The interplay of rock-paper-scissors competition and environments mediates species coexistence and intriguing dynamics

Abstract Asymmetrical rock-paper-scissors (RPS) competition has been perceived as a crucial factor in shaping species biodiversity, and understanding this ecological issue in a multi-species paradigm is rather difficult because community dynamics usually depend on distinct factors such as abiotic environments, biotic interactions and symmetry-breaking phenomenon. To address this problem, we employ a Lotka-Volterra competitive system consisting of both symmetrical, asymmetrical interactions and abiotic environment components. We discover that that asymmetrical RPS competition in heterogeneous environments can yield much richer dynamical behaviors, compared to the symmetrical and asymmetrical competition in homogeneous environments. While it is observed that species coexistence outcomes and/or oscillatory solutions are maintained as in the case of homogeneous environments, the nonuniformity in the environmental carrying capacities may lead to extra dynamics with regards to the appearance of survival states; for instance, coexistence of any two-species and single-species persistence states, which are not evident in the previous modelling studies. By means of bifurcation analysis, various salient features of the dynamical systems, including the emergence of certain attractors (e.g., different steady states, stable limit cycles and heteroclinic cycles) and co-dimension one bifurcations (e.g., transcritical and supercritical Hopf bifurcations) are realized in this ecological model. Overall, this modelling work provides a novel attempt to simultaneously encompass not only symmetry-breaking phenomenon through RPS competition, but also heterogeneity in the environments. This framework can provide additional insights to better understand various mechanisms underlying the effects of distinct ecological processes on multi-species communities.