Question: Does space stabilize or destabilize cooperation ?

Background and Previous Models: The emergence and abundance of cooperation in nature poses a challenging puzzle to evolutionary biology. Traditional approaches to studying the problem of cooperation assume constant population sizes and thus neglect the ecology of the interacting individuals. Ecological public goods game considers dynamics of group size in public goods game. As multiplication rate (total return on investment) is fixed, cooperation is adaptive strategy when public goods game is played by fewer members (because the return is shared by fewer members). We assume the average number of players in each public goods game is determined by population density. Then, low density facilitates evolution of cooperation and high density facilitates evolution of defection. On the other hand, large ratio of cooperators to defectors results in effective population growth. Thus, the system has a tendency toward coexistence of cooperators and defectors.

Model: We allow cooperators and defectors to diffuse in two-dimensional space. The spatial ecological public goods game is denoted by reaction-diffusion equations.

Results: Coexistence region always expands when both extinction and coexistence are locally stable without space. Coexistence is sometimes achieved by spatially heterogenous pattern. Furthermore, spatial coexistence is achieved for some parameters that do not allow coexistence without space. Such spatial effect is often achieved by spatially chaotic dynamics (Many funny movies are shown in the talk).