Metapopulation model of rock-scissors-paper game with subpopulation-specific victory rates stabilized by heterogeneity

The effect of habitats and fitness on species coexistence in systems with cyclic dominance

Cyclic dominance between species may yield spiral waves that are known to provide a mechanism enabling persistent species coexistence. This observation holds true even in presence of spatial heterogeneity in the form of quenched disorder. In this work we study the effects on spatio-temporal patterns and species coexistence of structured spatial heterogeneity in the form of habitats that locally provide one of the species with an advantage. Performing extensive numerical simulations of systems with three and six species we show that these structured habitats destabilize spiral waves. Analyzing extinction events, we find that species extinction probabilities display a succession of maxima as function of time, that indicate a periodically enhanced probability for species extinction. Analysis of the mean extinction time reveals that as a function of the parameter governing the advantage of one of the species a transition between stable coexistence and unstable coexistence takes place. We also investigate how efficiency as a predator or a prey affects species coexistence.

A potential game approach to modelling evolution in a connected society

When studying human behaviour, it is important to understand not just how individuals interact, but also interactions at the level of communities and populations. Most previous modelling of networks has focused on interactions between individual agents. Here we provide a modelling framework to study the evolution of behaviour in connected populations, by regarding subpopulations as the basic unit of interaction and focusing on the population-level connection structure. We find that when the underlying game played by individuals is a potential game, utilizing such a structure greatly simplifies analysis. In addition, according to known general results on the convergence of evolution dynamics to Nash equilibria in a potential game, our formulation provides a tractable model on behavioural dynamics in social networks that needs only conventional techniques from evolutionary game theory.