Tournament versus Circulant: On Simulating 7-Species Evolutionary Spatial Cyclic Games with Ablated Predator-Prey Networks as Models of Biodiversity

Abstract: Computer simulations of minimal population-dynamics models have long been used to explore questions in ecosystems coexistence and species biodiversity, via simple agent-based models of three interacting species, referred to as $R$, $P$, and $S$, and where individual agents compete with one another in predator/prey contests that are determined by the cyclic dominance rules of the Rock-Paper-Scissors game. Recent publications have explored the dynamics of five-species models, based on the Rock-Paper-Scissors-Lizard-Spock (RPSLS) game. A 2022 paper by Zhong et al. reported simulation studies of species coexistence in spatial RPSLS systems in which one or more directed edges are ablated from the five-vertex tournament digraph defining the RPSLS game: Zhong et al. showed that the ablation of a single inter-species interaction can lead to a collapse in biodiversity. In this paper I present first results from simulation studies of evolutionary spatial cyclic games where there are seven species, but where each species is still in its own local five-species RPSLS-like interaction network: the dominance networks I use for this are a subset of the $n$-node $k$-regular circulant digraphs $D(n,\Omega)$ for odd-numbered $n$ and $|\Omega|=2$. My results indicate that Zhong et al.'s results are due to the specific fully-connected tournament dominance network used in their RPSLS model: when other, equally realistic, RPSLS-style dominance networks are used instead, no such sudden collapse in biodiversity occurs. The Python source-code used for the work reported here is freely available on GitHub.