Density-dependent intraspecific competitions among cyclically competing three species

Abstract

Density-dependent processes often occur in ecological fields. In this paper, we propose a model for cyclically competing species who can do density-dependent intraspecific competition and investigate the effect of the balance between density-dependence for intraspecific competition and the coexistence. When intraspecific competition occur depending on species' density, we found robust coexistence of three species which is contrast to classic rock-paper-scissors games. The transition from coexistence to extinction is uncovered with a nonmonotonic behavior in the extinction probability which is especially occurred at small degree of the strength for density-dependence. Further, we found specific pattern formations on spatially extended systems. Whether the degree of density-dependence is low or high, plane wave formations arise for moderated of mobility when the coexistence occurs. Our results suggest that density-dependent process is quite important for species coexistence even cyclic structured populations.