Territorial expansions in public goods games

Demographic noise in ecological species can significantly alter deterministic outcomes, for example concerning the survival of producers (a less fit species) in public goods games. Here, we discuss the importance of stochastic effects, encoded in our work in two different classes of models for the prisoner's dilemma as one type of public goods game, on both producer stability and spatial properties (concerning the expansion of the dominant species). In one model, interaction and reproduction take place locally on a patch, while in the other model, single players on one patch each interact across patches. While pattern formation occurs for both models, it is crucial for determining producer stability only in the latter. We then discuss how these models affect spatial patterns as production costs vary, and focus specifically on the expansion velocity and front properties in these systems. By doing so, we intend to elucidate both the role of spatial habitats and migration between them, as well as identify behaviour that may help to distinguish between these models experimentally.