A desirable property of a diversity index is strict concavity. This implies that the pooled diversity of a given community sample is greater than or equal to but not less than the weighted mean of the diversity values of the constituting plots. For a strict concave diversity index, such as species richness S, Shannon's entropy H or Simpson's index 1-D, the pooled diversity of a given community sample can be partitioned into two non-negative, additive components: average within-plot diversity and between-plot diversity. As a result, species diversity can be summarized at various scales measuring all diversity components in the same units. Conversely, violation of strict concavity would imply the non-interpretable result of a negative diversity among community plots. In this paper, 1 apply this additive partition model generally adopted for traditional diversity measures to Aczél and Daróczy's generalized entropy of type α. In this way, a parametric measure of β-diversity is derived as the ratio between the pooled sample diversity and the average within-plot diversity that represents the parametric analogue of Whittaker's β-diversity for data on species relative abundances.

Additive partition of parametric information and its associated β-diversity measure / Ricotta, Carlo. - In: ACTA BIOTHEORETICA. - ISSN 0001-5342. - STAMPA. - 51:2(2003), pp. 91-100. [10.1023/a:1024539526618]

Additive partition of parametric information and its associated β-diversity measure

RICOTTA, Carlo
2003

Abstract

A desirable property of a diversity index is strict concavity. This implies that the pooled diversity of a given community sample is greater than or equal to but not less than the weighted mean of the diversity values of the constituting plots. For a strict concave diversity index, such as species richness S, Shannon's entropy H or Simpson's index 1-D, the pooled diversity of a given community sample can be partitioned into two non-negative, additive components: average within-plot diversity and between-plot diversity. As a result, species diversity can be summarized at various scales measuring all diversity components in the same units. Conversely, violation of strict concavity would imply the non-interpretable result of a negative diversity among community plots. In this paper, 1 apply this additive partition model generally adopted for traditional diversity measures to Aczél and Daróczy's generalized entropy of type α. In this way, a parametric measure of β-diversity is derived as the ratio between the pooled sample diversity and the average within-plot diversity that represents the parametric analogue of Whittaker's β-diversity for data on species relative abundances.
parametric diversity; generalized entropy of type α; information theory; diversity profiles
01 Pubblicazione su rivista::01a Articolo in rivista
Additive partition of parametric information and its associated β-diversity measure / Ricotta, Carlo. - In: ACTA BIOTHEORETICA. - ISSN 0001-5342. - STAMPA. - 51:2(2003), pp. 91-100. [10.1023/a:1024539526618]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/147161
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