Fisheries Research 63 (2003) 179–191 An exact time of release and recapture stock assessment model with an application to Macquarie Island Patagonian toothfish (Dissostichus eleginoides) G.N. Tuck a,∗ , W.K. de la Mare b , W.S. Hearn c , R. Williams d , A.D.M. Smith a , X. He e , A. Constable d a CSIRO Marine Research, GPO Box 1538, Hobart, Tasmania 7001, Australia b School of Resource and Environmental Management, Simon Fraser University, Burnaby, BC, Canada V5A 1S6 c CSIRO Marine Research, Private Bag No. 5, Wembley, WA 6913, Australia d Australian Antarctic Division, Channel Highway, Kingston, Tasmania 7050, Australia e Southwest Fisheries Science Center, 110 Shaffer Road, Santa Cruz, CA 95060, USA Received 19 June 2000; received in revised form 24 January 2003; accepted 4 February 2003 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. Crown Copyright © 2003 Published by Elsevier Science B.V. All rights reserved. Keywords: Patagonian toothfish; Macquarie Island; Stock assessment; Tagging experiment; Semi-parametric model; Available abundance ∗ Corresponding author. Tel.: +61-3-6232-5222; fax: +61-3-6232-5053. E-mail address: geoff.tuck@csiro.au (G.N. Tuck). 1. Introduction Bottom-set longline and trawl fisheries for Patago- nian toothfish (Dissostichus eleginoides) have devel- oped in waters around several of the Southern Ocean’s 0165-7836/03/$ – see front matter. Crown Copyright © 2003 Published by Elsevier Science B.V. All rights reserved. doi:10.1016/S0165-7836(03)00073-0