On the Statistical Distribution of Salmon in the Sea: Application of the Negative Binomial Distribution, and the Influence of Sampling Effort

Abstract

We examined the sampling statistics of Pacific salmon (Oncorhynchus spp.) caught in a series of experimental gillnet sets on the high seas and demonstrate how the reliability of the catch statistics varies with the amount of sampling effort. Our analysis indicates that the replicate catches, which were made under essentially identical conditions, are adequately described by the negative binomial distribution. We also extend the utility of this distribution for describing catch statistics by showing that (1) the shape parameter of the distribution can be directly interpreted as the number of degrees of freedom (df) associated with each observation of catch and (2) the df are related to the amount of sampling effort used and the size of the biological aggregation being encountered by the gear. For salmon caught on the high seas, approximately 1 df is obtained per 15 m of gill net used. Identification of the statistical model describing the uncertainty in high-seas gillnet catches should help in the design of better high seas surveys and in the analysis of historical data bases. As an example, we show how the statistical certainty associated with estimates of salmon density changes with the amount of sampling effort applied.