Shape matters: lifecycle of cooperative patches promotes cooperation in bulky populations

Natural cooperative systems take many forms, ranging from one-dimensional cyanobacteria arrays to fractal-like biofilms. We use in silico experimental systems to study a previously overlooked factor in the evolution of cooperation, physical shape of the population. We compare the emergence and maintenance of cooperation in populations of digital organisms that inhabit bulky (100 × 100 cells) or slender (4 × 2500) toroidal grids. Although more isolated subpopulations of secretors in a slender population could be expected to favor cooperation, we find the opposite: secretion evolves to higher levels in bulky populations. We identify the mechanistic explanation for the shape effect by analyzing the lifecycle and dynamics of cooperator patches, from their emergence and growth, to invasion by noncooperators and extinction. Because they are constrained by the population shape, the cooperator patches expand less in slender than in bulky populations, leading to fewer cooperators, less public good secretion, and generally lower cooperation. The patch dynamics and mechanisms of shape effect are robust across several digital cooperation systems and independent of the underlying basis for cooperation (public good secretion or a cooperation game). Our results urge for a greater consideration of population shape in the study of the evolution of cooperation across experimental and modeling systems.