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Theoretical Ecology

, Volume 10, Issue 2, pp 207–215 | Cite as

Dissecting the role of transitivity and intransitivity on coexistence in competing species networks

  • Julio M. AlcántaraEmail author
  • Manuel Pulgar
  • Pedro J. Rey
ORIGINAL PAPER

Abstract

It is well established that intransitively assembled interaction networks can support the coexistence of competing species, while transitively assembled (hierarchical) networks are prone to species loss through competitive exclusion. However, as the number of species grows, the complexity of ecological interaction networks grows disproportionately, and species can get involved simultaneously in transitive and intransitive groups of interactions. In such complex networks, the effects of intransitivity on species persistence are not straightforward. Dissecting networks into intransitive/transitive components can help us to understand the complex role that intransitivity may play in supporting species diversity. We show through simulations that those species participating in the largest group of intransitive interactions (the core of the network) have high probabilities of persisting in the long term. However, participation in a group of intransitive interactions other than the core does not always improve persistence. Likewise, participating in transitive interactions does not always decrease persistence because certain species (the satellites) transitively linked to the core have also a high persistence probability. Therefore, when networks contain transitive and intransitive structures, as it can be expected in real ecological networks, the existence of a large intransitive core of species can have a disproportionate positive effect on species richness.

Keywords

Competition Ecological networks Intransitive interactions Plant community Replacement dynamics Replacement networks 

Notes

Acknowledgements

During the elaboration of this study, the authors were funded by projects COEXMED (CGL2012-36776) and COEXMED II (CGL2015-69118-C2-1) of the Spanish Ministerio de Economía y Competitividad with partial funds from Fondo Europeo de Desarrollo Regional (FEDER) of the European Union.

References

  1. Alcántara JM, Rey PJ (2012) Linking topological structure and dynamics in ecological networks. Am Nat 180:186–199CrossRefPubMedGoogle Scholar
  2. Alcántara JM, Rey PJ (2014) Community dynamics: lessons from a skeleton. In: Benítez M, Miramontes O, Valiente-Banuet A (eds) Frontiers in ecology, evolution and complexity. CopIt ArXives, Mexico, pp. 40–47Google Scholar
  3. Alcántara JM, Rey PJ, Manzaneda AJ (2015) A model of plant community dynamics based on plant replacement networks. J Veg Sci 26:24–537CrossRefGoogle Scholar
  4. Allesina S, Levine JM (2011) A competitive network theory of species diversity. Proc Natl Acad Sci U S A 108:5638–5642CrossRefPubMedPubMedCentralGoogle Scholar
  5. Allesina S, Bodini A, Bondavalli C (2005) Ecological subsystems via graph theory: the role of strongly connected components. Oikos 110:164–176CrossRefGoogle Scholar
  6. Broder A, Kumar R, Maghoul F, Raghavan P, Rajagopalan S, Stata R et al (2000) Graph structure in the web. Comp Net 33:309–320CrossRefGoogle Scholar
  7. Chadwick, NE, Morrow KM (2011) Competition among sessile organisms in coral reefs. In: Dubinsky Z and Stambler N (eds.) Coral reefs: an ecosystem in transition. Springer, pp 347–371Google Scholar
  8. Chesson PL, Warner RR (1981) Environmental variability promotes coexistence in lottery competitive systems. Am Nat 117:923–943CrossRefGoogle Scholar
  9. Corominas-Murtra B, Goñi J, Solé RV, Rodríguez-Caso C (2013) On the origins of hierarchy in complex networks. Proc Natl Acad Sci U S A 110:13316–13321CrossRefPubMedPubMedCentralGoogle Scholar
  10. Dorogovtsev SN, Mendes JFF, Samukhin AN (2001) Giant strongly connected component of directed networks. Phys Revs E 64:025101CrossRefGoogle Scholar
  11. Gantmacher FR (1959) Matrix theory. Chelsea Publishing Company, New YorkGoogle Scholar
  12. Gilpin ME (1975) Limit cycles in competition communities. Am Nat 109:51–60CrossRefGoogle Scholar
  13. Gross K (2008) Positive interactions among competitors produce species-rich communities. Ecol Lett 11:929–936CrossRefPubMedGoogle Scholar
  14. Grubb PJ (1977) The maintenance of species richness in plant communities: the importance of the regeneration niche. Biol Revs 52:107–145CrossRefGoogle Scholar
  15. Halás M, Moog CH (2013) Definition of eigenvalues for a nonlinear system. In: Tarbouriech S, Krstic M (eds) Proceedings of the 9th IFAC Symposium on Nonlinear Control Systems. International Federation of Automatic Control. Toulouse, France, pp 600–605Google Scholar
  16. Hardin G (1960) The competitive exclusion principle. Science 131:1292–1297CrossRefPubMedGoogle Scholar
  17. Horn HS (1975) Markovian properties of forest succession. In: Cody ML, Diamond MJ (eds) Ecology and evolution of communities. Belknap Press, Cambridge, pp. 196–211Google Scholar
  18. Hubbell SP (2001) The unified neutral theory of biodiversity and biogeography. Princeton University Press, PrincetonGoogle Scholar
  19. Inderjit, Wardle DA, Karban R, Callaway RM (2011) The ecosystem and evolutionary contexts of allelopathy. Trends Ecol Evol 26:655–662CrossRefPubMedGoogle Scholar
  20. Janzen D (1970) Herbivores and the number of tree species in tropical forests. Am Nat 104:501–528CrossRefGoogle Scholar
  21. Keddy PA, Shipley B (1989) Competitive hierarchies in herbaceous plant communities. Oikos 54:234–241CrossRefGoogle Scholar
  22. Kirkup BC, Riley MR (2004) Antibiotic-mediated antagonism leads to a bacterial game of rock-scissors-paper in vivo. Nature 428:412–414CrossRefPubMedGoogle Scholar
  23. Laird RA, Schamp BS (2006) Competitive intransitivity promotes species coexistence. Am Nat 168:182–193CrossRefPubMedGoogle Scholar
  24. Laird RA, Schamp BS (2008) Does local competition increase the coexistence of species in intransitive networks? Ecology 89:237–247CrossRefPubMedGoogle Scholar
  25. Laird RA, Schamp BS (2009) Species coexistence, intransitivity, and topological variation in competitive tournaments. J Theor Biol 256:90–95CrossRefPubMedGoogle Scholar
  26. Lebrija-Trejos E, Wright SJ, Hernández A, Reich PB (2014) Does relatedness matter? Phylogenetic density-dependent survival of seedlings in a tropical forest. Ecology 95:940–951CrossRefPubMedGoogle Scholar
  27. May RM, Leonard WJ (1975) Nonlinear aspects of competition between three species. SIAM J Appl Math 29:243–253CrossRefGoogle Scholar
  28. Myster RW (2012) Plants replacing plants: the future of community modelling and research. Bot Revs 78:2–9CrossRefGoogle Scholar
  29. Quinn JF (1982) Competitive hierarchies in marine benthic communities. Oecologia 54:129–135CrossRefPubMedGoogle Scholar
  30. Rojas-Echenique J, Allesina S (2011) Interaction rules affect species coexistence in intransitive networks. Ecology 92:1174–1180CrossRefPubMedGoogle Scholar
  31. Snyder RE, Chesson P (2003) Local dispersal can facilitate coexistence in the presence of permanent spatial heterogeneity. Ecol Lett 6:301–309CrossRefGoogle Scholar
  32. Soliveres S, Maestre FT, Ulrich W, Manning P, Boch S, Bowker MA et al (2015) Intransitive competition is widespread in plant communities and maintains their species richness. Ecol Lett 18:790–798CrossRefPubMedPubMedCentralGoogle Scholar
  33. Tilman D (1994) Competition and biodiversity in spatially structured habitats. Ecology 75:2–16CrossRefGoogle Scholar
  34. Uriarte M, Swenson NG, Chazdon RL, Comita LS, John Kress W, Erickson D et al (2010) Trait similarity, shared ancestry and the structure of neighbourhood interactions in a subtropical wet forest: implications for community assembly. Ecol Lett 13:1503–1514CrossRefPubMedGoogle Scholar
  35. Vitali S, Glattfelder JB, Battiston S (2011) The network of global corporate control. PLoS One 6:e25995CrossRefPubMedPubMedCentralGoogle Scholar
  36. Wolfram Research, Inc. (2015), Mathematica, Versión 10.3, Champaign, ILGoogle Scholar
  37. Wright ES, Vetgesian KH (2016) Inhibitory interactions promote frequent bistability among competitive bacteria. Nat Commun 7:11274CrossRefPubMedPubMedCentralGoogle Scholar
  38. Zhao J, Yu H, Luo JH, Cao ZW, Li YX (2006) Hierarchical modularity of nested bow-ties in metabolic networks. BMC Bioinformatics 7:386CrossRefPubMedPubMedCentralGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Julio M. Alcántara
    • 1
    Email author
  • Manuel Pulgar
    • 1
  • Pedro J. Rey
    • 1
  1. 1.Departamento de Biología Animal, Biología Vegetal y EcologíaUniversidad de JaénJaénSpain

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