On long-term species coexistence in five-species evolutionary spatial cyclic games with ablated and non-ablated dominance networks

Abstract

I present a replication and, to some extent, a refutation of key results published by Zhong, Zhang, Li, Dai, & Yang in their 2022 paper “Species coexistence in spatial cyclic game of five species” (Chaos, Solitons and Fractals, 156: 111806), where ecosystem species coexistence was explored via simulation studies of the evolutionary spatial cyclic game (Escg) Rock–Paper–Scissors–Lizard–Spock (Rpsls) with certain predator–prey relationships removed from the game’s “interaction structure”, i.e. with specific arcs ablated in the Escg’s dominance network, and with the Escg run for $10^5$ Monte Carlo Steps (mcs) to identify its asymptotic behaviors. I replicate the results presented by Zhong et al. for interaction structures with one, two, three, and four arcs ablated from the dominance network. I then empirically demonstrate that the dynamics of the Rpsls Escg have sufficiently long time constants that the true asymptotic outcomes can often only be identified after running the ablated Escg for $10^7$ mcs or longer, and that the true long-term outcomes can be markedly less diverse than those reported by Zhong et al. as asymptotic. Finally I demonstrate that, when run for sufficiently many mcs, the original unablated Rpsls system exhibits essentially the same asymptotic outcomes as the ablated Rpsls systems, and in this sense the only causal effect of the ablations is to alter the time required for the system to converge to the long-term asymptotic states that the unablated system eventually settles to anyhow.