Dynamical patterns of coexisting strategies in a hybrid discrete-continuum spatial evolutionary game model
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, 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.
Citation
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
Publication
Mathematical Modelling of Natural Phenomena
Status
Peer reviewed
ISSN
0973-5348Type
Journal article
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