## 2 Materials and Methods
### Estimation of the Mesh Selectivity Curve  
We used [PERSON]'s (1968) method to estimate the mesh selectivity curve and the method developed by [PERSON] et al. (1996) to estimate the master curve. [PERSON]'s method of mesh selectivity curve estimation is based on the geometrical similarity theory proposed by [PERSON] (1914), which assumes that as the mesh size increases \(k\) times, the length of the fish caught also increases \(k\) times (Equation (1)). Based on this assumption, [PERSON] used the relative length (\(l/m\))--a normalization of the length (\(l\)) to the mesh size (\(m\))--as a variable to derive the selectivity curve \(S(l_{j}/m_{i})\) as follows ([PERSON], 1968; [PERSON], 1968; [PERSON], 1968):  
\[S(m,\ l)=s\big{(}l_{j}/m_{i}\big{)}S(km,\ kl)=s\big{(}k_{j}/km_{i}\big{)}=s \big{(}l_{j}/m_{i}\big{)} \tag{1}\]  
where \(k\) is a proportional constant. The number of catches per unit effort (\(c_{ij}\)) can be expressed as follows:  
\[c_{ij}=C_{ij}/X_{i}=s\ \big{(}l_{j}/m_{i}\big{)}\cdot q_{i}\cdot d_{j} \tag{2}\]  
Figure 3: Location of the sea trials’ site for the selectivity experiments.  
where \(C_{ij}\) is the number of catches of fish with a length of \(l_{j}\) in a net with a mesh size \(m_{i}\) and \(X_{i}\) is the catch effort of the net, while \(q_{i}\) represents the catching efficiency, indicating the effect of fishing conditions such as the fishing gear structure and soaking time, and \(d_{j}\) represents the relative stock density of fish with a length \(l_{j}\). By taking the logarithms of both sides of Equation (2) and rearranging the equation, the following equation can be derived [26,27]:  
\[In\ s\ \left(l_{j}/m_{i}\right)=ln\ C_{ij}-ln\ \left(q\cdot d_{j}\right) \tag{3}\]  
In Equation (3), the second term on the right-hand side is the correction related to the catching efficiency or stock density. [PERSON]'s method, similar to [PERSON]'s (1962) method, has a drawback in that it does not have a curve formula that can represent the selectivity curve. Therefore, in order to express the selectivity curve for the mesh as one master curve, [PERSON] et al. (1996) applied the master curve formula of polynomials to [PERSON]'s method as follows [24,28]:  
\[ln\ s\ (R)=a_{n}R^{n}+a_{n-1}R^{n-1}+a_{n-2}R^{n-2}+\ \cdots\ +a_{0} \tag{4}\]  
where \(R=l_{j}/m_{i}\). To estimate the selectivity curve, a symmetric quadratic polynomial and an asymmetric cubic polynomial are applied for estimation. However, for gillnets, the number of fish caught is often not in agreement with the theory of [PERSON], and higher reliability has been reported when using asymmetric polynomials than symmetric ones [4,24,25]. Therefore, in this study, the selectivity curve formula was estimated by setting cubic polynomials. In addition, the relative efficiency \(q\) was generally assumed to have a maximum value of 1, and the selectivity curve \(s(R)\) can be expressed by the following equation:  
\[s(R)=exp\Big{(}a_{n}R^{n}+a_{n-1}R^{n-1}+a_{n-2}R^{n-2}+\cdots+a_{0}\Big{)}-F_ {max} \tag{5}\]  
where \(F_{max}\) is the maximum value of Equation (4) and can be obtained by differentiation [24,29]. Each parameter of the function was obtained using the least-squares method, and the fit of the model was determined by obtaining the unbiased estimator (\(\rho\)) of the error.