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- Title
Dynamical Patterns of Coexisting Strategies in a Hybrid Discrete-continuum Spatial Evolutionary Game Model.
- Authors
Burgess, A. E. F.; Schofield, P.G.; Hubbard, S. F.; Chaplain, M. A. J.; Lorenzi, T.
- Abstract
We present a novel hybrid modelling framework that takes into account two aspects which have been largely neglected in previous models of spatial evolutionary games: random motion and chemotaxis. A stochastic individual-based model is used to describe the player dynamics, whereas the evolution of the chemoattractant is governed by a reaction-diffusion equation. The two models are coupled by deriving individual movement rules via the discretisation of a taxis-diffusion equation which describes the evolution of the local number of players. In this framework, individuals occupying the same position can engage in a two-player game, and are awarded a payoff, in terms of reproductive fitness, according to their strategy. As an example, we let individuals play the Hawk-Dove game. Numerical simulations illustrate how random motion and chemotactic response can bring about self-generated dynamical patterns that create favourable conditions for the coexistence of hawks and doves in situations in which the two strategies cannot coexist otherwise. In this sense, our work offers a new perspective of research on spatial evolutionary games, and provides a general formalism to study the dynamics of spatially-structured populations in biological and social contexts where individual motion is likely to affect natural selection of behavioural traits.
- Subjects
GAME theory; CHEMOTAXIS; PROBABILITY theory; DIFFUSION; DISCRETE &; continuous games
- Publication
Mathematical Modelling of Natural Phenomena, 2016, Vol 11, Issue 5, p49
- ISSN
0973-5348
- Publication type
Article
- DOI
10.1051/mmnp/201611504