Stock Assessment of Chub Mackerel ( Scomber japonicus ) in the Northwest Paciﬁc Ocean Based on Catch and Resilience Data

: This study aimed to evaluate the stock status of chub mackerel ( Scomber japonicus ) in the Northwest Paciﬁc Ocean. Chub mackerel is a commercially important ﬁsh species in South Korea. The ﬁshing grounds of chub mackerel are in the Northwest Paciﬁc Ocean, off South Korea and the neighboring countries of China and Japan. Previous chub mackerel stock assessments have mostly been based on catch data from a single country. However, in this study we used the total catch data on chub mackerel in the Northwest Paciﬁc Ocean to assess the stock status, owing to their migrations and occurrence in the waters of several different countries. We used a catch and maximum sustainable yield model, which is based on catch and resilience data, using the Monte Carlo method. Moreover, sensitivity analysis was conducted according to the availability of catch data by sea area and country. The results showed that the current level of chub mackerel biomass is lower than the biomass required to achieve a maximum sustainable yield based on median values. Furthermore, analysis of all scenarios showed the same results, while the current biomass showed a decreasing trend. These results indicate that improved cooperative resource management is required to prevent further stock status decline.


Introduction
Chub mackerel (Scomber japonicus) is a migratory fish widely distributed in subtropical and temperate seas, including the waters around South Korea. It migrates horizontally for spawning, feeding, and passing winters, and migrates vertically to shallow waters in spring and summer and to deeper waters in autumn [1]. Chub mackerel is captured worldwide, including in South Korea, China, Japan, Russia, and Taiwan [2]. In 2020, a total of 993,474 tons of chub mackerel were captured in the Pacific Northwest, of which 392,556 tons were caught in China, followed by 376,600 tons in Japan, 81,317 tons in Russia, 77,401 tons in South Korea, and 65,600 tons in Taiwan [3].
The fluctuating trend in the total amount of chub mackerel captured in the Northwest Pacific Ocean from 1970 to 2020 shows a continuous increase from 1,570,000 tons in 1970 to a maximum of 2,240,000 tons in 1978. However, an overall decreasing trend has been observed from the 1980s to date. The specific national fishing rate shows that fishing in Japan accounted for over half of the total catch before the 1990s. After the 2000s, the fishing rate in China was similar to that in Japan [4].
Several studies have been conducted on the chub mackerel resource in South Korea and nearby countries, and various efforts have been made to manage it. To regulate chub mackerel fishing by large purse seine fisheries in South Korea, a total allowable catch (TAC) was established and implemented from 1999 onwards. The TAC of chub mackerel from July 2022 to June 2023 is 145,905 tons [5][6][7]. Japan established a TAC from 1997 onwards to regulate chub mackerel fishing [8,9].

Analysis Method
The surplus production model for assessing fishery resources was developed to estimate the maximum sustainable yield (MSY) using catch and fishing effort data [13][14][15]. However, the fishing effort for chub mackerel in the Northwest Pacific Ocean is nation-and fishing industry-specific. Therefore, collecting and using these different data types in one model is not possible.
Despite the current lack of adequate analysis data, including fishing effort data, the CMSY model can assess resources based on catch data, and many studies have applied this model [11,12,14,16,17]. Therefore, this study uses the CMSY model to assess the chub mackerel resource in the Northwest Pacific Ocean.
The CMSY model assumes that the increase in a resource takes the form of a logistic function, similar to the assumption of Schaefer [13,18] (1954; 1957). Therefore, based on Sustainability 2023, 15, 358 3 of 14 time t, the stock biomass at t + 1 is represented by Equation (1). Here, B t is the stock biomass at time t, r is the intrinsic growth rate of the resource, k is the environmental carrying capacity, and C t is the catch amount at time t. Here, the case of stock biomass declining to one quarter of k or below is represented by Equation (2) [12,14,19].
The CMSY model that assesses the resource based on the catch data is able to estimate the stock biomass, fishing mortality rate, MSY, r, and k based on limited data. Specifically, the Monte Carlo method is used for r and k to estimate the 'r − k' pair by comparing the estimated stock biomass to the range of prior stock biomass and observed catch data. The prior information and range of r is set to the resilience and r value, and the resilience is classified into four types according to a certain range of r (Table 1) [12,14]. The prior information and range of k is determined by the range of the intrinsic growth rate based on the maximum value (max(C)) within the range of catch data used in the analysis, as shown in Equation (3). If the level of prior stock biomass is high, Equation (4) is applied to set the prior range of the environmental carrying capacity. Additionally, the prior information and range for the stock biomass are distinguished into high (0.5-0.9), medium (0.2-0.6), and low (0.01-0.4) according to the relative level (B/k) [14].
The process of estimating the 'r − k' pair consists of the selection of an arbitrary 'r − k' pair within the previously set range, followed by the selection of the stock biomass of the initial period from the prior range of stock biomass. Additionally, the stock biomass during the following period is determined through Equation (1) or (2). In the case of a significantly low level of the predicted stock biomass or deviation from the prior range of stock biomass, the 'r − k' pair is eliminated. Among the 'r − k' pairs, the value with the greatest possibility of determined stock biomass falling within the prior range is determined through the regression equation based on the Schaefer function shown in Equation (5) [11,14,20].
As a method of identifying the chub mackerel stock state using the CMSY model, the state of the fishery resource was defined based on the stock biomass in the last year of the analysis period compared to the B MSY used in several recent studies [11,12,21,22]. Depending on the rate of stock biomass to B MSY , the resource state is defined: collapsed, grossly overfished, overfished, slightly overfished, or healthy (Table 2). Source: [11,12,21,22].
Through this process, the Kobe plot was estimated by examining changes in chub mackerel biomass status and considering changes in chub mackerel biomass and fishing mortality by year. Specifically, the Kobe plot is presented as one point for each year according to B/B MSY on the x-axis and F/F MSY on the y-axis. In other words, in the case of the x-axis, it is considered that the biomass is low if it is ≤1.0, while in the case of ≥1.0 the biomass is in a good state. In contrast, in the case of the y-axis, when it is ≤1.0, the fishing rate is considered at a good level, while when it is ≥1.0 the fishing rate is high [23].
The Kobe plot is divided into four quadrants: red, orange, yellow, and green. The red area indicates an area that is overfished, and in which overfishing is occurring; orange indicates an area that is not overfished in which overfishing is occurring; yellow indicates an area that is overfished where there is no overfishing; and green indicates that the area is not overfishing and there is no overfishing [23]. Through this breakdown, this study attempted to understand additional information by estimating where the annual mackerel resource status is located on the quadrant.
Meanwhile, according to a study on the labeling of chub mackerel resources in Japan and an analysis of fatty acid components, the chub mackerel population is divided into the Pacific sub-population and Tsushima-warm current sub-population [24,25]. Previous studies have shown that the population dynamics between the two sub-populations are different [8,26,27]. In this way, even when the population of chub mackerel resources in the same sea area is classified, a limit to identification of the resource status may exist if it is analyzed as a single resource.
In addition, the CMSY model used in this study tends to have bias in the analysis results; thus, it is necessary to clarify uncertainty by presenting the sensitivity analysis results when presenting the estimation results [28].
Therefore, in this study, an assessment of the entire chub mackerel resource in the Northwest Pacific Ocean was conducted using the CMSY model, and sensitivity analysis was conducted depending on whether additional catch data by sea area and country were included (Table 3). Specifically, the scenarios were divided into five cases: (1) stock assessment was conducted on the chub mackerel catch in the northwest Pacific Ocean; (2) to consider different sub-populations captured in the Pacific Ocean, the analysis was conducted excluding chub mackerel caught in the Pacific region; (3) analysis excluding the Japanese catch in the entire northwest Pacific; (4) analysis excluding the Chinese catch; and (5) analysis excluding the Korean catch. Finally, the results of analysis for each of these scenarios were compared to determine the status of chub mackerel resources in the Northwest Pacific Ocean. Additionally, a correlation analysis was conducted to investigate the correlation between nations that fished chub mackerel in the Northwest Pacific Ocean. The statistical significance of the correlation analysis results was validated. The results were analyzed to review their relevance to the nation-specific fluctuation in catch and resource assessment results and present a comprehensive conclusion.

Data Used for the Analysis
The starting year of the available domestic time-series chub mackerel catch data is 1970. Hong and Kim used domestic data from 1970 to 2020 to assess the chub mackerel resource [12]. This study established a 51-year dataset from 1970 to 2020 to analyze the chub mackerel resource and compare results with previous studies.
To assess the chub mackerel resource in the Northwest Pacific Ocean using the CMSY model, the catch and resilience data are needed. For catch data, FAO's "FishStatJ" was referenced; for statistical data, the area of the Northwest Pacific Ocean (Figure 1) was set as the sea area, and the data from all nations that captured chub mackerel were searched. The total sum of catches from the acquirable data on the corresponding sea area and nations was used for analysis. Similarly, statistical data on chub mackerel fishing in the Northwest Pacific Ocean between 1970 and 2020 were obtained for China, Japan, South Korea, Russia, and Taiwan. The current catch data from Russia were only available for certain years; thus, only those years were used in the analysis. The chub mackerel catch for each nation is summarized in Table 4.
Additionally, a correlation analysis was conducted to investigate the c tween nations that fished chub mackerel in the Northwest Pacific Ocean. significance of the correlation analysis results was validated. The results we review their relevance to the nation-specific fluctuation in catch and resour results and present a comprehensive conclusion.

Data Used for the Analysis
The starting year of the available domestic time-series chub mackere 1970. Hong and Kim used domestic data from 1970 to 2020 to assess the c resource [12]. This study established a 51-year dataset from 1970 to 2020 t chub mackerel resource and compare results with previous studies.
To assess the chub mackerel resource in the Northwest Pacific Ocean us model, the catch and resilience data are needed. For catch data, FAO's "F referenced; for statistical data, the area of the Northwest Pacific Ocean (Fig as the sea area, and the data from all nations that captured chub mackerel w The total sum of catches from the acquirable data on the corresponding sea tions was used for analysis. Similarly, statistical data on chub mackerel Northwest Pacific Ocean between 1970 and 2020 were obtained for China Korea, Russia, and Taiwan. The current catch data from Russia were only certain years; thus, only those years were used in the analysis. The chub m for each nation is summarized in Table 4.   Before examining the full data on the chub mackerel catch, we examined the recent average catch to determine the proportion of per-nation catch of chub mackerel currently captured from the Northwest Pacific Ocean. The most recent five-year (2016-2020) data on average catches shows that Japan accounts for the highest rate (41.1% of the total amount), followed by China (37.8%), South Korea (9.5%), Taiwan (6.0%), and Russia (5.6%).
The total catch in the Northwest Pacific sea area continuously increased from 1,571,600 tons in 1970 and reached a maximum of 2,238,781 tons in 1978. However, an overall decreasing trend has been observed from the 1980s to date, and the catches in 2018, 2019, and 2020 were 1,297,215 tons, 1,177,254 tons, and 993,474 tons, respectively [4]. The change in chub mackerel catches in China increased from 173,100 tons in 1970 to approximately 300,000 tons after the 1990s and reached a maximum of 592,637 tons in 2008 ( Figure 2). However, it has subsequently been decreasing. In 2013, China accounted for approximately half (49.1%) of the total catch in the Northwest Pacific Ocean [4]. In 1971, Japan captured 87.3% of the total catch in the Northwest Pacific Ocean at 1,252,600 tons, and recorded a maximum of 1,625,753 tons in 1978. Nonetheless, their catches have been declining since the 1980s. Despite the decreasing trend, Japan accounts for approximately 40% of the total catch since 2000 [4]. In South Korea, approximately 100,000 tons or less was caught in the early 1970s; it continuously increased to a high of 415,003 in 1996, accounting for 25.8% of the total catch in the Northwest Pacific Ocean. However, chub mackerel catches in South Korean waters have been declining since the late 1990s. In Taiwan, chub mackerel catches continuously increased from 1980, reaching a maximum of 98,604 tons in 2011, which accounted for 8.3% of the total catch in the Northwest Pacific Ocean. In 2012 and 2013, fishing waned significantly, though it is now generally on the increasing trend (except on certain years), and they recorded catches of 65,600 tons in 2020 [4].  Table 5 shows the catch data used to analyze the stock assessment scenarios. Sp ically, in the case of scenario 1, the entire catch of chub mackerel in the Northwest P Ocean was used as analysis data. In scenario 2, the Pacific chub mackerel catch da NRIFS (2020) were excluded from the catch data used in scenario 1 in order to con  Table 5 shows the catch data used to analyze the stock assessment scenarios. Specifically, in the case of scenario 1, the entire catch of chub mackerel in the Northwest Pacific Ocean was used as analysis data. In scenario 2, the Pacific chub mackerel catch data by NRIFS (2020) were excluded from the catch data used in scenario 1 in order to consider the impact of different chub mackerel populations caught in the Pacific Ocean. The data in NRIFS (2020) are only available to check the catch data of Japan, China, and Russia, and the data period ranges from 1970 to 2018 with the annual catch referring to the catch from July to June. In addition, in the case of scenarios 3, 4, and 5, the total catch of chub mackerel in Japan, China, and Korea, respectively, was excluded from the catch of chub mackerel in the northwest Pacific (Scenario 1). Resilience data are essential for estimating the intrinsic growth rate of the target fish species before assessing the resource using the CMSY model. The resilience data for chub mackerel were obtained through FishBase. Specifically, the median value of the prior information of intrinsic growth rate was 0.48, and the 95% confidence interval (CI) was observed between the lowest limit of 0.32 and the highest limit of 0.73. The resilience capacity was determined to be at a medium level for use in further analysis.

Results
Resource assessment results from the CMSY model based on chub mackerel catch data in the Pacific Northwest from 1970 to 2020 are summarized in Table 6, and the estimated results for the 'r − k' pair are illustrated in Figure 3.     Specifically, the estimates for the variable r were within the range of prior determined resilience capacity (median, 0.2-0.8). Additionally, the k estimation median value was 16,264,802 tons, and the 95% CI range was 10,983,651-24,085,231 tons. The estimated MSY median value was 1,294,320 tons, which was between the lowest limit of 1,144,003 tons and the highest limit of 1,499,941 tons.
Based on the median value of 4,871,919 tons for chub mackerel stock biomass in 2020, the 95% CI ranged from 601,037 to 6,446,315 tons. Based on the median value of 8,132,401 tons, the 95% CI of B MSY ranged from 5,491,825 to 12,042,616 tons. Specifically, based on the median value, the Pacific Northwest chub mackerel B MSY to the 2020 stock biomass ratio was 0.60, and the current stock state was estimated to be "overfished." Additionally, the estimated range of 95% CI for B 2020 /B MSY was determined to be between 0.07 and 0.79 (Table 7). Based on the median value, the chub mackerel stock was higher than the B MSY at the beginning of 1970 and was approximately 9,000,000 tons ( Figure 4). However, due to the continuous decrease in the stock biomass, this amount decreased to below B MSY after 1975. This decreasing trend continued until 1990, when a partial increase was observed until the mid-1990s. However, the trend has been declining since then.  A Kobe plot accounting for fishing mortality, along with the yearly fluctuations in the chub mackerel resource, is shown in Figure 5. Estimations show that in 1970, the fishing mortality rate based on the MSY level was high (orange area, Figure 5) due to the high stock biomass. From 1970 to the 1980s, the stock biomass declined, and fishing mortality increased due to an increase in fishing, which is represented by a shift to the red area. Subsequently, the fishing mortality rate decreased, and there was a shift to the yellow area, though in 2020 the chub mackerel resource was estimated to fall within the red area. Specifically, the probability of the state of the chub mackerel resource remaining in the red area in 2020 was the highest, at 76.6%, followed by 18.3% in the yellow area and 5.1% in the green area. A Kobe plot accounting for fishing mortality, along with the yearly fluctuations in the chub mackerel resource, is shown in Figure 5. Estimations show that in 1970, the fishing mortality rate based on the MSY level was high (orange area, Figure 5) due to the high stock biomass. From 1970 to the 1980s, the stock biomass declined, and fishing mortality increased due to an increase in fishing, which is represented by a shift to the red area. Subsequently, the fishing mortality rate decreased, and there was a shift to the yellow area, though in 2020 the chub mackerel resource was estimated to fall within the red area. Specifically, the probability of the state of the chub mackerel resource remaining in the red area in 2020 was the highest, at 76.6%, followed by 18.3% in the yellow area and 5.1% in the green area. stock biomass. From 1970 to the 1980s, the stock biomass declined, and fishing mortality increased due to an increase in fishing, which is represented by a shift to the red area. Subsequently, the fishing mortality rate decreased, and there was a shift to the yellow area, though in 2020 the chub mackerel resource was estimated to fall within the red area. Specifically, the probability of the state of the chub mackerel resource remaining in the red area in 2020 was the highest, at 76.6%, followed by 18.3% in the yellow area and 5.1% in the green area. Comparing these analysis results with the analysis results of the other four scenarios, it can be confirmed that the decrease in stock biomass and the current chub mackerel stock biomass is lower than . Specifically, based on the median value, scenarios 1, 3, and 5 showed that the chub mackerel stock status was overfished, and scenario 4 showed that the stock was grossly overfished. In scenario 2, the stock was found to be slightly overfished, even though the stock level was the highest among all scenarios. In contrast, based on the upper limit of the 95% CI range, it was found that in scenarios 2 and 3 the stock biomass of chub mackerel was higher than . However, most of the changes in chub Comparing these analysis results with the analysis results of the other four scenarios, it can be confirmed that the decrease in stock biomass and the current chub mackerel stock biomass is lower than B MSY . Specifically, based on the median value, scenarios 1, 3, and 5 showed that the chub mackerel stock status was overfished, and scenario 4 showed that the stock was grossly overfished. In scenario 2, the stock was found to be slightly overfished, even though the stock level was the highest among all scenarios. In contrast, based on the upper limit of the 95% CI range, it was found that in scenarios 2 and 3 the stock biomass of chub mackerel was higher than B MSY . However, most of the changes in chub mackerel resources by year are in the direction of a continuous decrease (Figure 6), which is the same as the change in the resource in scenario 1 (Figure 4), except for the recent increase in certain resources in scenario 2.
The change in chub mackerel catches based on the estimated MSY from scenario 1 shows that catches were lower than the MSY, excluding those in the period between the 1970s and 1980s and a few years during the mid-1990s (Figure 7).
Excluding the recent decline in chub mackerel catches, the catch trend of the past shows an overall increase in China and Taiwan and a decline in Japan and South Korea. The correlation between catches in each nation was analyzed in order to better understand the relationships between each nation's catch trend.
The results showed that the correlation between catches in each nation was statistically significant (Figure 8). Catches in China were found to have a negative (−) relationship with those in Japan (p < 0.01), and the correlation was somewhat high at 0.65. In contrast, catches in China had a positive (+) relationship with catches in South Korea and Taiwan (p < 0.01), and the correlation values were 0.38 and 0.87, respectively. Catches in Japan had a negative relationship with catches in South Korea and Taiwan. The correlation between catches in Japan and South Korea was 0.33 (p < 0.05), and that between Japan and Taiwan was 0.69 (p < 0.01). Lastly, catches in Korea had a positive relationship with catches in Taiwan, and the correlation between the two countries was 0.30 (p < 0.05). In summary, South Korean, Chinese, and Taiwanese chub mackerel catches had a negative correlation with Japanese catches, while all other correlations showed a positive relationship. mackerel resources by year are in the direction of a continuous decrease (Figure 6), which is the same as the change in the resource in scenario 1 (Figure 4), except for the recent increase in certain resources in scenario 2. The change in chub mackerel catches based on the estimated from scenario 1 shows that catches were lower than the MSY, excluding those in the period between the 1970s and 1980s and a few years during the mid-1990s (Figure 7). Excluding the recent decline in chub mackerel catches, the catch trend of the past shows an overall increase in China and Taiwan and a decline in Japan and South Korea. The correlation between catches in each nation was analyzed in order to better understand the relationships between each nation's catch trend. mackerel resources by year are in the direction of a continuous decrease (Figure 6), which is the same as the change in the resource in scenario 1 (Figure 4), except for the recent increase in certain resources in scenario 2. The change in chub mackerel catches based on the estimated from scenario 1 shows that catches were lower than the MSY, excluding those in the period between the 1970s and 1980s and a few years during the mid-1990s (Figure 7). Excluding the recent decline in chub mackerel catches, the catch trend of the past shows an overall increase in China and Taiwan and a decline in Japan and South Korea. The correlation between catches in each nation was analyzed in order to better understand the relationships between each nation's catch trend. (p < 0.01), and the correlation values were 0.38 and 0.87, respectively. Catches in Japan had a negative relationship with catches in South Korea and Taiwan. The correlation between catches in Japan and South Korea was 0.33 (p < 0.05), and that between Japan and Taiwan was 0.69 (p < 0.01). Lastly, catches in Korea had a positive relationship with catches in Taiwan, and the correlation between the two countries was 0.30 (p < 0.05). In summary, South Korean, Chinese, and Taiwanese chub mackerel catches had a negative correlation with Japanese catches, while all other correlations showed a positive relationship.

Discussion and Conclusions
This study assessed the state of the chub mackerel resource fished in the Northwest Pacific Ocean by adjacent nations, including South Korea. Resource assessment was performed using the CMSY model based on chub mackerel catch data from 1970 to 2020. The results showed a declining trend, and the resource was assessed as "overfished" in 2020. Therefore, recovering and managing the chub mackerel resource in the Northwest Pacific Ocean is essential.
The following common findings were observed while comparing our findings with previous studies. First, the chub mackerel resource has recently been declining, corroborating the reports of the studies conducted by Liang et al. [11], Hong and Kim [12], and Jung [30]. Additionally, Wang et al. [31], Liang et al. [11], Park and Kwon [32], and Hong and Kim [12] estimated the biomass of the current chub mackerel resource to be lower than . In particular, Liang et al. [11] estimated chub mackerel to be overfished in South Korea, China, and Japan, while Hong and Kim [12] assessed chub mackerel to be

Discussion and Conclusions
This study assessed the state of the chub mackerel resource fished in the Northwest Pacific Ocean by adjacent nations, including South Korea. Resource assessment was performed using the CMSY model based on chub mackerel catch data from 1970 to 2020. The results showed a declining trend, and the resource was assessed as "overfished" in 2020. Therefore, recovering and managing the chub mackerel resource in the Northwest Pacific Ocean is essential.
The following common findings were observed while comparing our findings with previous studies. First, the chub mackerel resource has recently been declining, corroborating the reports of the studies conducted by Liang et al. [11], Hong and Kim [12], and Jung [30]. Additionally, Wang et al. [31], Liang et al. [11], Park and Kwon [32], and Hong and Kim [12] estimated the biomass of the current chub mackerel resource to be lower than B MSY . In particular, Liang et al. [11] estimated chub mackerel to be overfished in South Korea, China, and Japan, while Hong and Kim [12] assessed chub mackerel to be overfished in South Korea. In addition, comparison with the results of each stock assessment scenario showed a recent decline in chub mackerel resources and that the current chub mackerel biomass is lower than B MSY .
Currently, nations that cooperatively fish chub mackerel in the Northwest Pacific Ocean are undertaking various measures to manage this resource. For more effective management, a common resource management scheme is necessary beyond the measures currently being taken. South Korea is a member of the North Pacific Fisheries Commission (NPFC), along with China, Japan, Russia, and the United States. In light of the NPFC's conservation and management measures for chub mackerel, the adverse impact on chub mackerel resources due to the increase in the number of fishing vessels has been discussed. Fishing efforts should not be expanded without prior evaluation of the impact of fishing activities on the long-term sustainability of chub mackerel resources. Moreover, the measures include the need to periodically review the catch of chub mackerel in the conventional zone of all Member States [33]. According to the "Third Fisheries Resource Management Plan" in South Korea [10], marine resource recovery and management policies are planned for promotion by strengthening international cooperation, including information sharing and cooperative resource investigation by South Korea, Japan, and China. For improved future cooperative management, it is necessary for the Northwest Pacific Ocean nations to discuss methods to improve the effect of chub mackerel resource management through cooperation, conduct research on factors that impact chub mackerel resource changes, review and compare resource assessments on major fish species in each nation, and discuss resource assessment methods for each sea area unit considering the migratory characteristics of the species.
A correlation was observed between chub mackerel catches in the Northwest Pacific Ocean in each nation; thus, it is necessary to consult and negotiate on promotion of chub mackerel resource management in the future through an output control method such as TAC. For example, as in the case of the European Union (EU), it seems necessary to manage the catch harvested from the sea. Specifically, if any third-country vessels fish in Union waters and the fish catch exceeds the quota, the quota for that country is deducted from its catch quota in the following year [34].
Currently, in Korea the TAC is set at 145,905 tons for the large purse seine fishery, which catches chub mackerel from July 2022 to June 2023 [35]. However, because Korea's chub mackerel catch represents only approximately 9.5% of the total Northwest Pacific sea area (Figure 4), it is difficult to expect a recovery of the total chub mackerel resources in the sea only by restricting the catch of individual countries. Therefore, for recovering chub mackerel resources that are migratory it is necessary to consider the entire Northwest Pacific Ocean when setting the catch limit.
In this study, the levels of fishing effort for each nation could not be considered in the chub mackerel stock assessment. While the CMSY model used here is applicable despite the limited data on fishing effort, there is a possibility of bias in the analysis results owing to the lack of consideration of fishing effort or fishing circumstances [20,36,37]. Therefore, in the future improvements should be made in accounting for the fishing effort of each nation, environmental data, climate change impacts, cooperative fishing status, the accuracy of the stock assessment, and the predictability of stock fluctuations.