Stock assessment and management implications of sailfin sandfish (Arctoscopus japonicus) caught by multiple fishing gears with different selectivity in Korean waters

Selectivity and age at capture by fishing gears

The main sailfin sandfish fisheries analyzed in this study are the East Sea mid-sized Danish seine (DS) and coastal gillnet (GN) fisheries, which have different fishing selectivities owing to their different fishing gear and fishing methods. As illustrated in Fig. 2, the selectivity of the DS fishery follows the sigmoid curve of a cumulative normal distribution, whereas that of the GN fishery follows a bell-shaped normal distribution curve (Jones, 1963; Holt, 1963).

The age at which the fish enter the fishing ground (t_r) is the same for both fishing gear types. The probability of a fish being caught in fishing gear after t_r depends on the size (or age) of the fish. Even among fish of the same size, selectivity differs based on the specific characteristics of each gear (e.g., fishing method and mesh size).

In the case of sailfin sandfish (Fig. 2), the age at first capture (t_c), which corresponds to 50% of the selection ratio, occurs in t_cDS for the DS fishery and t_cGN for the GN fishery. After t_cDS, the rate of increase in the selection ratio with age gradually decreases in the DS fishery, as illustrated by the sigmoid curve in Fig. 2A. The selection ratio converges upon reaching a size corresponding to 100%, at which point all individuals exceeding this size are captured by the fishing gear. In other words, fish subject to fishing ranged from their age at first capture (t_c) to their maximum age (t_L).

Conversely, in the GN fishery, similar to the DS fishery, the rate of increase in the selection ratio after t_cGN decreases until it reaches the age of 100% (t_mGN), as illustrated by the bell-shaped curve in Fig. 2B. In contrast to the DS fishery, the selection ratio decreases to another 50% and continues to decrease thereafter. Two ages corresponded to a selection ratio of 50%: the age at which the catch starts (t_cGN) on the left and the age at which the catch ends (t_eGN) on the right (Fig. 2B). Therefore, t_e in the GN fishery is the same concept as t_L in the DS fishery, both representing the age at which fishing ends.

Models assessing yield per recruit and spawning biomass per recruit across multiple fishing gear

The single-gear YPR model developed by Beverton & Holt (1957) was modified into a multi-gear YPR model, as presented in Eq. (1). This multi-gear YPR model was applied to fish species captured using multiple fishing gears. To accurately reflect the characteristics of each fishing gear, as explained above, t_L was substituted with the age at last capture t_ei for each fishery. Additionally, the instantaneous fishing mortality was weighted (w_i) by the catch for each fishery to reflect the fishing mortality caused by each fishery. (1)${\displaystyle Multi-gear\frac{Y}{R}=\sum _{i=1}^g\left[w_i\cdot F\cdot exp\left\{-M\left(t_{c_i}-t_r\right)\right\}\cdot W_{\infty }\sum _{n=0}^3\frac{U_{n\cdot }exp\left\{-n\cdot K\left(t_{c_i}-t_0\right)\right\}}{F+M+n\cdot K}\cdot \left(1-exp\left\{-\left(F+M+n\cdot K\right)\left(t_{e_i}-t_{c_i}\right)\right\}\right)\right]}$ where g is the number of fishing gear (fishery); t_ci is the age at the first capture of gear i; t_ei is the age at the last capture of gear i; and F is the instantaneous fishing mortality. Furthermore, w_i is the weighting factor of the instantaneous fishing mortality for each gear ($=C_i/{\sum }_{i=1}^g{C}_i$); and C_i is the catch of gear i (where the w_i of DS and GN is w₁ = 0.59 and w₂ = 0.41, respectively), and the sum is 1. In addition, t_r is the age at recruitment to the fishing ground; M is the instantaneous natural mortality; W_∞ is the theoretical maximum weight; K is the growth coefficient; and t₀ is the theoretical age when the length is zero. These parameters are the same as those of the traditional YPR model.

This multi-gear YPR model has the same assumptions as those of the traditional model (Beverton & Holt, 1957). However, the assumption that after the age at first capture all fish coming into contact with fishing gear have an equal probability of capture is invalid in the multi-gear model because the selectivity by the GN fishery has different capture probabilities by age.

The multi-gear SBPR model considered the selection ratio of each fishing gear within the age-specific selection ratio of the traditional SBPR model (Zhang, 2010), which did not account for the selection ratio for individual fishing gears. The instantaneous fishing mortality of each fishing gear was weighted, as shown in Eq. (1). The model is expressed in Eq. (2). (2)${\displaystyle Multi-gear\frac{SB}{R}\left(\text{\%}\right)=\frac{m_0\cdot {\left\{1-e^{K{t}_0}\right\}}^3\cdot N_0+\sum _{t=1}^{t_{\lambda }}{m}_t\cdot {\left\{1-e^{-K\left(t-t_0\right)}\right\}}^3\cdot N_{t-1}\cdot e^{-\left(M+\sum _{i=1}^g{w}_i\cdot F\cdot S{\left(t-1\right)}_i\right)}}{m_0\cdot {\left\{1-e^{K{t}_0}\right\}}^3\cdot N_0+\sum _{t=1}^{t_{\lambda }}{m}_t\cdot {\left\{1-e^{-K\left(t-t_0\right)}\right\}}^3\cdot N_{t-1}\cdot e^{-M}}\times 100}$ where N_t is the population size at age t (where, N₀ = 1); m_t is the maturity ratio at age t (m₀ is the maturity ratio at age 0): Added m₀ for clarity since m₀ is in the formula; S(t)_i is the selection ratio at age t for the fishing gear i; t_λ is longevity; and the remaining parameters are consistent with those in Eq. (1).

Model parameters

The ecological characteristics of the sailfin sandfish used in the YPR and SBPR models were based on the results of previous studies. The parameters are listed in Table 1.

The analysis of the selectivity of the East Sea mid-sized Danish seine (DS) and coastal gillnet (GN) fisheries for sailfin sandfish involved determining the total length (TL) composition of the catch for each fishery. This was conducted using the latest 2019 data [modified from the (NIFS, 2022)], which provided a sufficient sample size and optimal representation of their characteristics (Fig. 3). The NIFS performed monthly port sampling to monitor the length composition of sailfin sandfish for catches from commercial fishing vessels. Samples acquired at landing ports were subsequently transported to the laboratory for length measurements. This study involved the random collection of more than 250 fish, which were measured monthly for each fishery whenever catches were available (all months except May for the DS fishery and November–December for the GN fishery). However, the sample sizes were small, comprising 57 fish in December for the DS fishery and 70 fish in November for the GN fishery, at periods of low catches. Moreover, given the samples were collected from commercial fishing vessels, there may have been sampling errors for extremely small and large individuals, especially for those within the DS fishery.

The main TL mode was 14 cm (range: 11–29 cm; 137,977 samples) for the DS fishery and 20 cm (range: 14–25 cm; 24,629 samples) for the GN fishery. This indicated that the fish caught by the GN fishery were larger than those caught by the DS fishery. The TL data from the DN and GN fisheries were combined as follows. First, the sample length data for each fishery were converted to body weight (W) using the relationship between TL and W (Table 1). Subsequently, the total weight of each sample was determined. The weighting factor for each fishery was calculated based on the respective catch amount and total sample weight corresponding to each fishery. Finally, the length composition representative of each fishery was generated by multiplying the sample length frequency by the weight factor, after which the results were combined.

The selectivity of the DS fishery was estimated using the logistic curve formula shown in Eq. (3), whereas that of the GN fishery was estimated using Eq. (4) as a third-order polynomial of Kitahara (1968) and Fujimori et al. (1996). (3)${\displaystyle S\left(t\right)=\frac{1}{1+exp\left(\alpha -\beta \cdot t\right)}}$ where t is the age, S(t) is the selection ratio for age t, and α and β are constants. (4)${\displaystyle S\left(R\right)=exp\left[\left\{a_3{R}^3+a_2{R}^2+a_{1}R+a_0\right\}-S_{max}\right]}$ where R is the ratio (R = TL/m) of the total length (TL) to the mesh size (m = 51 mm); S(R) is the selection ratio to R; S_max is the maximum value of the approximated curve; and a₃, a₂, a₁ and a₀ are constants. Because S(R) represented the selection ratio for length, the von Bertalanffy growth formula (Bertalanffy, 1938) was used to convert it into the selection ratio for age.

The instantaneous total mortality (Z) was estimated using the Pauly (1984) method based on the TL data from the catch. The Z for application to the single-gear model used the TL data (Fig. 3A) of the DS fishery, whereas those for application to the multi-gear model were weighted according to the catch from each fishery and summed (Fig. 3C). In addition, the instantaneous natural mortality (M) was estimated using the method of Zhang & Megrey (2006), which incorporates more comprehensive information on fish life history than other approaches, such as those by Alverson & Carney (1975) or Alagaraja (1984). The instantaneous fishing mortality (F) was obtained by subtracting M from Z.

Optimal fishing intensity (F_opt)

As the optimal fishing intensity (F_opt) for sailfin sandfish, an instantaneous fishing mortality of F_0.1 at a 10% slope inclination when F = 0 on the YPR curve was determined by the YPR model. In the SBPR model, we estimated an instantaneous fishing mortality of F_40%, which can sustain 40% of the spawning stock in the absence of fishing (F = 0) based on the SBPR curve. These optimal fishing intensities were estimated using single- and multi-gear models, respectively, and the results of these two models were analyzed and compared.

Sensitivity analysis

We assessed the impact of variations in the growth coefficient (K) and instantaneous natural mortality (M) in the multi-gear YPR and SBPR models on the estimates of each model. This was achieved by analyzing the sensitivity of the model estimates to 10% errors within a ±30% range of the two parameters based on the current values of these parameters.

Fishing gear selectivity

Figure 4 shows the selectivity curve and age-specific selection ratio of the East Sea mid-sized Danish seine (DS) and coastal gillnet (GN) fisheries for sailfin sandfish. The estimated selectivity equations for each fishery are as follows: $S\left(t\right)=\frac{1}{1+exp\left(18.94-13.67t\right)}$ for the DS fishery and $S\left(R\right)=exp\left[\left\{-0.48R^3+2.86R^2+0.06R-12\right\}-3.04\right]$ for the GN fishery. The age at first capture (t_c) for the DS fishery was calculated by dividing α by β, whereas the age corresponding to the 50% selection ratio on the left of the bell-shaped curve was selected as t_c for the GN fishery. The age at last capture (t_e) for the DS fishery was determined based on the lifespan of the sandfish, while the age corresponding to a 50% selection ratio on the right of the bell-shaped curve was selected for the GN fishery. Here, t_c and t_e represent the knife-edged ages.

The t_c of each fishing gear was estimated at 1.38 years for the DS fishery and 2.58 years for the GN fishery. This indicated a difference of 1.2 years higher for the t_c of the GN fishery than that of the DS fishery. In addition, the age at last capture (t_e) for each fishing gear was estimated at 4.40 years for the GN fishery, and was considered to be 7 years (Lee et al., 2009) for the DS fishery.

Mortalities

The instantaneous total mortality (Z) estimated by the Pauly (1984) method using TL data (Fig. 3A for single-gear and Fig. 3C for multi-gear) for the single- and multi-gear models was 1.346/year and 1.515/year, respectively. Because the instantaneous natural mortality (M) obtained using the method of Zhang & Megrey (2006) was 0.480/year, the current instantaneous fishing mortalities (F) for the single- and multi-gear models were calculated to be 0.866/year and 1.035/year, respectively. The current F of each fishery for the multi-gear model was estimated at 0.611/year for the DS fishery and 0.424/year for the GN fishery, using the 2019 catch ratio (Fig. 1B) as the weighting (0.59 for the DS fishery and 0.41 for the GN fishery).

Yield per recruit

At the current age at first capture (t_cDS = 1.38 years, t_cGN = 2.58 years) and the current fishing intensity (F_DS = 0.611/year, F_GN = 0.424/year) of each fishery, the YPR values estimated by the multi-gear YPR model were 10.24 g for the DS fishery and 6.99 g for the GN fishery. This resulted in a total YPR of 17.23 g (F_cMulti = 1.035/year) for the two fisheries (Fig. 5A).

As shown in Fig. 5A, at the current level of fishing intensity, the YPR was higher for the DS fishery than that for the GN fishery owing to the different selectivities (Figs. 2A–2B). Additionally, the current fishing intensity for the DS fishery was higher than the fishing intensity (F_maxDS), which yielded the maximum YPR.

The YPR was 17.40 g at the current age at first capture (t_cDS = 1.38 years) and current fishing intensity (F_cSingle = 0.866/year) as per the single-gear YPR model (considering only the DS fishery) (Fig. 5B). Comparing the results of the two models (Fig. 5B), the current fishing intensity (1.035/year) from the multi-gear YPR model exceeded that from the single-gear model (0.866/year). The YPR was lower in the multi-gear model (17.23 g) than that in the single-gear model (17.40 g), although the difference was negligible.

Spawning biomass per recruit

Compared with the virgin spawning stock biomass, the current spawning stock biomass at the current fishing intensity (F_cMulti = 1.035/year, F_cSingle = 0.866/year) was estimated to be approximately 21% for the multi-gear model and approximately 18% for the single-gear model (Fig. 6). The estimate of F_40% for the single-gear model, which only considered the DS fishery, was 0.400/year, which was lower than the estimate of 0.522/year for the multi-gear model.

Optimal fishing intensity and optimal age at first capture

In the case of F_0.1 based on the YPR models (Fig. 5B), the F_0.1Multi was estimated to be 0.540/year, and the F_0.1Single was estimated to be 0.422/year. The YPR values at this time were 14.99 g and 15.78 g, respectively, indicating that the estimate of F_0.1 was higher in the multi-gear model than that in the single-gear model. This phenomenon reflects the actual catch status, wherein the capture of older fish in the GN fishery gradually decreases because of their selectivity (Figs. 2 and 4). The F_0.1 derived from the multi-gear model, which accounted for the two different selectivity curves (sigmoid for DS and bell-shaped for GN), was estimated to be higher than that of the single-gear YPR model, which only considered the DS fishery.

Conversely, in the single-gear model (traditional model), the catch of older fish was maintained until the age at end capture because of the nature of their sigmoid selectivity; therefore, fishing mortality could be lower to compensate for the necessary catch level or necessary spawning biomass using low fishing intensity. The current fishing mortality was underestimated by 16% in the single-gear model compared with the multi-gear model because the single-gear model only considered DS selectivity (sigmoid curve) and not combined DS and GN (bell-shaped curve) selectivity.

According to the SBPR model, the F_40%Multi was 0.522/year and the F_40%Single was 0.400/year, and the estimates were similar to F_0.1. This also reflected the catch status of older fish in the GN fishery and YPR models; therefore, the estimate for the multi-gear model was higher than that for the single-gear model (Fig. 6).

Table 2 compares the YPR and SBPR at the current level of fishing intensity (F_c) estimated from the multi-gear and single-gear models and those at the optimal fishing intensity (F_0.1, F_40%) as management reference points. Overall, the fishing intensity was higher in the multi-gear model than that in the single-gear model.

The F_0.1 or F_40% levels for the appropriate management of the sailfin sandfish stock by the multi-gear model were approximately half lower than the current fishing intensity (F_c), with no significant difference observed between YPR and SBPR (Fig. 7). Reducing the fishing intensity to F_0.1 resulted in a YPR of 14.99 g, representing a 13% decrease from the current level. This also corresponded to a 46% increase in the SBPR from the current level. Compared to the current F_c level, F_40% increased the SBPR by 48% and decreased the YPR by 14% (Table 2).

Sensitivity analysis

A sensitivity analysis was conducted to examine the perturbation of variations in the growth coefficient (K) and natural mortality (M) parameters used in the multi-gear YPR and SBPR models on the estimates of each model. Figure 8A shows the sensitivity of YPR to errors of M and K. YPR showed an inverse relationship, decreasing with increasing M. If the error of M is -30%, the YPR increases by 35%, and if the error of M is +30%, the YPR decreases by 25%. Conversely, if K error is -30%, YPR decreases by 50%, and if it is +30%, YPR increases by 60%. Therefore, YPR was found to be more sensitive to variations in growth coefficient (K) values than those in natural mortality (M) values.

Figure 8B shows the sensitivity analysis results of M and K for the SBPR. As the errors of both M and K increased, SBPR also increased, and SBPR showed changes of −16% to +16% and −8% to +7%, respectively, indicating greater sensitivity to M than to K. However, M and K significantly affected YPR but minimally influenced SBPR.