This paper outlines a method of calculating suitable tagging rates and total allowable catches (TACs) that would be expected to yield a pre-specified precision in a resultant abundance estimate. With respect to the tagging-based abundance estimator, we use the Lincoln-Petersen method and derive a formula that gives the expected coefficient of variation of the abundance estimate in terms of the number of releases and recaptures, which can in turn be expressed in terms of the tagging rate per tonne caught, the catch taken and the postulated underlying exploitable biomass. This relationship is shown to be extremely useful in terms of defining suitable catch levels and tagging rates required to obtain a given precision in the Petersen abundance estimate. To show the reliability of the precision relationship we predict the expected abundance precision using the mark and recapture data for Patagonian toothfish (Dissostichus eleginoides) in sub-area 48.3, and compare this to the precision in the abundance predicted by the integrated stock assessment. To show the usefulness of the methodology to new and exploratory fisheries we estimate the required TAC, for a given range of observed tagging rates, that would give us an abundance estimate with a coefficient of variation of 30% for the Patagonian toothfish stock in sub-area 48.4.
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