Enumerating sparse organisms in ships' ballast water: why counting to 10 is not so easy

To reduce ballast water-borne aquatic invasions worldwide, the International Maritime Organization and United States Coast Guard have each proposed discharge standards specifying maximum concentrations of living biota that may be released in ships' ballast water (BW), but these regulations still lack guidance for standardized type approval and compliance testing of treatment systems. Verifying whether BW meets a discharge standard poses significant challenges. Properly treated BW will contain extremely sparse numbers of live organisms, and robust estimates of rare events require extensive sampling efforts. A balance of analytical rigor and practicality is essential to determine the volume of BW that can be reasonably sampled and processed, yet yield accurate live counts. We applied statistical modeling to a range of sample volumes, plankton concentrations, and regulatory scenarios (i.e., levels of type I and type II errors), and calculated the statistical power of each combination to detect noncompliant discharge concentrations. The model expressly addresses the roles of sampling error, BW volume, and burden of proof on the detection of noncompliant discharges in order to establish a rigorous lower limit of sampling volume. The potential effects of recovery errors (i.e., incomplete recovery and detection of live biota) in relation to sample volume are also discussed.