The mathematics of cooperation in spatially structured populations

Tommaso Lorenzi (University of St Andrews, UK)


Abstract:
The occurrence of cooperation is a major conundrum in the biological and social sciences. To unravel this evolutionary riddle, several models have been developed within the theoretical framework of spatial game theory. Generally, explicit movement is not considered in these models, with strategies moving via imitation or through colonisation of neighbouring sites. We present here a stochastic individual-based model and an equivalent partial differential equation model which describe the evolutionary dynamics of spatial games in the presence of diffusion-based dispersal. Analyses and numerical simulations of these models lead the way to a deeper understanding of the critical mechanisms underpinning the evolution of cooperation in spatially structured populations.

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