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Coexistence of many species in random ecosystems


Rich ecosystems harbour thousands of species interacting in tangled networks encompassing predation, mutualism and competition. Such widespread biodiversity is puzzling, because in ecological models it is exceedingly improbable for large communities to stably coexist. One aspect rarely considered in these models, however, is that coexisting species in natural communities are a selected portion of a much larger pool, which has been pruned by population dynamics. Here we compute the distribution of the number of species that can coexist when we start from a pool of species interacting randomly, and show that even in this case we can observe rich, stable communities. Interestingly, our results show that, once stability conditions are met, network structure has very little influence on the level of biodiversity attained. Our results identify the main drivers responsible for widespread coexistence in natural communities, providing a baseline for determining which structural aspects of empirical communities promote or hinder coexistence.

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Fig. 1: Number of coexisting species when interactions and intrinsic growth rates are randomly sampled from the standard normal distribution.
Fig. 2: Number of coexisting species for competitive interactions.
Fig. 3: Effect of network structure on coexistence for the case of nonzero means.


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We thank D. Maynard and G. Barabás for comments. C.A.S. and S.A. were supported by NSF-DEB 1148867; J.G. by the Human Frontier Science Program; and J.A.C. by the Spanish Ministerio de Economa y Competitividad project CGL2015-69034-P. A Fulbright Fellowship (programme FMECD-ST-2016, grant number CAS16/00096) allowed J.A.C. to visit the University of Chicago.

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S.A. and C.A.S. devised the study; C.A.S. and K.E.M. solved the mean-zero case; J.A.C. and J.G. the nonzero-mean case; S.A. wrote the main text; J.A.C., C.A.S. and J.G. wrote the Supplementary Information; C.A.S. drew the figures; all authors edited the manuscript.

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Correspondence to Stefano Allesina.

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Supplementary Methods, Supplementary Results, Supplementary Figures 1–5, Supplementary References

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Serván, C.A., Capitán, J.A., Grilli, J. et al. Coexistence of many species in random ecosystems. Nat Ecol Evol 2, 1237–1242 (2018).

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