Theoretical Ecology

, Volume 10, Issue 4, pp 443–450 | Cite as

Reduction of species coexistence through mixing in a spatial competition model

  • Senay YitbarekEmail author
  • John H. Vandermeer


Many ecological systems exhibit self-organized spatial patterns due to local interactions. Such patterns can promote species diversity and therefore serve as an important mechanism for biodiversity maintenance. Previous work has shown that when species interactions occurred at local spatial scales, species diversity was greatest when robust mosaic spatial patterns formed. Also, intransitive interactions led to the emergence of spiral patterns, frequently resulting in multispecies coexistence. In some instances, intransitive interactions reduced species diversity as the consequence of competitive hierarchies. Here, we extend and broaden this line of investigation and examine the role of global competition along a continuum ranging from spatial mosaics to spiral patterns. While previous models have predicted that species diversity is reduced when interactions occur over larger spatial scales, our model considers the effects of various levels of mixing on species diversity, in the context of various network structures as measured by the covariance of row and column sums of the competition matrix. First, we compare local competition (unmixed system) versus global competition (mixed systems) and show that greater species diversity is maintained under a positive covariance. Second, we show that under various levels of mixing, species diversity declines more rapidly under a negative covariance. Lastly, we demonstrate that time to extinction in our model occurs much more rapidly under a negative covariance.


Spatial self-organization Cellular automata Coexistence Biodiversity 


  1. Chesson P (2000) Mechanisms of maintenance of species diversity. Annu Rev Ecol Syst 31:343–366CrossRefGoogle Scholar
  2. Durrett R, Levin S (1998) Spatial aspects of interspecific competition. Theor Popul Biol 53:30–43. doi: 10.1006/tpbi.1997.1338 CrossRefPubMedGoogle Scholar
  3. Frean M, Abraham ER (2001) Rock–scissors–paper and the survival of the weakest. Proc R Soc Lond B Biol Sci 268:1323–1327. doi: 10.1098/rspb.2001.1670 CrossRefGoogle Scholar
  4. Gause GF (1932) Experimental studies on the struggle for existence I. Mixed population of two species of yeast. J Exp Biol 9:389–402Google Scholar
  5. Goldberg DE, Landa K (1991) Competitive effect and response: hierarchies and correlated traits in the early stages of competition. J Ecol 79:1013–1030. doi: 10.2307/2261095 CrossRefGoogle Scholar
  6. Hubbell SP (2001) The unified neutral theory of biodiversity and biogeography. Princeton Monographs in Population Biology. Princeton University Press, PrincetonGoogle Scholar
  7. Huisman J, Weissing FJ (1999) Biodiversity of plankton by species oscillations and chaos. Nature 402:407–410. doi: 10.1038/46540 CrossRefGoogle Scholar
  8. Huisman J, Weissing FJ (2001) Fundamental unpredictability in multispecies competition. Am Nat 157:488–494. doi: 10.1086/319929 CrossRefPubMedGoogle Scholar
  9. Kerr B, Riley MA, Feldman MW, Bohannan BJM (2002) Local dispersal promotes biodiversity in a real-life game of rock–paper–scissors. Nature 418:171–174. doi: 10.1038/nature00823 CrossRefPubMedGoogle Scholar
  10. Laird RA, Schamp BS (2008) Does local competition increase the coexistence of species in intransitive networks. Ecology 89:237–247. doi: 10.1890/07-0117.1 CrossRefPubMedGoogle Scholar
  11. Laird RA, Schamp BS (2015) Competitive intransitivity, population interaction structure, and strategy coexistence. J Theor Biol 365:149–158. doi: 10.1016/j.jtbi.2014.10.010 CrossRefPubMedGoogle Scholar
  12. May R, Leonard W (1975) Nonlinear aspects of competition between three species. SIAM J Appl Math 29:243–253. doi: 10.1137/0129022 CrossRefGoogle Scholar
  13. Rojas-Echenique J, Allesina S (2011) Interaction rules affect species coexistence in intransitive networks. Ecology 92:1174–1180. doi: 10.1890/10-0953.1 CrossRefPubMedGoogle Scholar
  14. Schreiber SJ, Killingback TP (2013) Spatial heterogeneity promotes coexistence of rock–paper–scissors metacommunities. Theor Popul Biol 86:1–11. doi: 10.1016/j.tpb.2013.02.004 CrossRefPubMedGoogle Scholar
  15. Sinervo B, Lively CM (1996) The rock–paper–scissors game and the evolution of alternative male strategies. Nature 380:240–243. doi: 10.1038/380240a0 CrossRefGoogle Scholar
  16. Szabó G, Szolnoki A, Izsák R (2004) Rock-scissors-paper game on regular small-world networks. J Phys Math Gen 37:2599. doi: 10.1088/0305-4470/37/7/006 CrossRefGoogle Scholar
  17. Vandermeer J, Yitbarek S (2012) Self-organized spatial pattern determines biodiversity in spatial competition. J Theor Biol 300:48–56. doi: 10.1016/j.jtbi.2012.01.005 CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Integrative BiologyUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of Ecology and Evolutionary BiologyUniversity of MichiganAnn ArborUSA

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