A double-edged aspect of basin entropy for predicting biodiversity in spatial rock–paper–scissors games

Abstract

Basin entropy is a useful tool for predicting uncertainty in nonlinear dynamical systems, and it is proposed as a way to present biodiversity in the rock–paper–scissors game in a classic manner. As new interaction can be allowed in the system, such biodiversity can be changed, and the system can present different features. In this paper, we investigate the role of basin entropy in the spatial rock–paper–scissors (RPS) game, where the system allows competition within the same species, which can lead to various biodiversity. From extensive numerical simulations, we found that calculating basin entropy may be ambiguous in identifying biodiversity in the spatial RPS game, even if it plays an important role in the system in a classic manner. As intraspecific competition is induced, it disturbs the collective behaviors of species associated with the coexistence state and leads to the change in the level of basin entropy having various values. Similar phenomena are found by considering the symmetry-breaking of intraspecific competition that leads to diverse survival states. Our findings address that basin entropy can be a candidate to predict biodiversity but not always, and they may provide new insight into basin entropy in a different framework- a double-edged effect.