A Recipe for Unconventional Evenness Measures

The degree to which abundances are evenly divided among the species of a given community is a basic property of any biological community. Several evenness indices have thus far been proposed in ecological literature. However, despite their vast potential applicability in ecological research, none seems to be generally preferred. In this paper, I first summarize the basic requirements that evenness measures should meet to adequately behave in ecological studies. Then, I discuss the major drawbacks of these requirements and propose an alternative family of measures that are based on the notion of specificity used in fuzzy set theory for measuring the uncertainty associated with a fuzzy set.

[1]  Catherine Potvin,et al.  BIODIVERSITY AND ECOSYSTEM FUNCTIONING: IMPORTANCE OF SPECIES EVENNESS IN AN OLD FIELD , 2000 .

[2]  Benjamin Smith,et al.  The relationship between community biomass and evenness: what does community theory predict, and can these predictions be tested? , 1998 .

[3]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[4]  Ronald Rousseau,et al.  The relationship between diversity profiles, evenness and species richness based on partial ordering , 1999, Environmental and Ecological Statistics.

[5]  R. Yager.  MEASURING TRANQUILITY AND ANXIETY IN DECISION MAKING: AN APPLICATION OF FUZZY SETS , 1982 .

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

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

[8]  P. Keddy,et al.  Relative abundance and evenness patterns along diversity and biomass gradients , 1999 .

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

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

[11]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[12]  L. Bulla.  An Index of Evenness and Its Associated Diversity Measure , 1994 .

[13]  Ronald Rousseau,et al.  The Lorenz curve: a graphical representation of evenness , 1998 .

[14]  G. Klir,et al.  Uncertainty-based information: Elements of generalized information theory (studies in fuzziness and soft computing). , 1998 .

[15]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[16]  Carlo Ricotta,et al.  On parametric evenness measures. , 2003, Journal of theoretical biology.

[17]  S. Hurlbert.  The Nonconcept of Species Diversity: A Critique and Alternative Parameters. , 1971, Ecology.

[18]  H. Dalton.  The Measurement of the Inequality of Incomes , 1920 .

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

[20]  C. Ricotta,et al.  On the Information-Theoretical Meaning of Hill's Parametric Evenness , 2002, Acta biotheoretica.

[21]  G. Stirling,et al.  Empirical Relationships between Species Richness, Evenness, and Proportional Diversity , 2001, The American Naturalist.

[22]  E. H. Simpson.  Measurement of Diversity , 1949, Nature.

[23]  A. Sheldon,et al.  Equitability Indices: Dependence on the Species Count , 1969 .

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

[25]  R. Yager.  On the specificity of a possibility distribution , 1992 .

[26]  Tarald O. Kvålseth,et al.  Note on biological diversity, evenness, and homogeneity measures , 1991 .

[27]  C. Ricotta,et al.  On the mutual relatedness of evenness measures , 2001 .

[28]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..