发表机构
Max Planck Institute of Molecular Cell Biology and Genetics; Center for Systems Biology Dresden; Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克分子细胞生物学与遗传学研究所; 德累斯顿系统生物学中心; 马克斯·普朗克科学数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过分类不可能生态网络并证明高阶互作可克服成对模型的符号障碍，揭示了生态与博弈中稳定共存的可行条件及与对称博弈均衡的联系。
AI 中文摘要
我们研究了Lotka-Volterra系统及其高阶扩展的可行稳定平衡点。我们完成了最多包含四个物种的不可能生态互作网络的分类，并将其中若干不可能性结果推广到具有任意多个物种的族。随后我们证明，这些符号模式障碍是成对Lotka-Volterra模型所特有的：任意给定的增长率与成对系数可以通过补充高阶互作，从而允许存在可行的渐近稳定平衡点。通过复制子动力学的对应关系，我们将高阶Lotka-Volterra系统的可行平衡点解释为对称多人博弈的全混合对称纳什均衡，推导出其数量的界，并研究其在支付张量扰动下的稳健性。最后我们证明，每个不可能的生态学都确定了一个非空的对称两人博弈开类，该类博弈不存在全混合进化稳定策略。
英文摘要
We study feasible stable equilibria of Lotka-Volterra systems and their higher-order extensions. We complete the classification of impossible ecological interaction networks with at most four species and extend several of these impossibility results to families with arbitrarily many species. We then show that these sign-pattern obstructions are specific to the pairwise Lotka-Volterra model: arbitrary prescribed growth rates and pairwise coefficients can be supplemented by higher-order interactions so as to admit a feasible asymptotically stable equilibrium. Through the correspondence with replicator dynamics, we interpret feasible equilibria of higher-order Lotka-Volterra systems as totally mixed symmetric Nash equilibria of symmetric multiplayer games, derive bounds on their number, and study their robustness under perturbations of the payoff tensors. We conclude by showing that every impossible ecology determines a nonempty open class of symmetric two-player games with no totally mixed evolutionarily stable strategy.
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