title: Additive partition of parametric information and its associated beta-diversity measure.
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, I apply this additive partition model generally adopted for traditional diversity measures to Aczél and Daróczy's generalized entropy of type alpha. In this way, a parametric measure of beta-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 beta-diversity for data on species relative abundances.
authors.affiliation: Department of Plant Biology, University of Rome La Sapienza, Piazzale Aldo Moro 5, 00185 Rome, Italy. carlo.ricotta@uniroma1.it
authors.forename: Carlo
authors.initials: C
authors.lastname: Ricotta
mesh_terms: D018533:Biomass; D017753:Ecosystem; D019277:Entropy; D019684:Magnoliopsida / Q000254:growth & development*; D008954:Models, Biological; D015233:Models, Statistical; D011157:Population Dynamics