Seasonal Variation in a Predator-Predator-Prey Model

Abstract

Seasonal shifts in predation habits, from a generalist in the summer to a specialist in the winter, have been documented for the great horned owl (Bulbo virginialis) in the boreal forest. This shift occurs largely due to varying prey availability. There is little study of this switching behaviour in the current literature. Since season length is predicted to change under future climate scenarios, it is important to understand resulting effects on species dynamics. Previous work has been done on a two-species seasonal model for the great horned owl and its focal prey, the snowshoe hare (Lepus americanus). In this thesis, we extend the model by adding one of the hare's most important predators, the Canadian lynx (Lynx canadensis). We study the qualitative behaviour of this model as season length changes using tools and techniques from dynamical systems. Our main approach is to determine when the lynx and the owl may invade the system at low density and ask whether mutual invasion of the predators implies stable coexistence in the three-species model. We observe that, as summer length increases, mutual invasion is less likely, and we expect to see extinction of the lynx. However, in all cases where mutual invasion was satisfied, the three species stably coexist.