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Update: A non-parametric method for the measurement of size diversity, with emphasis on data standardization. The measurement of the size evenness

A method for the measurement of the size diversity based on the classical Shannon–Wiener expression was proposed as a proxy of the shape of the size distribution. The summatory of probabilities of a discrete variable (such as species relative abundances) in the original Shannon–Wiener expression was substituted by an integral of the probability density function of a continuous variable (such as body size). Here, we propose an update of this method by including the measurement of the size e-evenness, just dividing the exponential of the size diversity by its possible maximum for a given size range. Assuming a domain of the size range of (0,∞), for a given logarithmic mean ( math formula) and a logarithmic standard deviation math formula, the distribution with the highest diversity is the Log-Normal. The size e-evenness ranges between 0 and 1 because of the division by the maximum exponential diversity. Size e-evenness is useful to discriminate whether variations in size diversity are due to changes in the shape of the size distribution or caused by differences in size dispersion

This work was supported by grants from the Generalitat de Catalunya (ref. 2014 SGR 484) and from the Ministerio de Ciencia e Innovaci on, Programa de Investigaci on Fundamental (CGL2011-23907)

Limnology and Oceanography: Methods, 2016, vol. 14, núm. 6, p. 408-413

http://hdl.handle.net/10256/9720

Association for the Sciences of Limnology and Oceanography (ASLO)

Author: Quintana Pou, Xavier
Egozcue, Juan José
Martínez-Abella, Omar
López-Flores, Rocio
Gascón Garcia, Stéphanie
Brucet Balmaña, Sandra
Boix Masafret, Dani
Date: 2016
Abstract: A method for the measurement of the size diversity based on the classical Shannon–Wiener expression was proposed as a proxy of the shape of the size distribution. The summatory of probabilities of a discrete variable (such as species relative abundances) in the original Shannon–Wiener expression was substituted by an integral of the probability density function of a continuous variable (such as body size). Here, we propose an update of this method by including the measurement of the size e-evenness, just dividing the exponential of the size diversity by its possible maximum for a given size range. Assuming a domain of the size range of (0,∞), for a given logarithmic mean ( math formula) and a logarithmic standard deviation math formula, the distribution with the highest diversity is the Log-Normal. The size e-evenness ranges between 0 and 1 because of the division by the maximum exponential diversity. Size e-evenness is useful to discriminate whether variations in size diversity are due to changes in the shape of the size distribution or caused by differences in size dispersion
This work was supported by grants from the Generalitat de Catalunya (ref. 2014 SGR 484) and from the Ministerio de Ciencia e Innovaci on, Programa de Investigaci on Fundamental (CGL2011-23907)
Format: application/pdf
ISSN: 1541-5856
Document access: http://hdl.handle.net/10256/13685
Language: eng
Publisher: Association for the Sciences of Limnology and Oceanography (ASLO)
Collection: MICINN/PN 2012-2015/CGL2011-23907
Reproducció digital del document publicat a: http://dx.doi.org/10.1002/lom3.10099
Articles publicats (D-CCAA)
Is part of: Limnology and Oceanography: Methods, 2016, vol. 14, núm. 6, p. 408-413
See also: http://hdl.handle.net/10256/9720
Rights: Attribution-NonCommercial-NoDerivs 3.0 Spain
Rights URI: http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Subject: Mostreig (Estadística)
Sampling (Statistics)
Estimació de paràmetres
Parameter estimation
Funcions de variables complexes
Functions of complex variables
Title: Update: A non-parametric method for the measurement of size diversity, with emphasis on data standardization. The measurement of the size evenness
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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