An exact time of release and recapture stock assessment model applied to Macquarie Island Patagonian toothfish (Dissostichus eleginoides)

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.