循环竞争群落中奇偶性的影响

中文摘要 AI 辅助

表现出循环（即“无赢家”）竞争的群落普遍存在于自然界中。这些系统根据物种间竞争的强度以及相互作用物种数量的一项特定属性——奇偶性，可以表现出性质上不同的长期行为。我们考虑生态群落如何适应并在奇数与偶数个循环竞争物种之间进行转变。先前的研究表明，在强烈的物种间竞争下，奇数奇偶性群落是动态不稳定的，而偶数奇偶性群落中的物种则形成最大非竞争集合的稳定联盟。我们追踪了两个May-Leonard型模型之间的同伦：奇数奇偶性的N=3模型和偶数奇偶性的N=4系统。我们识别了所有物理稳态并分析了它们的稳定性。我们证明了在我们的对称模型中存在的稳定过渡态的唯一性。然后，我们使用分段线性近似技术来表征异宿环的稳定性。我们使用数值模拟来描绘参数空间中的不同区域。我们的计算证实了我们的分析结果，并揭示了参数空间中一个出现极限环的窗口。我们说明奇偶性转变可能是复杂的，并以多种依赖于参数的路径为特征。

英文摘要

Communities exhibiting cyclic (i.e., ``winnerless'') competition occur throughout nature. These systems can exhibit qualitatively different long-term behavior depending on the strength of inter-species competition and a specific property of the number of interacting species: parity. We consider how ecological communities can adapt to and transition between an odd and an even number of cyclically competing species. Previous studies have shown that, for strong inter-species competition, odd parity communities are dynamically unstable, while species in even parity communities form stable alliances of maximal noncompeting sets. We trace a homotopy between two May-Leonard type models: the odd parity N=3 model and the even parity N=4 system. We identify all physical steady states and analyze their stabilities. We show the existence of stable transitional states that are unique to our symmetric model. We then use a piecewise linear approximation technique to characterize the stability of heteroclinic cycles. We use numerical simulations to map distinct regimes in parameter space. Our computations confirm our analytical results and also reveal a window in parameter space where limit cycles occur. We illustrate that parity transitions can be complex and characterized by diverse parameter-dependent pathways.

发表机构

• Northwestern University（西北大学）

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