On predator-prey interactions with predation dependent on age of prey

Abstract

This paper combines previously developed models for nonlinear age-dependent population dynamics with the classical Volterra-Lotka model of interacting predator and prey populations. For the resulting models the basic evolution equations of the theory reduce to systems of ordinary differential equations. The limiting dynamics of the predator and prey populations are shown to depend substantially on what ages of prey are eaten by predators. Two cases in particular are studied: where the predator eats all ages of prey indiscriminately, and where the predator eats only eggs (or newborns, equivalently). Indiscriminate eating is found to lead to stable periodic oscillations in numbers of predator and prey, such as occur in the Volterra-Lotka equations, while egg eating leads to oscillations which increase rapidly in amplitude and result, ultimately, in the extinction of both predator and prey. It is suggested that age-selective predation could be a more effective means of extinction than age-indiscriminate predation.