Diversity 2010, 2(3), 370-394; doi:10.3390/d2030370

Linking Diversity and Differentiation

Received: 15 December 2009; Accepted: 20 February 2010 / Published: 3 March 2010
(This article belongs to the Special Issue Diversity Theories and Perspectives)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: Generally speaking, the term differentiation refers to differences between collections for the distribution of specified traits of their members, while diversity deals with (effective) numbers of trait states (types). Counting numbers of types implies discrete traits such as alleles and genotypes in population genetics or species and taxa in ecology. Comparisons between the concepts of differentiation and diversity therefore primarily refer to discrete traits. Diversity is related to differentiation through the idea that the total diversity of a subdivided collection should be composed of the diversity within the subcollections and a complement called “diversity between subcollections”. The idea goes back to the perception that the mixing of differentiated collections increases diversity. Several existing concepts of “diversity between subcollections” are based on this idea. Among them, β-diversity and fixation (inadvertently called differentiation) are the most prominent in ecology and in population genetics, respectively. The pertaining measures are shown to quantify the effect of differentiation in terms of diversity components, though from a dual perspective: the classical perspective of differentiation between collections for their type compositions, and the reverse perspective of differentiation between types for their collection affiliations. A series of measures of diversity-oriented differentiation is presented that consider this dual perspective at two levels of diversity partitioning: the overall type or subcollection diversity and the joint type-subcollection diversity. It turns out that, in contrast with common notions, the measures of fixation (such as FST or GST ) refer to the perspective of type rather than subcollection differentiation. This unexpected observation strongly suggests that the popular interpretations of fixation measures must be reconsidered.
Keywords: diversity partitioning; dual perspectives; differentiation measures; diversity measures; concept of effective number; Hill-diversity; Rényi-diversity; alpha-diversity; beta-diversity; gamma-diversity; fixation measures; FST; GST; information measures; ecology; population genetics; subcollections; subpopulations
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MDPI and ACS Style

Gregorius, H.-R. Linking Diversity and Differentiation. Diversity 2010, 2, 370-394.

AMA Style

Gregorius H-R. Linking Diversity and Differentiation. Diversity. 2010; 2(3):370-394.

Chicago/Turabian Style

Gregorius, Hans-Rolf. 2010. "Linking Diversity and Differentiation." Diversity 2, no. 3: 370-394.

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