages within the developing cohort. The convergence method used to find the solutions should prove useful for other dynamic ecological models as well. The results indicate that the optimal levels of predator activity predicted by the model are particularly sensitive to parameter shifts; changes in activity mediate and damp growth, survival, and fitness responses. The ratio of mortality rate to growth rate may be approximately minimized (as predicted in other theoretical analyses) even within cannibalistic cohorts constrained by seasons, unless there is no advantage to reaching intermediate or larger sizes during the season. Except when cannibalism is particularly intense overall or increases in intensity with the absolute size of the potential cannibal, within-cohort cannibalism should generally tend to synchronize the cohort, yielding survivors more uniform in size than would result at lower intensities. Finally, stock-recruitment curves derived from the results imply stable generation-to-generation dynamics, though low alternative prey availabilities and high fecundities can generate oscillatory behavior consistent with published observations.