The Relation between Evenness and Diversity

Contrary to common belief, decomposition of diversity into independent richness and evenness components is mathematically impossible. However, richness can be decomposed into independent diversity and evenness or inequality components. The evenness or inequality component derived in this way is connected to most of the common measures of evenness and inequality in ecology and economics. This perspective justifies the derivation of measures of relative evenness, which give the amount of evenness relative to the maximum and minimum possible for a given richness. Pielou’s [1] evenness measure J is shown to be such a measure.

[1]  Rauno V. Alatalo,et al.  Problems in the measurement of evenness in ecology , 1981 .

[2]  M. Adelman,et al.  Comment on the "H" Concentration Measure as a Numbers-Equivalent , 1969 .

[3]  A. Chao,et al.  Nonparametric estimation of Shannon’s index of diversity when there are unseen species in sample , 2004, Environmental and Ecological Statistics.

[4]  Henri Theil,et al.  Economics and information theory , 1967 .

[5]  A. Chao,et al.  Partitioning diversity for conservation analyses , 2010 .

[6]  G. Patil,et al.  Diversity as a Concept and its Measurement , 1982 .

[7]  L. Jost.  Mismeasuring biological diversity: : Response to Hoffmann and Hoffmann (2008) , 2009 .

[8]  E. C. Pielou.  The measurement of diversity in different types of biological collections , 1966 .

[9]  Sönke Hoffmann,et al.  Generalized distribution based diversity measurement: Survey and unification , 2008 .

[10]  Benjamin Smith,et al.  A consumer's guide to evenness indices , 1996 .

[11]  Carlo H. R. Heip,et al.  A New Index Measuring Evenness , 1974, Journal of the Marine Biological Association of the United Kingdom.

[12]  R. Salas,et al.  Inequality foundations of concentration measures: An application to the Hannah-Kay indices , 2002 .

[13]  L. Hayek,et al.  Biodiversity resolution: an integrated approach , 1996 .

[14]  K. Song.  Rényi information, loglikelihood and an intrinsic distribution measure , 2001 .

[15]  I. Good,et al.  THE NUMBER OF NEW SPECIES, AND THE INCREASE IN POPULATION COVERAGE, WHEN A SAMPLE IS INCREASED , 1956 .

[16]  F. Gosselin.  Lorenz partial order: the best known logical framework to define evenness indices , 2001 .

[17]  Anne Chao,et al.  Sufficient sampling for asymptotic minimum species richness estimators. , 2009, Ecology.

[18]  L. Jost.  Partitioning diversity into independent alpha and beta components. , 2007, Ecology.

[19]  I. Good.  THE POPULATION FREQUENCIES OF SPECIES AND THE ESTIMATION OF POPULATION PARAMETERS , 1953 .

[20]  E. Ayanoglu,et al.  Diversity Analysis of , 2010 .

[21]  R. Routledge.  Evenness Indices: Are Any Admissible? , 1983 .

[22]  L. Jost.  Entropy and diversity , 2006 .

[23]  N. Starr,et al.  Optimal and Adaptive Stopping in the Search for New Species , 1979 .

[24]  F. Gosselin.  An assessment of the dependence of evenness indices on species richness. , 2006, Journal of theoretical biology.

[25]  M. Hill.  Diversity and Evenness: A Unifying Notation and Its Consequences , 1973 .

[26]  V. Latora,et al.  Nonextensivity: From Low-Dimensional Maps to Hamiltonian Systems , 2002, cond-mat/0209168.

[27]  C. Ricotta,et al.  A Recipe for Unconventional Evenness Measures , 2004, Acta biotheoretica.

[28]  L. Jost.  GST and its relatives do not measure differentiation , 2008, Molecular ecology.