On Long-Term Species Coexistence in Five-Species Evolutionary Spatial Cyclic Games with Ablated and Non-Ablated Dominance Networks

TL;DR

This paper replicates and refutes prior findings on species coexistence in a five-species spatial cyclic game, showing that true long-term outcomes require much longer simulations and that ablations mainly affect convergence time, not ultimate states.

Contribution

It demonstrates that long-term asymptotic behaviors in the five-species cyclic game are only observable after extensive simulations, challenging previous shorter-term results and clarifying the effects of network ablations.

Findings

Long simulation times are necessary to observe true asymptotic outcomes.

Ablations mainly affect the convergence time, not the final states.

Unablated and ablated systems tend to share similar long-term outcomes.

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 100,000 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 10,000,000MCS 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.