This paper presents an assessment of the harvested population of Patagonian toothfish at Macquarie Island based on data from a tag-recapture experiment initiated during the 1995/96 fishing season. Population models that include dynamics of tagged and un-tagged fish, daily releases, catches, recaptures, natural mortality, and annual net recruitment are used to assess the population of one of the main fishing regions of Macquarie Island: Aurora Trough. The pre-tagging abundance is estimated by incorporating a Petersen approach in a novel semi-parametric model using maximum likelihood methods. The model (the "base-case model") assumes the recaptures are Poisson distributed, and the recapture expectations are conditional on catch numbers and previous recaptures. A second model (the "selectivity model") attempts to account for apparent decreasing availability with length. It assumes a maximum age or length above which a fish is no longer available to the gear. Each released fish is assigned a length of time in the available population according to its estimated release age. Once this time has elapsed, the fish is removed from the analysis. The base-case model estimated that pre-tagging abundance was between 1.0 and 1.5 million fish, depending on assumed mixing levels between tagged and un-tagged fish. Estimates of net recruitment were occasionally negative, suggesting that emigration may have exceeded immigration. The estimated percentage of the pre-tagging available abundance remaining in Aurora Trough was about 35% in the base-case model. In general, the selectivity model estimated a lower available abundance, and a lower percent remaining, than the base-case model. The substantial decline in available abundance predicted by both models provides some evidence of large-scale emigration, and could not be due to fishing alone.
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