Neighborhood size-effects in nonlinear public goods games

Ecological and evolutionary dynamics can be strongly affected by population assortment and frequency-dependent selection. In growing populations, a particular challenge is to disentangle global ecological effects from local frequency-dependent effects. Here we implement a logistic growth and death model on the global scale, coupled to frequency-dependent growth rates influenced by a public goods game between cooperators and defectors. For each individual, the public good is only effective within a neighborhood of other individuals, and the public good-growth rate relationship can be nonlinear. At low numbers of cooperators, increases of public good accumulate synergistically; at high numbers, increases in public good only provide diminishing returns-the inflection point of this pattern is given by the strength of frequency-dependent selection in relation to the background fitness effect. We observed complex critical behavior in the evolutionary dynamics equilibria, determined by the relative magnitude of frequency-dependent to constant (background) growth benefits. We predict neighborhood-size-driven state changes, hysteresis between polymorphic and monomorphic equilibria, and observed that type-dependent differences in neighborhood sizes can destabilize monomorphic cooperative states but increase coexistence of cooperators and defectors. Stochastic neighborhood size fluctuations also led to coexistence and could stabilize the purely cooperative equilibrium. Our results quantify the role of assortment through neighborhood-size effects and nonlinearity of the gains function in eco-evolutionary dynamics, which is relevant for a variety of microbial and cellular public goods games.