Evolution of cooperation in spatially variable ecological landscapes

How do spatial variations in environmental conditions shape the evolution of cooperation in finite populations? Environmental and ecological interactions can alter the benefits and costs of cooperation, as well as the background fitness of cooperators and defectors. Existing models of evolutionary games on lattice graphs yield Hamilton-like rule indicating when selection favors cooperators. We extend this framework to spatially heterogeneous environments represented by an arbitrary coloring map of the graph, where each node’s color is the local environmental quality denoting the local benefit in a donation game. Under weak selection, we show that spatial correlation of the environmental field (coloring map) is a determinant of fixation probability of cooperators. We also find that environmental variation can strongly affect cooperator abundance and often produces long-lived metastable states in which cooperators and defectors coexist. Finally, we discuss related results for environments in which heterogeneity affects the background fitness of cooperators and defectors.