Contrasting effects of dispersal network heterogeneity on ecosystem stability in rock-paper-scissors games

Abstract

Intransitive competition, typically represented by the classic rock-paper-scissors game, provides an endogenous mechanism promoting species coexistence. As well known, species dispersal and interaction in nature might occur on complex patch networks, with species interacting in diverse ways. However, the effects of different interaction modes, combined with spatial heterogeneity in patch connectivities, have not been well integrated into our general understanding of how stable coexistence emerges in cyclic competition. We thus incorporate network heterogeneity into the classic rock-paper-scissors game, in order to compare ecosystem stability under two typical modes of interaction: species compete to fill empty sites, and species seize each other’s colony sites. On lattice-structured regular networks, the two interaction modes produce similar stability patterns through forming conspecific clusters to reduce interspecific competition. However, for heterogeneous networks, the interaction modes have contrasting effects on ecosystem stability. Specifically, if species compete for colony sites, increasing network heterogeneity stabilizes competitive dynamics. When species compete to fill empty sites, an increase in network heterogeneity leads to larger population fluctuations and therefore a higher risk of stochastic extinctions, in stark contrast to current knowledge. Our findings strongly suggest that particular attention should be devoted to testing which mode of interaction is more appropriate for modeling a given system.