THE EFFECT OF EASTERN ATLANTIC AND MEDITERRANEAN BLUEFIN TUNA SAMPLING ERROR ON THE CATCH AT AGE

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1 SCRS/2004/093 Col. Vol. Sci. Pap. ICCAT, 58(2): (2005) THE EFFECT OF EASTERN ATLANTIC AND MEDITERRANEAN BLUEFIN TUNA SAMPLING ERROR ON THE CATCH AT AGE H. Arrizabalaga 1 SUMMARY During the last BFT stock assessment session, three catch at age matrices were used in the ADAPT VPA: one for the total catch and one for each of the two indices that were ageaggregated, the Japanese Longline index and the Spanish Trap index, respectively. The aim of this study is to see what the effect of sampling error is on the catch at age estimates. For that purpose, catch at size is resampled according to the sampling fractions of each fleet, and catch at age is estimated with confidence intervals, using the slicing method used by the SCRS in previous assessments. Preliminary results seem to show some years and ages where the coefficients of variation of the estimates are important. RÉSUMÉ Lors de la dernière session d évaluation du stock de thon rouge, trois matrices de capture à l âge ont été utilisées dans l analyse ADAPT VPA : une pour la capture totale et une pour chacun des deux indices qui étaient regroupés par âge, l indice palangrier japonais et l indice de madrague espagnol, respectivement. Le but de la présente étude est d observer l effet de l erreur d échantillonnage sur les estimations de prise par âge. A cette fin, la prise par taille est ré-échantillonnée en fonction des fractions d échantillonnage de chaque flottille, et la prise par âge est estimée avec des intervalles de confiance, en utilisant la méthode de découpage employée par le SCRS dans des évaluations antérieures. Les résultats préliminaires semblent indiquer certaines années et âges où les coefficients de variation des estimations sont importants. RESUMEN Durante la última sesión de evaluación del stock de atún rojo se utilizaron tres matrices de captura por edad en el ADAPT VPA: una para la captura total y otra para cada uno de los dos índices que fueron agregados por edad, el índice de la pesquería palangrera japonesa y el índice de la pesquería de almadraba española, respectivamente. El objetivo de este estudio es detectar qué efecto tiene el error de muestreo según las estimaciones de captura por edad. Para ello se remuestreó la captura por talla de las fracciones de muestreo de cada flota, y se estimó la captura por edad con intervalos de confianza, utilizando el método de separación de edades (filo de cuchillo) empleado por el SCRS en anteriores evaluaciones. Los resultados preliminares parecen mostrar algunos años y edades en los que los coeficientes de variación de las estimaciones son importantes. KEYWORDS Sampling error, Catch at size, Ample size, Age composition, Slicing 1 AZTI. Herrera Kaia Portualdea z/g Pasaia. Basque Country. (Spain). harri@pas.azti.es 791

2 1. Introduction In the past, the eastern bluefin stock has being assessed using a VPA that was calibrated with several indices. This approach needs to have a total catch at age matrix. Moreover, in the last 2002 assessment a catch at age matrix for the Japanese longline fleet and for the Spanish trap fleet were used to split their abundance index into ages 8+ and 6+ respectively. The catch at age matrices were obtained using the knife edge slicing method applied to the catch at size on a monthly basis, based on Cort's (1991) growth equation and assuming June as birth date. It is important to note, however, that the catch at age estimates may vary if we consider different error sources like sampling error or growth process error, and also if we use a different method to split the catch at size into catch at age or different substitution rules for the unsampled strata. The objective of this paper is to have an insight of the effect of sampling error in the catch at age estimates for the total international catch and for the Japanese longline and the Spanish traps. 2. Materials and methods Monthly catch at size data and sample sizes for the total international catch and for the two fleets were provided by ICCAT Secretariat. The monthly catch at size was resampled assuming a multinomial distribution. As many fish as the original sample size for each month-fleet combination were boostrapped with replacement. If the sampling proportion was missing for a given month, the mean sampling proportion for that fleet was assigned. In each iteration (400), the new sample was raised to the total catch in number for the given month-fleet strata, and the obtained catch at size distribution was converted into catch at age using the knife edge slicing method, in the same way as it is done in the working group, and described in Turner (1994). Birth date was established in June, it was assumed that all the catch was extracted in the middle of a given month, and Cort's (1991) growth equation was used to estimate the upper and lower cutting points for each age and month. These limits were used to split the catch at size into catch at age. Mean catch at age estimates and coefficients of variation as well as correlation between ages was estimated. 3. Results and discussion The historical evolution of the sampling proportion for the total international catch and for the Japanese longline and Spanish trap fisheries is shown in Figure 1. In general, the sample proportion is quite variable among years, but it seems that the sampling proportion is higher in the second part of the series than in the first one. Estimated mean proportions for the total catch, Japanese longline and Spanish traps were , and respectively. However, the Japanese longline and Spanish trap sample proportion series were not complete, with only 117 and 17 monthly observations (out of 372 months). In the case of Spanish traps, most of the observations belong to the latest period and the mean value seems to be too high. Some sampling proportions showed values higher than 1, which suggests the need to revise the data used. estimates are shown in Table 1. Coefficients of variation increased with age (Figure 2) and were lower in the second period of the time series (Figure 3). These coefficients of variation are very high, over 100% in the first years (corresponding to low sample sizes), and rather low in the last 10 years. The estimated catch at age for the total catch, Japanese longline and Spanish traps are shown in Figures 4 to 6, respectively appeared like an unusual year for the Japanese longline, as the catch in number was larger than usual, especially for young ages. In spite of this, this index only applies to ages 8+. The CAA trends for these ages show a decreasing confidence interval along the series. In the case of Spanish traps, there are some years in which the younger ages are unusually well represented. In spite of this, the abundance index applies to ages 6-10+, the confidence interval for the catch at age for these ages showing a decreasing trend and being specially narrow in the latest years, due to the high mean proportion sampled that was estimated with the limited information available. In fact, the real sample size could be overestimated as some records that are submitted as samples may already be raised to some intermediate strata and do not reflect the real number of fish measured. 792

3 In order to see the effect of the sampling error on the stock assessment, estimated CAA values could be introduced in the VPA framework to estimate abundance and fishing mortality rates. According to the value of CV obtained, it is expected to have an important effect. Other sources of error may be also important, and even more important than sampling error. For the western stock, Turner and Restrepo (1992) analysed the effect of different sources. In the case of the eastern stock, the effect using different substitutions was assessed in Turner and Restrepo (1995). It could be useful to analyse simultaneously the effect of sampling error, substitutions, incorporating growth process error and considering different methods for converting CAS into CAA in the eastern bluefin stock assessment. 4. Acknowledgements To Steve Turner for his help implementing the slicing method. References CORT, J.L Age and growth of the bluefin tuna, Thunnus thynnus (L.) of the Northwest Atlantic. Collect. Vol. Sci. Pap. ICCAT 35: TURNER, S A review of the recent information on size at age and the calculation of age from size for Atlantic bluefin tuna. Collect. Vol. Sci. Pap. ICCAT 42: TURNER, S. and V. Restrepo Method of incorporating uncertainty in size composition of catches of east Atlantic bluefin tuna in assessments. Collect. Vol. Sci. Pap. ICCAT 44: TURNER, S. and V. Restrepo Sensitivity of bluefin tuna virtual population analysis and projections to uncertainty in inputs. Collect. Vol. Sci. Pap. ICCAT 39: Table 1. Mean catch at age estimates after 400 iterations #### ####

4 Proportion sampled Total :Month Proportion sampled Japan LL :Month Proportion sampled Spain TRAP :Month Figure 1. Historical evolution of sampling proportions. Mean CV Mean CV Age Figure 2. Mean coefficient of variation for the different catch at age estimates by age Age Figure 3. Mean coefficient of variation for the different catch at age estimates by year. 794

5 Age1 Age2 0 e+00 1 e+06 2 e+05 Age3 Age Age Age6 Age Age8 Age Age Figure 4. CAA estimates for the total international catch, with 95% CI. 795

6 Age1 Age Age3 Age Age Age6 Age Age8 Age Age10 0 Figure 5. CAA estimates for the Japanesse longline fishery, with 95% CI. 796

7 Age1 Age Age3 Age Age Age6 Age Age8 Age Age Figure 6. CAA estimates for the Spanish trap fishery, with 95% CI. 797