Diversification of investment strategies in an ecological public goods game driven by the spatial structure of the population

Ecology and evolution work in tandem to create biodiversity, especially when they act on similar timescales, as can happen in microbial populations. Frequency and density dependent ecological models, like the public goods game, are known to be capable of supporting diverse populations. Recent experiments have shown diversification of gene expression in a bacterial population for a gene expressing a public good. Motivated by these observations we study an ecological public goods model and compare the extent to which mutations can fix in a population and generate diversity in a well-mixed situation and one with spatial structure. We show that rapid diversification within an ecological public goods game can drastically vary depending on the time scale of evolution and the time scale of ecological dynamics. While populations in a well-mixed model quickly come to equilibrium, limiting the amount of diversity typically to two dominant investment strategies; models with spatial structure prolong the time to equilibrium and allow multiple mutants to fix themselves in the population. Our theoretical studies agree with the experimental observations and point to a general principle how ecological public good games in spatially extended microbial population can lead to rapid diversification.