SCRS/2004/093 Col. Vol. Sci. Pap. ICCAT, 58(2): 791-797 (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. 20110 Pasaia. Basque Country. (Spain). harri@pas.azti.es 791
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 0.1520993, 0.1038385 and 0.5936522 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. 1974 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
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. 1991. Age and growth of the bluefin tuna, Thunnus thynnus (L.) of the Northwest Atlantic. Collect. Vol. Sci. Pap. ICCAT 35:213-230. TURNER, S. 1994. 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 42:97-99. TURNER, S. and V. Restrepo. 1995. Method of incorporating uncertainty in size composition of catches of east Atlantic bluefin tuna in assessments. Collect. Vol. Sci. Pap. ICCAT 44:159-165. TURNER, S. and V. Restrepo. 1992. Sensitivity of bluefin tuna virtual population analysis and projections to uncertainty in inputs. Collect. Vol. Sci. Pap. ICCAT 39:793-802. Table 1. Mean catch at age estimates after 400 iterations. 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1 135327 134440 120482 146001 331931 859689 196306 476305 369892 130770 2 70851 33628 127822 54694 109266 272185 196816 306217 178944 49359 3 24003 28443 62136 56559 57918 45903 237449 98015 131708 83438 4 14974 4841 14827 7571 50500 18429 50111 47273 24428 43885 5 7617 636 9225 2307 10445 6808 18741 7790 5174 8779 6 6541 1146 6307 2328 4700 4547 6206 5172 1692 2794 7 2330 3844 3387 4534 2903 3189 3644 4387 2288 2336 8 624 4696 1436 5054 3548 3507 2308 2724 1737 3792 9 249 4547 1499 4605 8657 4577 3064 2670 1406 3702 10 1582 18933 2402 1811 37523 47911 39417 36443 25278 22725 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1 235924 188997 641965 #### 169101 597757 #### 329928 794387 447764 2 138609 308426 242528 183357 593331 316733 273214 401019 195553 374519 3 112133 112219 169562 118363 77853 263509 108271 126647 214720 100516 4 35065 16745 34289 27499 29869 53664 57859 33390 46065 51796 5 10895 12845 6898 11651 19144 11457 10458 13180 12245 28211 6 4837 6094 3576 4876 9718 7194 5427 8004 10003 7236 7 3314 4402 5077 8600 5554 2971 3285 8563 11191 10434 8 2312 4736 8976 6441 6286 2884 2112 4539 6195 7356 9 2322 3431 5204 5169 10294 3189 2829 3768 5375 5122 10 24454 17664 38901 38594 41400 29585 25898 23606 33196 24083 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 1 459509 369165 419543 307367 333220 468715 529001 337915 446409 265373 892019 2 324980 399053 476450 749987 513431 312207 755143 583778 611442 275836 384675 3 198756 186307 268030 363442 169392 290549 258957 185431 351563 152436 191824 4 55771 42495 47187 64547 55264 64654 142472 59221 75555 92350 51179 5 39260 40377 18430 27080 40923 54093 41006 44685 13450 29814 57145 6 8432 8641 12290 16877 33482 36155 19901 29151 89665 9339 38170 7 7402 5415 11905 11684 28738 20678 18045 19399 6824 3680 13158 8 10991 6279 10844 8294 23463 15635 16009 28852 9053 5052 14042 9 12776 14179 12372 8419 22970 16196 18551 35360 12952 6575 14469 10 24625 41620 47963 41243 87792 87519 88896 82520 50407 35288 44215 793
Proportion sampled 0.0 1.0 2.0 Total 0 100 200 300 :Month Proportion sampled 0.0 0.6 1.2 Japan LL 0 100 200 300 :Month Proportion sampled 0.0 0.6 1.2 Spain TRAP 0 100 200 300 :Month Figure 1. Historical evolution of sampling proportions. Mean CV 0.2 0.4 0.6 0.8 1.0 1.2 Mean CV 0 1 2 3 4 5 6 2 4 6 8 10 Age Figure 2. Mean coefficient of variation for the different catch at age estimates by age. 1970 1975 1980 1985 1990 1995 2000 Age Figure 3. Mean coefficient of variation for the different catch at age estimates by year. 794
Age1 Age2 0 e+00 1 e+06 2 e+05 Age3 Age4 50000 300000 0 60000 Age5 0 30000 Age6 Age7 0 40000 5000 20000 Age8 Age9 0 15000 0 15000 Age10 0 40000 Figure 4. CAA estimates for the total international catch, with 95% CI. 795
Age1 Age2 0 40 80 0 200 400 Age3 Age4 2500 Age5 2500 Age6 Age7 0 1500 3000 Age8 Age9 0 1500 Age10 0 Figure 5. CAA estimates for the Japanesse longline fishery, with 95% CI. 796
Age1 Age2 0 6000 14000 0.0 1.5 Age3 Age4 0 40 80 0 200 500 Age5 0 40 Age6 Age7 0 500 1500 Age8 Age9 0 1500 Age10 0 6000 Figure 6. CAA estimates for the Spanish trap fishery, with 95% CI. 797