SCRS/2011/050 Collect. Vol. Sci. Pap. ICCAT, 68(4): 1531-1542 (2012) 

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STANDARDIZED CPUE SERIES OF BLUE MARLIN AND WHITE MARLIN CAUGHT BY BRAZILIAN TUNA LONGLINE FISHERIES IN

THE SOUTHWESTERN ATLANTIC OCEAN (1980-2010) Humberto G. Hazin, Bruno Mourato, Fabio Hazin, Felipe Carvalho,

Thierry Frédou, Paulo Travassos, José Carlos Pacheco

SUMMARY

In the present paper, blue marlin and white marlin catch and effort data from the Brazilian commercial tuna longline fishery, from 1980 to 2010, were analyzed. The catch per unit of effort (CPUE), as the number of fish caught per 1,000 hooks, was standardized by zero inflated negative binomial, delta-log normal and tweedie GLM, based on 57,365 longline sets. The frequency of zero catches was equal to 83% for white marlin and 74% for blue marlin. The following factors were considered in the analyses: year, month, area and fleet strategy. The total fishing ground, ranging from 10°N to 35°S, was divided into two areas, by 15°S of latitude. Abundance indices of both species showed a strong inter-annual oscillation. The CPUE of blue marlin, after peaking in 2001, showed a decreasing trend since then, except for 2010, when it increased again. The CPUE of white marlin, after peaking in 1996, declined until 2006, remained more stable from 2006 to 2009, and, like blue marlin, increased again in 2010.

RÉSUMÉ

Le présent document analyse les données de prise et d’effort du makaire bleu et du makaire blanc de la pêcherie palangrière commerciale de thonidés du Brésil entre 1980 et 2010. La capture par unité d’effort (CPUE), correspondant au nombre de poissons capturés pour 1.000 hameçons, a été standardisée au moyen des modèles GLM binomial négatif modifié en zéro, delta log-normal et tweedie, sur la base de 57.365 opérations à la palangre. La fréquence des prises nulles s'élevait à 83 % dans le cas du makaire blanc et à 74 % dans le cas du makaire bleu. Les facteurs suivants ont été pris en compte dans les analyses : année, mois, zone et stratégie de la flottille. La zone de pêche totale, s’étendant de 10ºN à 35ºS, a été divisée en deux zones, à la latitude 15ºS. Les indices d’abondance des deux espèces indiquaient une forte oscillation interannuelle. La CPUE du makaire bleu, après avoir atteint un sommet en 2001, a présenté une tendance à la baisse depuis lors jusqu’en 2010, année à partir de laquelle elle a repris son ascension. La CPUE du makaire blanc, après avoir culminé en 1996, a connu une baisse jusqu'en 2006, est restée plus stable entre 2006 et 2009 et, à l'instar du makaire bleu, a recommencé à croître en 2010.

RESUMEN

En este documento se analizan los datos de captura y esfuerzo de la aguja blanca y la aguja azul de la pesquería de palangre comercial de túnidos de Brasil, entre 1980 y 2010. La captura por unidad de esfuerzo (CPUE) y el número de peces capturados por 1.000 anzuelos fueron estandarizados mediante GLM binomial negativo de ceros aumentados, delta lognormal y tweedie, basándose en 57.365 lances de palangre. La frecuencia de capturas cero era igual al 83% para la aguja blanca y al 74% para la aguja azul. En los análisis se consideraron los siguientes factores: año, mes, área y estrategia de la flota. El caladero total, entre 10ºN y 35ºS, fue dividido en dos zonas, en 15ºS de latitud. Los índices de abundancia de ambas especies mostraban una fuerte oscilación interanual. La CPUE de la aguja azul, tras alcanzar un pico en 2001, presentó una tendencia descendente a partir de entonces, excepto en 2010, año en que volvió a aumentar. La CPUE de la aguja blanca, tras alcanzar un pico en 1996, descendió hasta 2006, permaneció más estable entre 2006 y 2009 y, al igual que la aguja azul, volvió a aumentar en 2010.

KEYWORDS

Catch/effort, abundance, regression analysis

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1. Introduction

The blue marlin, Makaira nigricans, and the white marlin, Kajika albida (formerly Tetrapturus albidus), are distributed in the Atlantic ocean between 50oN and 45oS (Nakamura, 1985). Although the structure of the blue marlin population is not yet well defined, there seems to be two stocks separated roughly by 5oN. For white marlin the population structure is also not well defined. Although the last assessment considered a single stock for the western Atlantic, there is growing evidence that the stocks from the northern and southern Atlantic are distinct. The last assessment for both species indicated that both stocks were likely overfished (Restrepo et al., 2003). In the present paper, a GLM analysis was used to standardize the blue marlin and white marlin CPUE trends in the Brazilian Tuna longline fishery, from 1980 to 2010, considering two different approachs: Zero inflated and Delta-lognormal. 2. Material and methods

In the present study, catch and effort data from 57,365 tuna longline sets reported by the Brazilian tuna longline fleet, including both national and foreign chartered vessels, from 1980 to 2010 (31 years) were analyzed. All the data were obtained from the logbooks filled in by the skippers of the vessels. The longline sets were distributed along a wide area of the Equatorial and South Atlantic Ocean, ranging from 0º to 60ºW of longitude, and from 07ºN to 50ºS of latitude (Figure 1). The resolution of 1º latitude x 1º longitude, per fishing day, was used for the analysis of the geographical distribution of catches. The factors considered as explanatory variables were “Year”, “Quarter”, “Area”, and “Fleet strategy”. The total fishing ground was divided into 2 areas, following the definitions used by ICCAT (International Commission for the Conservation of Atlantic Tunas) for the assessment of the blue marlin and white marlin stocks: Region 1, to the north of 15oS, and Region 3, to the south of that latitude. Calendar quarters were used to account for seasonal fishery distribution through the year (Jan-Mar, Apr-Jun, Jul-Sep, and Oct-Dec). The fleet Strategy was defined by multivariate analysis previously run (Hazin et al., 2010- SCRS-10-49) for the same data set, as follows: Strategy 1 (YFT), Strategy 2 (SWO-BSH ), Strategy 3 (ALB) and Strategy 4 (YFT; ALB; BET and SWO). Due to the very large proportion of sets with zero catches of blue marlin (74%) and white marlin (83%), stemming from its bycatch nature in this fishery, tree standardized CPUE series were generated, assuming different error structures: Tweedie, Delta-lognormal and Zero Inflated Negative Binomial. The delta lognormal and tweedie models were previously employed by Hazin et al. (2011). The Zero inflated Negative Binomial is a mixture of two distributions, the delta distribution on zero (the distribution that takes only the value zero; ‘perfect state’) and a distribution on the non-negative integers (i.e., including the value zero; ‘imperfect state’). A sample is in the perfect state with probability p and the imperfect state with probability 1 − p. If a sample is in the perfect state, it takes only the value zero; if it is in the imperfect state, it follows the distribution on non-negative integers (Lambert, 1992). Based on the suggestion of the working group (SCRS) in 2010, the standardized CPUE series for white and blue marlins were constructed without interaction. The tree different models could then be described as: For the Tweedie models (family = tweedie and var. power = 1.42): CPUE= Year + Quarter + Area + Strategy + ε For the positive sets in the Delta model (family = gaussian, link = identify): Log(CPUE)= Year + Quarter + Area +Strategy+ ε For the Zero Inflated Negative Binomial (Part 1: count models- Negative Binomial; Part 2: Binomial, link = logit): Catch= Year + Quarter + Area + Strategy + offset (effort) + ε The accuracy of the three models was evaluated using 5,000 datasets to calculate parameter estimates that were then used to predict the remaining half of the observations. This was repeated for 500 random samples of the data with the percentage prediction error at each count (between the observed and predicted data) and the resulting parameter estimates stored at each iteration. The relative prediction error given by each model structure was then estimated.

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The residual plots of zero inflated models are difficult to interpret because the response variable has a mixed distribution (Albert and Chib, 1995). This fact accounts for unusual residual distribution, i.e. the Q-Q plot shows a straight line fragmented into two sections. To convert the residuals into a form which is easier to interpret, a binned plot was constructed. The data were divided into categories (bins) of different fitted values with the mean fitted value being then plotted against the mean residual for each bin (Gelman and Hill, 2007). The dotted lines on the binned plot represent the bounds of the standard errors (i.e. 95% of the points should be found within these bounds). The models were fit using the general linear model (glm) and zero-inflated model (zeroninfl) functions in R (R Development Core Team 2005). These packages use maximum likelihood to estimate coefficients for the generalized linear models as well as for the zero-inflated models. The standardized CPUE predictions were obtained for every Year, fixing the level of remaining factors at the level with the highest number of observations. 3. Results The distribution of blue and white marlin counts during the period of study is overdispersed with respect to a Tweedie distribution (φ =2.8 and 4.5) suggesting the appropriateness of a ZINB regression (φ=0.28 and 0.37) or Delta log models (φ=0.63 and 0.69) (Figures 2, 3 and 4). Because of this, lower values appear to be consistently underestimated by the model, although not to a significant degree, for delta lognormal and zero inflated negative binomial models. Therefore, the model can be considered to be explaining adequately the variation in the data. Overall prediction error was highest in the tweedie models, for both species (Figure 2). The delta-lognormal and zero inflated negative binomial models had the lowest prediction error of any of the model structures, showing little to no prediction error across the entire range of catch events. Given the substantially improved fit and reduced prediction error, the zero inflated negative binomial and Delta lognormal models were selected for subsequent inferences. In the delta log models (positive and proportion) both for blue and white marlin the Year and Strategy was the most important factors (Table 1). The delta-lognormal (positive model) explained 14% (blue marlin) and 16% (white marlin) of the variance in CPUE. The zero inflated negative binomial explained 52% (blue marlin) and 46% (white marlin) of the total variance of the model. The zero component of ZINB to blue marlin (count model) was most related to Year (OR=1.62), Strategy (OR=1.39) and Area (OR=1.32), but relatively unrelated to Quarter. In the case of the white marlin, on the contrary, the zero component of ZINB (model count) was most related to Quarter (OR=1.12), but relatively unrelated to Year, Strategy and area (Table 2). The standardized CPUE series for blue and white marlins by the zero inflated negative binomial and by the delta-lognormal were not much different from each other (Figures 5 and 6). Abundance indices of both species showed a strong inter-annual oscillation. The CPUE of blue marlin, after peaking in 2001, showed a decreasing trend since then, except for 2010, when it increased again. The CPUE of white marlin, after peaking in 1996, declined until 2006, remained more stable from 2006 to 2009, and, like the blue marlin, increased in 2010. References  Albert, J. H. and Chib, S. 1995, Bayesian Residual Analysis for Binary Response Regression Models.

Biometrika. 82, 747-759. Gelman, A. and Hill, J. 2007, Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge.

601p. Hazin, H., Hazin, F., Travassos, P. and Freduo, T. 2011, Standardized CPUE series of blue marlin caught by

Brazilian tuna longline fisheries in the southwestern Atlantic ocean (1980-2008). Collect. Vol. Sci. Pap. ICCAT, 66(4): 1725-1734.

Nakamura, I. 1985, FAO Species catalogue. Billfishes of the World. An annotated and illustrated catalogue of

marlins, sailfishes, spearfishes and swordfishes know to date. FAO Fish. Synop. (125) Vol.5: 65 p. Restrepo, V., Prince, E.D., Scott, G.P. and Uozumi, Y. 2003, ICCAT stock assessments of Atlantic billfish.

Marine and Freshwater Research, 54: 361-367.

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Table 1. Deviance analysis of explanatory variables for the models used to standardize the CPUE series of blue and white marlins caught by the Brazilian tuna longline fleet, from 1980 to 2010.

Covariates Df Deviance Resid.

Df Resid.

deviance P(>|Chi|)

Explained deviance (%)

Explained model (%)

Blue Marlin-Delta log

Positive

NULL 10146 7490.2

Year 30 545.40 10116 6944.8 0.00 52.2% 7.3%

Quarter 3 6.79 10113 6938.0 0.01 0.6% 7.4%

Área 2 136.23 10111 6801.8 0.00 13.0% 9.2%

Strategy 3 356.97 10108 6444.8 0.00 34.1% 14.0%

Proportion

NULL 697 21663.2

Year 30 5192.25 667 16471.0 0.00 81.8% 24.0%

Quarter 3 546.68 664 15924.3 0.00 8.6% 26.5%

Área 2 26.71 662 15897.6 0.00 0.4% 26.6%

Strategy 3 585.09 659 15312.5 0.00 9.2% 29.3%

White Marlin-Delta-log

Positive

NULL 7673 6257.3

Year 30 690.63 7643 5566.7 0.00 68.2% 11.0%

Quarter 3 65.18 7640 5501.5 0.00 6.4% 12.1%

Área 2 15.42 7638 5486.1 0.00 1.5% 12.3%

Strategy 3 241.48 7635 5244.6 0.00 23.8% 16.2%

Proportion

NULL 697 21776.0

Year 30 6318.76 667 15457.3 0.00 70.0% 29.0%

Quarter 3 675.16 664 14782.1 0.00 7.5% 32.1%

Área 2 412.41 662 14369.7 0.00 4.6% 34.0%

Strategy 3 1621.09 659 12748.6 0.00 18.0% 41.5%

Blue Marlin-Tweedie

NULL 56982 143851

Year 30 7752.1 56952 136098 0.00 71.0% 5.4%

Quarter 3 586.5 56949 135512 0.00 5.4% 5.8%

Área 2 212.4 56947 135300 0.00 1.9% 5.9%

Strategy 3 2369.8 56944 132930 0.00 21.7% 7.6%

White Marlin-Tweedie

NULL 56982 162362

Year 30 16020.6 56952 146342 0.00 61.8% 9.9%

Quarter 3 1195.1 56949 145147 0.00 4.6% 10.6%

Área 2 677.9 56947 144469 0.00 2.6% 11.0%

Strategy 3 8044.9 56944 136424 0.00 31.0% 16.0%

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Table 2. Estimative coefficients of predictors for the Zero Inflated Negative Binomial and Delta-lognormal, their standard errors (SE) and Odd Ratios (OR).

Zero inflated models Delta-lognormal models

Blue marlin White marlin Blue marlin White marlin

Covariates Coefficient SE OR Coefficient SE OR Coefficient SE OR Coefficient SE OR

Part 1- Count

(Intercept) -8.44 0.25 0.00 -6.48 0.22 0.00 -0.43 0.12 0.65 0.70 0.12 2.02

Year1981 -0.10 0.34 0.91 -1.29 0.42 0.28 -0.13 0.20 0.88 -0.57 0.21 0.56

Year1982 0.20 0.32 1.22 -1.39 0.34 0.25 -0.23 0.16 0.79 -0.67 0.17 0.51

Year1983 1.33 0.30 3.76 -1.19 0.32 0.31 0.22 0.15 1.24 -0.54 0.17 0.58

Year1984 0.30 0.33 1.35 -1.32 0.29 0.27 -0.11 0.16 0.89 -0.79 0.15 0.46

Year1985 -0.13 0.42 0.88 -0.83 0.35 0.44 -0.16 0.20 0.85 -0.64 0.18 0.53

Year1986 -0.64 0.30 0.53 -0.44 0.26 0.65 -0.09 0.15 0.91 -0.32 0.14 0.73

Year1987 1.38 0.29 3.97 -0.28 0.25 0.76 0.61 0.15 1.84 -0.17 0.13 0.84

Year1988 0.04 0.29 1.04 -0.30 0.25 0.74 0.13 0.15 1.14 -0.26 0.14 0.77

Year1989 0.68 0.29 1.97 0.11 0.27 1.11 0.27 0.14 1.31 0.06 0.15 1.07

Year1990 0.25 0.41 1.28 0.05 0.28 1.06 0.38 0.20 1.46 0.23 0.15 1.26

Year1991 0.58 0.29 1.79 0.38 0.27 1.46 0.17 0.14 1.18 0.13 0.15 1.14

Year1992 1.42 0.29 4.14 0.88 0.27 2.41 0.55 0.14 1.72 0.28 0.14 1.32

Year1993 0.80 0.45 2.22 -0.01 0.33 0.99 0.48 0.20 1.62 -0.03 0.18 0.98

Year1994 0.12 0.30 1.12 -0.49 0.29 0.61 0.17 0.15 1.19 0.02 0.15 1.02

Year1995 0.72 0.26 2.05 -0.39 0.24 0.68 0.30 0.13 1.35 -0.14 0.13 0.87

Year1996 0.21 0.28 1.23 0.95 0.23 2.59 0.53 0.15 1.69 0.56 0.13 1.76

Year1997 0.80 0.25 2.22 0.50 0.22 1.66 0.65 0.13 1.93 0.30 0.12 1.35

Year1998 0.75 0.26 2.12 0.11 0.22 1.11 0.53 0.13 1.70 0.15 0.12 1.16

Year1999 0.73 0.24 2.08 0.47 0.21 1.60 0.45 0.12 1.58 0.26 0.11 1.30

Year2000 1.04 0.24 2.83 0.35 0.20 1.42 0.63 0.12 1.87 0.20 0.11 1.23

Year2001 1.93 0.24 6.87 -0.30 0.21 0.74 0.89 0.12 2.43 0.15 0.12 1.16

Year2002 1.28 0.25 3.60 -0.37 0.23 0.69 0.65 0.13 1.91 -0.05 0.12 0.95

Year2003 0.41 0.26 1.51 -0.68 0.24 0.51 0.53 0.13 1.70 -0.05 0.13 0.95

Year2004 0.86 0.24 2.35 -0.76 0.22 0.47 0.49 0.12 1.64 -0.27 0.12 0.77

Year2005 0.67 0.24 1.95 -1.15 0.22 0.32 0.42 0.12 1.52 -0.37 0.12 0.69

Year2006 0.18 0.24 1.20 -1.68 0.22 0.19 0.20 0.12 1.23 -0.48 0.12 0.62

Year2007 0.00 0.25 1.00 -1.40 0.22 0.25 0.21 0.13 1.23 -0.34 0.12 0.71

Year2008 -0.13 0.25 0.88 -1.78 0.25 0.17 0.16 0.13 1.18 -0.40 0.13 0.67

Year2009 -0.64 0.27 0.53 -1.70 0.25 0.18 0.14 0.13 1.15 -0.45 0.13 0.63

Year2010 -0.50 0.26 0.60 -0.47 0.23 0.63 0.09 0.14 1.09 0.01 0.13 1.01

Quarter2 -0.31 0.04 0.73 -0.24 0.05 0.79 -0.03 0.02 0.97 0.00 0.03 1.00

Quarter3 -0.60 0.05 0.55 0.32 0.06 1.38 -0.03 0.03 0.97 0.21 0.03 1.24

Quarter4 -0.19 0.04 0.83 0.27 0.05 1.31 -0.05 0.02 0.95 0.10 0.03 1.10

area2 0.24 0.04 1.27 0.13 0.05 1.14 0.12 0.02 1.13 0.13 0.03 1.14

area3 0.33 0.05 1.39 -0.20 0.06 0.82 0.20 0.03 1.22 0.01 0.03 1.01

Strategy2 0.42 0.06 1.52 -0.39 0.08 0.68 0.33 0.03 1.39 -0.30 0.04 0.74

Strategy3 0.45 0.09 1.57 -0.44 0.10 0.65 -0.45 0.04 0.64 -0.89 0.05 0.41

Strategy4 0.14 0.06 1.15 -0.18 0.07 0.83 0.10 0.03 1.11 -0.33 0.03 0.72

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Part 2- Zero Inflation

(Intercept) -8.77 0.61 0.00 -7.34 0.29 0.00 -1.28 0.13 0.28 0.26 0.10 1.30

Year1981 -15.77 1561.84 0.00 -2.55 3.11 0.08 0.52 0.22 1.69 -0.56 0.21 0.57

Year1982 0.84 0.66 2.32 0.23 0.45 1.26 0.05 0.17 1.05 -1.51 0.16 0.22

Year1983 0.70 0.66 2.02 -0.10 0.45 0.91 1.32 0.15 3.76 -0.97 0.15 0.38

Year1984 1.87 0.67 6.51 -0.05 0.38 0.96 -0.05 0.16 0.95 -1.24 0.14 0.29

Year1985 2.31 0.78 10.03 1.05 0.39 2.84 -0.80 0.20 0.45 -1.49 0.16 0.23

Year1986 -0.64 2.25 0.53 0.82 0.32 2.26 -0.64 0.16 0.53 -0.89 0.12 0.41

Year1987 1.86 0.66 6.40 0.50 0.34 1.66 0.65 0.15 1.92 -0.83 0.12 0.43

Year1988 0.72 0.75 2.06 0.62 0.33 1.86 -0.18 0.16 0.83 -0.73 0.11 0.48

Year1989 1.06 0.72 2.87 1.15 0.32 3.17 0.29 0.15 1.33 -0.90 0.12 0.41

Year1990 1.94 0.90 6.93 0.57 0.38 1.78 -0.55 0.21 0.58 -0.60 0.13 0.55

Year1991 1.47 0.62 4.34 1.11 0.31 3.03 0.15 0.15 1.17 -0.67 0.11 0.51

Year1992 2.47 0.60 11.81 1.52 0.30 4.55 0.48 0.14 1.62 -0.86 0.11 0.42

Year1993 2.31 0.75 10.03 0.75 0.42 2.13 -0.26 0.21 0.77 -0.82 0.15 0.44

Year1994 1.73 0.63 5.66 0.99 0.34 2.69 -0.36 0.15 0.70 -1.12 0.12 0.33

Year1995 2.02 0.60 7.55 1.09 0.30 2.97 0.25 0.14 1.28 -1.10 0.11 0.33

Year1996 1.74 0.64 5.71 0.73 0.30 2.07 -0.19 0.15 0.82 0.05 0.10 1.06

Year1997 1.40 0.61 4.06 1.09 0.29 2.98 0.56 0.13 1.76 -0.34 0.10 0.71

Year1998 0.91 0.60 2.47 1.07 0.29 2.92 1.01 0.13 2.75 -0.49 0.10 0.62

Year1999 2.04 0.59 7.71 0.85 0.28 2.34 0.05 0.13 1.05 -0.31 0.09 0.73

Year2000 1.79 0.59 6.01 0.68 0.28 1.97 0.49 0.13 1.64 -0.24 0.09 0.79

Year2001 2.23 0.59 9.29 1.43 0.28 4.19 0.85 0.13 2.33 -1.08 0.09 0.34

Year2002 2.94 0.59 18.95 1.87 0.29 6.52 -0.20 0.13 0.82 -1.59 0.10 0.20

Year2003 2.71 0.61 14.97 1.87 0.30 6.48 -0.84 0.14 0.43 -1.90 0.11 0.15

Year2004 0.90 0.60 2.47 1.21 0.28 3.34 0.45 0.13 1.56 -1.59 0.10 0.20

Year2005 -0.25 0.63 0.78 0.70 0.29 2.00 0.58 0.13 1.79 -1.71 0.10 0.18

Year2006 -15.05 477.28 0.00 -0.61 0.37 0.54 0.05 0.13 1.06 -1.59 0.10 0.20

Year2007 0.93 0.61 2.53 -0.38 0.36 0.69 -0.55 0.14 0.57 -1.38 0.10 0.25

Year2008 -16.70 1258.93 0.00 -1.19 0.80 0.30 -0.30 0.14 0.74 -1.60 0.11 0.20

Year2009 -0.10 0.98 0.90 0.32 0.38 1.38 -0.85 0.15 0.43 -1.94 0.11 0.14

Year2010 -17.77 3665.09 0.00 0.25 0.34 1.28 -0.67 0.15 0.51 -0.50 0.11 0.60

Quarter2 -0.33 0.08 0.72 -0.44 0.07 0.65 -0.31 0.02 0.73 0.09 0.02 1.09

Quarter3 -0.36 0.10 0.70 -0.37 0.06 0.69 -0.44 0.02 0.64 0.49 0.02 1.63

Quarter4 -0.13 0.07 0.88 -0.41 0.06 0.67 -0.03 0.02 0.97 0.46 0.02 1.59

area2 0.36 0.07 1.44 0.14 0.06 1.15 0.06 0.02 1.06 0.08 0.02 1.08

area3 1.14 0.08 3.13 0.32 0.07 1.38 -0.06 0.02 0.94 -0.25 0.03 0.78

Strategy2 -0.05 0.13 0.95 0.24 0.09 1.27 0.33 0.03 1.40 -0.68 0.03 0.50

Strategy3 -0.60 0.14 0.55 0.76 0.09 2.15 0.48 0.03 1.62 -1.09 0.03 0.34

Strategy4 -1.53 0.13 0.22 -0.28 0.07 0.75 0.62 0.03 1.86 -0.22 0.02 0.80

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Figure 1. Distribution of fishing effort, in number of hooks, from Brazilian tuna longliners (national and chartered vessels), from 1980 to 2010.

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Figure 2. Binned plot with data divided into categories and plotting mean residuals vs. average fitted values and Relative bias plot between observed and predicted CPUE from blue and white marlins. There appears to be a slight pattern in the residuals; lower values are consistently underestimated by the model but not to a significant degree.

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Figure 3. Binned plot with data divided into categories and plotting mean residuals vs. average fitted values and Relative bias plot between observed and predicted CPUE from blue and white marlins. There appears to be a slight pattern in the residuals; lower values are consistently underestimated by the model but not to a significant degree.

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Figure 4. Binned plot with data divided into categories and plotting mean residuals vs. average fitted values and Relative bias plot between observed and predicted CPUE from blue and white marlins. There appears to be a slight pattern in the residuals; lower values are consistently underestimated by the model but not to a significant degree.

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Figure 5. Nominal and standardized CPUE of blue marlin for Brazilian tuna longliners, from 1980 to 2010.

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Figure 6. Nominal and standardized CPUE of white marlin for Brazilian tuna longliners, from 1980 to 2010.