Researches on Population Ecology

, Volume 22, Issue 1, pp 51–68 | Cite as

A model of the species rank-abundance relation for a community in an open habitat

  • Shiro Kobayashi


A mathematical model is proposed to describe the relationship between the abundance and the rank of species in order from the most abundant to the least in a community in an open habitat. This model is derived as a corollary of a species-area equation (Kobayashi, 1975) which could be expected in the case where the individuals of each species are uniformly distributed over a habitat area. Numerical simulation reveals that a rank-abundance curve for a universe results in different species-area or species-individual curves according to the spatial distribution of individuals, and that the relative abundance of each species in a sample varies with sample size unless the spatial distribution of individuals is uniform. A species-individual curve obtained bySanders’s (1968) rarefaction method agrees with that observed actually only for the spatially uniform distribution. Change in the pattern of rank-abundance curve with species diversity and with sample size is discussed in relation to the present model.


Break Line Open Habitat Diatom Community Thin Solid Line Geometrical Progression 
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  1. Bazzaz, F. A. (1975) Plant species diversity in old-field successional ecosystems in southern Illinois.Ecology 56: 485–488.CrossRefGoogle Scholar
  2. Boswell, M. T. andG. P. Patil (1971) Chance mechanisms generating the logarithmic series distribution used in the analysis of number of species and individuals. InStatistical ecology, Vol. 1 (ed.G. P. Patil, E. C. Pielou andW. E. Waters). Penn. State. Univ. Press. 99–127.Google Scholar
  3. Fisher, R. A., A. S. Corbet andC. B. Williams (1943) The relation between the number of species and the number of individuals in a random sample of an animal population.J. Anim. Ecol. 12: 42–58.CrossRefGoogle Scholar
  4. Gleason, H. A. (1922) On the relation between species and area.Ecology 3: 158–162.CrossRefGoogle Scholar
  5. Hairston, N. G. (1959) Species abundance and community organization.Ecology 40: 404–416.CrossRefGoogle Scholar
  6. Horn, H. S. (1975) Markovian properties of forest succession. InEcology and evolution of communities (ed.M. L. Cody andJ. M. Diamond). Belknap Press, Cambridge. 196–211.Google Scholar
  7. Hurlbert, S. H. (1971) The nonconcept of species diversity: A critique and alternative parameters.Ecology 52: 577–586.CrossRefGoogle Scholar
  8. Kobayashi, S. (1974) The species-area relation. I. A model for discrete sampling.Res. Popul. Ecol. 15: 223–237.CrossRefGoogle Scholar
  9. Kobayashi, S. (1975) The species-area relation. II. A second model for continuous sampling.Res. Popul. Ecol. 16: 265–280.CrossRefGoogle Scholar
  10. Kobayashi, S. (1976) The species-area relation. III. A third model for a delimited community.Res. Popul. Ecol. 17: 243–254.Google Scholar
  11. Kobayashi, S. (1979a) Species-area curves. InStatistical distributions in ecological work (ed.)J. K. Ord, G. P. Patil andC. Taillie). Internat. Co-op. Publ. House, Fairland, Maryland. 349–368.Google Scholar
  12. Kobayashi, S. (1979b) Another model of the species rank-abundance relation for a delimited community. InContemporary quantitative ecology and related ecometrics (ed.G. P. Patil andM. L. Rosenzweig). Internat. Co-op. Publ. House, Fairland, Maryland. 89–108.Google Scholar
  13. Margalef, R. (1958) Information theory in ecology.Gen. System. 3: 36–71.Google Scholar
  14. May, R. M. (1975) Patterns of species abundance and diversity. InEcology and evolution of communities (ed.M. L. Cody andJ. M. Diamond). Belknap Press, Cambridge. 81–120.Google Scholar
  15. Motomura, I. (1932) A statistical treatment of animal associations.Jap. J. Zool. 44: 379–383 (in Japanese).Google Scholar
  16. Motomura, I. (1935) Relation between the area of sampling and the number of species in the animal association.Ecol. Rev. 1: 195–199 (in Japanese).Google Scholar
  17. Motomura, I. (1943) A statistical treatment of animal associations (continued report).Ecol. Rev. 9: 117–119 (in Japanese).Google Scholar
  18. Motomura, I. (1947) Further notes on the law of geometrical progression of the population density in animal association.Physiol. Ecol. 1: 55–60 (in Japanese with English summary).Google Scholar
  19. Numata, M., H. Nobuhara andK. Suzuki (1953) The quantitative composition of plant populations from the viewpoint ofMotomura’s law of geometrical progression. Studies on the fundamental structure of biological universes I.Bull. Soc. Plant Ecol. Jap. 3: 89–94 (in Japanese with English summary).Google Scholar
  20. Odum, H. T., J. E. Cantlon andL. S. Kornicker (1960) An organizational hierarchy postulate for the interpretation of species-individual distributions, species entropy, ecosystem evolution, and the meaning of a species-variety index.Ecology 41: 395–399.CrossRefGoogle Scholar
  21. Patrick, R. (1968) The structure of diatom communities in similar ecological conditions.Amer. Natur. 102: 173–183.CrossRefGoogle Scholar
  22. Preston, F. W. (1962) The canonical distribution of commonness and rarity.Ecology 43: 185–215, 410–432.CrossRefGoogle Scholar
  23. Sanders, H. L. (1968) Marine benthic diversity: A comparative study.Amer. Natur. 102: 243–282.CrossRefGoogle Scholar
  24. Shinozaki, K. (1955) Several problems on the law of geometrical progression.Physiol. Ecol. 6: 127–144 (in Japanese with English summary).Google Scholar
  25. Simpson, E. H. (1949) Measurement of diversity.Nature 163: 688.Google Scholar
  26. Utida, S. (1943) Consideration onMotomura’s law of geometrical progression in animal association.Ecol. Rev. 9: 173–178 (in Japanese).Google Scholar
  27. Whittaker, R. H. (1965) Dominance and diversity in plant communities.Science 147: 250–260.CrossRefGoogle Scholar
  28. Whittaker, R. H. (1969) Evolution of diversity in plant communities. InDiversity and stability in ecological systems. Brookhaven Symposia in Biology, No. 22, 178–196.Google Scholar
  29. Whittaker, R. H. (1972) Evolution and measurement of species diversity.Taxon 21: 213–251.CrossRefGoogle Scholar
  30. Williams, C. B. (1964)Patterns in the balance of nature. Academic Press, London.Google Scholar

Copyright information

© The Society of Population Ecology 1980

Authors and Affiliations

  • Shiro Kobayashi
    • 1
  1. 1.Faculty of AgricultureYamagata UniversityTsuruokaJapan

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