## 3 Results
### Estimation of the Mesh Size Selectivity Curve  
The selectivity of the four mesh sizes for blackfin flounders was analyzed using [PERSON]'s and [PERSON]'s methods using the catch data listed in Table 3. Each mesh size selectivity curve showed a shift to the right with an increase in the mesh size, and the length of the fish caught increased with the mesh size. The mesh size selectivity curves of the four groups of experimental nets are shown in Figure 5.  
The parameters of the polynomial equation for the master curve were estimated using the least-squares method based on the catch data, and the results are shown in Table 4.  
The estimated polynomial for the master curve can be expressed as follows, and the master curve is shown in Figure 6:  
\[s(R)\equiv s(l/m)=exp\Big{\{}\Big{(}-1.1275R^{3}+5.5905R^{2}-5.5255R+0.6519 \Big{)}-4.9439\Big{\}} \tag{6}\]  
In the master curve for mesh selectivity, the optimal length/mesh size (\(l/m\)) value with a retention probability of 1 was 2.70, and the 50% selection range was 2.225-3.116 with an interval of 0.891. This suggests that with the increasing mesh size, the fish with longer total lengths exhibited the same retention probability. This confirmed that the catch rate of small fish decreased with an increase in the mesh size. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Total Length**} & \multicolumn{5}{c}{**Mesh Size (Catch Number)**} & \multirow{2}{*}{**Total**} \\ \cline{2-2} \cline{4-5}
**(mm)** & **84 mm** & **90 mm** & **105 mm** & **120 mm** \\ \hline \(<\)160 & 0 & 0 & 0 & 0 & 0 \\
160–170 & 0 & 1 & 0 & 0 & 1 \\
170–180 & 13 & 4 & 0 & 0 & 17 \\
180–190 & 10 & 5 & 2 & 1 & 18 \\
190–200 & 19 & 8 & 4 & 3 & 34 \\
200–210 & 13 & 16 & 16 & 2 & 47 \\
210–220 & 34 & 15 & 15 & 2 & 66 \\
220–230 & 59 & 29 & 23 & 7 & 118 \\
230–240 & 77 & 57 & 31 & 11 & 176 \\
240–250 & 68 & 83 & 44 & 16 & 211 \\
250–260 & 48 & 72 & 37 & 11 & 168 \\
260–270 & 16 & 41 & 51 & 17 & 125 \\
270–280 & 6 & 16 & 37 & 8 & 67 \\
280–290 & 7 & 12 & 29 & 5 & 19 \\
290–300 & 0 & 1 & 9 & 9 & 14 \\
300–310 & 0 & 3 & 6 & 5 & 9 \\
310–320 & 3 & 0 & 2 & 2 & 7 \\ \(>\)320 & 0 & 0 & 1 & 2 & 3 \\ \hline Total & 373 & 363 & 307 & 101 & 1144 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Distribution of total lengths of blackfin flounders caught by the experimental nets. Table 5 outlines the 25% (L\({}_{25}\)), 50% (L\({}_{50}\)), and 75% (L\({}_{75}\)) selection lengths and selection ranges--the criteria for selectivity evaluation--obtained from the master curve. The net with a mesh size of 84 mm showed the smallest selection range, and the larger the mesh size, the higher the selection range was. The relationship between the mesh size and selection length is presented in Figure 7. The fishing of blackfin flounder with a total length \(\leq\)170 mm is currently prohibited by relevant laws and regulations. In the nets with a mesh size of 84 mm currently used for blackfin flounder fishing, the 50% selection length was estimated to be 186.9 mm, which was approximately 17 mm larger than the length limit. Figure 4: Frequency distributions of the total lengths of blackfin flounders caught by the experimental nets with four different mesh sizes. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Model**} & \multicolumn{6}{c}{**Parameters**} \\ \hline [PERSON]’s and & \(a3\) & \(a2\) & \(a1\) & \(a0\) & \(R\) & \(\rho\) & \(F_{\text{max}}\) \\ \cline{2-7} [PERSON]’s methods & \(-1.1275\) & \(5.5905\) & \(-5.5255\) & \(0.6519\) & \(2.7005\) & \(0.3562\) & \(4.9439\) \\ \hline \hline \end{tabular} \(a3\)-\(a0\): parameter of the polynomial for the master curve. \(R\): variable, length/mesh (l/m). \(\rho\): unbiased estimator \(F_{\text{max}}\): maximum value of the polynomial for logarithm selectivity.  
\end{table} 
Table 4: Selectivity parameters estimated with [PERSON]’s and [PERSON]’s methods. Figure 5: Selectivity curve of each experimental net, as estimated using [PERSON]’s and [PERSON]’s methods.