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

Abstract

This paper presents an exact time of release and recapture stock assessment model that unifies the semi-parametric approach with the Petersen method. It allows for the expectation that a fish tagged early in a fishing season has a higher chance of being recaptured during the season than a fish tagged later in the season. The model is applied to the harvested population of Patagonian toothfish at Macquarie Island utilising data from a tag-recapture experiment initiated during the 1995/1996 fishing season. The population models of the assessment include dynamics of tagged and untagged fish, daily releases, catches, recaptures, natural mortality, and annual net recruitment. Two assessment models are presented. The first, referred to as the ‘length-independent selection’ (LIS) model, assumes the recaptures are Poisson distributed, and the recapture expectations are conditional on catch numbers and the estimated abundance of tagged fish. The second, the ‘length-dependent selection’ (LDS) model, attempts to account for apparent decreasing availability with length. It assumes that the likelihood of recapturing a tagged fish is proportional to the relative selectivity for fish of the corresponding length. The assessment models were applied to the population inhabiting the Aurora Trough region; one of the main fishing areas surrounding Macquarie Island. The models estimated that pre-tagging abundance was between 0.6 and 0.8 million fish, depending on assumed mixing levels between tagged and untagged fish. The LDS model estimated a lower available abundance than the LIS model. Estimates of net recruitment were occasionally negative, suggesting that emigration may have exceeded immigration. Estimates of available abundance to the fishery showed a decline to approximately 30% of the pre-tagging available abundance in 1998 before recovering to between 50 and 75%, depending on the assumed mixing level.