Niche Overlaps and the Evolution of Competitive Interactions

  • H. Reşit Akçakaya
  • L. R. Ginzburg
Conference paper

Abstract

Several theoretical studies have suggested that the nature of interactions between species effect the structure of communities. Most of these studies were based on the analysis of an interaction matrix A, and its stability properties. The elements of this matrix describe the interactions between species: diagonal elements α ii describe the effect of the population of species i on itself (i.e., self-limitation as a result of density-dependent factors), and off-diagonal elements α ij describe the effect of species j on the growth rate of species i. The signs of the two corresponding elements of the matrix, α ij and α ji together define the type of interaction between species i and species j: (0,0) for no interaction, (−,−) for competition, (−,+) for predation/parasitism, (0,−) for amensalism, (0,+) for commensalism, and (+,+) for mutualism. The number of species (i.e., the dimension of the matrix), m, and the proportion of non-zero elements of the matrix (connectance), C, were used as measures of the complexity of the system (May, 1972).

Keywords

Ordovician Palaeontology Anolis 

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References

  1. Abrams P (1980) Comments on measuring niche overlap. Ecology 61: 44–49CrossRefGoogle Scholar
  2. Aoki K (1980) A criterion for the establishment of a stable polymorphism of a higher order with an application to the evolution of polymorphism. J Math Biol 9: 133–146PubMedCrossRefGoogle Scholar
  3. Brown JH, Lieberman GA (1973) Resource utilization and coexistence of seed-eating desert rodents in sand dune habitats. Ecology 54: 788–797CrossRefGoogle Scholar
  4. Clark AG, Feldman MV (1986) A numerical simulation of the one-locus multiple-allele fertility model. Genetics 113: 161–176PubMedGoogle Scholar
  5. Cody ML (1974) Competition and community structure. Princeton University Press New JerseyGoogle Scholar
  6. Colwell RK, Futuyma DJ (1971) On the measurement of niche breadth and overlap. Ecology 52: 567–576CrossRefGoogle Scholar
  7. Colwell RK, Winkler DW (1984) A null model for null models in biogeography. Pp. 344–359 in: DR Strong, D Simberloff, LB Abele, AB Thistle (eds) Ecological communities: conceptual issues and the evidence. Princeton University Press New JerseyGoogle Scholar
  8. Connor EF, Simberloff D (1979) The assembly of species communities: chance or competition? Ecology 60: 1132–1140CrossRefGoogle Scholar
  9. Culver DC (1970) Analysis of simple cave communities: niche separation and species packing. Ecology 51: 949–958CrossRefGoogle Scholar
  10. Deakin MAB (1975) The steady state of ecosystems. Math BioSci 24: 319–331CrossRefGoogle Scholar
  11. DeAngelis DL (1975) Stability and connectance in food web models. Ecology 56: 238–243CrossRefGoogle Scholar
  12. DeAngelis DL, Goldstein RA, O’Neill RV (1975) A model for trophic interactions. Ecology 56: 881–892CrossRefGoogle Scholar
  13. Diamond JM, Gilpin ME (1982) Examination of the “null” model of Connor and Simberloff for species co-occurances on islands. Oecologia 52: 64–74CrossRefGoogle Scholar
  14. Endler JA (1977) Geographic variation, speciation and clines. Princeton University Press New JerseyGoogle Scholar
  15. Gardner MR, Ashby WR (1970) Connectance of large dynamic (cybernetic) systems: critical values for stability. Nature 228: 784PubMedCrossRefGoogle Scholar
  16. Gibbons JRH (1979) A model for sympatric speciation in Megarhyssa. (Hymenoptera: Ichneumonidae): competitive speciation. Am Natur 114: 719–741CrossRefGoogle Scholar
  17. Gillespie JH (1977) A general model for enzyme variation in natural populations. III. Multiple alleles. Evolution 31: 85–90CrossRefGoogle Scholar
  18. Gilpin ME, Case TJ (1976) Multiple domains of attraction in competition communities Nature 61: 40–42Google Scholar
  19. Ginzburg LR, Akçakaya HR, Kim J (1988) Evolution of community structure: Competition. J theor Biol 133: 513–523CrossRefGoogle Scholar
  20. Gould SJ, Raup DM, Sepkoski JJ, Schopf TJM, Simberloff DS (1977) The shape of evolution: a comparison of real and random clades. Paleobiology 3: 23–40Google Scholar
  21. Karlin S (1981) Some natural viability systems for a multiallelic locus: a theoretical study. Genetics 97: 457–473PubMedGoogle Scholar
  22. Karlin S, Feldman MW (1981) A theoretical and numerical assessment of genetic variability. Genetics 97: 475–493PubMedGoogle Scholar
  23. Levins R (1968) Evolution in changing environments. Princeton University Press New JerseyGoogle Scholar
  24. Lewontin RC, Ginzburg LR, Tuljapurkar SD (1978) Heterosis as an explanation for large amounts of polymorphism. Genetics 88: 149–170PubMedGoogle Scholar
  25. Margalef R (1968) Perspectives in ecological theory. University of Chicago Press ChicagoGoogle Scholar
  26. Margalef R (1968) Perspectives in ecological theory. University of Chicago Press ChicagoGoogle Scholar
  27. May RM (1972) Will a large complex system be stable? Nature 238: 413–414PubMedCrossRefGoogle Scholar
  28. May RM (1973) Stability and complexity in model ecosystems. Princeton University Press New JerseyGoogle Scholar
  29. May RM (1975) Some notes on estimating the competition matrix, a. Ecology 56: 737–741CrossRefGoogle Scholar
  30. McMurtie RE (1975) Determinants of stability of large randomly connected systems. J theor Biol 50: 1–11CrossRefGoogle Scholar
  31. Pianka ER (1973) The structure of lizard communities. Ann Rev Ecol Syst 4: 53–74CrossRefGoogle Scholar
  32. Post WM, Pimm SL (1983) Community assembly and food web stability. Math BioSci 64: 169–192CrossRefGoogle Scholar
  33. Roberts A (1974) The stability of a feasible random ecosystem. Nature 251: 607–608CrossRefGoogle Scholar
  34. Roberts A, Tregonning K (1980) The robustness of natural systems. Nature 288: 265–266CrossRefGoogle Scholar
  35. Robinson JV, Valentine WD (1979) The concepts of elasticity, invulnerability and invadability. J theor Biol 81: 91–104PubMedCrossRefGoogle Scholar
  36. Roughgarden J (1979) Theory of population genetics and evolutionary ecology: an introduction. MacMillan New YorkGoogle Scholar
  37. Rosenzweig ML (1978) Competitive speciation. Biol J Linn Soc 10: 275–289CrossRefGoogle Scholar
  38. Rosenzweig ML, Taylor JA (1980) Speciation and diversity in Ordovician invertebrates: filling niches quickly and carefully. Oikos 35: 236–243CrossRefGoogle Scholar
  39. Schoener TW (1968) The Anolis 1imrds of Bimini: resource partitioning in a complex fauna. Ecology 49: 704–726CrossRefGoogle Scholar
  40. Schoener TW (1974) Some methods for calculating competition coefficients from resource-utilization spectra. Amer Natur 104: 73–83Google Scholar
  41. Siljak DD (1975) When is a complex ecosystem stable? Math BioSci 25: 25–50CrossRefGoogle Scholar
  42. Smith AB (1988) Patterns of diversification and extinction in early palaeozoic echinoderms. Palaeontology 31: 799–828Google Scholar
  43. Spencer HG, Marks RW (1988) The maintenance of single-locus polymorphism. I. Numerical Studies of a viability selection model. Genetics 120: 605–613PubMedGoogle Scholar
  44. Strong DR, Simberloff D, Abele LB, Thistle AB (eds) (1984) Ecological communities: conceptual issues and the evidence. Princeton University Press New JerseyGoogle Scholar
  45. Tauber CA, Tauber MJ (1977) Sympatric speciation based on allelic changes at three loci: evidence from natural populations in two habitats. Science 197: 1298–1299PubMedCrossRefGoogle Scholar
  46. Taylor PJ (1985) Construction and turnover of multispecies communities: a critique of approaches to ecological complexity Ph.D. Thesis. Harvard University Cambridge MAGoogle Scholar
  47. Tregonning K, Roberts A (1978) Ecosystem-like behavior of a random interaction model I. Bull Math Biol 40: 513–524Google Scholar
  48. Tregonning K, Roberts A (1979) Complex systems which evolve towards homeostasis. Nature 281: 563–564CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • H. Reşit Akçakaya
    • 1
  • L. R. Ginzburg
    • 1
  1. 1.Department of Ecology and EvolutionState University of New YorkStony BrookUSA

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