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The effects of subsampling and between-haul variation on the size-selectivity estimation of Chilean hake (Merluccius gayi gayi)/Los efectos de submuestreo y variacion entre lances en la estimacion de la selectividad a la talla de la merluza comun (Merluccius gayi gayi).

INTRODUCTION

Chilean hake (Merluccius gayi gayi) occurs along the coast of Chile between 23[degrees] and 47[degrees]S at depths from 50 to 500 m. It is the main demersal species caught along the central coast. The biomass of this resource decreased dramatically as a consequence of natural (cannibalism and predation) and fishing mortality from 2002 to 2005 and the current stock assessment indicates that it is overexploited (SUBPESCA, 2010). The proportion of fish below the size-at-maturity has increased since 2004 (more than 70% of the catches) and the present spawning biomass is below the limit reference level of 20% established for the fishery (SUBPESCA, 2010).

Regulation of mesh size is one of the most common management measures in fisheries. Specification and use of an appropriate mesh size can contribute to increases in the size of first capture and can reduce the mortality of smaller fish. Only one experiment on size selectivity has been performed for the Chilean hake trawling fishery over the last decade. Galvez et al. (2000) analysed the selectivity of four mesh sizes (100, 110, 130 and 140 mm) using the covered codend method and the results were later published by Galvez & Rebolledo (2005). These authors estimated similar [l.sub.50] values among the different mesh sizes used, although the escape proportions increased with increasing mesh size. These results were compared with different selectivity studies carried out in Gadiformes (Fig. 1). A linear relation was found for this group of fishes between the mesh size and the 50% retention length, with a slope of ~0.4. Because Galvez & Rebolledo (2005) found a lower value of the slope for this relationship (~0.1), the procedures were reviewed. In fact, the sampling proportions of the codend and cover were not considered in their analysis. Subsampling is necessary when the catch is so large that it is not possible to measure every single individual (Wileman et al., 1996). The effect of subsampling can be incorporated in two ways: (i) expanding the sample to the total catch or (ii) correcting the estimated parameters by a subsampling factor. Millar (1994) points out that the second case is preferable because it uses raw (unscaled) data and thereby ensures statistical rigour.

Replicate hauls using the same trawl and configuration indicate that codend selectivity changes from one haul to another. Fryer (1991) indicated that the between-haul variation could be due to a number of "uncontrolled" factors. Examples of such factors include the haul duration, catch size, fishing season and depth among others (O'Neill & Kynoch, 1996; Millar & Fryer, 1999; Fonseca et al., 2007; Grimaldo et al., 2008; Sala & Lucchetti, 2010).

The objective of this study was to estimate the selectivity parameters so as to account for subsampling proportions. Moreover, explanatory variables were added in order to incorporate the effects of between-haul variation. The resulting parameter values were compared with previous estimates.

MATERIALS AND METHODS

Selectivity experiments were conducted during March-April 2000 on board a stern trawler (41.7 m overall length; 1900 HP) in the central-southern area of Chile (between 34[degrees]50'-35[degrees]40'S). Hauls were made during daylight hours at depths from 90 to 260 m. The duration of each haul varied between 14 and 135 min. Towing speed fluctuated between 3.0 and 4.0 knots (3.4 knots average speed) (Table 1). The hauls were carried out using a 53-m headline and 37-m footrope Engel Balloon Trawl, with four experimental codends of 100, 110, 130 and 140 mm mesh size opening. The covered codend method was used to retain the fish that escaped through the meshes (Galvez & Rebolledo, 2005). A length-frequency dataset was obtained from 32 covered codend experimental hauls (Table 1).

The data from each of the two compartments (codend and cover) were analysed separately. The catch weight for each compartment j was estimated for each haul. In order to estimate the catch in numbers of Chilean hake, a length-weight function was applied based on data recorded by Lillo et al. (2001). The average specimen weight was then determined ([[bar.w].sub.j]). The number of retained specimens by haul and compartment was obtained according to [N.sub.j] = [W.sub.j]/[[bar.w.].sub.j] where [W.sub.j] is the catch weight in each compartment.

For each haul, the retention probability r(l) of the codend was modelled using a logistic curve: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where r(l) is the (conditional) retention probability of a fish of length l given that it entered the codend (Wileman et al., 1996), and v = [([v.sub.1] + [v.sub.2]).sup.T] is the vector of the selectivity parameters. The correction for the effects of subsampling was performed according to Millar (1994) who showed that for subsampled hauls [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [v.sup.*.sub.1] = [v.sub.1] + ln(q) and q = [P.sub.1]/[P.sub.2] is the rate of sampling proportions in the codend and cover, respectively. The selectivity parameters [v.sup.*.sub.1] and [v.sub.2] of the logistic curve were estimated by means of haul-by-haul maximum likelihood using the CC2000 software (ConStat).

[FIGURE 1 OMITTED]

The 50% retention length ([l.sub.50]) and the selection range (SR) were estimated as [l.sub.50] = -[v.sub.1]/[v.sub.2] and SR = 2ln(3)/[v.sub.2], respectively. The model proposed by Fryer (1991) was then used to investigate the between-haul variation of the selectivity parameters [v.sup.*.sub.1] and [v.sub.2] for each configuration, thereby allowing an average curve to be estimated for the codends. Analysis was done using the ECModel software (ConStat) based on the residual maximum likelihood (REML) method proposed by Fryer (1991). The individual contributions of various explanatory variables to the selectivity parameters were tested using the ECModel according to the REML method (Fryer, 1991). The variables considered were mesh size, catch (in number and weight), tow duration, depth and towing speed. The choice of the best fit model was based on the lowest value for Akaike's Information Criterion (AIC) (Fryer & Shepherd, 1996).

RESULTS

To calculate the sample weight in each compartment (codend and cover), the length-weight relationship [w.sub.i] = 7.76[e.sup.-6] [l.sup.2.979.sub.i] ([R.sup.2] = 0.97) was used for both sexes. The catch in numbers for each haul was calculated using this relationship and the catch weight. The resulting values ranged between 437 and 37,345 specimens in the codend and between 83 and 10,507 in the cover (Table 1). The corresponding sample proportions ([P.sub.1] and [P.sub.2]) varied between 0.005 and 0.185 in the codend and between 0.028 and 0.724 in the cover. Accordingly, the relationship between the sample proportions (q) ranged between 0.01 and 1.68 ([bar.q] =0.26). The q values for all hauls were taken into account in order to fit the selectivity models.

Fig. 2 shows the fitted curves for each haul. For all hauls, the estimated model resulted in good fits (P > 0.05) (Table 2). With the selection parameters [v.sup.*.sub.1] and [v.sub.2] taken into consideration in the haul-by-haul analysis, the resulting estimates of [l.sub.50] ranged between 26.4 and 35.6 cm for the 100 mm mesh; between 22.9 and 35.4 cm for the 110 mm mesh; between 23.7 and 34.0 cm for the 130 mm mesh and between 35.3 and 45.6 cm for the 140 mm mesh. Using the fit of the average curve based on between-haul variation, values of [l.sub.50] were estimated as 30.8, 29.9, 30.0 and 41.2 cm for each mesh size, respectively (Table 2). Selection range (SR) tended to increase with increasing mesh size. However, the 130 mm mesh exhibited a value higher than expected from the general tendency observed. The average values of SR were 6.9, 7.2, 11.9 and 8.3 cm for the 100, 110, 130 and 140 mm meshes, respectively (Table 2).

Addition of the explanatory variables to account for between-haul variation indicated that the parameter [v.sup.*.sub.1] depends significantly on the catch in numbers (P = 0.01) and the towing speed (P = 0.023), whereas [v.sub.2] depends on the mesh size (P < 0.001) (Table 3). This analysis yields a direct relation between [l.sub.50] and the mesh size. On the other hand, the [l.sub.50] value decreases as catch and towing speed increase. The model that best described selectivity was:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [c.sub.i] is the catch (in numbers), [s.sub.i] is the towing speed (knots) and [m.sub.i] is the mesh size (mm). The depth and duration variables did not contribute significantly to the model.

The effect of the catch for each mesh size used in the model was analysed for a range of 1,000 to 35,000 specimens caught and for a fixed towing speed corresponding to the average value of 3.4 knots. A significant decrease of at least 6 cm TL in the [l.sub.50] value for extreme catches was observed for all mesh sizes (Fig. 3). For example, the [l.sub.50] of the 100 mm mesh was 29.9 cm for a small catch (1,000 specimens), while this value decreases to 23.1 cm for a large catch (35,000 specimens).

Likewise, the model with towing speeds between 3 and 4 knots was evaluated assuming a constant catch of 10,000 individuals. A decrease of at least 4.5 cm TL in the [l.sub.50] value for extreme speeds was observed (Fig. 4). For the 140 mm mesh at a towing speed of 3 knots, the [l.sub.50] was 39.0 cm. This value decreased to 33.1 cm for a towing speed of 4 knots.

Note that [v.sub.2] depends only on the mesh size. Accordingly, the SR values estimated using the model were 7.2, 7.7, 8.9 and 9.6 cm for the meshes of 100, 110, 130 and 140 mm, respectively.

DISCUSSION

This study was based on the same data used by Galvez & Rebolledo (2005). However, the results of the two studies differ (Fig. 5). The main analytic difference is that these authors assume that the sampling proportions in the codend and in the cover are equal. This assumption leads to a significant overestimation of the selectivity parameters. When this effect and the between-haul variation are both taken into account, the [l.sub.50] estimate decreased by 9 cm for the 100, 110 and 130 mm mesh. The difference is lower (~4 cm) in the 140 mm mesh (Fig. 5).

Incorporation of subsampling effects produced a high dispersion of the [l.sub.50] values. This effect is the result of other variables included in the selection process. This consideration led us to introduce explanatory variables to the model and by including the mesh size, the catch (in numbers) and the towing speed, it was possible to achieve significant reductions in the dispersion of the estimates (Fig. 5). The effect of catch size on codend selectivity has been discussed in numerous studies. Some authors find that increasing catch size reduces [l.sub.50] (Ehrhardt et al., 1996; Erickson et al., 1996; Tschernij & Holst, 1999; Madsen et al., 2002; Grimaldo et al., 2007). However, others have obtained the opposite result (O'Neill & Kynoch, 1996; Dahm et al., 2002), while emphasising that selectivity tends to decrease when the catch size is very high. On the other hand, the studies of Madsen et al. (1998), O'Neill et al. (2006) and Grimaldo et al. (2008) yielded inconclusive results or found only a weak effect of the catch variable.

[FIGURE 2 OMITTED]

Many different factors are involved in gear selectivity. For example, alterations in and obstructtions of the escape channels can be produced, and changes can also occur in the tension-deformation relation of the meshes. Indeed, Erickson et al. (1996) point out that large catch sizes can obstruct the codend meshes and thereby reduce the potential escape channels for fish. Additionally, in some Gadidae, haddock and whiting for example, "opportunistic escape" is more common than "active escape" (Jones et al., 2008). This difference results in a reduced probability of escape as the catch size increases. Tension-deformation is also an important factor. The increased size of the mesh opening and the change in the shape of the codend would both favour increased selectivity (O'Neill & Kynoch, 1996; Herrmann, 2005; Madsen, 2007). Nevertheless, the increased drag produced by the operation of the trawl can increase the tension on the mesh bars. This increased tension can make escape more difficult (O'Neill et al., 2005) or can injure fish, thereby conditioning their post-escape survival (Suuronen, 2005).

Increased trawl speed thus affects selectivity adversely for two different reasons. Increased speed increases the resistance encountered by the gear, raises the tension on the codend meshes, and consequently reduces the mesh opening (Dahm et al., 2002; O'Neill et al., 2005). On the other hand, an increase in trawl speed also reduces the swimming performance of fish (Dahm et al., 2002; Breen et al., 2004). In this study, we did not have enough information to identify a particular mechanism responsible for the [l.sub.50] decrease. However, Queirolo et al. (2010) noted in hake that when fish are close to the codend at a towing speed of 4 knots, most fish exhibit no movement, appear exhausted and drop back into the codend.

The model obtained in this study indicates that the selectivity decreases as the catch size increases. This effect could be explained by the obstruction of the escape channels and by the closure of the meshes due to the increase of the tension. In the model, selectivity also decreased with increased towing speed. This effect can be attributed to the lower swimming performance of the fish. The significance found for the explanatory variables in the selectivity model indicates that these variables could be included in management "good practices" recommendations for users. Although the tow duration was not significant in our results, we recognize that this variable plays an important role both during the escape phase and postescape survival (Suuronen, 2005), so it should be consider in subsequent studies.

[FIGURE 3 OMITTED]

In order to reduce the juvenile catch and avoid growth overfishing, the recommended value of [l.sub.50] should be greater than or equal to the size at sexual maturity estimated as 34 cm TL by Lillo et al. (2009). Likewise, assuming an average catch of 10,000 fish and an average towing speed of 3.4 knots, an estimate of the minimum mesh size recommended for the fishery is 125 mm. However, at present, the use of 100 mm mesh and a 90-mm square mesh panel are mandatory (see Queirolo et al., 2008). For this reason, it is fundamental to evaluate and compare the whole selectivity of these codends for the fishery. These recommendations demonstrate ways in which the addition of the subsampling effect and the use of explanatory variables to model between-haul variation can allow fisheries scientists to improve selectivity estimates for Chilean hake.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

DOI: 10.3856/vol40-issue2-fulltext-9

ACKNOWLEDGEMENTS

We thank the Fondo de Investigacion Pesquera (FIP) for authorising this reanalysis of the data and for facilitating access to the databases of the FIP 96-25 project. Special thanks to the Centro Andaluz de Ciencia y Tecnologia Marinas (CACYTMAR) for logistical support and anonymous reviewers for their valuable comments. Dante Queirolo also thanks the Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT, Programa Becas Chile) for the fellowship awarded.

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Received: 17 May 2011; Accepted: 23 May 2012

Dante Queirolo (1), Mauricio Ahumada (1), Carlos F. Hurtado (1), Milagrosa C. Soriguer (2) & Karim Erzini (3)

(1) Escuela de Ciencias del Mar, Facultad de Recursos Naturales Pontificia Universidad Catolica de Valparaiso, P.O. Box 1020, Valparaiso, Chile

(2) Departamento de Biologia, Facultad de Ciencias del Mar y Ambientales Universidad de Cadiz, 11510 Puerto Real, Cadiz, Espana

(3) Centro de Ciencias do Mar (CCMAR), Faculdade de Ciencias do Mar e do Ambiente Universidade do Algarve, 8005-139, Faro, Portugal

Corresponding author: Dante Queirolo (dante.queirolo@ucv.cl)
Tabla 1. Resumen de los lances y variables explicatorias usados en
los experimentos de selectividad de la merluza chilena. Las
proporciones de submuestreo por compartimento (copo y cubrecopo)
tambien son incluidas.

Table 1. Summary of hauls and explanatory variables used in the
Chilean hake selectivity experiments. Subsampling proportions by
compartment (codend and cover) are also included.

Haul   Mesh size    Depth    Speed     Duration        Codend
          (mm)       (m)     (knots)     (min)
                                                   Catch    Sample
                                                    (kg)      (n)

1         100        209       3.3        45        2737      149
2         100        227       3.3        84        4426      110
3         100        200       3.3        55       10999      85
4         100        205       3.2        59        6253      98
5         100        146       3.3        25        1698      109
6         100        144       3.2        35        4320      144
7         100        143       3.3        20        8996      321
8         100        158       3.2        19       10725      304
9         100        217       3.3        45        2543      50
1         110        200       3.9        84        1526      122
2         110        175       3.6        45        4909      229
3         110        165       4.0        44        1529      132
4         110        220       3.7        24       14606      102
5         110        100       3.7        120       3884      377
6         110         98       3.7        39       10508      316
7         110         93       3.7        40        1776      181
8         110         90       3.2        14        730       91

Haul                     Codend                          Cover

       Av. length    Av. weight    Catch     p1     Catch    Sample
          (cm)          (kg)        (n)              (kg)      (n)

1         49.27         0.861       3177    0.046    115       145
2         46.68         0.733       6036    0.018     69       61
3         48.91         0.842      13056    0.006     58       97
4         49.66         0.881       7091    0.013     69       77
5         46.83         0.739       2293    0.047     69       88
6         46.55         0.727       5938    0.024     69       145
7         43.73         0.604      14894    0.021    184       460
8         40.07         0.465      23048    0.013    184       304
9         48.36         0.814       3121    0.016     46       28
1         43.32         0.587       2598    0.046     23       55
2         43.91         0.611       8035    0.028    1150      152
3         41.24         0.507       3016    0.043     23       92
4         46.36         0.718      20328    0.005     23       77
5         45.33         0.672       5778    0.065    276       577
6         46.81         0.739      14207    0.022    161       241
7         46.87         0.742       2392    0.075     92       282
8         47.14         0.755       967     0.094     23       232

Haul                             Cover

       Av. length    Av. weight    Catch (n)    p2       q
          (cm)          (kg)

1         37.03         0.367         313      0.463   0.099
2         36.03         0.339         204      0.299   0.060
3         25.46         0.121         477      0.203   0.029
4         34.72         0.303         227      0.339   0.038
5         34.34         0.293         235      0.374   0.125
6         33.74         0.278         247      0.587   0.040
7         28.93         0.176        1043      0.441   0.047
8         34.89         0.308         597      0.509   0.025
9         38.46         0.411         112      0.251   0.064
1         33.72         0.278         83       0.662   0.069
2         35.53         0.325        3534      0.043   0.651
3         29.16         0.179         127      0.724   0.059
4         27.12         0.145         158      0.487   0.010
5         28.95         0.176        1561      0.369   0.176
6         37.34         0.377         427      0.564   0.039
7         26.51         0.135         677      0.416   0.180
8         21.12         0.069         333      0.696   0.135

       Mesh size    Depth    Speed     Duration         Codend
          (mm)       (m)     (knots)     (min)
Haul                                               Catch    Sample
                                                    (kg)      (n)

1         130        138       4.0        45        4656      445
2         130        132       4.0        90        3196      585
3         130        136       3.1        55        1736      592
4         130        135       3.2        105       5194      374
5         130        139       3.3        69        3588      358
6         130        188       3.1        40        3442      305
7         130        200       3.1        120      26510      298
1         140        147       3.2        65        6024      245
2         140        159       3.3        110       7484      281
3         140        184       3.0        135       6736      249
4         140        260       3.1        50        895       112
5         140        134       3.2        45        288       81
6         140        130       3.2        45        5417      203
7         140        135       3.1        64        6585      220
8         140        185       3.2        90        4518      191

                           Codend                        Cover

Haul   Av. length    Av. weight    Catch     p1     Catch    Sample
          (cm)          (kg)        (n)              (kg)      (n)

1         41.96         0.534       8718    0.051    460       449
2         40.03         0.463       6889    0.084    644       462
3         39.29         0.438       3955    0.149    460       378
4         41.53         0.517      10031    0.037    1288      361
5         41.97         0.534       6714    0.053    598       361
6         45.97         0.701       4913    0.062    276       192
7         46.17         0.709      37345    0.007    483       263
1         46.26         0.714       8436    0.029    2438      259
2         47.95         0.794       9417    0.029    4278      304
3         49.67         0.882       7633    0.032    2406      216
4         48.83         0.839       1067    0.104     92       83
5         45.02         0.658       437     0.185    749       233
6         48.91         0.842       6428    0.031    699       211
7         47.11         0.753       8741    0.025    845       226
8         51.84         1.002       4506    0.042    311       188

                                 Cover

Haul   Av. length    Av. weight    Catch       p2        q
          (cm)          (kg)        (n)

1         36.71         0.358       1284     0.349     0.146
2         35.75         0.331       1944     0.237     0.354
3         36.37         0.348       1319     0.286     0.520
4         35.67         0.329       3914     0.092     0.402
5         34.49         0.297       2007     0.179     0.296
6         40.92         0.495       557      0.344     0.180
7         40.52         0.481       1004     0.261     0.026
1         38.89         0.425       5724     0.045     0.644
2         38.31         0.407      10507     0.028     1.035
3         44.38         0.631       3812     0.056     0.571
4         45.18         0.665       138      0.601     0.173
5         36.63         0.356       2103     0.109     1.681
6         40.72         0.488       1432     0.147     0.210
7         40.12         0.467       1809     0.124     0.201
8         45.27         0.669       465      0.404     0.103

Tabla 2. Analisis de la selectividad de la merluza chilena por
redes de arrastre de fondo. Estimados del modelo SELECT de los
parametros de seleccion ([v.sub.1]* and [v.sub.2]) para cada lance.
Se presenta tambien la variacion intra lance, los estadisticos
de bondad de ajuste, la curva media estimada usando variacion entre
lances (Fryer, 1991) y los estimados de [l.sub.50] y rango de
seleccion (SR).

Table 2. Analysis of the Chilean hake selectivity by bottom trawls.
The SELECT (Share Each Length Catch Total) model estimates of the
selection parameters ([v.sub.1]* and [v.sub.2]) for each haul. The
within-haul variance, goodness of fit statistics, mean curve
estimated by using between-haul variation (Fryer, 1991).
Estimates of [l.sub.50] and selection range (SR) are also given.

Haul        Mesh   [v.sub   [v.sub     var       var       var
            size    .1]      .2]     ([v.sub   ([v.sub    ([v.sub
                                      .1])     .1] x [v.   .2])
                                                sub.2)

1           100    -12.96    0.36     2.8528   -0.0685    0.0017
2           100     -6.73    0.24     2.4762   -0.0601    0.0015
3           100    -11.73    0.38     5.8228   -0.1398    0.0034
4           100     -8.94    0.28     3.5168   -0.0788    0.0018
5           100     -9.56    0.30     2.6499   -0.0681    0.0018
6           100    -12.70    0.40     3.2103   -0.0832    0.0022
7           100     -8.09    0.29     0.7791   -0.0203    0.0005
8           100     -9.12    0.35     1.8463   -0.0504    0.0014
9           100    -12.80    0.37     9.9798   -0.2283    0.0053
Mean                -9.75    0.32     2.2042   -0.0361    0.0009
  curve
  (Fryer)

1           110    -13.43    0.44     7.4438   -0.1995    0.0054
2           110     -6.96    0.20     0.7907   -0.0201    0.0005
3           110     -6.15    0.26     2.2284   -0.0618    0.0017
4           110     -7.07    0.31     3.4963   -0.0882    0.0023
5           110    -12.43    0.37     0.7251   -0.0194    0.0005
6           110     -4.47    0.18     0.6554   -0.0146    0.0003
7           110    -12.46    0.36     1.7202   -0.0419    0.0011
8           110    -12.32    0.38     4.7162   -0.1173    0.0030
Mean                -9.07    0.30    10.6178   -0.2463    0.0069
  curve
  (Fryer)

1           130     -5.47    0.19     0.4096   -0.0104    0.0003
2           130     -5.86    0.19     0.4315   -0.0115    0.0003
3           130     -3.14    0.11     0.3357   -0.0089    0.0002
4           130     -7.61    0.22     0.6221   -0.0164    0.0004
5           130     -8.67    0.26     0.6926   -0.0187    0.0005
6           130     -3.60    0.13     0.6452   -0.0145    0.0003
7           130     -4.29    0.18     0.7302   -0.0164    0.0004
Mean                -5.53    0.18     3.5308   -0.0858    0.0023
  curve
  (Fryer)

1           140     -7.08    0.18     0.5382   -0.0127    0.0003
2           140    -13.76    0.32     1.1333   -0.0270    0.0007
3           140    -11.04    0.25     1.7664   -0.0377    0.0008
4           140     -6.16    0.17     3.7661   -0.0797    0.0017
5           140    -12.21    0.27     1.5847   -0.0392    0.0010
6           140    -12.83    0.32     1.8690   -0.0410    0.0009
7           140     -8.26    0.23     0.9884   -0.0224    0.0005
8           140    -17.13    0.40     5.2595   -0.1082    0.0022
Mean               -10.96    0.27    10.2228   -0.2080    0.0044
  curve
  (Fryer)

Haul        Deviance  dof   P-value   [l.sub    SR
                                       .50]

1            23.37    39     0.98     35.62     6.04
2            24.08    33     0.87     27.56     9.00
3            25.60    45     0.99     31.27     5.86
4            28.61    39     0.89     31.52     7.74
5            28.11    35     0.79     32.11     7.38
6            19.75    36     0.99     31.50     5.45
7            22.90    39     0.98     28.37     7.70
8            15.78    33     1.00     26.39     6.36
9            20.03    20     0.46     34.55     5.93
Mean                                  30.79     6.94
  curve
  (Fryer)

1            33.83    25     0.11     30.43     4.98
2            41.06    32     0.13     35.36    11.16
3            20.66    37     0.99     23.60     8.43
4            18.33    40     1.00     22.97     7.14
5            42.33    45     0.59     33.45     5.92
6            30.05    45     0.96     24.25    11.92
7            19.55    43     1.00     34.60     6.10
8            18.22    41     1.00     32.61     5.82
Mean                                  29.90     7.24
  curve
  (Fryer)

1             9.19    35     1.00     28.95    11.63
2            32.11    34     0.56     30.99    11.61
3            38.94    35     0.30     27.89    19.53
4            30.96    36     0.71     33.98     9.81
5            24.25    39     0.97     32.85     8.33
6            35.06    33     0.37     27.29    16.67
7            15.72    30     0.99     23.71    12.15
Mean                                  30.00    11.92
  curve
  (Fryer)

1            16.40    35     1.00     39.91    12.38
2            21.72    38     0.98     42.44     6.78
3            21.09    35     0.97     43.99     8.76
4            15.64    24     0.90     35.27    12.58
5            35.17    27     0.13     45.60     8.20
6            29.24    34     0.70     40.10     6.87
7            22.55    33     0.91     36.50     9.71
8            15.10    35     1.00     42.78     5.49
Mean                                  41.20     8.26
  curve
  (Fryer)

Tabla 3. Analisis de la selectividad de la merluza chilena
por redes de arrastre de fondo. Contribucion de variables
explicatorias en los parametros de seleccion; estimados
del parametro alpha, desviacion estandar, valor t, grados de
libertad (dof) y valor P.

Table 3. Analysis of the Chilean hake selectivity by
bottom trawls. Contribution of explanatory variables on the selection
parameters; alpha parameter estimates, standard deviation,
t-value, degrees of freedom (dof) and P-value.

Parameter     Estimate     Standard      t-value   dof   P-value
                           deviation

[alfa.sub.1]  -13.970      2.098         -6.66     56    <0.001
([v.sub.1],
intcpt)

[alfa.sub.2]  4.886 x      3.219 x       15.18     56    <0.001
([v.sub.2],   [10.sup.-1]  [10.sup.-2]
intcpt)

[alfa.sub.3]  5.713 x      2.145 x       2.66      56    0.010
([v.sub.1],   [10.sup.-5]  [10.sup.-5]
catch)

[alfa.sub.4]  1.363        5.843 x       2.33      56    0.023
([v.sup.1],                [10.sup.-1]
speed)

[alfa.sub.5]  -1.850 x     2.401 x       -7.72     56    <0.001
([v.sub.2],   [10.sup.-3   [10.sup.-4]
mesh size)
COPYRIGHT 2012 Pontificia Universidad Catolica de Valparaiso, Escuela de Ciencias del Mar
No portion of this article can be reproduced without the express written permission from the copyright holder.
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Article Details
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Title Annotation:merluza, estimacion de la selectividad, lances
Author:Queirolo, Dante; Ahumada, Mauricio; Hurtado, Carlos F.; Soriguer, Milagrosa C.; Erzini, Karim
Publication:Latin American Journal of Aquatic Research
Date:Jul 1, 2012
Words:6625
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