Fitting the truncated negative binomial distribution to count data A comparison of estimators, with an application to groundfishes from the Mauritanian Exclusive Economic Zone

Type Article
Date 2016-09
Language English
Author(s) Mante Claude1, Kide Saikou Oumar2, Yao-Lafourcade Anne-Francoise3, Merigot Bastien4
Affiliation(s) 1 : Aix Marseille Univ, Univ Sud Toulon Var, CNRS INSU, IRD,MIO,UM 110, F-13288 Marseille 09, France.
2 : Inst Mauritanien Rech Oceanog & Peches, Lab Biol & Ecol Organismes Aquat, BP 22, Nouadhibou, Mauritania.
3 : Univ Clermont Ferrand, CNRS, Math Lab, UMR 6620, Campus Cezeaux, F-63171 Aubiere, France.
4 : Univ Montpellier 2, Ctr Rech Halieut Mediterraneenne, UMR Ecosyst Marins Exploites EME IFREMER, IRD,UM2, Ave Jean Monnet,BP 171, F-34203 Sete, France.
Source Environmental And Ecological Statistics (1352-8505) (Springer), 2016-09 , Vol. 23 , N. 3 , P. 359-385
DOI 10.1007/s10651-016-0343-1
WOS© Times Cited 4
Keyword(s) Birth-and-dead models, Habitat, Log-series, Minimum Hellinger distance, Negative binomial, Species abundance
Abstract

Modeling empirical distributions of repeated counts with parametric probability distributions is a frequent problem when studying species abundance. One must choose a family of distributions which is flexible enough to take into account very diverse patterns and possess parameters with clear biological/ecological interpretations. The negative binomial distribution fulfills these criteria and was selected for modeling counts of marine fish and invertebrates. This distribution depends on a vector of parameters, and ranges from the Poisson distribution (when ) to Fisher's log-series, when . Moreover, these parameters have biological/ecological interpretations which are detailed in the literature and in this study. We compared three estimators of K, and the parameter of Fisher's log-series, following the work of Rao CR (Statistical ecology. Pennsylvania State University Press, University Park, 1971) on a three-parameter unstandardized variant of the negative binomial distribution. We further investigated the coherence underlying parameter values resulting from the different estimators, using both real count data collected in the Mauritanian Exclusive Economic Zone (MEEZ) during the period 1987-2010 and realistic simulations of these data. In the case of the MEEZ, we first built homogeneous lists of counts (replicates), by gathering observations of each species with respect to "typical environments" obtained by clustering the sampled stations. The best estimation of was generally obtained by penalized minimum Hellinger distance estimation. Interestingly, the parameters of most of the correctly sampled species seem compatible with the classical birth-and-dead model of population growth with immigration by Kendall (Biometrika 35:6-15, 1948).

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Mante Claude, Kide Saikou Oumar, Yao-Lafourcade Anne-Francoise, Merigot Bastien (2016). Fitting the truncated negative binomial distribution to count data A comparison of estimators, with an application to groundfishes from the Mauritanian Exclusive Economic Zone. Environmental And Ecological Statistics, 23(3), 359-385. Publisher's official version : https://doi.org/10.1007/s10651-016-0343-1 , Open Access version : https://archimer.ifremer.fr/doc/00352/46332/