Claude Manté¹ ; Saikou Oumar Kidé² ; Anne-Francoise Yao-Lafourcade³ ; Bastien Mérigot⁴

1 : Université du Sud Toulon-Var, CNRS/INSU, IRD, MIO, UM 110, Aix-Marseille Université, 13288 Marseille Cedex 09, France ; 2 : , Institut Mauritanien de Recherches Océanographiques et des Pêches, Laboratoire de Biologie et Ecologie des Organismes Aquatiques, BP 22, Nouadhibou, Mauritania ; 3 :  Laboratoire de Mathématiques, Université Blaise Pascal, UMR 6620 – CNRS Campus des Cézeaux, 63171 Aubière Cedex, France ; 4 UMR Ecosystèmes Marins Exploités EME (IFREMER, IRD, UM2), Centre de Recherche Halieutique Méditerranéenne, Université de Montpellier 2, Avenue Jean Monnet, BP 171, 34203 Sète Cedex, France

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 (K,P) of parameters, and ranges from the Poisson distribution (when K →+∞) to Fisher’s log-series, when K → 0. Moreover, these parameters have biologi cal/ecological interpretations which are detailed in the literature and in this study. We compared three estimators of K,Pand the parameter α 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 (K,P) 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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