Local densities connect spatial ecology to game, multilevel selection and inclusive fitness theories of cooperation.

Cooperation plays a crucial role in many aspects of biology. We use the spatial ecological metrics of local densities to measure and model cooperative interactions. While local densities can be found as technical details in current theories, we aim to establish them as central to an approach that describes spatial effects in the evolution of cooperation. A resulting local interaction model neatly partitions various spatial and non-spatial selection mechanisms. Furthermore, local densities are shown to be fundamental for important metrics of game theory, multilevel selection theory and inclusive fitness theory. The corresponding metrics include structure coefficients, spatial variance, contextual covariance, relatedness, and inbreeding coefficient or F-statistics. Local densities serve as the basis of an emergent spatial theory that draws from and brings unity to multiple theories of cooperation.