Skip to main content
SpringerLink
Log in

Measurement of Biodiversity: Richness and Evenness

  • Chapter
  • First Online:
Mathematics of Planet Earth

Part of the book series: Mathematics of Planet Earth ((MPE,volume 5))

Abstract

Evidence about the health of ecosystems is often thought to be related to biodiversity. Traditional attempts to define biodiversity consider two components: richness—the number of species in the ecosystem—and evenness—the extent to which species are evenly distributed. This chapter studies attempts to make both concepts precise using mathematical approaches. It describes a number of evenness indices that have been widely used, studies axioms for evenness that an index could be required to satisfy, and explores which evenness indices satisfy those axioms. The chapter also considers evenness indices that “preserve” certain partial orders. The relationship between richness and evenness and attempts to derive measures of biodiversity based on both richness and evenness are explored.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Arrhenius, O.: Species and area. J. Ecol. 9, 95–99 (1921)

    Article  Google Scholar 

  2. Arrow, K.: Social Choice and Individual Values. Cowles Commission Monograph, vol. 12. Wiley, New York (1951). Second edition (1963)

    Google Scholar 

  3. Bock, C.E., Jones, Z.F., Bock, J.H.: Relationships between species richness, evenness, and abundance in a southwestern savanna. Ecology 88, 1322–1327 (2007)

    Article  Google Scholar 

  4. Boulinier, T., Nichols, J.D., Sauer, J.R., et al.: Estimating species richness: the importance of heterogeneity in species detectability. Ecology 79, 1018–1028 (1998)

    Article  Google Scholar 

  5. Buckland, S.T., Magurran, A.E., Green, R.E., et al.: Monitoring change in biodiversity through composite indices. Philos. Trans. R. Soc. B 360, 243–254 (2005)

    Article  Google Scholar 

  6. Daget, J.: Les Modèles Mathématiques en Écologie. Masson, Paris (1976)

    MATH  Google Scholar 

  7. Dalton, H.: The measurement of inequality of incomes. Econ. J. 30, 348–361 (1920)

    Article  Google Scholar 

  8. Daly, A.J., Baetens, J.M., De Baets, B.: The impact of initial evenness on biodiversity maintenance for a four-species in silico bacterial community. J. Theor. Biol. 387, 189–205 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  9. Egghe, L., Rousseau, R.: Elements of concentration theory. In: Egghe, L., Rousseau, R. (eds.) Informetrics, pp. 97–137. Elsevier, Amsterdam (1990)

    Google Scholar 

  10. Egghe, L., Rousseau, R.: Transfer principles and a classification of concentration measures. J. Am. Soc. Inf. Sci. 42, 479–489 (1991)

    Article  Google Scholar 

  11. Firebaugh, G.: Empirics of world income inequality. Am. J. Sociol. 104, 1597–1630 (1999)

    Article  Google Scholar 

  12. Firebaugh, G.: Inequality: What it is and how it is measured. In: The New Geography of Global Income Inequality. Harvard University Press, Cambridge (2003)

    Google Scholar 

  13. Gini, C.: Il diverso accrescimento delle classi sociali e la concentrazione della richezza. Giornale degli Economisti, serie II 38, 27–83 (1909)

    Google Scholar 

  14. Gini, C.: Variabilite mutabilita, Parte II. Technical report, Univ. di Cagliari III, Studi Economicoaguridic della Facotta di Giurisprudenza (1912)

    Google Scholar 

  15. Gosselin, F.: Lorenz partial order: the best known logical framework to define evenness indices. Commun. Ecol. 2, 197–207 (2001)

    Article  Google Scholar 

  16. Gotelli, N.J., Colwell, R.K.: Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness. Ecol. Lett. 4, 379–391 (2001)

    Article  Google Scholar 

  17. Grabchak, M., Marcon, E., Lang, G., et al.: The generalized Simpson’s entropy is a measure of biodiversity. PLoS One 12 (2017). https://doi.org/10.1371/journal.pone.0173305

    Article  Google Scholar 

  18. Jost, L.: The relation between evenness and diversity. Diversity 2, 207–232 (2010). https://doi.org/10.3390/d2020207

    Article  Google Scholar 

  19. Kemeny, J.G., Snell, J.L.: Mathematical Models in the Social Sciences. Blaisdell, New York (1962). Reprinted by M.I.T Press, Cambridge, MA, 1972

    Google Scholar 

  20. Lamas, G., Robbins, R.K., Harvey, D.J.: A preliminary survey of the butterfly fauna of Pakitza, Parque Nacional Del Manu, Peru, with an estimate of its species richness. Technical report, Publicaciones Del Museo de Historia Natural, Universidad Nacional Mayor de San Marcos, A40, 1–19 (1991)

    Google Scholar 

  21. Lamb, E.G., Bayne, E., Holloway, G., et al.: Indices for monitoring biodiversity change: are some more effective than others? Ecol. Indic. 9, 432–444 (2009)

    Article  Google Scholar 

  22. Leyesdorff, L., Rafols, I.: Indicators of the interdisciplinarity of journals: diversity, centrality, and citations. J. Informet. 5, 87–100 (2011)

    Article  Google Scholar 

  23. Lorenz, M.O.: Methods of measuring the concentration of wealth. Publ. Am. Stat. Assoc. 9, 209–219 (1905). https://doi.org/10.2307/2276207

    Google Scholar 

  24. Ma, M.: Species richness vs evenness: independent relationship and different responses to edaphic factors. Oikos 111, 192–198 (2005)

    Article  Google Scholar 

  25. Magurran, A.E.: Ecological Diversity and Its Measurement. Chapman and Hall, London (1991)

    Google Scholar 

  26. Magurran, A.E.: Measuring Biological Diversity. Blackwell, Oxford (2004)

    Google Scholar 

  27. Nijssen, D., Rousseau, R., Van Hecke, P.: The Lorenz curve: a graphical representation of evenness. Coenoses 13, 33–38 (1998)

    Google Scholar 

  28. Patil, G.P., Taillie, C.: Diversity as a concept and its measurement. J. Am. Stat. Assoc. 77, 548–561 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  29. Pielou, E.C.: The measurement of diversity in different types of biological collections. J. Theor. Biol. 13, 131–144 (1966)

    Article  Google Scholar 

  30. Pielou, E.C.: Ecological Diversity. Wiley, New York (1975)

    Google Scholar 

  31. Prathap, P.: Second order indicators for evaluating international scientific collaboration. Scientometrics 95, 563–570 (2012)

    Article  Google Scholar 

  32. Preston, F.W.: The commonness, and rarity, of species. Ecology 29, 254–283 (1948)

    Article  Google Scholar 

  33. Preston, F.W.: The canonical distribution of commonness and rarity: Part I. Ecology 43, 185–215 (1962)

    Article  Google Scholar 

  34. Ricotta, C.: On parametric evenness measures. J. Theoret. Biol. 222, 189–197 (2003)

    Article  MathSciNet  Google Scholar 

  35. Roberts, F.S.: Discrete Mathematical Models, with Applications to Social, Biological, and Environmental Problems. Prentice-Hall, Englewood Cliffs (1976)

    MATH  Google Scholar 

  36. Rousseau, R.: Concentration and diversity of availability and use in information systems: a positive reinforcement model. J. Am. Soc. Inf. Sci. 43, 391–395 (1992)

    Article  MathSciNet  Google Scholar 

  37. Rousseau, R., Van Hecke, P.: Measuring biodiversity. Acta Biotheor. 47, 1–5 (1999)

    Article  Google Scholar 

  38. Rousseau, R., Van Hecke, P., Nijssen, D., et al.: The relationship between diversity profiles, evenness and species richness based on partial ordering. Environ. Ecol. Stat. 6, 211–223 (1999)

    Article  Google Scholar 

  39. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423, 623–656 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  40. Shapley, L.S.: A value for n-person games. In: Kuhn, H.W., Tucker, A.W. (eds.) Contributions to the Theory of Games. Annals of Mathematics Studies, vol. 28, pp. 307–317. Princeton University Press, Princeton (1953)

    Google Scholar 

  41. Simpson, E.H.: Measurement of diversity. Nature 163, 688 (1949)

    Article  MATH  Google Scholar 

  42. Smith, B., Wilson, J.: A consumer’s guide to evenness indices. Oikos 76, 70–82 (1996)

    Article  Google Scholar 

  43. Soberon, J., Llorente, B.: The use of species accumulation functions for the prediction of species richness. Conserv. Biol. 7, 480–488 (1993)

    Article  Google Scholar 

  44. Sugihara, G.: Minimal community structure: an explanation of species abundance patterns. Am. Nat. 11, 770–787 (1980)

    Article  MathSciNet  Google Scholar 

  45. Takacs, D.: The Idea of Biodiversity: Philosophies of Paradise. Johns Hopkins Press, Baltimore (1996)

    Google Scholar 

  46. Tuomisto, H.: A diversity of beta diversities: straightening up a concept gone awry. Part 1, Defining beta diversity as a function of alpha and gamma diversity. Ecography 33, 2–22 (2010)

    Article  Google Scholar 

  47. Tuomisto, H.: A diversity of beta diversities: straightening up a concept gone awry. Part 2, Quantifying beta diversity and related phenomena. Ecography 33, 23–45 (2010)

    Article  Google Scholar 

  48. Tuomisto, H.: An updated consumer’s guide to evenness and related indices. Oikos 121, 1203–1218 (2012)

    Article  Google Scholar 

  49. UNEP: Convention on biological diversity (1992). https://www.cbd.int/doc/legal/cbd-en.pdf. Accessed 14 Jul 2018

  50. UNEP: Report of the Sixth Meeting of the conference of the Parties to the Convention on Biological Diversity (UNEP/CBD/COP/6/20 (2002). https://www.cbd.int/doc/meetings/cop/cop-06/official/cop-06-20-en.pdf. Accessed 14 Jul 2018

  51. Whittaker, R.H.: Evolution and measurement of species diversity. Taxon 21, 213–251 (1972)

    Article  Google Scholar 

  52. Wilsey, B., Chalcraft, D.R., Bowles, C.M., et al.: Relationships among indices suggest that richness is an incomplete surrogate for grassland biodiversity. Ecology 86, 1178–1184 (2005)

    Article  Google Scholar 

  53. Wilson, E.O., Peters, F.M. (eds.): Biodiversity. National Academy Press, Washington (1988)

    Google Scholar 

  54. Zhang, H., John, R., Peng, Z., et al.: The relationship between species richness and evenness in plant communities along a successional gradient: a study from sub-alpine meadows of the Eastern Qinghai-Tibetan Plateau, China. PLoS One (2012). https://doi.org/10.1371/journal.pone.0049024

    Article  Google Scholar 

Download references

Acknowledgements

Parts of this chapter (in particular, some of the Introduction, parts of the nontechnical discussion of Richness in Sect. 8.2 and Evenness in Sect. 8.3, and a portion of the concluding Sect. 8.10) were used in a book (report) Mathematical and Statistical Challenges for Sustainability edited by Margaret Cozzens and Fred Roberts, and in particular in Fred Roberts’ contribution to the Working Group I Report on Human Well-Being and the Natural Environment, included in the aforementioned book and authored by Alejandro Adem, Michelle Bell, Margaret Cozzens, Charmaine Dean, Francesca Dominici, Avner Friedman, Fred Roberts, Steve Sain, and Abdul-Aziz Yakubu. The author thanks the National Science Foundation for its support under grant DMS-1246305 to Rutgers University.

Author information

Authors and Affiliations

  1. DIMACS Center, Rutgers University, Piscataway, NJ, USA

    Fred S. Roberts

Authors
  1. Fred S. Roberts
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fred S. Roberts .

Editor information

Editors and Affiliations

  1. Mathematics and Statistics, Georgetown University, Washington, DC, USA

    Hans G. Kaper

  2. DIMACS Center, Rutgers University, Piscataway, NJ, USA

    Fred S. Roberts

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Roberts, F.S. (2019). Measurement of Biodiversity: Richness and Evenness. In: Kaper, H., Roberts, F. (eds) Mathematics of Planet Earth. Mathematics of Planet Earth, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-030-22044-0_8

Download citation

Publish with us

Policies and ethics

Search

Navigation