On Long-Term Species Coexistence in Five-Species Evolutionary Spatial Cyclic Games with Ablated and Non-Ablated Dominance Networks
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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 (E scg ) Rock-Paper-Scissors-Lizard-Spock (R psls ) with certain predator-prey relationships removed from the game’s “interaction structure”, i.e. with specific arcs ab-lated in the E scg ’s dominance network, and with the E scg 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 empiri-cally demonstrate that the dynamics of the R psls E scg have sufficiently long time constants that the true asymptotic outcomes can often only be identified after running the ablated E scg 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 R psls system exhibits essentially the same asymptotic outcomes as the ablated R psls 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.
Graphical Abstract
Highlights
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I replicate key results from Zhong et al. (2022) where biodiversity was explored via the game Rock-Paper-Scissors-Lizard-Spock (R psls ).
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Zhong et al. reported results from R psls games where specific predatorprey interactions were ablated from the game’s dominance network.
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My replication reveals problems in Zhong et al.’s design of experiments.
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Zhong et al. did not run their simulations for sufficiently long to reveal the true asymptotic behavior of the ablated R psls systems.
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Zhong et al. did not present control outcomes from the unablated R p - sls system, so there is no baseline data for comparison to the treatment outcomes.
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I present results from simulations that are run for 100 to 1000 times longer than the experiments reported by Zhong et al., thereby revealing the true asymptotic behaviors of the system.
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The asymptotic outcomes are remarkably uniform – practically indistinguishable – in the cases where one, two, or three arcs are ablated from the R psls dominance network.
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My asymptotic results for the baseline original unablated system are also very similar to those for the one-two- and three-ablation systems.
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My results question whether the ablations have any effect other than speeding the system’s convergence to its eventual asymptotic state.
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Results from Zhong et al.’s four-ablation system do not fit so well with the lower-ablation-count systems: potential reasons for this, and avenues for further research on it, are discussed.
