CSIRO PUBLISHING Marine and Freshwater Research, 2009, 60, 168–182 www.publish.csiro.au/journals/mfr Performance of methods for estimating size–transition matrices using tag–recapture data André E. Punt A,B,F , Rik C. Buckworth C , Catherine M. Dichmont D and Yimin Ye D,E A CSIRO Marine and Atmospheric Research, GPO Box 1538, Hobart, Tas. 7001, Australia. B School of Aquatic and Fishery Sciences, Box 355020, University of Washington, Seattle, WA 98195-5020, USA. C Fisheries, Department of Regional Development, Fisheries and Resources, GPO Box 3000, Darwin, NT 0810, Australia. D CSIRO Marine and Atmospheric Research, PO Box 120, Cleveland, Qld 4163, Australia. E Current address: Fishery Management & Conservation Service, FAO of the United Nations, Viale delleTermi diCaracalla, 00153, Rome, Italy. F Corresponding author. Email: andre.punt@csiro.au Abstract. Management advice for hard-to-age species such as prawns, crabs and rock lobsters are usually based on size-structured population dynamics models. These models require a size–transition matrix that specifies the probabilities of growing from one size-class to the others. Many methods exist to estimate size–transition matrices using tag–recapture data. However, they have not been compared in a systematic way. Eight of these methods are compared using Monte Carlo simulations parameterised using the data for the tiger prawn (Penaeus semisulcatus). Four of the methods are then applied to tag–recapture data for three prawn species inAustralia’s Northern Prawn Fishery to highlight the considerable sensitivity of model outputs to the method for estimating the size–transition matrix. The simulations show that not all methods perform equally well and that some methods are extremely poor. The ‘best’methods, as identified in the simulations, are those that allow for individual variability in the parameters of the growth curve as well as the age-at-release. A method that assumes that ℓ ∞ rather than k varies among individuals tends to be more robust to violations of model assumptions. Additional keywords: Australia, prawns, size-structured models, tagging data. Introduction Crustacean species support some of the most commercially valuable fisheries worldwide. For example, there are major fish- eries for crabs, lobsters and prawns in many regions of the world and FAO fishery statistics indicate that almost 6000kt of crustaceans were caught during 2006, 7% of global marine production (Food and Agriculture Organization 2008). Within Australia, crustaceans form the basis for the most valuable State (WesternAustralian rock lobster, de Lestang and Melville-Smith 2006) and Commonwealth (prawn) fisheries (Galeano et al. 2006; McLoughlin 2006). A wide variety of methods of stock assessment has been used to provide scientific advice for crus- tacean fisheries (Smith and Addison 2003). Of these methods, the most sophisticated attempt to track the size of stocks over time rather than simply assessing equilibrium relationships between yield and fishing mortality. However, stock assessments for many crustacean species cannot be based on age-structured population dynamics models and must be based instead on size-structured models because of difficulties assigning ages to individual ani- mals (e.g. Hobday and Punt 2001; Kim et al. 2004; Chen et al. 2005). A key feature of size-structured stock assessment meth- ods is the size–transition matrix, i.e. the matrix that defines the probability of an animal growing from one size-class to the oth- ers over a certain time-step. This matrix is analogous to the growth curve in conventional age-structured stock assessment methods, although it plays a more fundamental role in deter- mining the dynamics of the population in size-structured stock assessment methods. Considerable focus, including extensive simulation studies, has been placed on estimating the parameters of growth curves (usually, but not always, the von Bertalanffy growth curve), specifically in the presence of individual variation in growth (e.g. Sainsbury 1980; Wang et al. 1995; Troynikov 1998; Laslett et al. 2002; Eveson et al. 2007). However, this previous work has concentrated on estimating the parameters determining the mean length-at-age of individuals in the population rather than the information needed to apply size-structured stock assess- ment methods, i.e. the entries of the size–transition matrix. These entries are defined not only in terms of the mean growth incre- ment as a function of size, but also in terms of the variability associated with this increment. A variety of methods has been proposed for estimating size– transition matrices for use in size-structured stock assessments (e.g. Sullivan et al. 1990; Punt et al. 1997, 2006; McGarvey et al. © CSIRO 2009 10.1071/MF08217 1323-1650/09/020168