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 EA 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 delle Termi diCaracalla, 00153, Rome, Italy.
F Corresponding author. Email: andre.punt@csiro.au
Marine and Freshwater Research 60(2) 168-182 https://doi.org/10.1071/MF08217
Submitted: 25 July 2008 Accepted: 25 October 2008 Published: 20 February 2009
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 in Australia’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.
Acknowledgements
This work was supported by FRDC project 2004/022 and CSIRO Marine and Atmospheric Research. Bill Venables, Nick Ellis and Shijie Zhou (CSIRO Marine and Atmospheric Research), Richard McGarvey (SARDI), Malcolm Haddon (TAFI), and an anonymous reviewer are thanked for their comments on an earlier version of this paper.
Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control 19, 716–723.
| Crossref | GoogleScholarGoogle Scholar |
Chen, Y. , Kanaiwa, M. , and Wilson, C. (2005). Developing and evaluating a size-structured stock assessment model for the American lobster, Homarus americanus, fishery. New Zealand Journal of Marine and Freshwater Research 39, 645–660.
Dichmont, C. M. , Punt, A. E. , Deng, A. , Dell, Q. , and Venables, W. (2003). Application of a weekly delay-difference model to commercial catch and effort data in Australia’s Northern Prawn Fishery. Fisheries Research 65, 335–350.
| Crossref | GoogleScholarGoogle Scholar |
Hobday, D. , and Punt, A. E. (2001). Size-structured population modelling and risk assessment of the Victorian southern rock lobster, Jasus edwardsii, fishery. Marine and Freshwater Research 52, 1495–1507.
| Crossref | GoogleScholarGoogle Scholar |
Laslett, G. M. , Eveson, J. P. , and Polacheck, T. (2002). A flexible maximum likelihood approach for fitting growth curves to tag–recapture data. Canadian Journal of Fisheries and Aquatic Sciences 59, 976–986.
| Crossref | GoogleScholarGoogle Scholar |
Pauly, D. (1990). Length converted catch curves and the seasonal growth of fishes. ICLARM Fishbyte 8, 33–38.
![](../../media/share/OpenURL_Image.gif)
Pauly, D. , Soriano-Bertz, M. , Moreau, J. , and Jarre-Teichmann, A. (1992). A new model accounting for seasonal growth cessation in fishes. Australian Journal of Marine and Freshwater Research 43, 1151–1156.
| Crossref | GoogleScholarGoogle Scholar |
![](../../media/share/OpenURL_Image.gif)
Punt, A. E. , Kennedy, R. B. , and Frusher, S. (1997). Estimating the size-transition matrix for Tasmanian rock lobster, Jasus edwardsii. Marine and Freshwater Research 48, 981–992.
| Crossref | GoogleScholarGoogle Scholar |
![](../../media/share/OpenURL_Image.gif)
Punt, A. E. , Hobday, D. , Gerhard, J. , and Troynikov, V. S. (2006). Modelling growth of rock lobsters, Jasus edwardsii, off Victoria, Australia using models that allow for individual variation in growth parameters. Fisheries Research 82, 119–130.
| Crossref | GoogleScholarGoogle Scholar |
![](../../media/share/OpenURL_Image.gif)
Sainsbury, K. J. (1980). Effect of individual variability on the von Bertalanffy growth equation. Canadian Journal of Fisheries and Aquatic Sciences 37, 241–247.
| Crossref | GoogleScholarGoogle Scholar |
![](../../media/share/OpenURL_Image.gif)
Schnute, J. (1981). A versatile growth model with statistically stable parameters. Canadian Journal of Fisheries and Aquatic Sciences 38, 1128–1140.
| Crossref | GoogleScholarGoogle Scholar |
![](../../media/share/OpenURL_Image.gif)
Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics 6, 461–464.
| Crossref | GoogleScholarGoogle Scholar |
![](../../media/share/OpenURL_Image.gif)
Smith, M. T. , and Addison, J. T. (2003). Methods for stock assessment of crustacean fisheries. Fisheries Research 65, 231–256.
| Crossref | GoogleScholarGoogle Scholar |
![](../../media/share/OpenURL_Image.gif)
Somers, I. F. , and Kirkwood, G. P. (1991). Population ecology of the grooved tiger prawn, Penaeus semisulcatus, in the north-western Gulf of Carpentaria, Australia: growth, movement, age structure and infestation by the bopyrid parasite Epipenaeon ingens. Australian Journal of Marine and Freshwater Research 42, 349–367.
| Crossref | GoogleScholarGoogle Scholar |
![](../../media/share/OpenURL_Image.gif)
Sullivan, P. J. , Lai, H. L. , and Gallucci, V. F. (1990). A catch-at-length analysis that incorporates a stochastic model of growth. Canadian Journal of Fisheries and Aquatic Sciences 47, 184–198.
| Crossref | GoogleScholarGoogle Scholar |
![](../../media/share/OpenURL_Image.gif)
Troynikov, V. S. (1998). Probability density functions useful for parameterization of heterogeneity in growth and allometry data. Bulletin of Mathematical Biology 60, 1099–1121.
| Crossref | GoogleScholarGoogle Scholar |
![](../../media/share/OpenURL_Image.gif)
Wang, Y.-G. , Thomas, M. R. , and Somers, I. F. (1995). A maximum likelihood approach for estimating growth from tag-recapture data. Canadian Journal of Fisheries and Aquatic Sciences 52, 252–259.
| Crossref | GoogleScholarGoogle Scholar |
![](../../media/share/OpenURL_Image.gif)