# The relationship between diversity profiles, evenness and species richness based on partial ordering

The relationship between diversity profiles, evenness and species richness based on partial ordering Problems with the notion of evenness, such as ambiguity, proliferation of indices, choice of indices, etc. can be overcome by a more fundamental, mathematical approach. We show that the Lorenz curve is an adequate representation of evenness. The corresponding Lorenz order induces a partial order in the set of equivalent abundance vectors. Also diversity can adequately be studied through a partial order and represented by a curve derived from the classical Lorenz curve. This curve is known as the intrinsic diversity profile (or k-dominance curve) and was introduced by Patil and Taillie (1979) and Lambshead et al. (1981). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Environmental and Ecological Statistics Springer Journals

# The relationship between diversity profiles, evenness and species richness based on partial ordering

, Volume 6 (2) – Oct 3, 2004
13 pages

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# References (22)

Publisher
Springer Journals
Subject
Life Sciences; Ecology; Statistics, general; Mathematical and Computational Biology; Evolutionary Biology
ISSN
1352-8505
eISSN
1573-3009
DOI
10.1023/A:1009626406418
Publisher site
See Article on Publisher Site

### Abstract

Problems with the notion of evenness, such as ambiguity, proliferation of indices, choice of indices, etc. can be overcome by a more fundamental, mathematical approach. We show that the Lorenz curve is an adequate representation of evenness. The corresponding Lorenz order induces a partial order in the set of equivalent abundance vectors. Also diversity can adequately be studied through a partial order and represented by a curve derived from the classical Lorenz curve. This curve is known as the intrinsic diversity profile (or k-dominance curve) and was introduced by Patil and Taillie (1979) and Lambshead et al. (1981).

### Journal

Environmental and Ecological StatisticsSpringer Journals

Published: Oct 3, 2004