标题： 循环优势的八种物种群体中的联盟竞争 显示英文标题

标题： Competition of alliances in a cyclically dominant eight-species population

摘要： 在一个包含许多物种的多样化群体中，竞争者可以在个体和集体层面为生存而竞争。 特别是，那些在个体层面上能够互相击败的物种，可能会形成一种特定的联盟，从而确保它们在面对外来物种入侵时的稳定共存。 我们的主要目标是识别决定这种形成物活力的一般特征。 因此，我们在这里研究了一个传统的八物种Lotka-Volterra模型，其中两个四物种循环体可以争夺空间。 除了这些形成物之外，当入侵率变化时，还可能有其他解出现。 我们探索了完整的参数范围，并发现大多数情况下占优势的是由实力相等的成员组成的联盟。 有趣的是，存在一些区域，其中对称性被打破，系统由由七个物种形成的解主导。 我们的工作还强调了严重的有限尺寸效应可能出现，这会阻止在小系统中观察到有效的解。 显示英文摘要

摘要： In a diverse population, where many species are present, competitors can fight for surviving at individual and collective levels. In particular, species, which would beat each other individually, may form a specific alliance that ensures them stable coexistence against the invasion of an external species. Our principal goal is to identify those general features of a formation which determine its vitality. Therefore, we here study a traditional Lotka-Volterra model of eight-species where two four-species cycles can fight for space. Beside these formations, there are other solutions which may emerge when invasion rates are varied. The complete range of parameters is explored and we find that in most of the cases those alliances prevail which are formed by equally strong members. Interestingly, there are regions where the symmetry is broken and the system is dominated by a solution formed by seven species. Our work also highlights that serious finite-size effects may emerge which prevent observing the valid solution in a small system.