SCRS/2002/076

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STANDARDIZED CATCH RATES FOR BLUE MARLIN (MAKAIRA NIGRICANS) AND WHITE MARLIN (TETRAPTURUS ALBIDUS) FROM THEVENEZUELAN

PELAGIC LONGLINE FISHERY OFF THE CARIBBEAN SEA AND THE WESTERN CENTRAL ATLANTIC

Freddy Arocha1 and Mauricio Ortiz2

SUMMARY Indices of abundance of blue marlin (Makaira nigricans) and white marlin (Tetrapturus albidus) from the Venezuelan Pelagic Longline fishery are presented for the period 1991-2001. The index of number of fish per number of hooks (thousand) was estimated from numbers of marlins caught and reported in the Observer data forms recorded by scientific observers aboard longline (Venezuelan Pelagic Longline Observer Program) vessels since 1991. The standardization analysis procedure included the following variables: year, area, season, fishing operation characteristics (main line length, hook density, target species), fishing time, and fishing depth. The standardized index was estimated using Generalized Linear Mixed Models under a delta lognormal model approach.

RÉSUMÉ

Les indices d’abondance du makaire bleu (Makaira nigricans) et du makaire blanc (Tetrapturus albidus) de la pêcherie palangrière pélagique du Venezuela sont présentés pour la période 1991-2001. L’indice du nombre de poissons par nombre d’hameçons (mille) a été estimé à partir du nombre de makaires capturés et déclarés dans les formulaires de données d’observation remplis par les observateurs scientifiques postés à bord de palangriers depuis 1991 (Programme d’observateurs à bord de palangriers pélagiques vénézuéliens). La procédure d’analyse de la standardisation a inclus les variables suivantes : année, zone, saison, caractéristiques des opérations de pêche (longueur de la ligne principale, densité des hameçons, espèces-cibles), le temps de pêche et la profondeur de la pêche. L’indice standardisé a été estimé en utilisant des modèles mixtes linéaires généralisés selon une approche du modèle delta-lognormal.

RESUMEN

Se presentan los índices de abundancia de la aguja azul (Makaira nigricans) y aguja blanca (Tetrapturus albidus) de la pesquería de palangre pelágico de Venezuela para el periodo 1991-2001. El índice del número de peces por número de anzuelos (mil) se estimó partiendo del número de marlines capturado y comunicado en los formularios de datos de observadores cumplimentados por observadores científicos embarcados en palangreros (Programa de observadores de Palangre Pelágico de Venezuela), desde 1991. El procedimiento de análisis de estandarización incluía las siguientes variables: año, zona, temporada, características de la operación pesquera (longitud de la línea principal, densidad de anzuelos, especies objetivo), tiempo de pesca y profundidad de la pesca. El índice estandarizado se estimó utilizando Modelos Lineales Mixtos Generalizados en el marco de un enfoque de modelo delta-lognormal.

KEY WORDS

Blue marlin, white marlin, catch rates, Venezuelan longline fishery.

1 Instituto Oceanográfico de Venezuela, Universidad de Oriente, Apartado de Correos No. 204, Cumaná 6101 – VENEZUELA. e-mail: farocha@sucre.udo.edu.ve 2 U.S. Department of Commerce, National Marine Fisheries Service, Southeast Fisheries Science Center, 75 Virginia Beach Drive, Miami, Florida 33149 U.S.A.

Col. Vol. Sci. Pap. ICCAT, 55(2): 649-659 (2003)

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1. INTRODUCTION Information about changes in the abundance of blue marlin (Makaira nigricans) and white marlin (Tetrapturus albidus), are necessary to tune stock assessment models that are required for the management of billfish in the Atlantic. The utility of indices of abundance based on catch and effort data can be improved by standardizing them to remove the impact of factors such as changes over time in the efficiency of the fleet. Since 1991, ICCAT’s Enhanced Billfish Research Program (EBRP) started placing scientific observers on board Venezuelan pelagic longliners targeting tuna and swordfish. Due to the difficulties in obtaining pelagic longline logbook data by species, the data collected from the EBRP from the Venezuelan fleet was chosen to develop standardized catch per unit of effort (CPUE) indices of abundance for the billfish caught by the Venezuelan fleet (ICCAT, 2001; Arocha and Ortiz, 2001). The Venezuelan longline fleet operates over an important geographical area in the western central Atlantic and its main target species is yellowfin tuna, thus imposing an important fishery mortality on by-catch species (e.g. white marlin, blue marlin, and sailfish) fished in the western tropical Atlantic. This document updates the catch and effort information through 2001 and re-estimates the standardize catch rates of blue and white marlin using a Generalized Linear Mixed Model with random factor interactions particularly for the year effect. 2. MATERIALS AND METHODS The data used in this paper came from the database of the Venezuelan Pelagic Longline Observer Program (VPLOP) for the period 1991-2001. Arocha and Marcano (2001) describe the main features of the fleet and Marcano et al. (2001) review the available catch and effort data from the Venezuelan Pelagic Longline fishery covered by the observer program. Yellowfin tuna and swordfish are the main target species for the Venezuelan Pelagic Longline fleet, where blue marlin represents 2.4% of the total catch in numbers and white marlin constitutes 4% (Arocha et al., 2001). Since 1991, trained scientific observers have recorded detailed information on gear characteristics, fishing operations as well morphometric and biological information from a sub-sample of the Venezuelan longline Pelagic vessels (Arocha and Marcano, 2001). The VPLOP surveys on average 14% of the Venezuela longline fleet trips (1991-2001). The data collected comprises a total of 10,590 record-sets from 1991 through 2001. Of these sets, blue marlin was reported caught in 973 sets (27.9%) and white marlin in 869 sets (24.8%). The information collected in the VPLOP includes specifics of gear configuration such as main line material, total length; gangion and leader length; number of baskets; number of hooks between floats; distance between floats; distance between hooks. Also, specifics of fishing configuration such as depth of float line, soak time, specific targeted species, bait type and number/weight of bait per set, direction of begin set and direction of begin haul. As well as some general environmental information such as sea surface temperature at the beginning and end of the set and haul retrieval. The longline fishing grounds for the Venezuelan fleet extend from northwest of Puerto Rico (22°N-68°W) to off the coast of northeastern Brazil (4°N-44°W), and the western Caribbean Sea. Three geographical areas of longline fishing were used for classification. These include: the Caribbean (CAR, area 1), the Guyana-Amazon (GUY-AMZN, area 2), and the Sargasso (SAR, area 3) (Figure 1). Three seasons were defined to account for seasonal fishery distribution through the year (Jan-Apr, May-Aug, and Sep-Dec). Other factors included in the analyses of catch rates included: time of the set (hour-set), depth of the hooks, size of the vessel, sea surface temperature and duration of the set (soaking time). Fishing effort is reported in terms of the total number of hooks per trip and number of set per trip, as number of hooks per set vary, catch rates were calculated as number of billfish caught per 1000 hooks.

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For the Venezuelan longline observer data, relative indices of abundance for all three billfish species were estimated by Generalized Linear Modeling approach assuming a delta lognormal model distribution using the same protocol as it appeared in Arocha and Ortiz (2001). The delta model estimates separately the proportion of positive to total number of sets assuming a binomial error distribution, and the mean catch rate of positive for a given marlin species by assuming a lognormal error distribution. The standardized index is the product of these model-estimated components. The estimated proportion of successful sets per stratum is assumed to be the result of n positive sets of a total r number of sets, and each one is an independent Bernoulli-type realization. The estimated proportion is a linear function of fixed effects and interactions. The logit function was used as link between the linear factor component and the binomial error. For sets that caught at least one of the marlin species (positive observations), estimated CPUE rates were assumed to follow a lognormal error distribution (lnCPUE) of a linear function of fixed factors and random effect interactions, particularly when the year effect was within the interaction. A step-wise regression procedure was used to determine the set of systematic factors and interactions that significantly explained the observed variability. The difference of deviance between two consecutive models follows a χ2 (Chi-square) distribution; this statistic was used to test for the significance of an additional factor in the model. The number of additional parameters associated with the added factor minus one corresponds to the number of degrees of freedom in the χ2 test (McCullagh and Nelder, 1989, pp 393). Deviance analysis tables are presented for the data series, including the deviance for the proportion of positive observations (i.e., pos itive sets/total sets), and the deviance for the positive catch rates. Final selection of explanatory factors was conditional to: a) the relative percent of deviance explained by adding the factor in evaluation (normally factors that explained more than 5 or 10% were selected) and b) The χ2 significance. Once a set of fixed factors was specified, possible interactions were evaluated, in particular interactions between the year effect and other factors. Selection of the final mixed model was based on the Akaike’s Information Criterion (AIC), the Schwarz’s Bayesian Criterion (SBC), and a χ2 test of the difference between the [–2 loglikelihood] statistic of a successive model formulations (Littell et al., 1996). Relative indices for the delta model formulation were calculated as the product of the year effect least square means (LSmeans) from the binomial and the lognormal model components. The LSmeans estimates use a weighted factor of the proportional observed margins in the input data to account for the non-balance characteristics of the data. LSMeans of lognormal positive trips were bias corrected using Lo et al., (1992) algorithms. Analyses were done using the GLIMMIX and MIXED procedures from the SAS statistical computer software (SAS Institute Inc. 1997). 3. RESULTS AND DISCUSSION Combined spatial distribution of nominal CPUE from the VPLOP data set for the two marlin species are presented in Figures 2 and 3. Each marlin species appear to show a species-specific spatial distribution. In the case of blue marlin, important catch rates are obtained in the Caribbean Sea area, with almost insignificant catches in the other two areas. In the case of white marlin, the highest catch rates are also observed in the Caribbean area, but also important catch rates are obtained in the Sargasso and the Guyana-Amazon areas. Of the two marlin species, white marlin appears to be only species with significance presence in the catches from sets fishing in the Sargasso area. The log-transformed frequency distribution of catch rates (lnCPUE) for sets that caught blue and white marlin are shown in Figure 4. 3.1 Blue marlin Table 1 shows the deviance analysis for blue marlin from the Venezuela Longline Observer data analyses. For the proportion of positive/total sets; year, area, and catboat and the interactions

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year*catboat, year*area, year*bait-type, and year*season were the major factors that explained whether or not a set caught at least one fish. For the mean catch rate given that it is a positive set, only the main factors: year, area, and catboat were more significant. Once a set of fixed factors was selected, we evaluated first level random interaction between the year and other effects. Table 2 shows the results from the random test analyses for blue marlin and the three-model selection criterion. For the proportion of positive/total sets, the final model included the year, area, catboat, season, bait-type as main fixed factors and the random interaction of year* area and year*season. For the conditional mean catch rate (i.e., positive observations), the final mixed model included the year, area, and catboat as fixed factor and the random interaction of year*area and year*catboat. Figure 5 shows the normalized cumulative plot of residuals for the positive set model fit. The diagnostic plot for the delta model of the proportions of positive/total from the assumed binomial error distribution is presented in Figure 6. Standardized CPUE series for blue marlin are shown in Table 3 and Figure 7. Coefficients of variation range from 26.2 to 50%. The standardized CPUE series show that the relative abundance of blue marlin caught by the observed Venezuelan longline fleet reflects a slow descending trend after its highest catch rate in 1994, with only a small increase in 1998, catch rates for blue marlin fall to a minimum in 2001. The nominal CPUE series show a similar trend as the standardized values. 3.2 White marlin Table 4 shows the deviance analysis for white marlin from the Venezuela Longline Observer data analyses. For the proportion of positive/total sets; year, area, season, and catboat and the interactions year*area, year*catboat, year*season, and were the major factors that explained whether or not a set caught at least one fish. For the mean catch rate given that it is a positive set, the factors: year, area, catboat, and season and the interactions year* catboat, year*bait type and year*season were more significant. Once a set of fixed factors was selected, we evaluated first level random interaction between the year and other effects. Table 5 shows the results from the random test analyses for white marlin and the three-model selection criterion. For the proportion of positive/total sets, the final model included the year, area, catboat, season, bait type as main fixed factors and the random interaction of year*season and year*bait type. For the conditional mean catch rate (i.e., positive observations), the final mixed model included the year, area, catboat and season as fixed factor and the random interaction of year* season and year* catboat. Figure 5 shows the normalized cumulative plot of residuals for the positive set model fit. The diagnostic plot for the delta model of the proportions of positive/total from the assumed binomial error distribution is presented in Figure 6. Standardized CPUE series for white marlin are shown in Table 6 and Figure 8. Coefficients of variation range from 33.3 to 104.7%. The standardized CPUE series show that the relative abundance of white marlin caught by the observed Venezuelan longline fleet reflects an uneven trend for the middle part of the series, but the overall trend is a stepwise decline that started in 1995 to reach its minimum in 2001. Although the standardized CPUE series based on the delta lognormal model approach estimated large confidence intervals for both marlin species, the resulting standardized series from the VPLOP account for about 14% of the annual trips of the Venezuelan pelagic longline fleet. Considering that the information that exists in logbooks do not reflect the catch of billfish and that there is a high degree of under-reporting of all species caught, the standardized CPUE index based on the VPLOP data could be used to reflect the overall trend in relative abundance of the tow marlin species caught by the longline fleet in the southeastern Caribbean Sea and east of the Guiana’s.

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REFERENCES AROCHA, F. and L. Marcano. 2001. Monitoring large pelagic fishes in the Caribbean Sea and the

western central Atlantic by an integrated monitoring program from Venezuela. pp. 557-576. In: Proceedings of the 52nd GCFI meeting. Key West, Fl. November 1999.

AROCHA, F. and M. Ortiz. 2001. Standardized catch rates for sailfish (Istiophorus platypterus) from

the Venezuelan Pelagic Longline Fishery off the Caribbean sea and the western central Atlantic. ICCAT, SCRS/01/094.

AROCHA, F., L. Marcano, J. Marcano, X. Gutierrez and J. Sayegh. 2001. Captura incidental

observada de peces de pico en la pesquería industrial de palangre venezolana en el mar Caribe y en el Atlántico centro-occidental: 1991-1999. ICCAT-Col. Vol. Sci. Pap.,53:131-140.

ICCAT. 2001. Report of the fourth ICCAT Billfish Workshop. ICCAT-Col. Vol. Sci. Pap.,53:1-110. LITTELL, R.C., G.A. Milliken, W.W. Stroup, and R.D Wolfinger. 1996. SAS® System for Mixed

Models, Cary NC:SAS Institute Inc., 1996. 663 pp. LO, N.C., L.D. Jacobson, and J.L. Squire. 1992. Indices of relative abundance from fish spotter data

based on delta-lognormal models. Can. J. Fish. Aquat. Sci. 49: 2515-2526. MARCANO, L., F. Arocha, J. Marcano and A. Larez. 2001. Actividades desarrolladas en el Programa

expandido de ICCAT para peces pico en Venezuela: período 1991-2001. ICCAT, SCRS/01/145. MCCULLAGH, P. and J.A. Nelder. 1989. Generalized Linear Models 2nd edition. Chapman & Hall. SAS Institute Inc. 1997, SAS/STAT® Software: Changes and Enhancements through Release

6.12. Cary, C: Sas Institute Inc., 1997. 1167 pp.

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Table 1. Deviance analysis table for explanatory variables in the delta lognormal model for blue marlin catch rates from the Venezuelan Pelagic Longline Observer Program (VPLOP). Percent of total deviance refers to the deviance explained by the full model; p value refers to the 5% Chi-square test between two nested models. The mean catch rate for positive observations assumed a lognormal error distribution.

Table 2. Analyses of delta lognormal mixed model formulations for blue marlin catch rates from the Venezuelan Pelagic Longline Observer Program (VPLOP). Likelihood ratio tests the deference of –2 REM log likelihood between two nested models. The highlighted model indicates the selected model for each component of the delta mixed model.

Model Delta Binomial Proportion of Positive obs

d.f.Residual deviance

Change in deviance

% of total deviance p

1 _ 1042.7Year 10 836.3 206.35 32.9% < 0.001Year Area 2 787.8 48.52 7.7% < 0.001Year Area Catboat 2 563.4 224.43 35.8% < 0.001Year Area Catboat Season 3 535.7 27.70 4.4% < 0.001Year Area Catboat Season Baittype 4 509.3 26.32 4.2% < 0.001Year Area Catboat Season Baittype Depth 1 506.8 2.54 0.4% 0.111Year Area Catboat Season Baittype Depth Year*Depth 9 477.8 29.04 4.6% < 0.001Year Area Catboat Season Baittype Depth Year*Catboat 15 455.8 50.99 8.1% < 0.001Year Area Catboat Season Baittype Depth Year*Area 17 453.6 53.19 8.5% < 0.001Year Area Catboat Season Baittype Depth Year*Baittype 24 428.0 78.84 12.6% < 0.001Year Area Catboat Season Baittype Depth Year*Season 29 415.2 91.60 14.6% < 0.001

Model Delta lognormal Positive obs

d.f.Residual deviance

Change in deviance

% of total deviance p

1 _ 589.0Year 10 539.4 49.61 14.0% < 0.001Year Area 2 493.5 45.87 13.0% < 0.001Year Area Catboat 2 263.3 230.26 65.2% < 0.001Year Area Catboat Season 3 262.0 1.25 0.4% 0.741Year Area Catboat Season Baittype 4 257.8 4.22 1.2% 0.378Year Area Catboat Season Baittype Depth 1 253.5 4.26 1.2% 0.039Year Area Catboat Season Baittype Depth Year*Depth 9 244.6 8.89 2.5% 0.447Year Area Catboat Season Baittype Depth Year*Area 14 243.9 9.66 2.7% 0.787Year Area Catboat Season Baittype Depth Year*Catboat 14 242.6 10.92 3.1% 0.692Year Area Catboat Season Baittype Depth Year*Baittype 23 240.4 13.14 3.7% 0.949Year Area Catboat Season Baittype Depth Year*Season 29 235.6 17.95 5.1% 0.945

Proportion positives Binomial Model-2 REM

Log likelihook

Akaike's Information

Criterion

Schwart'z Bayesian Criterion

Year Area Catboat Season Baittype 688.8 690.8 694Year Area Catboat Season Baittype Year*Area 686.8 690.8 693.6 2 0.1573Year Area Catboat Season Baittype Year*Area Year*Season 684.2 690.3 694.4 2.6 0.1069Year Area Catboat Season Baittype Year*Area Year*Season Year*baittype 685.4 693.4 699 -1.2 #¡NUM!Year Area Catboat Season Baittype Year*Area Year*Season Year*baittype Year*Catboat 684.1 694.1 701.1 1.3 0.2542

Positive Observations logNormal Model-2 REM

Log likelihook

Akaike's Information

Criterion

Schwart'z Bayesian Criterion

Year Area Catboat 1547.3 1549.4 1554.3Year Area Catboat Year*Area 1540 1544.4 1547 7.3 0.0069Year Area Catboat Year*Area Year*Catboat 1528.5 1534.5 1554.2 11.5 0.0007

Likelihood Ratio Test

Likelihood Ratio Test

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Table 3. Nominal and standardized (Delta lognormal mixed model) CPUE series (number of fish / 1000 hooks) for blue marlin catch rates from the Venezuelan Pelagic Longline Observer Program (VPLOP).

Table 4. Deviance analysis table for explanatory variables in the delta lognormal model for white marlin catch rates from the Venezuelan Pelagic Longline Observer Program (VPLOP). Percent of total deviance refers to the deviance explained by the full model; p value refers to the 5% Chi-square test between two nested models. The mean catch rate for positive observations assumed a lognormal error distribution.

Year N Obs Nominal CPUE

Standard CPUE SE CV upper lower

1991 98 0.634 0.303 0.135 44.5% 0.71 0.131992 261 0.373 0.198 0.077 38.8% 0.42 0.091993 458 0.196 0.100 0.046 46.1% 0.24 0.041994 159 1.110 0.620 0.193 31.1% 1.14 0.341995 453 0.430 0.242 0.080 33.0% 0.46 0.131996 359 0.381 0.184 0.065 35.6% 0.37 0.091997 377 0.328 0.201 0.073 36.3% 0.41 0.101998 422 0.578 0.369 0.097 26.2% 0.62 0.221999 354 0.280 0.187 0.076 40.4% 0.41 0.092000 332 0.312 0.206 0.076 37.0% 0.42 0.102001 219 0.176 0.136 0.068 50.0% 0.35 0.05

Model Delta Binomial Proportion of Positive obs

d.f.Residual deviance

Change in deviance

% of total deviance p

1 _ 1040.6Year 10 871.7 168.86 27.5% < 0.001Year Area 2 762.4 109.28 17.8% < 0.001Year Area Catboat 2 724.1 38.33 6.2% < 0.001Year Area Catboat Season 3 605.1 118.97 19.4% < 0.001Year Area Catboat Season Baittype 4 588.3 16.85 2.7% 0.002Year Area Catboat Season Baittype Depth 1 566.8 21.49 3.5% < 0.001Year Area Catboat Season Baittype Depth Year*Depth 9 541.3 25.49 4.1% 0.002Year Area Catboat Season Baittype Depth Year*Area 17 506.6 60.21 9.8% < 0.001Year Area Catboat Season Baittype Depth Year*Catboat 15 504.9 61.85 10.1% < 0.001Year Area Catboat Season Baittype Depth Year*Season 29 448.2 118.55 19.3% < 0.001Year Area Catboat Season Baittype Depth Year*Baittype 24 426.2 140.63 22.9% < 0.001

Model Delta lognormal Positive obs

d.f.Residual deviance

Change in deviance

% of total deviance p

1 _ 611.6Year 10 538.9 72.66 24.5% < 0.001Year Area 2 519.7 19.21 6.5% < 0.001Year Area Catboat 2 369.3 150.36 50.6% < 0.001Year Area Catboat Season 3 349.3 20.01 6.7% < 0.001Year Area Catboat Season Baittype 4 346.8 2.53 0.9% 0.640Year Area Catboat Season Baittype Depth 1 343.0 3.81 1.3% 0.051Year Area Catboat Season Baittype Depth Year*Depth 8 338.9 4.12 1.4% 0.846Year Area Catboat Season Baittype Depth Year*Area 14 328.8 14.19 4.8% 0.436Year Area Catboat Season Baittype Depth Year*Catboat 14 321.5 21.49 7.2% 0.090Year Area Catboat Season Baittype Depth Year*Baittype 20 319.0 24.03 8.1% 0.241Year Area Catboat Season Baittype Depth Year*Season 29 314.4 28.56 9.6% 0.488

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Table 5. Analyses of delta lognormal mixed model formulations for white marlin catch rates from the Venezuelan Pelagic Longline Observer Program (VPLOP). Likelihood ratio tests the deference of –2 REM log likelihood between two nested models. The highlighted model indicates the selected model for each component of the delta mixed model.

Table 6. Nominal and standardized (Delta lognormal mixed model) CPUE series (number of fish / 1000 hooks) for white marlin catch rates from the Venezuelan Pelagic Longline Observer Program (VPLOP).

Proportion positives Binomial Model-2 REM

Log likelihook

Akaike's Information

Criterion

Schwart'z Bayesian Criterion

Year Area Catboat Season Baittype 731.1 733.1 736.3Year Area Catboat Season Baittype Year*Season 726.6 73.6 734.1 4.5 0.0339Year Area Catboat Season Baittype Year*Season Year*Baittype 718.6 724.6 729.9 8 0.0047Year Area Catboat Season Baittype Year*Season Year*Baittype Year*Catboat 718.5 726.7 733.5 0.1 0.7518

Positive Observations logNormal Model-2 REM

Log likelihook

Akaike's Information

Criterion

Schwart'z Bayesian Criterion

Year Area Catboat Season 1735 1737 1741.7Year Area Catboat Season Year*Season 1721.5 1725.5 1729 13.5 0.0002Year Area Catboat Season Year*Season Year*Catboat 1715.6 1721.6 1721.6 5.9 0.0151

Likelihood Ratio Test

Likelihood Ratio Test

Year N Obs Nominal CPUE

Standard CPUE SE CV upper lower

1991 99 0.579 0.363 0.266 73.4% 1.35 0.101992 261 0.296 0.297 0.150 50.6% 0.77 0.111993 459 0.367 0.379 0.179 47.2% 0.93 0.151994 159 0.644 0.537 0.277 51.6% 1.42 0.201995 455 0.759 0.823 0.274 33.3% 1.57 0.431996 360 0.427 0.413 0.180 43.6% 0.95 0.181997 377 0.660 0.717 0.282 39.3% 1.53 0.341998 422 0.320 0.333 0.150 45.0% 0.79 0.141999 355 0.682 0.501 0.221 44.1% 1.16 0.222000 336 0.208 0.199 0.129 64.6% 0.65 0.062001 223 0.096 0.098 0.103 104.7% 0.55 0.02

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Figure 1. Area of the Atlantic Ocean and Caribbean Sea where the Venezuelan longline vessels operate. The divisions correspond to the fishing areas related in the text.

Figure 2. Spatial distribution of proportional nominal CPUE of blue marlin (numbers/1000 hooks) caught by the Venezuelan pelagic longline fleet during 1991-2001 and recorded by the VPLOP.

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Figure 3. Spatial distribution of proportional nominal CPUE of white marlin (numbers/1000 hooks) caught by the Venezuelan pelagic longline fleet during 1991-2001 and recorded by the VPLOP.

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Figure 4. Frequency distribution of log-transformed nominal CPUE (fish/1000 hooks) of trips that caught blue marlin and white marlin from the Venezuela Pelagic Longline Fishery from 1991 through 2001.

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Figure 5. Diagnostic plot delta lognormal positive observations model component. Cumulative normalized deviance residuals or qq-plot of the positive trips for blue marlin and white marlin fit for the lognormal error distribution.

Figure 6. Diagnostic plot delta model. Frequency distribution of observed (bars) and predicted (solid line) proportion of positive/total observations from the assumed binomial error distribution for blue marlin and white marlin from the Venezuela Pelagic Longline Fishery from 1991 through 2001.

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Figure 7. Observed and predicted VPLOP blue marlin scaled CPUE with 95% CI