Persistence of cooperation in diffusive public goods games

Journal article, 2019

Diffusive public goods (PG) games are difficult to analyze due to population assortment affecting growth rates of cooperators (producers) and free-riders. We study these growth rates using spectral decomposition of cellular densities and derive a finite cell-size correction of the growth rate advantage which exactly describes the dynamics of a randomly assorted population and approximates the dynamics under limited dispersal. The resulting effective benefit-to-cost ratio relates the physical parameters of PG dynamics to the persistence of cooperation, and our findings provide a powerful tool for the analysis of diffusive PG games, explaining commonly observed patterns of cooperation.