Search and Stock Depletion: Theory and Applications

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Abstract
A general theory for the estimation of stock size from search data is developed. In the theory, it is assumed that discrete aggregations (schools of fish, beds of clams) are encountered. The search model is an extension of the Poisson process to include depletion. The theory provides a way of estimating stock size and confidence intervals around the estimate, as well as the ability to predict future catches for a given level of effort. Three applications of theory are described: (1) estimating stock size when there is no catch; (2) determining, in real time, the length of fishing seasons; and (3) an empirical study of stock assessment of Pacific ocean perch (Sebastes alutus) near Rennell Sound, British Columbia.

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