Abstract
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.
Highlights
In predator-prey communities, population dynamics strongly depend on the way in which a prey responds to a predator, i.e., how many prey are killed and how frequently [9, 23]
We model the three-species system with a set of ordinary differential equations (ODEs), where we express the rate of change in a species density as a function of the density itself
Our study is inspired by the snowshoe hare, Canadian lynx and great horned owl system in western Canada, where the owl acts as a generalist predator in the summer and as a specialist in the winter, while the lynx is a specialist predator year round [17]
Summary
In predator-prey communities, population dynamics strongly depend on the way in which a prey responds to a predator, i.e., how many prey are killed and how frequently [9, 23]. The authors divided the year into two seasons and modelled the owl as a generalist in the summer and a specialist in the winter. In most of our analysis, we highlight and distinguish the parameter T , which represents in our model the proportion of the year corresponding to summer, and we discuss the effects of this parameter on such ecologically relevant issues as species coexistence and extinction In this way, it is possible to make predictions on the potential effects of global warming and climate change on these issues. The summer model alone (i.e., setting T = 1) contains a two-dimensional invariant subsystem of hare and owl dynamics (i.e., y = 0) that was independently analyzed in [8]; see [19] for a related model It exhibits periodic orbits, bistability, and nonlocal bifurcations. The region where 0 ≤ x ≤ 1, 0 ≤ y ≤ Y and 0 ≤ z ≤ Z is compact and forward invariant
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