Abstract
Delay-difference models are intermediate between simple surplus-production models and complicated age-structured models. Such intermediate models are more efficient and require less data than age-structured models. In this study, a delay-difference model was applied to fit catch and catch per unit effort (CPUE) data (1975–2011) of the southern Atlantic albacore (Thunnus alalunga) stock. The proposed delay-difference model captures annual fluctuations in predicted CPUE data better than Fox model. In a Monte Carlo simulation, white noises (CVs) were superimposed on the observed CPUE data at four levels. Relative estimate error was then calculated to compare the estimated results with the true values of parameters α and β in Ricker stock-recruitment model and the catchability coefficient q. a is more sensitive to CV than β and q. We also calculated an 80% percentile confidence interval of the maximum sustainable yield (MSY, 21756 t to 23408 t; median 22490 t) with the delay-difference model. The yield of the southern Atlantic albacore stock in 2011 was 24122 t, and the estimated ratios of catch against MSY for the past seven years were approximately 1.0. We suggest that care should be taken to protect the albacore fishery in the southern Atlantic Ocean. The proposed delay-difference model provides a good fit to the data of southern Atlantic albacore stock and may be a useful choice for the assessment of regional albacore stock.
Similar content being viewed by others
References
Akaike, H., 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19 (6): 716–723.
Deriso, R. B., 1980. Harvesting strategies and parameter estimation for an age-structured model. Canadian Journal of Fisheries and Aquatic Sciences, 37: 268–282.
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 for tiger prawns in Australia’s Northern Prawn Fishery. Fisheries Research, 65: 335–350.
Efron, B., and Tibshirani, R. J., 1993. An Introduction to the Bootstrap. Chapman and Hall/CRC, New York, London, 416pp.
Fogarty, M. J., and Murawski, S. A., 1986. Population dynamics and assessment of exploited invertebrate stocks. In: North Pacific Workshop on Stock Assessment and Management of Invertebrates. Canadian Special Publication of Fisheries and Aquatic Sciences 92. Jamieson, G. S., and Bourne, N., eds., T & H Printers Ltd., Ottawa, Ontario, 228–244.
Fournier, D. A., and Doonan, I. J., 1987. A length-based stock assessment method utilizing a generalized delay-difference model. Canadian Journal of Fisheries and Aquatic Sciences, 44: 422–437.
Gray, C. A., Silberschneider, V., and Stewart, J., 2009. Age, growth, maturity and the overfishing of the iconic sciaenid, Argyrosomus japonicus, in south-eastern, Australia. Fisheries Research, 95: 220–229.
Hall, N. G., 1997. Delay-difference model to estimate the catch of different categories of the western rock lobster (Panuliruscygnus) for the two stages of the annual fishing season. Marine and Freshwater Research, 48: 949–958.
Hilborn, R., and Walters, C. J., 1992. Quantitative Fisheries Stock Assessment, Choices, Dynamics and Uncertainty. Chapman and Hall/CRC, New York, London, 449pp.
ICCAT, 1999. Detailed report on albacore. ICCAT, Collective Volume of Scientific Papers, 49 (4): 1–92.
ICCAT, 2011. ICCAT Statistical Bulletin, Vol. 40. Madrid, Spain, 156pp.
ICCAT, 2012. Report of the 2011 ICCAT south Atlantic and Mediterranean albacore stock assessment sessions. ICCAT, Collective Volume of Scientific Papers, 68 (2): 387–491.
ICCAT, 2013. Report of the 2013 ICCAT North and South Atlantic Albacore Data Preparatory Meeting. Madrid, Spain, 68pp.
Jensen, O. P., Gilroy, D. J., Hogan, Z., and Allen, B. C., 2009. Evaluating recreational fisheries for an endangered species: A case study of taimen, Huchotaimen, in Mongolia. Canadian Journal of Fisheries and Aquatic Sciences, 66: 1707–1718.
Jacobson, L. D., Cadrin, S. X., and Weinberg, J. R., 2002. Tools for estimating surplus production and FMSY in any stock assessment model. North American Journal of Fisheries Management, 22: 326–338.
Kimura, D. K., Balsiger, J. W., and Ito, D. H., 1984. Generalized stock reduction analysis. Canadian Journal of Fisheries and Aquatic Sciences, 41: 1325–1333.
Kimura, D. K., 1985. Changes to stock reduction analysis indicated by Schnute’s general theory. Canadian Journal of Fisheries and Aquatic Sciences, 42: 2059–2060.
Lee, L. K., and Yeh, S. Y., 2007. Age and growth of south Atlantic albacore–A revision after the revelation of otolith daily ring counts. ICCAT, Collective Volume of Scientific Papers, 60 (2): 443–456.
Lee, L. K., and Yeh, S. Y., 2008. Assessment of south Atlantic albacore resource based on 1959–2005 catch and effort statistics from ICCAT. ICCAT, Collective Volume of Scientific Papers, 62 (3): 870–883.
Mesnil, B., 2012. The hesitant emergence of maximum sustainable yield (MSY) in fisheries policies in Europe. Marine Policy, 36: 473–480.
Murphy, G. I., 1966. Population biology of the Pacific sardine (Sardinopscaerulea). Proceedings of the California Academy of Sciences, 34: 1–84.
Musick, J. A., Bonfil, R., and Stevens, J. D., 2005. Management Techniques for Elasmobranch Fisheries. FAO, Rome, 474pp.
Pallare, P., and Restrepo, V., 2003. Use of delay-difference models to assess the India bigeye stock. IOCT Proceedings, 6: 148–150.
Penney, A. J., 1994. Morphometric relationships, annual catches and catch-at-size for South African caught South Atlantic albacore (Thunnus alalunga). ICCAT, Collective Volume of Scientific Papers, 42 (1): 371–382.
Prager, M. H., 2005. A stock production model incorporating covariates (version 5) and auxiliary programs, CCFHR (NOAA) Miami laboratory document MIA-92/93-55, Beaufort Laboratory Document BL-2004-01.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., 1986. Numerical Recipes. Cambridge Press, Cambridge, UK, 848pp.
Quinn II, T. J., and Deriso, R. B., 1999. Quantitative Fish Dynamics. Oxford University Press, New York, 542pp.
Ricker, W. E., 1975. Computation and Interpretation of Biological Statistics of Fish Populations. Bulletin of the Fisheries Research Board of Canada, The Blackburn Press, 400pp.
Saville, A., 1980. The assessment and management of pelagic fish stock. A symposium held in Aberdeen, 3–7 July 1978. Rapports et Proces-Verbaux des Reunions Conseil International pour l'Exploration de la Mer, 177: 517pp.
Schnute, J. T., 1985. A general theory for analysis of catch and effort data. Canadian Journal of Fisheries and Aquatic Sciences, 42: 414–429.
Schnute, J. T., 1987. A general fishery model for a size-structured fish population. Canadian Journal of Fisheries and Aquatic Sciences, 44: 924–940.
Sun, C. L., Ehrhardt, N. M., Porch, C. E., and Yeh, S. Z., 2002. Analyses of yield and spawning stock biomass per recruit for the South Atlantic albacore (Thunnus alalunga). Fisheries Research, 56: 193–204.
Su, Z. M., and Liu, Q., 1998. A continuous Fox-form of the surplus production observation-error estimator. Fisheries Research, 34: 59–76.
Walter, G. G., 1973. Delay-differential equation models for fisheries. Journal of the Fisheries Board of Canada, 30: 939–945.
Walters, C. J., and Martell, S. J. D., 2004. Fisheries Ecology and Management. Princeton University Press, Princeton, New Jersey, 448pp.
Yeh, S. Y., Liu, H. C., and Tsou, T. S., 1990. Assessment of the south Atlantic albacore resource by using surplus production models, 1967–1988. ICCAT, Collective Volume of Scientific Papers, 31: 236–240.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhang, K., Liu, Q. & Kalhoro, M.A. Application of a Delay-difference model for the stock assessment of southern Atlantic albacore (Thunnus alalunga). J. Ocean Univ. China 14, 557–563 (2015). https://doi.org/10.1007/s11802-015-2517-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11802-015-2517-0