Trawls are one of the most widely used fishing gears around the world. They have been adapted to many fisheries, and are capable of being towed on many types of seabed and in the most difficult of weather conditions. As a result, they and more specifically their selectivity are among the most commonly investigated fields within fisheries technology. A variety of experimental methodologies have been developed for carrying out selectivity experiments, the main ones being the covered codend and paired gear methods (Wileman et al. 1996). In the covered codend method, fish escaping from the gear are retained in one or more small mesh covers and hence an accurate estimate of the fish that entered the gear can be made. The twin trawl, trouser trawl, parallel haul and alternate haul methods are classified by Wileman et al. (1996) as paired gear methods. In these methods an estimate of the population fished is obtained from a small mesh control gear that is either towed simultaneously on one side of the twin/trouser trawl or from a different vessel (parallel), or towed consecutively from the same vessel which alternates test and control gears. A range of statistical methods have been developed to analyse the data collected during these experiments and to estimate the selective properties of the gears tested (Millar and Fryer 1999). Carrying out these studies at sea is challenging because of operational, environmental and biological factors which are difficult, if not impossible, to control. Consequently, repeat tows generally have large amounts of between-haul variation, which must be accounted for to avoid making incorrect inferences about the selection of the gear (Fryer 1991).

For scientific or operational reasons, it may not always be possible to use the covered codend or any of the above paired gear methods to estimate selectivity. There are, for instance, fisheries where the presence of small mesh covers may influence the fishing performance of the gear (by modifying hydrodynamic conditions or by altering fish behaviour); it may be difficult to deal with two codends on deck simultaneously (twin/trouser trawl); financial or economic considerations may preclude the use of two vessels (parallel haul); and difficulties and/or time constraints associated with repeated converting of a trawl from test to control may preclude the use of alternate hauls.

Under these circumstances, the most practicable and pragmatic way forward may be to first carry out a number of test hauls and then to carry out a number of control hauls. However, this leads to problems in analysing the subsequent data, as there is no obvious way of pairing the individual test and control hauls. Accordingly, alternative statistical methods must be explored. Here, to address this problem, we combine the test and the control hauls to produce two pooled data sets, from which we estimate the selectivity of the test gear. We then estimate the variance of the corresponding selection parameters by applying a double bootstrapping approach to account for both within-haul and between-haul variation.

We illustrate this approach by applying it to data from selectivity trials in the Barents Sea cod (Gadus morhua) fishery using pelagic trawls with T90 codends or exit windows (EWs). Pelagic trawling is one of the most efficient fishing methods to catch cod at certain times of the year because the species concentrates itself in dense schools in the water column. Although the fishery was banned in the late 1970s, owing to the high percentage of juveniles caught, in recent years a number of vessels have received special permits to exploit it again. At present, these vessels have to use three different types of grids combined with a 130 mm codend (Herrmann et al. 2013a). There are, however, concerns that, at high entry densities, fish accumulate in front of and behind these grids, blocking the passage to the codend, and hence a desire to test the selectivity of T90 codends and EWs which have proved effective in demersal cod trawls (Grimaldo et al. 2007).

The dimensions of the gears, their catch sizes (which are often >30 t) and space limitations on deck precluded the use of the covered codend or twin/trouser trawl methods, and the fact that the trials were carried out under commercial conditions prevented the use of the alternate haul method. From an operational point of view, the practicable way forward was to carry out a number of consecutive tows with the test codend followed by a number of consecutive tows with the small mesh control codend. As set out above, this leads to a situation in which there is no obvious way of pairing the individual test and control hauls. Thus, it precludes the use of the traditional paired gear statistical methodologies and necessitates the development of alternative approaches of the type we introduce here.

A total of 9 test hauls and 13 control hauls were carried out with the two tested devices. Catch rates were high, with rates >3000 kg h^–1 in 21 out of the 22 hauls, up to a maximum of 125009 kg h^–1. As a result, all the hauls needed to be subsampled and sampling factors ranged from 0.066 to 0.378. An overview of haul information is given in Table 1.

Of the 9 test hauls, 5 were carried out with the EW codend and 4 with the T90 codend. Table 1 presents the hauls in chronological order and highlights that there is no obvious way of pairing the test and control hauls. Hence, the relevant data were pooled and the mean selectivity parameters for each of the four selectivity curves were calculated for both test gears. The analysis was carried out using the analysis tool SELNET (Herrmann et al. 2012), which implements the method described in the data analysis section. All models considered resulted in deviance >DOF but, since the corresponding residuals showed no defined patterns, it was considered caused by overdispersion in the data (Wileman et al. 1996). Model selection was therefore based on the QAIC. The Probit and the Richard models respectively had the lowest QAIC values for the EW codend and the T90 codend data (Table 2). Table 3 and Figure 2A-C document the fit for the selected models.

The mean L50 and SR values were 59.54 and 15.07 cm for the EW codend and 51.55 and 6.56 cm for the T90 codend (Table 3). There were no significant differences (at the 95% level) between the mean L50 values of the two test gears, but there was a significant difference between their mean SR values. Furthermore, as shown in Figure 2C, the EW codend was significantly more selective for fish in the length range ~55-76 cm.

In this study, we present a methodology for analysing unpaired test and control selectivity data. We have developed a double bootstrapping approach to calculate the mean selectivity parameters and their 95% confidence ranges. This approach permits us to analyse selectivity data from fisheries, where for scientific or operational reasons it may be difficult to use the covered codend or any of the paired gear methods described in the introduction. There may also be circumstances in which, although a paired method may have been used, there is uncertainty regarding the validity of the assumption that similar populations enter the gear at the paired haul level. As long as it can be assumed that, on average, over the course of an experimental trip, similar populations enter the test and control gears, the approach described here may be preferable and provide more realistic estimates of the confidence intervals of the selectivity parameters. This is particularly the case for alternate haul methods applied to fisheries such as Danish/Scottish seining, in which there is likely to be both temporal and spatial differences between hauls/shots.

We demonstrate this approach by applying it to data from selectivity trials in the Barents Sea pelagic trawl cod fishery. We show that the mean L50 and SR values are 59.5 and 15.1 cm for the EW codend and 51.6 and 6.6 cm for the T90 codend (Table 3). We can compare these results with those of some previous studies for similar gears on demersal trawls. Grimaldo et al. (2007) tested EWs with mesh sizes of 128, 132 and 153 mm, and obtained L50 values of 53.6, 56.4 and 57.3 cm, respectively, while, Grimaldo et al. (2008) found that another 128 mm EW had a mean L50 of 53.9 cm. In terms of their selection factor (L50/mesh size), these results are respectively 0.42, 0.43, 0.37 and 0.42, which compare extremely well with the 0.42 of our trials. The corresponding SRs were respectively 9.3, 8.0, 6.8 and 8.5 cm, which are lower than the results obtained in our trials. Our selectivity results are obtained based on fishing trials consisting of only 22 hauls: 5 hauls with the EW codend, 4 with the T90 codend and 13 with the control codend. This limited number of hauls affects the uncertainty of the results presented, and therefore they need to be interpreted with care. However, the method presented accounts correctly for the uncertainty in the results caused by the limited dataset. This limitation is reflected in the confidence bands of the size selection curves and parameters that are provided together with the results (Table 3, Fig. 2). Therefore, as long as these confidence bands are considered when making conclusions, the limited number of hauls in the study should not be a major concern.

Herrmann et al. (2013b) tested the performance of a 124.4 mm mesh size T90 codend built with 8-mm PE twine in the Baltic and obtained a mean L50 value of 38.90 cm, while Wienbeck et al. (2013) found that a 126-mm T90 codend had a mean L50 of 43.4 cm. These sets of results give a selection factor of 0.31 and 0.34 respectively, which again correspond well with the 0.37 of the trials reported here. The SRs estimated in these two studies were respectively 5.01 and 6.7 cm, which correspond well with that obtained in our study (Table 3).

One of the objectives of this study was to investigate whether the grid systems being used in the Barents Sea cod fishery can be replaced by alternative selective gears. The minimum target size for cod in the Barents Sea is 44 cm and no more than 15% of the catch (by number) can be made up of undersized fish. Thus, an optimal selection device for this fishery should provide a sharp selection profile just above 44 cm so that the majority of fish above 44 cm would be retained and the majority below would be released from the gear. Sistiaga et al. (2010) have shown that a 55-mm Sort-V grid combined with diamond mesh codends had L50 values in the range 51.6-55.9 cm, which are not significantly different from the results we have here for either the EW or T90 gears (at the 95% level). There is, however, a significant difference between the mean SR values of these two gears and, as shown in Figure 2C, the T90 codend is closer to the 44 cm minimum landing size and retains significantly more fish in the length range 55-76 cm. Based on these results, this study suggests that from the fishers point of view the T90 codend is perhaps a more acceptable alternative device than that with the EW. We must be cautious, however, in drawing this conclusion, because the results are based on very few hauls and, as described above, the average catch rate observed for the test hauls carried out with the codend with the EWs was 13500 kg h^–1, whereas the average catch rate observed when testing the T90 codend was 6600 kg h^–1 (Table 1). These differences in the entry rate are substantial and may have contributed to the significant differences in SR estimated between the systems. In addition, the SR estimates for the EW codend are high when compared with other studies.

The analysis approach in this study provides an assessment of the average size selectivity of a group of hauls carried out with a specific test gear. This is what Millar et al. (2004) named a fishery selectivity curve. The approach of estimating a fishery selectivity curve based on a group of hauls has been applied in several recent trawl selectivity studies (Brčić et al. 2015, Herrmann et al. 2015, Özbilgin et al. 2015, Sala et al. 2015, Sistiaga et al. 2015, Lövgren et al. 2016). However, all these studies were based on covered or paired data collection, and the bootstrapping method applied to account for the uncertainty in the results is different from the one described in this study. Furthermore, the analysis carried out in all these other studies would not allow the uncertainty due to the unpaired nature of the data collection to be incorporated in the results. As long as we consider correctly the confidence limits obtained using the unpaired analysis method, the results and the fishery selectivity curves estimated with the method presented here would not be significantly biased compared with the results that would have been obtained with a paired data collection method. This is so because both approaches estimate the selectivity curves and parameters based on pooling data over hauls. The main difference is that only the unpaired analysis method is able to account correctly for the increased uncertainty in the results caused by the unpaired nature of the data collection process. Since the analysis is made at haul group level and not at individual haul level, the analysis method described does not account for the potential effect of uncontrolled variables (e.g. codend catch size) between hauls. However, this is not a problem for the assessment of size selectivity as long as these uncontrolled parameters vary between hauls in the same way as they vary in the commercial fishery.

The unpaired analysis approach described is here applied to estimate the size selectivity in the aft part of a pelagic trawl. However, this approach can also be applied to quantify other aspects of the catch performance of a fishing gear while accounting correctly for the uncertainties resulting from using an unpaired data collection method. Specifically, Sistiaga et al. (2015 and 2016) used the unpaired analysis approach to investigate the effect of lifting the sweeps of a trawl from the seabed on the catch performance of respectively cod and haddock. Further, Notti et al. (2016) applied the unpaired analysis approach to investigate the relative catch performance of a surrounding net without the purse line in the Mediterranean Sea. However, the current study is the first in which the unpaired analysis approach has been developed and adopted to study size selectivity in the aft of a trawl gear.