An age-structured Lotka-Volterra model and the emergence of overcompensation

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. We construct an age-structured single-species population model that incorporates a Lotka-Volterra-type cannibalism interaction. Depending on the structure of the interaction, our model can exhibit overcompensation as well as oscillations of the total population; both phenomena 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.