A differential game theoretical analysis of mechanistic models for territoriality.
In this paper, elements of differential game theory are used to analyze a spatially explicit home range model for interacting wolf packs when movement behavior is uncertain. The model consists of a system of partial differential equations whose parameters reflect the movement behavior of individuals within each pack and whose steady-state solutions describe the patterns of space-use associated to each pack. By controlling the behavioral parameters in a spatially-dynamic fashion, packs adjust their patterns of movement so as to find a Nash-optimal balance between spreading their territory and avoiding conflict with hostile neighbors. On the mathematical side, we show that solving a nonzero-sum differential game corresponds to finding a non-invasible function-valued trait. From the ecological standpoint, when movement behavior is uncertain, the resulting evolutionarily stable equilibrium gives rise to a buffer-zone, or a no-wolf's land where deer are known to find refuge.
Hamelin
Frédéric M
FM
Centre for Mathematical Biology, Mathematical and Statistical Sciences, University of Alberta, 632 Central Academic Building, Edmonton, AB, T6G 2G1, Canada. fhamelin@agrocampus-ouest.fr
Lewis
Mark A
MA
D000465:Algorithms; D000818:Animals; D017753:Ecosystem; D005246:Feedback; D005716:Game Theory; D008954:Models, Biological; D011235:Predatory Behavior; D013731:Territoriality; D019596:Wolves / Q000502:physiology*