Journal of Mathematical Biology

, Volume 61, Issue 5, pp 665–694 | Cite as

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.


Spatial ecology Behavioral ecology Home range analysis Evolutionary games Function-valued traits 

Mathematics Subject Classification (2000)

35Q84 49K15 91A23 91A22 92B05 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Centre for Mathematical Biology, Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  2. 2.Écologie et Sciences PhytosanitairesAGROCAMPUS OUESTRennes CedexFrance

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