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.