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Marine and Freshwater Research Marine and Freshwater Research Society
Advances in the aquatic sciences
RESEARCH ARTICLE

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
+ Author Affiliations
- Author Affiliations

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 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.


References

Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control 19, 716–723.
Crossref | GoogleScholarGoogle Scholar | Burnham K. P., and Anderson D. R. (2002). ‘Model Selection and Inference: A Practical Information-Theoretic Approach.’ 2nd edn. (Springer-Verlag: New York.)

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.
de Lestang S., and Melville-Smith R. (2006). West coast rock lobster managed fishery status report. In ‘State of the Fisheries Report 2005/06’. (Eds W. J. Fetcher and F. Head.) pp. 14–21. (Western Australian Department of Fisheries: Perth.)

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 | Food and Agriculture Organization (2008). Statistics. Available online at http://www.fao.org/corp/statistics/en/ [Verified January 2008].

Galeano D., Vieira S., Shafron W., and Newton P. (2006). Australian fisheries surveys report 2005. ABARE report prepared for the Fisheries Research Fund, Canberra.

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 | Kim S. W., Bentley N., Starr P. J., and Breen P. A. (2004). Assessment of red rock lobsters (Jasus edwardsii) in CRA 4 and CRA 5 in 2003. New Zealand Fisheries Assessment Report 2004(8).

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 | McLoughlin K. (2006). Northern Prawn Fishery. In ‘Fishery Status Reports 2005: Status of Fish Stocks Managed by the Australian Government’. (Ed. K. McLoughlin.) pp. 23–34. (Bureau of Rural Sciences: Canberra.)

Pauly, D. (1990). Length converted catch curves and the seasonal growth of fishes. ICLARM Fishbyte 8, 33–38.


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 |

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 |

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 |

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 |

Schnute, J. (1981). A versatile growth model with statistically stable parameters. Canadian Journal of Fisheries and Aquatic Sciences 38, 1128–1140.
Crossref | GoogleScholarGoogle Scholar |

Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics 6, 461–464.
Crossref | GoogleScholarGoogle Scholar |

Smith, M. T. , and Addison, J. T. (2003). Methods for stock assessment of crustacean fisheries. Fisheries Research 65, 231–256.
Crossref | GoogleScholarGoogle Scholar |

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 |

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 |

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 |

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 |