Implications of heterogeneous distributions of organisms on ballast water sampling

Ballast water sampling is one of the problems still needing investigation in order to enforce the D-2 Regulation of the International Convention for the Control and Management of Ship Ballast Water and Sediments. Although statistical "representativeness" of the sample is an issue usually discussed in the literature, neither a definition nor a clear description of its implications are presented. In this context, we relate it to the heterogeneity of the distribution of organisms in ballast water and show how to specify compliance tests under different models based on the Poisson and negative binomial distributions. We provide algorithms to obtain minimum sample volumes required to satisfy fixed limits on the probabilities of Type I and II errors. We show that when the sample consists of a large number of aliquots, the Poisson model may be employed even under moderate heterogeneity of the distribution of the organisms in the ballast water tank.