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A nonparametric method for the measurement of size diversity with emphasis on data standardization

The most suitable method for estimation of size diversity is investigated. Size diversity is computed on the basis of the Shannon diversity expression adapted for continuous variables, such as size. It takes the form of an integral involving the probability density function (pdf) of the size of the individuals. Different approaches for the estimation of pdf are compared: parametric methods, assuming that data come from a determinate family of pdfs, and nonparametric methods, where pdf is estimated using some kind of local evaluation. Exponential, generalized Pareto, normal, and log-normal distributions have been used to generate simulated samples using estimated parameters from real samples. Nonparametric methods include discrete computation of data histograms based on size intervals and continuous kernel estimation of pdf. Kernel approach gives accurate estimation of size diversity, whilst parametric methods are only useful when the reference distribution have similar shape to the real one. Special attention is given for data standardization. The division of data by the sample geometric mean is proposedas the most suitable standardization method, which shows additional advantages: the same size diversity value is obtained when using original size or log-transformed data, and size measurements with different dimensionality (longitudes, areas, volumes or biomasses) may be immediately compared with the simple addition of ln k where kis the dimensionality (1, 2, or 3, respectively). Thus, the kernel estimation, after data standardization by division of sample geometric mean, arises as the most reliable and generalizable method of size diversity evaluation

This work was supported by the grants from the Ministerio de Ciencia y Tecnología of the Spanish Government, Programa Nacional de Biodiversidad, Ciencias de la Tierra y Cambio Global (ref. CGL2004- 05433/BOS) and the project MEASURE (MTM2006-03040/)

Association for the Sciences of Limnology and Oceanography (ASLO)

Author: Quintana Pou, Xavier
Brucet Balmaña, Sandra
Boix Masafret, Dani
López i Flores, Rocío
Gascón Garcia, Stéphanie
Badosa i Salvador, Anna
Sala Genoher, Jordi
Moreno i Amich, Ramon
Egozcue, Juan José
Abstract: The most suitable method for estimation of size diversity is investigated. Size diversity is computed on the basis of the Shannon diversity expression adapted for continuous variables, such as size. It takes the form of an integral involving the probability density function (pdf) of the size of the individuals. Different approaches for the estimation of pdf are compared: parametric methods, assuming that data come from a determinate family of pdfs, and nonparametric methods, where pdf is estimated using some kind of local evaluation. Exponential, generalized Pareto, normal, and log-normal distributions have been used to generate simulated samples using estimated parameters from real samples. Nonparametric methods include discrete computation of data histograms based on size intervals and continuous kernel estimation of pdf. Kernel approach gives accurate estimation of size diversity, whilst parametric methods are only useful when the reference distribution have similar shape to the real one. Special attention is given for data standardization. The division of data by the sample geometric mean is proposedas the most suitable standardization method, which shows additional advantages: the same size diversity value is obtained when using original size or log-transformed data, and size measurements with different dimensionality (longitudes, areas, volumes or biomasses) may be immediately compared with the simple addition of ln k where kis the dimensionality (1, 2, or 3, respectively). Thus, the kernel estimation, after data standardization by division of sample geometric mean, arises as the most reliable and generalizable method of size diversity evaluation
This work was supported by the grants from the Ministerio de Ciencia y Tecnología of the Spanish Government, Programa Nacional de Biodiversidad, Ciencias de la Tierra y Cambio Global (ref. CGL2004- 05433/BOS) and the project MEASURE (MTM2006-03040/)
Document access: http://hdl.handle.net/2072/242861
Language: eng
Publisher: Association for the Sciences of Limnology and Oceanography (ASLO)
Rights: Tots els drets reservats
Subject: Mostreig (Estadística)
Sampling (Statistics)
Estimació de paràmetres
Parameter estimation
Funcions de variables complexes
Functions of complex variables
Title: A nonparametric method for the measurement of size diversity with emphasis on data standardization
Type: info:eu-repo/semantics/article
Repository: Recercat

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