Linear model analysis of net catch data using the negative binomial distribution

Abstract

Sampling with nets or trawls remains a common technique for determining the comparative abundances of aquatic organisms, and the objective of such studies is frequently to evaluate relationships among the counts of individuals caught and exogenous variables. Analysis of such data is often done with a general linear model (e.g., ANOVA, ANCOVA, regression), assuming an underlying normal probability distribution. Such analyses are not fully satisfactory because of the symmetry and continuous nature of the assumed normal probability distribution and the high variance to low mean value relationships common to counts of biological populations. The negative binomial is a discrete probability distribution that is recognized as a suitable descriptor of organism count data. We present an approach for undertaking linear model analyses of net catch data that permits estimation of model parameters (including the negative binomial k parameter) and hypothesis testing of both continuous and discrete model effects and their interactions using bootstrap replication. The analysis incorporates adjustment for varying element sizes, such as differences in the amounts of water filtered during sampling.Résumé : L'échantillonnage au filet droit ou au chalut reste une technique couramment utilisée pour mesurer et comparer l'abondance des organismes aquatiques, et l'objectif de ces études est souvent d'évaluer les relations entre les effectifs des individus capturés et certaines variables exogènes. L'analyse de ces données se fait souvent à l'aide d'un modèle linéaire général (p.ex. analyse de variance, analyse de covariance, régression) supposant à la base une distribution normale des probabilités. De telles analyses ne sont pas parfaitement satisfaisantes à cause de la symétrie et de la nature continue de la distribution normale supposée des probabilités, et des relations entre la forte variance et la faible valeur moyenne qui caractérisent les dénombrements des populations vivantes. La distribution binômiale négative est une distribution discrète qui est considérée comme un descripteur acceptable des données de dénombrement des organismes. Nous présentons un mode d'analyse par modèle linéaire des données sur les prises au filet qui permet d'estimer les paramètres du modèle (y compris le paramètre k de la distribution binômiale négative) et de vérifier l'hypothèse sur les effets à la fois continus et discrets du modèle et leurs interactions avec la réplication par bootstrap. L'analyse intègre un ajustement pour des tailles variables des éléments, comme des différences dans les quantités d'eau filtrées pendant l'échantillonnage.[Traduit par la Rédaction] Power and Moser 200

Columbia River plume fronts. I. Hydrography, zooplankton distribution, and community composition

“…Although the counts were converted to densities based on volume of water sampled, count-based models were still appropriate because volume sampled represents exposure time to the underlying distribution (Lawless 1987). The 2 alternative models we considered were a Poisson model, which assumes that the mean is equal to the variance, and the negative binomial model, which is applicable to 'over-dispersed' data where the variance is larger than the mean (Welch & Ishida 1993, Power & Moser 1999. To chose between these 2 models, we performed an analysis of deviance (ANODEV) to determine whether the more complex negative binomial model was warranted.…”

Columbia River plume fronts. II. Distribution, abundance, and feeding ecology of juvenile salmon

“…Lawless 1987), and countbased generalized linear models are still appropriate in this application. We used a negative binomial error model to account for over-dispersion in the data (Welch & Ishida 1993, Power & Moser 1999.…”

Aggregation on the edge: effects of hypoxia avoidance on the spatial distribution of brown shrimp and demersal fishes in the Northern Gulf of Mexico

“…Estimates of the model parameters were obtained by maximum likelihood assuming uncertainty in individual trawl CPUEs were described by a negative binomial distribution. A negative binomial distribution was chosen be cause the distribution of CPUE was typically highly skewed with numerous small catches and a few very large catches, as is typical with trawl survey data (Power & Moser 1999). For display purposes, CPUE was log (x + 1) transformed and standardized for differences in abundance among years by dividing by μ 2.…”