While natural communities can contain hundreds of species, modern coexistence theory focuses primarily on species pairs. Alternatively, the structural stability approach considers the feasibility of equilibria, gaining scalability to larger communities but sacrificing information about dynamic stability. Three‐species competitive communities are a bridge to more‐diverse communities. They display novel phenomena while remaining amenable to mathematical analysis, but remain incompletely understood. Here, we combine these approaches to identify the key quantities that determine three‐species competition outcomes. We show that pairwise niche overlap and fitness differences are insufficient to completely characterize competitive outcomes, which requires a strictly triplet‐wise quantity: cyclic asymmetry, which underlies intransitivity. Low pairwise niche overlap stabilizes the triplet, while high fitness differences promote competitive exclusion. The effect of cyclic asymmetry on stability is complex and depends on pairwise niche overlap. In summary, we elucidate how pairwise niche overlap, fitness differences and cyclic asymmetry determine three‐species competition outcomes.

中文翻译：

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三物种问题：将竞争性不对称性和不及物性纳入现代共存理论

虽然自然群落可以包含数百个物种，但现代共存理论主要关注物种对。或者，结构稳定性方法考虑平衡的可行性，获得更大社区的可扩展性，但牺牲有关动态稳定性的信息。三物种竞争性群落是通向更加多样化群落的桥梁。它们展示了新颖的现象，同时仍然适合数学分析，但仍然不完全被理解。在这里，我们结合这些方法来确定决定三种物种竞争结果的关键数量。我们表明，成对的生态位重叠和适应度差异不足以完全表征竞争结果，这需要严格的三元组数量：循环不对称性，它是不及物性的基础。低的成对生态位重叠可以稳定三联体，而高的适应度差异会促进竞争排斥。循环不对称对稳定性的影响很复杂，并且取决于成对的生态位重叠。总之，我们阐明了成对生态位重叠、适应度差异和循环不对称性如何决定三物种竞争结果。