Population overcompensation, transients, and oscillations in age-structured Lotka-Volterra models

There has been renewed interest in understanding the mathematical structure of ecological population models that lead to overcompensation, the process by which a population recovers to a higher level after suffering an increase in predation or harvesting. Here, we construct an age-structured single-species population model that includes a Lotka-Volterra-type cannibalism interaction. Depending on the age-dependent structure of the interaction, our model can exhibit transient or steady-state overcompensation–as well as oscillations of the total population–phenomena that have been observed in ecological systems. Analytic and numerical analysis of our model reveals sufficient conditions for overcompensation and oscillations. We also show how our structured population PDE model can be reduced to coupled ODE models representing piecewise constant parameter domains, providing additional mathematical insight into the emergence of overcompensation.