ESTIMATION OF NORTHEAST ATLANTIC BLUEFIN TUNA (THUNNUS THYNNUS) GROWTH PARAMETERS FROM TAGGING DATA

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1 SCRS/6/96 Col. Vol. Sci. Pap. ICCAT, (4): (7) ESTIMATION OF NORTHEAST ATLANTIC BLUEFIN TUNA (THUNNUS THYNNUS) GROWTH PARAMETERS FROM TAGGING DATA Cristina Rodríguez-Cabello 1, Víctor R. Restrepo, Enrique Rodríguez-Marín 1, José Luis Cort 1 and José Miguel de la Serna 3 SUMMARY Tag-recapture data of bluefin tuna (Thunnus thynnus) recorded from 1977 to 1 in the Bay of Biscay (North of Spain) have been analysed to estimate the von Bertalanffy growth parameters of this species. Growth models incorporating individual variability in growth among individuals and model error have been applied. The results provided were L =81.9 cm and K=.1. A bootstrap of the data resulted in large standard errors for these parameter estimates. The estimates currently adopted for the stock fell within the bootstrap ranges. It is concluded that these data could contribute useful information to future studies on growth for the stock. RÉSUMÉ Les données de marquage-recapture du thon rouge (Thunnus thynnus) enregistrées de 1977 à 1 dans le Golfe de Gascogne (au nord de l Espagne) ont été analysées afin d estimer les paramètres de croissance de von Bertalanffy. Un modèle de croissance incluant la variabilité individuelle de la croissance et de l erreur du modèle a été appliqué. Les résultats étaient les suivants = L =81,9 cm et K=,1. Une analyse des données par bootstrap a donné lieu à des valeurs élevées de l erreur standard pour les paramètres estimés. Les paramètres de croissance actuellement appliqués au stock s inscrivent dans la gamme des valeurs obtenues par bootstrap. On peut donc en conclure que ces données pourraient s avérer utiles pour les futures études de la croissance du stock. RESUMEN Se ha utilizado información de recapturas de atún rojo (Thunnus thynnus) en el Golfo de Vizcaya procedente de campañas de marcado realizadas en aguas de la península ibérica en los años 1977 a 1 para estimar los parámetros de crecimiento de la ecuación de von Bertalanffy. Se ha utilizado un modelo que incorpora la variación individual del crecimiento y del error del modelo. Los resultados obtenidos son L =81.9 cm y K=.1. Un análisis de los datos mediante bootstrap proporcionó valores altos del error estándar para los parámetros estimados. Los parámetros de crecimiento actualmente aplicados al stock se encuentran dentro del rango de valores obtenidos con el bootstrap. Se concluye que la información aquí presentada es útil para futuros estudios sobre el crecimiento de este stock. KEYWORDS Thunnus thynnus, growth, tag-recapture data, NE Atlantic 1 IEO Santander, Spain. c.cabello@st.ieo.es ICCAT Secretariat, Madrid, Spain. victor.restrepo@iccat.int 3 IEO Málaga, Spain. delaserna@ma.ieo.es 158

2 1. Introduction The most common techniques used for studying fish growth can be summarised in: (a) direct ageing estimated from the interpretation of bands in calcified structures like otoliths, spines or vertebrae, (b) analysis of length frequency data from commercial catches or research surveys or c) analysis of length increment and time at liberty from tagrecapture data. The two first ones have been widely used for the bluefin tuna eastern stock. However, tag-recapture data have only been used to compare the results obtained with previous techniques (Cort, 199) although no thorough analyses have been performed. Recently, a new revision of the growth curves currently used for both bluefin tuna stocks has been proposed (Restrepo et al., 6). The aim of this study is to estimate the growth parameters of bluefin tuna eastern stock using tag-recapture data and contribute to enhance growth information of this species.. Material and methods Between 1977 and 1991 tagging surveys were carried out systematically in the Bay of Biscay by the Instituto Español de Oceanografía (IEO) and have been performed in the Mediterranean Sea from 1983 to the present. In recent years tagging effort has been resumed in both areas (Rodríguez-Marín et al., 6; de la Serna et al., 1). A total of 61 bluefin tuna had been tagged in waters around the Iberian Peninsula. The fish were tagged with conventional spaghetti tags. For each specimen the fork length was measured to the inferior centimetre and date and released position was noted. A total of 41 recaptures were recovered up to date, % corresponding to fish which were at liberty for less than one year. Taking this into account, different data sets were constructed according to the time at liberty. One data set included recaptures with at least 9 days at liberty (n=33), while the second data set included recaptures with more than six months at liberty (n=179). This criteria was applied after exploring the residuals in order to eliminate the possible effect that tagging might have on short-term growth and to minimize the possible effects of seasonal fluctuations in growth on parameter estimation. The computations were carried out by using a Solver-based spreadsheet in MS Excel. Bootstrap estimates of the growth parameters (L, K) were obtained using Poptools, an Excel add-in. The range of recapture lengths used in the study was 5 cm to 5 cm although most of the fish were between 8 and 15 cm; the times at liberty ranged from 6 months up to 11 years (Figure 1). A large body of literature exists on statistical approaches for estimating growth from tag-return data (Fabens, 1965, Sainsbury, 198, Kirkwood and Somers, 1984; Hampton, 1991; Wang et al., 1995). The most appropriate approach depends on the error structure assumed for the model. We followed the model recommended by Hampton (1991) for southern bluefin tuna, based on Kirkwood and Somers (1984), which allows for individual growth variability by assuming that the asymptotic size is a random variable normally distributed with a mean (μ L and variance (σ L ). Hampton (1991) modified it so as to also include a model error term having a mean of zero and a variance (σ e ). In this model the expected growth increment is given by: E (δli) = (μ L -li) (1- e -Kδt ) where, δ l i = change in length between release and recapture, li = release length, δ t i = time at liberty, μ L = mean asymptotic length. and the variance of the length increment is given by: var (δli) = σ L (1- e -Kδt ) + σ e The estimates of μ L, K, σ L and σ e are obtained by minimizing the negative log-likelihood: 159

3 n ln LL = i = 1 [ π var( δli) ] [ δli E( δli )] + var( δli ) 3. Results Examination of residuals from the first data set after applying the model, suggested that the fitted model might not be appropriate (Figure ). Inspection of the original data by plotting growth (length increment divided by time at liberty) against time at liberty showed that some values had very high growth rates when time at liberty was very short (Figure 3a). For that reason the second data set was used. The results provided by the model fit to this second dataset are shown in Table 1. Examination of length increment versus time at liberty reveals an even distribution (Figure 3b) although the comparison of observed length increments against predicted ones suggests that large length increments are not fitted very well (Figure 4). The pattern of residuals in both figures shows the effect of the seasonal fishery on the number of recoveries. Examination of standardized residuals against release length for the model fit to data set reveals a quite regular distribution around zero (Figure 5). A bootstrap was carried out by re-sampling, with replacement, the data and re-fitting the model to each sample. The results of 5 bootstrap pairs of K and μ L estimates id shown in Figure 6. The 9% confidence intervals based on percentiles were [ ] for K and [7-3] for μ L. The model-based coefficient of variation for the asymptotic size is σ L /μ L =.15. For comparison, the estimates of asymptotic size and K from Cort (1991) which are currently used for the East and Mediterranean stock are also plotted in Figure 6. Cort's (1991) estimates fall within the range of bootstrapped pairs, suggesting that growth information inferred from the tagging data is consistent with the adopted growth curve. 4. Discussion Tag-recapture is one of the most important methods for estimating growth parameters (K and L ) and it has been widely used for several tuna species. In particular for the western Atlantic bluefin tuna stock, the growth curve currently used by the ICCAT Standing Committee on Research and Statistics (SCRS) has been estimated using tag-recapture data (Turner et al., 1991; Turner and Restrepo, 1994) and previously the one used by Parrack and Phares (1979). However, growth parameters have not been estimated from tagging data for the eastern bluefin tuna stock. The growth curve used for the eastern stock is based on modal length analysis and age-length keys, although tag-recapture data was also used to check previous results (Cort, 199). Cort (199) adjusted the mean length of release and recaptured data to a curve and used a linear and parabolic fit to compare the results with the other methods used in that study. No further analyses have been performed using these data. The estimates of the growth parameters in this document are rather imprecise (see Figure 6), perhaps as a result of various sources of uncertainty such as small sample size, inaccurate size measurements at the time of tagging and/or recapture, preponderance of short times at liberty, the potential effects of tagging on growth, etc. Nevertheless, the tagging data used appear to be consistent with the currently-adopted growth curve for the stock. We recommend that if the growth curve for eastern bluefin tuna were to be revisited, this tagging dataset be considered as a source of information. References CORT, J.L Biología y pesca del atún rojo, Thunnus thynnus (L.), del mar Cantábrico (Tesis doctoral). Publicaciones Especiales. Instituto Español de Oceanografía. Num. 4, 7 pp. CORT, J.L Age and growth of the bluefin tuna, Thunnus thynnus (L.) of the Northeast Atlantic. Col. Vol. Sci. Pap. ICCAT, 35():

4 De la SERNA, J.M., V. Ortiz de Zárate and M.J. Gómez. 1. Actualización de los datos de marcado-recaptura de atún rojo (Thunnus thynnus L.) en el Atlántico Este y Mediterráneo. Col. Vol. Sci. Pap. ICCAT, 5(): FABENS, A.J., Properties and fitting of the von Bertalanffy growth curve. Growth, 9: HAMPTON, J., Estimation of southern bluefin tuna Thunnus maccoyii growth parameters from tagging data using von Bertalanffy models incorporating individual variation. Fish. Bull. U.S. 89: PARRACK, M.L. and P.L. Phares Aspects of the growth of Atlantic bluefin tuna determined from markrecapture data. Col. Vol. Sci. Pap. ICCAT, 8(): KIRKWOOD, G.P. and I.F. Somers Growth of two species of tiger prawn, Penaeus esculentus and P. semisulcatus in the western Gulf of Carpentaria. Aust. J. Mar. Freshw. Res., 35: RESTREPO, V.R., E. Rodríguez-Marín, J.L. Cort and C. Rodríguez-Cabello, (in prep.). Are the growth curves currently used for Atlantic bluefin tuna statistically different? Col. Vol. Sci. Pap. ICCAT. SCRS/6/79. RODRIGUEZ-MARIN, E., C. Rodríguez-Cabello, S. Barreiro, M. Quintans, J. Valeiras, M. Ruiz, H. Arrizabalaga, J.M. de la Serna and J.L. Cort. 6. Bluefin tuna (Thunnus thynnus) tagging survey in the Bay of Biscay in summer 5. Col. Vol. Sci. Pap. ICCAT, 59(3): SAINSBURY, K.J., 198. Effect of individual variability on the von Bertalanffy growth equation. Can. J. Fish. Aquat. Sci. 37: TURNER, S.C., V.R. Restrepo, and A.M. Eklund A review of the growth of Atlantic bluefin tuna, Thunnus thynnus. Col. Vol. Sci. Pap. ICCAT, 35(): TURNER, S.C., and V.R. Restrepo A review of the growth rate of West Atlantic bluefin tuna, Thunnus thynnus, estimated from marked and recaptured fish. Col. Vol. Sci. Pap. ICCAT, 4(1): WANG Y., M.R. Thomas and L.F. Somers A maximum likelihood approach for estimating growth from tagrecapture data. Can. J. Fish. Aquat. Sci. 5:

5 Table 1. Summary of other growth parameters previously reported for bluefin tuna based on tag-recaptured data. Author Loo K σ L σ ε LL to Area Parrack and Phares, (1979) Atlantic NW Turner et al., (1991) Atlantic NW Turner and Restrepo, (1994) Atlantic NW This study Atlantic NE Figure 1. Length distribution of bluefin tuna fish released and recaptured used in this study. dl pred Number dl obs 135 Fork Length Release Recaptured Figure. Observed length increment versus predicted length increment for the model fitted using data set 1. dl obs/ dt 1 8 a) 16 dl obs/dt 5 3 b) 1

6 Figure 3. Plot of growth rates against time at liberty for a) the data set 1 and b) data set dl esp dl obs Figure 4. Observed length increment versus predicted length increment for the model fitted with data set. standardised residuals Length at release (cm) Figure 5. Plot of standardized residuals against release length following fit of model to the data set. 163

7 k,18,16,14,1,1,8,6,4, Linf Figure 6. Bootstrap estimates of L and K. Centre square indicates VBGF parameters currently adopted for the eastern stock (Cort, 1991). 164