Diversity indices: which ones are admissible?

Abstract Many indices have been proposed for measuring diversity. If we demand that any index satisfy a few basic properties, including that it contain hierarchical components, then only the subset, {Na for a > 0} of Hill's family need be considered. (This subset includes indices related to the Shannon-Wiener index, H′ = log N1, and Simpson's index of concentration, λ = 1/N2.) Ecological components can also be defined for any of these indices. Only N2, however, can be used consistently to define local diversity and segregation components. These observations suggest that N2 is the best, single measure of diversity, and that the only other index worth considering is N1 .

[1]  E. C. Pielou,et al.  Species-diversity and pattern-diversity in the study of ecological succession. , 1966, Journal of theoretical biology.

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

[3]  S. Zacks.  The theory of statistical inference , 1972 .

[4]  E. C. Pielou.  Niche Width and Niche Overlap: A Method for Measuring Them , 1972 .

[5]  Aleksandr Yakovlevich Khinchin,et al.  Mathematical foundations of information theory , 1959 .

[6]  R. Whittaker.  Vegetation of the Siskiyou Mountains, Oregon and California , 1960 .

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

[8]  C. Peterson.  Measurement of Community Pattern by Indices of Local Segregation and Species Diversity , 1976 .

[9]  R. Routledge.  On Whittaker's Components of Diversity , 1977 .

[10]  R. P. McIntosh.  An Index of Diversity and the Relation of Certain Concepts to Diversity , 1967 .

[11]  H. Tverberg.  A New Derivation of the Information Function. , 1958 .

[12]  R. Whittaker.  Evolution and measurement of species diversity , 1972 .

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

[14]  J. Aczél,et al.  Lectures on Functional Equations and Their Applications , 1968 .

[15]  R. May,et al.  Stability and Complexity in Model Ecosystems , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[16]  E. C. Pielou.  Population and Community Ecology: Principles and Methods , 1974 .