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.
Dynamical Patterns of Coexisting Strategies in a Hybrid Discrete-continuum Spatial Evolutionary Game Model / Burgess, A. E. F.; Schofield, P. G.; Hubbard, S. F.; Chaplain, M. A. J.; Lorenzi, T.. - In: MATHEMATICAL MODELLING OF NATURAL PHENOMENA. - ISSN 0973-5348. - STAMPA. - 11:5(2016), pp. 49-64.
|Titolo:||Dynamical Patterns of Coexisting Strategies in a Hybrid Discrete-continuum Spatial Evolutionary Game Model|
|Data di pubblicazione:||2016|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1051/mmnp/201611504|
|Appare nelle tipologie:||1.1 Articolo in rivista|
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