Dynamical patterns of coexisting strategies in a hybrid discrete-continuum spatial evolutionary game model
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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 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, interms 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.
Burgess , A E F , Schofield , P G , Hubbard , S F , Chaplain , M A J & Lorenzi , T 2016 , ' Dynamical patterns of coexisting strategies in a hybrid discrete-continuum spatial evolutionary game model ' , Mathematical Modelling of Natural Phenomena , vol. 11 , no. 5 , pp. 49-64 . https://doi.org/10.1051/mmnp/201611504
Mathematical Modelling of Natural Phenomena
© 2016, ESO. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.mmnp-journal.org / https://dx.doi.org/10.1051/mmnp/201611504