Structural stability of coexistence in evolutionary dynamics of cyclic competition

One of the common assumptions in previous spatial dynamics of cyclic competition is that, regardless of competing structure and strength among species, the spatial size of a network is considered as large as possible to avoid finite size effect for species biodiversity. In real ecosystems, however, species richness, which can be defined by spatial size and competition strength, can sensitively affect species coexistence as a competition among individuals becomes complicated. In this paper, we investigate the structural stability of coexistence of mobile species in three cyclic competition games due to network complexity in which imposes a size of a square lattice and competition strength among species. By exploiting the coexistence probability, our computations quantitatively reveal that the network complexity due to changes in the competition rate and lattice size can strongly affect the structural stability of coexistence in each model. In particular, intense intraspecific competition can yield the robust coexistence at small-sized lattices regardless of mobility, and strengthening interspecific competition simultaneously induces changes in critical mobility that hampers coexistence and in spatial size for stable coexistence. Qualitatively, we find that such structural stability of coexistence relates to the degree of stability of fixed points in deterministic systems. Our finding can be useful to gain insights into species coexistence on spatially extended systems with respect to network complexity. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

The study investigates the structural stability of coexistence of mobile species in cyclic competition games, finding that network complexity strongly affects the stability of coexistence by changes in competition rate and lattice size. Intense intraspecific competition leads to more robust coexistence in small-sized lattices, while strengthening interspecific competition changes critical mobility and spatial size for stable coexistence. The finding provides insights into species coexistence on spatially extended systems with respect to network complexity.