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by claude@2026-07, 2026-07-03
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The paper studies when multispecies coexistence can emerge in competitive communities even if every pair of species does not coexist, using simple trade-off models and random competitive communities. Across simulations and analyses, it shows that emergent coexistence can arise in communities where interactions are competitive, transitive, and pairwise, and it often occurs in hierarchical trade-off models and even in random model communities without pronounced intransitivity. The main caveat is that the study uses abstract ecological models rather than direct empirical data on real organisms. This paper does not explicitly discuss endometriosis or adenomyosis; it was included in the corpus via a keyword match in the upstream search index.
Abstract
Competitive coexistence is often understood as an additive process where coexisting species pairs, triplets, etc. combine to form larger communities. However, emergent coexistence – where multi-species persistence occurs without pairwise coexistence – can arise through mechanisms including intransitive loops, facilitation, or higher-order interactions. Emergent coexistence has functional consequences, for example constraining community assembly and reducing robustness to extinctions. Here, we demonstrate that emergent coexistence can arise without intransitivity in competitive communities with pairwise interactions. First, we develop a simple trade-off model where interactions are competitive, transitive, and pairwise, yet coexistence is emergent. Second, we show that coexistence is typically emergent in well-known hierarchical trade-off models. Third, we find that emergent coexistence frequently occurs without pronounced intransitivity in random model communities. Our results suggest that competitive coexistence may often be emergent, highlighting a need to better understand the mechanisms and prevalence of this phenomenon in order to reliably predict community assembly, robustness, and biodiversity maintenance.
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Abstract
Competitive coexistence is often understood as an additive process where coexisting species pairs, triplets, etc. combine to form larger communities. However, emergent coexistence – where multi-species persistence occurs without pairwise coexistence – can arise through mechanisms including intransitive loops, facilitation, or higher-order interactions. Emergent coexistence has functional consequences, for example constraining community assembly and reducing robustness to extinctions. Here, we demonstrate that emergent coexistence can arise without intransitivity in competitive communities with pairwise interactions. First, we develop a simple trade-off model where interactions are competitive, transitive, and pairwise, yet coexistence is emergent. Second, we show that coexistence is typically emergent in well-known hierarchical trade-off models. Third, we find that emergent coexistence frequently occurs without pronounced intransitivity in random model communities. Our results suggest that competitive coexistence may often be emergent, highlighting a need to better understand the mechanisms and prevalence of this phenomenon in order to reliably predict community assembly, robustness, and biodiversity maintenance.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
(zachary.miller{at}yale.edu)
(dmax2{at}ucla.edu)
Data Accessibility: Code to implement the models and reproduce all simulations and figures is available at https://github.com/zacharyrmiller/emergent_coexistence.
We made several clarifications in all sections of the manuscript. In particular, we added two new supplementary figures that help explain the mechanism behind emergent coexistence in our randomly simulated communities. We also discussed a new, relevant pre-print that complements our work.
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