Generalized entropy indices to measure α- and β-diversities of macrophytes

Abstract

A family of entropy indices constructed in the framework of Tsallis entropy formalism is used to investigate ecological diversity. It represents a new perspective in ecology because a simple equation can incorporate all aspects of α−diversity, from richness to dominance and can be also related to a measure of species rarity. In addition, a generalized Kullback-Leibler distance, constructed in the framework of a nonextensive formalism, is recalled and used as a measure of β−diversity between two systems. These tools are applied to data relative to the macrophytes collected from two not far apart arms of Itaipu Reservoir, in Paraná River basin.

Comparison of diversity indices applied to macrophyte incidence-based data

“…In other words, with regard to the content S q* , the value of the parameter q is a property found only for a specific system (in the present case, a sample or a community) and it acquires a specific meaning because it is determined by the sample itself to which it is applied. This approach could be considered a new perspective when indices are used to analyze the communities (Mendes et al 2008;Evangelista et al 2009). It is worth noting that when the S q family is used as the Tsallis entropy in the statistical mechanics, there is no clear criterion for determining the optimal value of q (Mendes et al 2008), unlike what occurs with a biological community.…”

“…With the relative abundances estimated with frequency data, the Shannon (H) and Simpson (D) diversity was estimated. The other index used (the target index) was the Sq * (Mendes et al 2008), which was from a family of diversity indices (Evangelista et al 2009). In this work, a simplified methodology was developed for determining this number, using the software Mathematica 6.0 (Wolfram 1991), in which all the indices of diversity were also calculated.…”

Tsallis Entropy for Assessing Spatial Uncertainty Associated with Mean Annual Runoff of Quaternary Catchments of the Middle Vaal Basin in South Africa

“…In other cases, many details of the system influence the q-values and the determination of q for all existing systems is still at an early stage [ 6 ]. In many instances, the system details are not known a priori [ 6 ], and determining q-values is not an easy task [ 17 ]. Hence, for physical, biological and ecological systems, and so forth, there is no general methodology to determine the q-values [ 18 ].…”

Multi-Way Multi-Group Segregation and Diversity Indices

“…What measure of diversity will detect white women being exclusively hired in clerical positions, people of colour being hired in custodial positions, and white males being hired in white-collar positions? A robust diversity statistic would have to measure whether traditionally under-represented groups have an equal footing in all departments and all job descriptions, what ecologists call β -diversity [1] , [2] . Quantification should allow comparison of an industry's employment diversity or segregation against itself at an earlier time, or against another industry at the same time.…”