Seasonal dynamics of a generalist and a specialist predator on a single prey

In ecological communities, the behaviour of individuals and the interaction between species may change between seasons, yet this seasonal variation is often not represented explicitly in mathematical models. As global change is predicted to alter season length and other climatic aspects, such seasonal variation needs to be included in models in order to make reasonable predictions for community dynamics. The resulting mathematical descriptions are nonautonomous models with a large number of parameters, and are therefore challenging to analyze. We present a model for two predators and one prey, whereby one predator switches hunting behaviour to seasonally include alternative prey when available. We use a combination of temporal averaging and invasion analysis to derive simplified models and determine the behaviour of the system, in particular to gain insight into conditions under which the two predators can coexist in a changing climate. We compare our results with numerical simulations of the temporally varying model.