Evolutionary dynamics in the cyclic competition system of seven species: Common cascading dynamics in biodiversity

Complex systems in ecological science can be generally defined by either the number of different species or the structure among species having many relations, and understanding the given interaction structure is essential to predict the evolution of ecosystems. In this paper, we propose a multi-species system whose competition can occur cyclically. By exploiting the generalized system of cyclic competition among seven species, we explore how species biodiversity can appear when the generalized system is established by possessing the underlying mechanism of rock–paper–scissors (RPS) and rock–paper–scissors–lizard–spock (RPSLS) games. Through Monte-Carlo simulations, similar to the RPSLS system having the phase transition in biodiversity from five to one containing the three species survival in the middle, the model for seven species also exhibits similar cascading features in the biodiversity as mobility increases, validated by measuring the survival probability. We also found that not every cyclic structured system among seven species exhibits a common cascading feature in the transition in biodiversity. It is revealed that such a characteristic may require sufficient structures of RPS-like subgroups. Our findings may provide insights into the biodiversity of cyclically competing species and the link to predict biodiversity associated with the interaction structure in the microscopic framework.