STANDARDIZED CPUE SERIES OF SWORDFISH, XIPHIAS GLADIUS,
CAUGHT BY BRAZILIAN LONGLINERS IN THE
SOUTHWESTERN ATLANTIC OCEAN
Humberto G. Hazin^{1}, Fábio H.V. Hazin^{1} and Paulo Travassos^{1}
SUMMARY
Relative abundance indices by number of swordfish (Xiphias gladius) caught by the Brazilian tuna longline fishery in the South Atlantic Ocean were estimated by analyzing catch and effort data from individual sets (~60,000) collected for the period 19782006. A Generalized Linear Model was used to standardize the CPUE series (fish/ 1000hooks), assuming two different error distributions: delta lognormal and quasiPoisson (link= log and variance= µ,). For the deltalognormal distribution, the model explained 40.6% of the variance for the positive catches and about 77.8% of the proportion of positives. The quasiPoisson model explained 57.9% of the variance. For both models the “Target” and
“Year” variables explained most of the deviance. The results obtained seem to confirm the optimistic scenario of a continuing trend of CPUE increase for the species, in the southwestern Atlantic, in recent years.
RÉSUMÉ
Les indices d’abondance relative en nombre d’espadons (Xiphias gladius) capturés par la pêcherie palangrière brésilienne ciblant les thonidés dans l’Océan Atlantique Sud ont été estimés en analysant les données de prise et d’effort d’opérations individuelles (~60.000), collectées pour la période 19782006. Un Modèle Linéaire Généralisé a été utilisé pour standardiser la série de CPUE (poissons/1.000 hameçons), en postulant deux distributions d’erreur différentes : delta lognormale et quasiPoisson (lien= log et variance= µ,). Pour la distribution deltalognormale, le modèle a expliqué 40,6% de la variance des prises positives et environ 77,8% de la proportion des valeurs positives. Le modèle quasiPoisson a expliqué 57,9% de la variance. Pour les deux modèles, les variables “Cible” et “Année” expliquaient la plupart de la déviance. Les résultats obtenus semblent confirmer le scénario optimiste d’une tendance ascendante constante de la CPUE dans l’Atlantique SudOuest pour cette espèce, ces dernières années.
RESUMEN
Se estimaron índices de abundancia relativa por número de peces espada (Xiphias gladius) capturados por la pesquería de palangre atunera de Brasil en el Atlántico sur analizando datos de captura y esfuerzo de lances individuales (~60.000) recopilados para el periodo 19782006. Se utilizó un modelo lineal generalizado para estandarizar la serie de CPUE (peces/1000 anzuelos), asumiendo dos distribuciones de error diferentes: delta lognormal y quasiPoisson (vínculo= log y varianza= µ,).Para la distribución delta lognormal, el modelo explicaba el 40,6% de la varianza para las capturas positivas y aproximadamente el 77,8% % de la proporción de positivos. El modelo quasiPoisson explicaba el 57,9% de la varianza. Para ambos modelos, las variables de “objetivo” y “año” explicaban la mayoría de la desvianza. Los resultados obtenidos parecen confirmar el escenario optimista de una tendencia continua de aumento de la CPUE para la especie en el Atlántico sudoccidental en años recientes.
KEYWORDS
CPUE, swodfish, GLM, QuasiPoisson, Delta log
1. Introduction
Catch per unit of effort (CPUE) is often the main information used in the assessment of fish stocks. Generally assumed to be proportional to the actual number of fish available to the fishery, the CPUE is commonly included in the models as a relative index of abundance, a premise, however, that is rarely, if ever, entirely true (Gulland 1964; Harley et al. 2001). Of particular concern is the trend of hyperstability of CPUE, i.e. since fishers tend to do whatever they can to improve or maintain their catch rates, including through increases in fishing power and methods, the resulting CPUE does not reflect the actual state of exploited stocks (Hilborn and Walters 1992), which are, in many instances, more depleted than realized from CPUE trends. Besides, discrepancies between model predictions and observed catches are often attributed to variations in catchability that are linked to environmental fluctuations or to changes in targeting, in multispecies fisheries. The importance of targeting strategy on the CPUE of fish species caught by the tuna longline fishery has been recognized by several authors (Ward et al., 1996; He et al., 1997; Wu and Yeh, 2001; Alemany and Álvarez, 2003).
Important changes in the fishing strategy of the Brazilian tuna longline fishery have been frequently observed and reported (Arffeli, 1996; Hazin, 2006; Hazin, et al. 2007). Recently, clustering methods (e.g. cluster analysis) have been applied in the analysis of fishing data, aiming at categorizing fishing effort based on the proportion of the several species in the catches, as a way to detect changes in targeting strategy (Hazin, 2006; Hazin et al. 2007; Hazin et al., 2008). The main advantage of such method, instead of using the percentage of a single species as an expression of the targeting strategy, relies in the fact that they consider the frequency distribution of all species in each set, thus providing, probably, a more reliable estimation.
In the present paper, a GLM analysis was used to standardize the swordfish CPUE trend in the Brazilian Tuna longline fishery, from 1978 to 2006, considering 2 different distributions: deltalognormal and quasiPoisson. Besides, in order to take the targeting strategy into account, the target species was included in both models, as inferred from a cluster analysis previously run.
2. Material and methods
In the present study, catch and effort data from 60,103 tuna longline sets done by the Brazilian tuna longline fleet, including both national and foreign chartered vessels, from 1978 to 2006 (29 years) were analysed. The logbooks were filled in by the skippers of the vessels and delivered to the Special Secretariat of Fisheries and Aquaculture (SEAP). 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 fishing ground was subdivided into 2 areas, according to the biological and spatial fishing characteristics of the species, reported by Hazin et al. (2007): A1, from 10ºN to 15ºS, and A2, to the south of 15ºS.
The percentage of sets with no catch was relatively low (24.7%). The Generalized Linear Models (GLM) were fitted using SPlus 7 (Insightful Corp., Seattle, WA, USA) and were specified with a quasilikelihood estimate of the error distribution (quasiPoisson; link= log and variance=µ,) and delta lognormal. Forward and backward stepwise, using the AIC protocol, was used to quantify the relative importance of the main factors explaining the CPUE variance and concluded that only four out of eight variables primarily investigated were significant (p<0.05) in the GLM analyses, for both models: Year, Target, Area, and Quarter, as well as the interaction Year*Quarter. The target species was defined by a cluster analysis, using the Kmeans method (FASTCLUS, Johnson e Wichern, 1988; SAS Institute Inc, 1989), to identify the number of ideal clusters.
The fits were done in SPlus and the predictions were obtained for every Year, fixing the level of remaining factors at the level with the highest number of observations. The general formulation used in the present study was expressed by the following equation:
CPUE (fish/1000 hooks) = Year+Quarter+Area+Target+Year:Quarter
3. Results and discussion
For the deltalognormal distribution, the model explained 40.6% of the variance for the positive catches and about 77.8% of the proportion of positives. The “Target” and “Year” variables were those which explained most of the deviance with 70.0% and 22.8% for the positive catches and 77.8% and 10.5% for the proportion of positives (Table 1). The histogram of residuals for the sets with positive swordfish catches (Figure 2) was very close to the normal curve.
For the quasiPoisson model, the variables chosen explained 57.9% of the variance (Table 3). Similarly to previous works (Hazin et al., 2007), the target species (cluster) was the most important factor, explaining 73.8% of the deviance, followed by Year (21.1%), while quarter (2.7%), year*quarter (2.3%), and area (0.1%) played a minor role (Table 3). Histogram of residuals for the sets from the quasiPoisson model is presented in Figure 3.
The scaled nominal CPUE series showed a clear difference to the scaled standardized values by both methods (Table 4 and Figure 4). The CPUE series standardized by the quasiPoisson and the deltalognormal, however, were not much different from each other, showing a strong oscillation along time, with an increasing trend from 2000 on. The results were also close to a CPUE series standardized by the deltalognormal, up to 2005 (Hazin et al. 2007), which also showed an increase in CPUE for the most recent years.
The confidence intervals were relatively narrow for both models (quasiPoisson: CV= 2% to 27%; deltalognormal: CV= 14% to 36%), particularly considering the high variance usually associated to CPUE series, based in a set by set data, with no data aggregation (Punt et al., 2000). The quasi family in SPlus allows for parameter estimation without directly specifying the error distribution (Campos et al., 1997, Anon., 1999). The quasilikelihood method provides a more accurate estimate of the standard errors around estimated coefficients because it accounts for the dispersion parameter estimated from the data rather than assuming Ø equals some theoretical value (e.g., Ø = 1 when Poisson or negative binomial distributions are specified).
The results obtained in the present paper are similar to the ones presented during the last swordfish stock assessment, in 2006 (Hazin et al., 2007), and seem to confirm the optimistic scenario of a continuing trend of CPUE increase for the species, in the southwestern Atlantic, in recent years.
Acknowledgements
This work was made possible by the Secretariat of Fisheries and Aquaculture (SEAP) of the Brazilian Government and by Fundação de Amparo à Ciência e Tecnologia do Estado de PernambucoFACEPE.
References
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Table 1. Deviance analysis table of explanatory variables in the deltalognormal model for swordfish CPUE, for positive catches and for the proportion of positives.
Positive catches

Df

Deviance

Resid. DF

Resid. Dev

PR (Chi)

Explained Deviance (%)

Explained by the Model (%)

NULL



47242

73158.37




Quarter

3

863.76

47239

72294.61

0.00000

2.9%

1.2%

Year

28

6779.89

47211

65514.72

0.00000

22.8%

10.4%

Área

1

4.93

47210

65509.79

0.02642

0.0%

10.5%

Target

5

20817.13

47205

44692.66

0.00000

70.0%

38.9%

Quarter:year

84

1256.89

47121

43435.77

0.00000

4.2%

40.6%

Proprtion of positives

Df

Deviance

Resid. DF

Resid. Dev

PR (Chi)

Explained Deviance (%)

Explained by the Model (%)

NULL



1042

19624.95




Quarter

3

481.32

1039

19143.62

0.00000

3.2%

2.5%

Year

28

1599.41

1011

17544.21

0.00000

10.5%

10.6%

Área

1

134.52

1010

17409.69

0.00000

0.9%

11.3%

Target

5

11878.16

1005

5531.54

0.00000

77.8%

71.8%

Quarter:year

84

1180.84

921

4350.7

0.00000

7.7%

77.8%

Table 2. Deviance analysis table of explanatory variables in the QuasiPoisson model for swordfish CPUE.

DF

Deviance

Resid. DF

Resid. Dev

PR (Chi)

Explained Deviance (%)

Explained by the Model (%)

NULL



60103

428860.3




Quarter

3

6690.2

60100

422170.1

0.00000

2.7%

1.6%

Year

28

52423.6

60072

369746.5

0.00000

21.1%

13.8%

Área

1

237.9

60071

369508.5

0.00000

0.1%

13.8%

Target

5

183484.2

60066

186024.3

0.00000

73.8%

56.6%

Quarter:year

84

5679.2

59982

180345.1

0.00000

2.3%

57.9%

Table 3. Nominal and standardized (QuasiPoisson and Delta lognormal) CPUE series (number of fish/ 1000 hooks) for swordfish catch rates from the Brazilian tuna longline.
Year

STANDARDIZED (QuasiPoisson)

SE

CV

SCALED
(QuasiPoisson)

STANDARDIZED (Deltalog)

SE

CV

SCALED (Deltalog)

CPUE (Nominal)

SCAL (nominal)

1978

8.786

0.840

10%

0.815

6.259

1.586

25%

0.805

3.965

0.882

1979

8.462

0.954

11%

0.785

5.720

1.215

21%

0.736

4.105

0.913

1980

8.873

0.513

6%

0.823

7.454

1.222

16%

0.959

6.901

1.535

1981

5.810

1.578

27%

0.539

7.122

1.514

21%

0.916

10.568

2.351

1982

14.811

0.830

6%

1.374

9.539

2.599

27%

1.227

10.923

2.430

1983

12.985

1.382

11%

1.204

10.664

2.181

20%

1.372

5.742

1.277

1984

8.328

0.679

8%

0.772

6.110

1.244

20%

0.786

3.141

0.699

1985

11.204

0.916

8%

1.039

8.078

2.005

25%

1.039

4.377

0.974

1986

8.920

0.565

6%

0.827

6.436

0.933

14%

0.828

4.795

1.067

1987

9.928

0.838

8%

0.921

8.862

1.703

19%

1.140

5.527

1.230

1988

14.311

0.784

5%

1.327

10.202

2.055

20%

1.313

4.687

1.043

1989

9.427

0.879

9%

0.874

6.071

1.845

30%

0.781

2.601

0.579

1990

20.671

2.769

13%

1.917

14.748

3.520

24%

1.898

5.366

1.194

1991

10.742

0.953

9%

0.996

10.380

2.518

24%

1.336

2.944

0.655

1992

4.610

0.608

13%

0.428

4.001

1.184

30%

0.515

1.361

0.303

1993

4.168

0.854

20%

0.387

3.017

0.624

21%

0.388

2.045

0.455

1994

5.001

0.557

11%

0.464

3.727

1.080

29%

0.480

2.090

0.465

1995

6.476

0.510

8%

0.601

4.515

1.150

25%

0.581

1.672

0.372

1996

10.713

0.868

8%

0.994

7.116

1.911

27%

0.916

2.248

0.500

1997

13.098

0.625

5%

1.215

7.674

2.098

27%

0.987

3.852

0.857

1998

21.296

0.565

3%

1.975

9.132

2.605

29%

1.175

5.581

1.242

1999

10.513

0.349

3%

0.975

6.723

1.436

21%

0.865

2.052

0.456

2000

10.531

0.241

2%

0.977

7.321

1.683

23%

0.942

2.699

0.600

2001

14.399

0.248

2%

1.335

8.672

2.079

24%

1.116

2.353

0.523

2002

8.083

0.200

2%

0.750

5.994

1.358

23%

0.771

2.466

0.549

2003

10.113

0.592

6%

0.938

9.306

1.260

14%

1.197

6.853

1.525

2004

13.967

0.315

2%

1.295

10.293

2.597

25%

1.324

4.593

1.022

2005

11.549

0.236

2%

1.071

7.180

2.599

36%

0.924

5.118

1.139

2006

14.928

0.330

2%

1.384

13.078

2.369

18%

1.683

9.723

2.163

A1
B2
Figure 1. Distribution of the longline sets done by the Brazilian tuna longline fishery in the Atlantic Ocean, from 1978 to 2006 (29 years).
Figure 2. Histogram of residuals for the sets with positive swordfish catches
Figure 3. Histogram of residuals for the sets from QuasiPoisson model.
Figure 4. Scaled nominal and standardized CPUE of swordfish for Brazilian tuna longliners, from 1978 to 2006.
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