Eco-evolutionary spatial dynamics of non-linear social dilemmas

Spatial dynamics can promote the evolution of cooperation. While dispersal processes have been studied in simple evolutionary games, real-world social dilemmas are much more complicated. The public good, in many cases, does not increase linearly as per the investment in it. When the investment is low, for example, every additional unit of the investment may help a lot to increase the public good, but the effect vanishes as the number of investments increase. Such non-linear behaviour is the norm rather than an exception in a variety of social as well as biological systems. We take into account the non-linearity in the payoffs of the public goods game as well as the natural demographic effects of population densities. Population density has also been shown to impact the evolution of co-operation. Coupling these non-linear games and population size effect together with an explicitly defined spatial structure brings us one step closer to the complexity of real eco-evolutionary spatial systems. We show how the non-linearity in payoffs, resulting in synergy or discounting of public goods can alter the effective rate of return on the cooperative investment. Synergy or discounting in public goods accumulation affects the resulting spatial structure, not just quantitatively but in some cases, drastically changing the outcomes. In cases where a linear payoff structure would lead to extinction, synergy can support the coexistence of cooperators and defectors. The combined eco-evolutionary trajectory can thus be qualitatively different in cases on non-linear social dilemmas.