Application of a Delay-Difference Model for the Stock Assessment of Southern Atlantic Albacore(Thunnus alalunga)

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. α 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.

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-differ- ence 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 a and fl in Ricker stock-recruitment model and the catchability coefficient q. a is more sensitive to CV than fl 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 24122t, and the estimated ratios of catch against MSY for the past seven years were approxi- mately 1.0. We suggest that care should be taken to protect the albacore fishery in the southern Atlantic Ocean. The proposed de- lay-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.