Evolutionarily Stable Relative Abundance Distributions

  • Tania L. S. Vincent
  • Thomas L. Vincent
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 9)


Modified versions of a wellknown model for coexistence are used to examine the conditions that determine the relative abundance of species that are in an evolutionarily stable state. Relative abundance is a term used to refer to the ranking of the number of individuals present within trophically similar species in an ecosystem. We use the G-function approach to understand why relative abundance relationships take the form so often found in field data. We assume that the ecosystem is at or near an evolutionary equilibrium and seek evolutionarily stable strategies to identify a coalition of individual species. In order to have a coalition greater than one, the G-function must produce frequency dependence, implying that the fitness of any given individual depends on the strategies used by all individuals in the population. This is an essential element of the evolutionary game. Otherwise, evolution would drive the population to a single strategy (i.e., a coalition of one) that is an optimal or group fitness strategy. We start with a classical version of the Lotka-Volterra competition equation that is not frequency dependent and make it frequency dependent in three different ways, thus allowing for the modeling of relative abundance. The first two methods involve a single resource niche and rely on modifications of the competitive effects to provide for a coalition of two or more. These models yield relative abundance distribution curves that are generally convex and are not typical of most field data. The third method creates several resource niches, and the simulated results generally create concave curves that are much closer to the field data obtained for natural systems.


Relative Abundance Evolutionary Game Evolutionarily Stable Strategy Adaptive Landscape Competitive Cost 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Benkman, C. W.: 2003, Divergent selection drives the adaptive radiation of crossbills, Evolution 57(5), 1176–1181.Google Scholar
  2. [2]
    Brown, J. S. and Vincent, T. L.: 1987, Coevolution as an evolutionary game, Evolution 41, 66–79.Google Scholar
  3. [3]
    Case, T. J.: 1982, Coevolution in resource-limited competition communities, Theoretical Population Biology 21, 69–91.Google Scholar
  4. [4]
    Fargione, J., Brown, C. S. and Tilman, D.: 2003, Community assembly and invasion: An experimental test of neutral versus niche processes, PNAS 100(15), 8916–8920.Google Scholar
  5. [5]
    Fisher, R. A., Corbet, A. S. and Williams, C. B.: 1943, The relation between the number of species and the number of individuals in a random sample of an animal population, Journal of Animal Ecology 12, 42–58.Google Scholar
  6. [6]
    Hubbell, S. P.: 2001, The Unified Neutral Theory of Biodiversity and Biogeography, Princeton University Press, Princeton, NJ.Google Scholar
  7. [7]
    Jones, G. P., Munday, P. L. and Caley, M. J.: 2002, Coral Reef Fishes, Dynamics and Diversity in a Complex Ecosystem, Academic Press, New York, chapter Rarity in coral reef fish communities, pp. 81–101.Google Scholar
  8. [8]
    Kelly, C. K. and Woodward, F. I.: 1996, Ecological correlates of plant range size: Taxonomies and phylogenies in the study of plant commonness and rarity in Great Britain, Phil. Trans. R. Soc. Lond. B 351(1), 1261–1269.Google Scholar
  9. [9]
    Link, W. A. and Sauer, J.: 1998, Estimating population change from count data: Application to the North American breeding bird survey, Ecological Applications 8(2), 258–268.Google Scholar
  10. [10]
    Magurran, A. E.: 1988, Ecological Diversity and its Measurement, Princeton University Press, Princeton, NJ.Google Scholar
  11. [11]
    Magurran, A. E. and Henderson, P. A.: 2003, Explaining the excess of rare species in natural species abundance distributions, Nature 422, 714–716.Google Scholar
  12. [12]
    May, R. M.: 1975a, General Introduction. In Ecological Stability, Chapman & Hall, London, pp. 1–14.Google Scholar
  13. [13]
    May, R. M.: 1975b, Patterns of Species Abundance and Diversity, Belknap Press of Harvard University Press, Cambridge, MA, pp. 81–120.Google Scholar
  14. [14]
    McGill, B. J.: 2003, A test of the unified neutral theory, Nature 422, 881–885.Google Scholar
  15. [15]
    Murray, B. R., Thrall, P. H., Gill, A. M. and Nicotra, A. B.: 2002, How plant life-history and ecological traits relate to species rarity and commonness at varing spatial scales, Austral Ecology 27, 291–310.Google Scholar
  16. [16]
    Roughgarden, J.: 1983, The Theory of Coevolution, Sinauer, Sunderland, MA, pp. 383–403.Google Scholar
  17. [17]
    Rummel, J. D. and Roughgarden, J.: 1983, Some differences between invasion-structured and coevolution-structured competitive communities: A preliminary theoretical analysis, Oikos 41, 477–486.Google Scholar
  18. [18]
    Sugihara, G.: 1980, Minimal community structure: An explanation of species abundance patterns, Am. Nat. 116, 770–787.Google Scholar
  19. [19]
    Tilman, D., Reich, P., Knops, J., Wedin, D., Mielke, T. and Lehman, C.: 2001, Diversity and productivity in a long term grassland experiment, Science 294, 843–845.Google Scholar
  20. [20]
    Vincent, T. L. and Brown, J. S.: 2005, Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics, Cambridge University Press, Cambridge.Google Scholar
  21. [21]
    Vincent, T. L., Cohen, Y. and Brown, J. S.: 1993, Evolution via strategy dynamics, Theoretical Population Biology 44, 149–176.Google Scholar
  22. [22]
    Whittaker, R. H.: 1970, Communities and Ecosystems, Macmillan, New York.Google Scholar

Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • Tania L. S. Vincent
    • 1
  • Thomas L. Vincent
    • 2
  1. 1.Alaska Pacific University4101 University Drive AnchorageUSA
  2. 2.Department of Aerospace and Mechanical EngineeringUniversity of ArizonaTucsonUSA

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