Fluctuations-induced coexistence in public goods dynamics
Cooperative interactions, their stability and evolution, provide an interesting context in which to study the interface between cellular and population levels of organization. Such interactions also open the way for the discovery of new population dynamics mechanisms.
We have studied a version of the public goods model relevant to microorganism populations actively extracting a growth resource from their environment. Cells can display one of two phenotypes – a productive phenotype that extracts the resources at a cost, and a non-productive phenotype that only consumes the same resource. We analyze the continuous differential equation model as well as simulate stochastically the full dynamics. It is found that the two sub-populations, which cannot coexist in a well-mixed environment, develop spatio-temporal patterns that enable long-term coexistence in the shared environment. These patterns are solely fluctuation-driven, since the continuous system does not display Turing instability. The average stability of the coexistence patterns derives from a dynamic mechanism in which one sub-population holds the environmental resource close to an extinction transition of the other, causing it to constantly hover around its critical transition point, forming a mechanism reminiscent of selforganized criticality. Accordingly, power-law distributions and long-range correlations are found.
When a time scale separation occurs between two dynamic parameters is defined, a structurally unstable point emerges and any small perturbation of the dynamics with additive noise leads to an equilibrium distribution in which both species coexist in context of additive but not multiplicative noise.