Ecological communities are characterized by the interactions among the species living within a given habitat and can be conveniently represented as networks of interactions. Variation in the way the interactions are organized in the network determines whether the ecological community is able to support coexistence and resist collapse. Analyzing network properties can thus provide insights as to why some species persist while others go extinct and provide solutions to one of community ecology’s central aim, the prediction of community structure at equilibrium. In this work, we highlight an approach that makes use of the properties of the network to determine the equilibrium species composition and richness in a number of competition networks represented by complete directed graphs (tournaments). We show that in any tournament, all non-kings get eliminated resulting in a smaller tournament in which every species is a king. At this point, the pairwise interactions among species are not sufficient to determine community structure and it is the interactions among the intransitive triads of the tournament that fundamentally determine how many species persist.

中文翻译：

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在生态竞争网络中消除非国王，不及格的三合会互动和物种共存

生态群落的特征是生活在给定栖息地内的物种之间的相互作用，可以方便地表示为相互作用网络。网络中交互组织方式的变化决定了生态社区是否能够支持共存和抵抗崩溃。因此，分析网络特性可以提供一些物种为何存留而其他物种却灭绝的原因的见解，并为解决社区生态学的中心目标之一-平衡状态下的社区结构的预测-提供解决方案。在这项工作中，我们重点介绍一种利用网络的属性来确定由完全有向图（锦标赛）表示的多个竞争网络中的平衡物种组成和丰富度的方法。我们证明在任何比赛中 所有非国王都将被淘汰，从而导致规模较小的锦标赛，其中每个物种都是国王。在这一点上，物种之间的成对相互作用不足以确定群落结构，而比赛的不及格三合会之间的相互作用从根本上决定了有多少物种存在。