We used the FISHSELECT methodology to predict size selection of European hake (henceforth hake) for a wide range of mesh configurations through simulations following Herrmann et al. (2009) and Tokaç et al. (2016). The FISHSELECT software can be obtained from the first author of Herrmann et al. (2009). To evaluate the validity of the results, we compared them with experimental selectivity results from sea trials. Table 1 and 2 summarizes hake experimental selectivity results for diamond mesh (D) and square mesh (S) codends in bottom trawl fisheries. In addition, we used selectivity estimates obtained with the predictive model of Sala and Lucchetti (2011) based on their experimental data. We quantify codend size selectivity for hake by two parameters: L50, the length of hake with a 50% probability of being retained given that they enter the codend; and selection range (SR), the difference in the lengths of fish having 75% and 25% probability of being retained (Wileman et al. 1996).

Individual hake were caught by trawling on daily cruises in the Aegean Sea (İzmir Bay) in September 2014 using the research vessel R/V EGESÜF. Several short 20- to 30-minute tows at 30-50 m depth were conducted and individual fish were kept alive in holding tanks until the FISHSELECT measurements were taken (following Herrmann et al. 2009 and Krag et al. 2011). Hake are fragile compared with other species and were therefore transferred to the holding tanks on land, and measurements of the individuals were conducted as quickly as possible thereafter. Holding tanks helped keep the fish alive so that each individual was as fresh as possible when measurements were taken. To obtain the correct morphometric measures for each fish using FISHSELECT, it is very important that the shape of the fish measured is not affected by dehydration, depressurization, rigor mortis, or any other factor that could alter the original shape (Sistiaga et al. 2011). Hake is a physoclistous species. Individuals with overinflated swim bladders, commonly observed when caught in trawl, had difficulties obtaining normal swimming behaviour in the on-board holding tanks, and gently had their swim bladder punctured using a syringe. About 200 individuals were transferred to holding tanks on land, and 74 individuals ranging from 15 to 66 cm in length with all length classes being represented by between one and eight individuals were selected and used in the subsequent FISHSELECT experiments. The 74 hake were selected to cover as wide a length interval as possible and with an approximately uniform size distribution in order to subsequently be able to make predictions for size selection of hake for a wide range of mesh size and shapes based on the collected information.

The FISHSELECT methodology is based on establishing descriptions of the significant cross-section shapes determining size selection for the given species. We first determined the most relevant cross-section for mesh penetration for hake. The morphological measurements of four hake were thoroughly examined during an initial laboratory experiment. Extensive cross-section measures on these individuals, combined with fall-through trials, revealed three cross-sections to be potentially critical for mesh penetration (Fig. 1). CS1 represents the widest bony part of the fish’s head. CS2 is larger but more compressible than CS1 and is positioned at the posterior end of the opercula. CS3 is the largest, but most compressible cross-section of the three and represents the maximum girth of the fish, i.e. stomach girth. The cross-sectional morphology was measured for each fish using a morphometer (Herrmann et al. 2009) (Fig. 2A, B) and the shapes formed by the morphometer were scanned and converted into digital images using a flatbed scanner (Fig. 2C, D). The outlines of the cross-sections were modelled using four different parametric models: ellipse, flexellipse 1, flexdrope and superdrope [see Appendix A in Tokaç et al. (2016)]. The ellipse is fully described by two parameters, c₁ and c₂, while each of the three other shapes requires an additional parameter, c₃ [see Appendix A in Tokaç et al. (2016) for a mathematical description of the shapes]. The Akaike information criterion (AIC) (Akaike 1974) and R² were calculated for each individual for each of the four models for CS1, CS2 and CS3 [see Appendix A in Tokaç et al. (2016) for details].

The shape model with the lowest mean AIC value was chosen to describe each of the three cross-sections individually. The mean R² value was applied to judge how well the selected models described the cross-section shapes on average. When the best shape models had been chosen for CS1, CS2 and CS3, the parameters describing these shapes (c₁, c₂, and c₃) were related to total fish length and these functions were used to simulate the cross-sections (CS1, CS2 and CS3) for a virtual population of 5000 individuals with uniform length distributed between 1 and 90 cm to be subsequently used in the simulation of size selection.

After measuring fish morphology, we conducted fall-through experiments in order to examine and quantify potential compression of the measured cross-sections during a mesh penetration. A total of 478 stiff mesh templates, including diamond, square, rectangular, and hexagonal meshes with different mesh sizes and OAs were made with 5-mm-thick nylon plates (see Tokaç et al. 2016). In the fall-through trials, each fish was held by the tail and lowered vertically head-first and with optimal orientation for penetration into each of the 478 stiff mesh templates, and the results in terms of penetration (yes or no) were recorded. We used the pull of gravity as a proxy for fish swimming ability during mesh penetration, following Krag et al. (2011), as shown in Figure 3. A total of 35372 fall-through trials were carried out (74 fish × 478 mesh templates).

The cross-section shape and its compressibility will determine whether or not a fish will be able to pass through a mesh. The penetration models implemented in FISHSELECT simulate the compressibility of the fish for each measured cross-section. An initial inspection of the deformability of hake carried out by simply squeezing the tissue of a few individuals by hand revealed that the dorsal and the ventral compressibilities of the species are not symmetric. Therefore, we applied a penetration model which allows asymmetrical compression. This model, previously used for redfish (Sebastes spp.) by Herrmann et al. (2012) and for red mullet (Mulllus barbatus) by Tokaç et al. (2016), included the estimation of three parameters representing the dorsal, lateral and ventral compressibility of the fish. To establish an optimal penetration model for hake, each CS1, CS2 and CS3 individually and combined was tested with compression models with different assumed values for the dorsal, lateral and ventral compression. Thus, we simulated the penetration of the modelled CS1, CS2 and CS3 shapes of each fish through the 478 different mesh templates included in the fall-through trials using the FISHSELECT software. Models considering one cross-section at a time were created, where the dorsal, lateral and ventral compression were varied independently from 0% to 32% in 2% and 4% increments. This made 216 penetration models for each CS1 and CS2, 324 penetration models for CS3, and 15116544 combined models. Finally, we compared the results obtained from all the different penetration models with the experimental fall-through results using the FISHSELECT software. The evaluation was based on the degree of agreement value (DA-value) for the different models. The DA-value expresses the percentage of the fall-through results where the simulated result from FISHSELECT was the same as that obtained experimentally (“yes” or “no”).

We needed an appropriate description of how the meshes in diamond and square mesh codends would behave during fishing in order to predict size selection of hake in codends relevant to the bottom trawl fishery.

For the diamond mesh codends, we assumed that because none of the mesh bars is perpendicular to the towing direction, there would be tension in all the four mesh bars of a diamond mesh during the fishing process (Krag et al. 2011, Herrmann et al. 2012, Tokaç et al. 2016). Further, we assumed that the diamond meshes will remain diamond-shaped and the mesh openness will not change when a hake attempts to escape through the mesh.

For square mesh codends, the circumferential mesh bars are perpendicular to the towing direction during fishing, which implies that these mesh bars are not under tension. For partly open square meshes we used the model established in Krag et al. (2011), assuming that the fish can bend or distort the circumferential mesh bars outwards during an escape attempt as these mesh bars are not under tension. Krag et al. (2011) approximated this situation with the hexagonal mesh description. Definitions of OAs for diamond and square meshes are completely different. One is an angle between adjacent bars; the other is the angle through which a single bar is distorted. Two related measures are applied to describe the openness of a diamond mesh and a hexagonal modelled distorted square mesh. These are the OA and the relative openness (OP), which quantifies the circumferential opening of the mesh relative to the longitudinal opening. More detailed information and a diagram regarding the definition of OA for a diamond mesh and a hexagonally distorted square mesh can be found in Tokaç et al. 2016.

To predict size selection of hake in diamond and square mesh codends, the population of 5000 virtual fish was simulated with a total of 528 diamond meshes of 40 to 100 mm mesh size ranging from 10° to 90° OAs and 1085 hexagonally distorted square meshes of 40 to 100 mm mesh size with 10° to 180° OAs using the FISHSELECT software. We followed the same protocol as that described by Tokaç et al. 2016 for the modelling of mesh shapes of diamond-and square-mesh codends during fishing.

Sala and Lucchetti (2011) established an empirical model based on experimental data describing the effect of number of meshes in the circumference of the codend for hake. They found that values of L50 tend to decrease if the number of meshes in circumference in the codend increase, in agreement with the theoretical findings in Herrmann et al. (2007). From a mechanical point of view, the mechanism can be explained if we assume that the codend diameter is nearly independent of the number of meshes in circumference. This assumption implies that the OA value tends to decrease with an increasing number of meshes around (n). To investigate this in more detail, we plotted L50 values estimated from the model of Sala and Lucchetti (2011) for a codend mesh size of 50 mm for the number of meshes in the circumference equal to 240, 260, 280, 300 and 320. Then, based on FISHSELECT, we determined the extent to which we obtained a similar pattern for the L50 values assuming that OA is a specific decreasing function of n. A detailed explanation of the steps needed to apply the model to be used in the investigation of this effect can be found in Tokaç et al. 2016.

Based on AIC values (Table 3), the flexellipse1 model was chosen to model CS1 and CS3 while the flexdrope was chosen to model CS2. The mean R² values indicate that the cross-section shapes were well described by these models. Table 4 contains the values for the parameters describing CS1, CS2 and CS3 as a function of the length for hake.

Based on the results from the 35372 fall-through trials, we selected a penetration model (compression model) to use for simulating size selection of hake. CS1 gave a DA value at 97.67% which was the highest. This result indicates that CS1 to a large extent determines the morphological limits for size selectivity for hake. We also tested combined models, CS1-CS2 and CS1-CS3, to find the best model, and they resulted in a DA value of 97.70% and 97.62%, respectively. Although the CS1-CS2 combined model gave a marginally higher DA value than CS1, we decided to use the CS1 single model as a best model for the predictions. The left panel of Figure 4 illustrates the fits of CS1 to the cross-section of a hake. The compressibility for this model of CS1 was 8% lateral, 0% dorsal and 0% ventral. The right panel of Figure 4 illustrates the selected penetration model where the red (outer) curve represents the uncompressed fish and the green (inner) curve the maximal compressibility of a hake during a mesh penetration.

We compared our FISHSELECT-based simulations of the selectivity of diamond meshes with experimental results for diamond mesh codends (Table 1). It is clearly seen in Figure 5 that the Italian data are different from the other experimental results. To show this difference more clearly, we plotted five linear trend lines with a 5° increment between the minimum (OA 20°) and maximum (OA 40°) L50 values for mesh sizes ranging from 40 to 100 mm (Fig. 5). The exception is the Italian estimates (Lucchetti 2008, Sala and Lucchetti 2010, 2011) which generally report lower selectivity, suggesting a lower and narrower OA range (20° to 30°) in the codend (Fig. 5). As a general result, the range of FISHSELECT predictions represents the experimental data fairly well, and most experimental results correspond to the size selection in diamond meshes with OAs of between 20° and 40° (Fig. 5). We will therefore use this range to predict the expected size selection in diamond mesh codends for hake.

For square meshes we simulated the size selection for meshes between 40 and 100 mm. We plot these FISHSELECT predictions (Fig. 6) against experimentally obtained historical data in Table 2. The few available experimental results show that the experimental L50 values mostly correspond to those of meshes that are far from fully open. We see from Figure 6 that the FISHSELECT predictions represent the experimental square mesh codend selectivity data well for OAs between 70° and 120°, and we therefore use this range for comparison with diamond mesh codend size selection, as seen in Figure 8. FISHSELECT values for OA=180° represent a mesh that is fully open in Figure 6.

L50 values for a diamond mesh codend depend on the mesh OA. To investigate this, we plotted L50 values for 240, 260, 280, 300 and 320 meshes in the codend circumference based on the model of Sala and Lucchetti (2011) for a codend mesh size of 50 mm. These values were plotted against values obtained from FISHSELECT simulations and compared for similarity. Figure 7 compares the results from the model of Sala and Lucchetti (2011) for 240, 260, 280, 300 and 320 meshes around the codend (squares) with those obtained from FISHSELECT (curve), which are represented by black diamonds. The black square corresponds to the result for 280 meshes in circumference, which has been applied to find the expected codend diameter. The unfilled squares are then placed according to the calculated OA, assuming that codend diameter is constant over this range of meshes around the circumference. We are now able to model and predict the effect of number of meshes in the codend circumference for hake size selection in diamond mesh codends.

When comparing FISHSELECT results with diamond and square mesh codend experimental results, we assumed the most suitable OA to be between 20° and 40° in diamond mesh codends and 70° and 120° in square mesh codends for prediction of the size selection of hake. For these ranges, we plotted the minimum and maximum L50 values predicted by FISHSELECT for mesh sizes ranging from 40 to 100 mm. We considered a fully open square mesh codend as the most likely mean situation and therefore also plotted FISHSELECT predictions based on OA=180° (Fig. 8). It is clearly seen in Figure 8 that square mesh codends in practice are more size-selective for hake than diamond mesh codends, simply because the square meshes are closer to being fully open during fishing than the diamond meshes. This is illustrated by Figure 8, which shows that the square mesh has an expected L50 range closer to that of the 100% open mesh than the diamond mesh.

The size selection predicted by FISHSELECT can be applied to produce design guides in the form of iso-curves for L50 values dependent on mesh size and mesh OAs. Figure 9 shows design guides for both diamond meshes and hexagonally distorted square meshes. For example, for diamond mesh sizes of 40, 44 and 50 mm for OAs fixed between 20° and 40°, L50s are predicted to be between 7.8 and 12.8 cm, 8.2 and 14.0 cm and 9.4 and 15.8 cm, respectively. The results demonstrate that for diamond meshes used in demersal trawl codends L50 increases with increasing mesh size and OA value. We used OAs fixed at 20° and 40° to predict the expected size selection in diamond mesh codends for hake because most experimental results corresponded to the size selection L50 parameters between these ranges of OAs.

From this design guide, we also see that for 40-mm square mesh sizes and OAs between 70° and 120°, L50s are predicted to range from 12 to 17.7 cm (Fig. 9). The design guides also show that L50 varies considerably with OA for a given mesh size. Figure 9 illustrates that much higher L50 can be obtained especially for square mesh codends if the mesh OA can be controlled.