Ecological feedback on diffusion dynamics

Spatial patterns are ubiquitous across different scales of organization. Animal coat pattern, spatial organization of insect colonies, and vegetation in arid areas are prominent examples from such diverse ecologies. Typically, pattern formation has been described by reaction-diffusion equations, which considers individuals dispersing between sub-populations of a global pool. This framework applied to public goods game nicely showed the endurance of populations via diffusion and generation of spatial patterns. However, how the spatial characteristics, such as diffusion, are related to the eco-evolutionary process as well as the nature of the feedback from evolution to ecology and vice versa, has been so far neglected. We present a thorough analysis of the ecologically driven evolutionary dynamics in a spatially extended version of ecological public goods games. We show how these evolutionary dynamics feedback into shaping the ecology thus together determining the fate of the system.