Geodesic
Dynamical Patterns of Coexisting Strategies in a Hybrid Discrete-continuum Spatial Evolutionary Game Model
A.E.F. Burgess1 ; P.G. Schofield2 ; S.F. Hubbard2 ; M.A.J. Chaplain3 ; T. Lorenzi3
1 Division of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland
2 College of Life Sciences, University of Dundee, Dundee DD1 4HN, Scotland
3 School of Mathematics and Statistics, University of St Andrews St Andrews KY16 9SS, Scotland
Mathematical modelling of natural phenomena, Tome 11 (2016) no. 5, pp. 49-64 Cet article a éte moissonné depuis la source EDP Sciences

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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 discretisa- tion 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.
DOI : 10.1051/mmnp/201611504

A.E.F. Burgess 1 ; P.G. Schofield 2 ; S.F. Hubbard 2 ; M.A.J. Chaplain 3 ; T. Lorenzi 3

1 Division of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland
2 College of Life Sciences, University of Dundee, Dundee DD1 4HN, Scotland
3 School of Mathematics and Statistics, University of St Andrews St Andrews KY16 9SS, Scotland 
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A.E.F. Burgess; P.G. Schofield; S.F. Hubbard; M.A.J. Chaplain; T. Lorenzi. Dynamical Patterns of Coexisting Strategies in a Hybrid Discrete-continuum Spatial Evolutionary Game Model. Mathematical modelling of natural phenomena, Tome 11 (2016) no. 5, pp. 49-64. doi: 10.1051/mmnp/201611504

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