Role of adaptive intraspecific competition on collective behavior in the rock–paper–scissors game

Density-dependent selection is a universal feature in the evolution of populations, and such an adaptive behavior can change the survival strategy of species during evolution. In this paper, we investigate the role of adaptive behavior in biodiversity in the system of cyclic competition. By incorporating a density-dependent mechanism into intraspecific competition, which is well-known as a key mechanism leading to biodiversity, we studied how such adaptive intraspecific competition can affect biodiversity and collective behavior during the evolution of cyclically competing species. Microscopically, we found that species can coexist strongly and are spirally entangled or collectively united by presenting two distinct pattern formations on spatially extended systems. While the adaptive mechanism can always promote species coexistence in a mean-field manner for particular sensitivity to the group scale, corresponding spatial dynamics exhibit nonmonotonic features for the robustness of extinction at moderately high mobility regime over the critical mobility when the associated mean-field system exhibits asymptotically stable heteroclinic cycles. The findings can shed light on a new aspect of the collective behavior of coexisting populations which may indicate the possibility of changing the survival strategies of each group to maintain the coexistence of cyclically competing populations.