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Theoretical ecology

Coexistence holes fill a gap in community assembly theory

The mathematics of counting holes reveals hidden paths to species coexistence and the obstacles that block the way.

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Fig. 1: Alternative assembly hypergraphs, constructed from a collection of four species, and their corresponding Betti numbers.


  1. Gamow, G. Biography of Physics (Harper, 1961).

  2. Cang, Z., Mu, L. & Wei, G.-W. PLoS Comput. Biol. 14, e1005929 (2018).

    Article  Google Scholar 

  3. Reimann, M. W. et al. Front. Comput. Neurosci. 11, 48 (2017).

    Article  Google Scholar 

  4. Angulo, M. T., Kelley, A., Montejano, L., Song, C. & Saavedra, S. Nat. Ecol. Evol. (2021).

    Article  PubMed  Google Scholar 

  5. Ghrist, R. Bull. Am. Math. Soc. 45, 61–75 (2008).

    Article  Google Scholar 

  6. Chesson, P. Annu. Rev. Ecol. Syst. 31, 343–366 (2000).

    Article  Google Scholar 

  7. Friedman, J., Higgins, L. M. & Gore, J. Nat. Ecol. Evol. 1, 0109 (2017).

    Article  Google Scholar 

  8. Grilli, J., Barabás, G., Michalska-Smith, M. J. & Allesina, S. Nature 548, 210–213 (2017).

    CAS  Article  Google Scholar 

  9. Grainger, T. N., Levine, J. M. & Gilbert, B. Trends Ecol. Evol. 34, 925–935 (2019).

    Article  Google Scholar 

  10. Gould, A. L. et al. Proc. Natl Acad. Sci. USA 115, E11951–E11960 (2018).

    CAS  Article  Google Scholar 

  11. Letten, A. D. & Stouffer, D. B. Ecol. Lett. 22, 423–436 (2019).

    Article  Google Scholar 

  12. Fukami, T. Annu. Rev. Ecol. Evol. Syst. 46, 1–23 (2015).

    Article  Google Scholar 

Download references

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Correspondence to Andrew D. Letten.

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Letten, A.D. Coexistence holes fill a gap in community assembly theory. Nat Ecol Evol 5, 1062–1063 (2021).

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