Enhancement of persistence in the rock-paper-scissors dynamics through higher-order interactions

Higher-order interactions (HOIs) are ubiquitous in real systems, and HOIs among individuals complicate the exploration of species diversity for populations in ecosystems. Therefore, understanding how higher-order interactions affect biodiversity is essential but poses significant challenges. In this paper, we consider higher-order interactions in the competitive processes of spatial rock-paper-scissors (RPS) dynamics, specifically within spatially embedded hyper-lattices, and investigate what biodiversity can be driven by HOIs. Considering hyperedges, species in hyperedges can be different, and different relationships are considered, which can eventually demonstrate the strength of competition. With the competition intensity modulated by the sensitivity of HOIs, extensive simulations have shown that higher-order competitive processes can promote coexistence. We also found that stratification of species densities occurs when three species coexist due to HOIs, which are closely related to the increase of empty sites and disordered spiral entanglement. From investigating the extinction probability in a broad aspect, it has been found that, even if HOIs are working, the coexistence in the system is eventually broken at high mobility regimes. The intensified sensitivity to HOIs can somewhat alleviate extinction, although no striking change has occurred. Our findings may address that modeling predator-prey interactions incorporating HOIs is important for gaining insights into biodiversity, and we hope our study may provide a broad aspect for exploring complex ecosystems.