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Abstract 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. 

Abstract Ongoing climate change is shifting species distributions and increasing extinction risks globally. It is generally thought that large population sizes and short generation times of marine phytoplankton may allow them to adapt rapidly to global change, including warming, thus limiting losses of biodiversity and ecosystem function. Here, we show that a marine diatom survives high, previously lethal, temperatures after adapting to above‐optimal temperatures under nitrogen (N)‐replete conditions. N limitation, however, precludes thermal adaptation, leaving the diatom vulnerable to high temperatures. A trade‐off between high‐temperature tolerance and increased N requirements may explain why N limitation inhibited adaptation. Because oceanic N limitation is common and likely to intensify in the future, the assumption that phytoplankton will readily adapt to rising temperatures may need to be reevaluated.