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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Mar. Sci.</journal-id>
<journal-title>Frontiers in Marine Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Mar. Sci.</abbrev-journal-title>
<issn pub-type="epub">2296-7745</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fmars.2024.1474996</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Marine Science</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Recovery of <italic>Coilia nasus</italic> resources after implementation of the 10-year fishing ban in the Yangtze River: implied from the Yangtze River Estuary and its adjacent sea areas</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Wang</surname>
<given-names>Shuyan</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
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</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Xiong</surname>
<given-names>Ying</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="author-notes" rid="fn001">
<sup>*</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1346148"/>
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<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Hushun</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
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<contrib contrib-type="author">
<name>
<surname>Song</surname>
<given-names>Dade</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
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<contrib contrib-type="author">
<name>
<surname>Wang</surname>
<given-names>Yanping</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
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<contrib contrib-type="author">
<name>
<surname>Ge</surname>
<given-names>Hui</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/data-curation/"/>
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<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Chengbin</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
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<contrib contrib-type="author">
<name>
<surname>Liang</surname>
<given-names>Long</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
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<contrib contrib-type="author" corresp="yes">
<name>
<surname>Zhong</surname>
<given-names>Xiaming</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="author-notes" rid="fn001">
<sup>*</sup>
</xref>
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<aff id="aff1">
<sup>1</sup>
<institution>College of Marine Living Resource Sciences and Management, Shanghai Ocean University</institution>, <addr-line>Shanghai</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Jiangsu Marine Fisheries Research Institute</institution>, <addr-line>Nantong</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>State Key Laboratory of Estuarine and Coastal Research, East China Normal University</institution>, <addr-line>Shanghai</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>Edited by: Hui Zhang, Chinese Academy of Sciences (CAS), China</p>
</fn>
<fn fn-type="edited-by">
<p>Reviewed by: Oumar Sadio, Institut de recherche pour le d&#xe9;veloppement, Senegal</p>
<p>Chao Song, Chinese Academy of Fishery Sciences (CAFS), China</p>
<p>Yuan Li, Ministry of Natural Resources, China</p>
</fn>
<fn fn-type="corresp" id="fn001">
<p>*Correspondence: Ying Xiong, <email xlink:href="mailto:yxiongshfu@126.com">yxiongshfu@126.com</email>; Xiaming Zhong, <email xlink:href="mailto:oceanxmzh@163.com">oceanxmzh@163.com</email>
</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>05</day>
<month>12</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="collection">
<year>2024</year>
</pub-date>
<volume>11</volume>
<elocation-id>1474996</elocation-id>
<history>
<date date-type="received">
<day>02</day>
<month>08</month>
<year>2024</year>
</date>
<date date-type="accepted">
<day>11</day>
<month>11</month>
<year>2024</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2024 Wang, Xiong, Zhang, Song, Wang, Ge, Zhang, Liang and Zhong</copyright-statement>
<copyright-year>2024</copyright-year>
<copyright-holder>Wang, Xiong, Zhang, Song, Wang, Ge, Zhang, Liang and Zhong</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<sec>
<title>Introduction</title>
<p>The implementation of the 10-year fishing ban in the Yangtze River has provided a crucial opportunity for the recovery of rare and endangered diadromous species, such as <italic>Coilia nasus</italic>.</p>
</sec>
<sec>
<title>Methods</title>
<p>In this study, we utilized electronic length&#x2013;frequency analysis (ELEFAN) and length-based Bayesian biomass estimation (LBB) method to fit the body length data of C. nasus from the Yangtze River Estuary and its adjacent sea areas before and after the fishing ban (2019-2023), and the resource changes of C. nasus population were evaluated. Additionally, combined the catch production monitoring data from 2020 to 2022, we comprehensively analyzed the impact of the Yangtze River fishing ban on the recovery of C. nasus resources.</p>
</sec>
<sec>
<title>Results</title>
<p>The results showed that: (1) The proportion of quantity, weight and occurrence frequency of <italic>C. nasus</italic> in catches showed a significant increasing trend year by year. (2) 4,994 <italic>C. nasus</italic> were caught from 2021&#x2013;2023, with body lengths ranging from 13&#x2013;410 mm. In 2023, the average body length and weight of C. nasus had increased by 39.93% and 133.89%, respectively, from those in 2021. (3) ELEFAN estimated that the growth parameters after fishing ban, including asymptotic length, growth coefficient, and the theoretical age at length zero, were determined to be 42.92 cm, 0.43 year<sup>-1</sup>, and -0.31 year, respectively. The total mortality rate, fishing mortality rate, and exploitation rate were determined to be 1.47 year<sup>-1</sup>, 0.79 year<sup>-1</sup>, and 0.54, respectively. (4) LBB estimated that the relative fishing mortality of <italic>C. nasus</italic> before the fishing ban increased from 1.22 in 2019 to 2.65 in 2020, while the relative biomass decreased from 0.34 to 0.22. After the fishing ban, the relative fishing mortality decreased from 0.85 in 2021 to 0.06 in 2023, and the relative biomass increased from 0.26 in 2021 to 0.90 in 2023, with a significant increase in 2022, indicating a clear recovery trend in <italic>C. nasus</italic> resources.</p>
</sec>
<sec>
<title>Discussion</title>
<p>By quantifying the resource characteristics of <italic>C. nasus</italic> before and after the 10-year fishing ban on the Yangtze River, this research revealed the impact of the ban and provided a reference for future systematic evaluations of the <italic>C. nasus</italic> population.</p>
</sec>
</abstract>
<kwd-group>
<kwd>10-year fishing ban</kwd>
<kwd>Yangtze River</kwd>
<kwd>
<italic>Coilia nasus</italic>
</kwd>
<kwd>ELEFAN</kwd>
<kwd>LBB</kwd>
<kwd>resource recovery</kwd>
</kwd-group>
<counts>
<fig-count count="7"/>
<table-count count="5"/>
<equation-count count="22"/>
<ref-count count="83"/>
<page-count count="15"/>
<word-count count="7419"/>
</counts>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-in-acceptance</meta-name>
<meta-value>Marine Fisheries, Aquaculture and Living Resources</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1" sec-type="intro">
<label>1</label>
<title>Introduction</title>
<p>The Yangtze River, the longest river in Asia with a basin rich in fishery resources, is not only a representative of biodiversity but also a cradle of freshwater fisheries in China. In recent decades, aquatic biological resources have sharply declined owing to long-term overfishing, construction of water conservancy projects, and water pollution (<xref ref-type="bibr" rid="B5">Chen et&#xa0;al., 2009</xref>; <xref ref-type="bibr" rid="B36">Liu et&#xa0;al., 2019</xref>). Consequently, the biological integrity index once plummeted to the lowest level, indicating a state of &#x201c;no fish&#x201d; (<xref ref-type="bibr" rid="B79">Zhang et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B7">Chen T. et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B14">Dong et&#xa0;al., 2023</xref>). The fish community within the river basin has undergone significant changes, and many endemic and rare aquatic species such as <italic>Lipotes vexillifer</italic>, <italic>Psephurus gladius</italic>, <italic>Acipenser sinensis</italic>, and <italic>Acipenser dabryanus</italic> have become functionally extinct. Since the late 1990s, the Yangtze River is in a vicious cycle of &#x2018;the fewer resources are caught, the worse the ecology is caught, and the poorer the fishermen are caught&#x2019; (<xref ref-type="bibr" rid="B5">Chen et&#xa0;al., 2009</xref>; <xref ref-type="bibr" rid="B25">He et&#xa0;al., 2019</xref>; <xref ref-type="bibr" rid="B6">Chen et&#xa0;al., 2021</xref>). Thus, as part of China&#x2019;s intensive efforts to protect the Yangtze River and prevent large-scale development, the 10-year fishing ban was officially launched on January 1, 2020 and fully implemented on January 1, 2021 (<xref ref-type="bibr" rid="B42">Mei et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B40">Ma et&#xa0;al., 2022</xref>). This ban primarily targeting the Yangtze River Basin, including the main stream, the Yangtze Estuary, Poyang Lake, Dongting Lake, and the seven tributaries that connect to it: the Dadu, Min, Tuo, Chishui, Jialing, Wu, and Han River. The ban represents the most extensive and strict management measures ever implemented in the basin. Among them, the Yangtze River Estuary plays a crucial role in the resource recovery of diadromous species. The ban is a critical initiative for China to restore aquatic biological resources and protect the ecosystem, and it can also serve as a reference for global fisheries management and ecological conservation efforts. Therefore, long-term monitoring and objective evaluation of aquatic biological resources in the Yangtze River basin have become important needs to assess the effectiveness of the fishing ban. Currently, the effect of the 10-year ban on fishing in the Yangtze River has been widely publicized in the world.</p>
<p>
<italic>Coilia nasus</italic>, an anadromous migratory fish species, has historically been a significant target in the Yangtze River Basin, known as one of the &#x2018;Three Delicacies of the Yangtze River&#x2019; (<xref ref-type="bibr" rid="B27">Jiang et&#xa0;al., 2023</xref>). In China, the Yangtze River Estuary and its adjacent sea areas serve as the main habitats for <italic>C. nasus</italic> (<xref ref-type="bibr" rid="B74">Yuan, 1988</xref>; <xref ref-type="bibr" rid="B62">Wang and Cui, 2019</xref>). According to ecotypes, the population of <italic>C. nasus</italic> in the Yangtze River can be divided into two phenotypes: freshwater residents (<italic>Coilia brachygnathus</italic>) and anadromous migrants (<italic>C. nasus</italic>). Anadromous <italic>C. nasus</italic> has developed a unique flavor and taste because of its distinct lifestyle habits, which also makes it highly esteemed in the aquatic product market and very popular among consumers. Therefore, this type has the highest economic value and is the primary fishing target (<xref ref-type="bibr" rid="B28">Jiang et&#xa0;al., 2020</xref>). Anadromous <italic>C. nasus</italic> grows and fattens in coastal areas and undergoes spawning migration after reaching sexual maturity. Mature adults initiate this journey in February each year, moving from the near-sea waters toward the Yangtze River Estuary, then ascending through the estuary to the spawning grounds where they reproduce and lay eggs (<xref ref-type="bibr" rid="B75">Yuan et&#xa0;al., 1980</xref>). The spawning period of <italic>C. nasus</italic> extends from late May to early October each year. After completing the spawning process, <italic>C.&#xa0;nasus</italic> adults move downstream with the current, and return to the ocean. After hatching, juveniles live for a time at the spawning ground, before eventually entering the ocean in batches, carried by water currents (<xref ref-type="bibr" rid="B75">Yuan et&#xa0;al., 1980</xref>; <xref ref-type="bibr" rid="B82">Zhang et&#xa0;al., 2005</xref>; <xref ref-type="bibr" rid="B19">Ge and Zhong, 2010</xref>; <xref ref-type="bibr" rid="B22">Guan et&#xa0;al., 2010</xref>). Historically, the Yangtze River was abundant in <italic>C. nasus</italic>, with the catch reaching 3,750 t in the 1970s (<xref ref-type="bibr" rid="B82">Zhang et&#xa0;al., 2005</xref>). However, multiple factors such as long-term high-intensity fishing, blocked migratory channels, and intensified water pollution have resulted in a sharp decline in <italic>C. nasus</italic> resources in the Yangtze River (<xref ref-type="bibr" rid="B82">Zhang et&#xa0;al., 2005</xref>; <xref ref-type="bibr" rid="B29">Jiang et&#xa0;al., 2022</xref>). The migratory range has also greatly shortened, the distribution area has progressively shrunk, and the catch in various river sections has continued to significantly decline (<xref ref-type="bibr" rid="B55">Shi et&#xa0;al., 2009</xref>; <xref ref-type="bibr" rid="B22">Guan et&#xa0;al., 2010</xref>; <xref ref-type="bibr" rid="B40">Ma et&#xa0;al., 2022</xref>). By 2016, the catch of <italic>C. nasus</italic> had decreased to 3.7 &#xd7; 10<sup>3</sup>kg, a decrease of 99.06% from the historical peak catch (<xref ref-type="bibr" rid="B82">Zhang et&#xa0;al., 2005</xref>; <xref ref-type="bibr" rid="B68">Xuan et&#xa0;al., 2021</xref>). Accordingly, the management department implemented a series of measures to alleviate fishing pressure, including reducing fishing time, issuing fewer <italic>C. nasus</italic> fishing licenses since 2004, and establishing the <italic>C.&#xa0;nasus</italic> National Aquatic Germplasm Resources Protection Area on December 7, 2012 (<xref ref-type="bibr" rid="B82">Zhang et&#xa0;al., 2005</xref>; <xref ref-type="bibr" rid="B11">Dai et&#xa0;al., 2020</xref>). However, stimulated by high profits, these measures have not effectively reduced the fishing intensity. To protect <italic>C. nasus</italic>, the Ministry of Agriculture and Rural Affairs stopped issuing special fishing licenses for <italic>C. nasus</italic>, <italic>Coilia mystus</italic>, and <italic>Eriocheir</italic> sinensis on February 1, 2019, and banned productive fishing of these species. Subsequently, on Jan. 1, 2021, the comprehensive implementation of the 10-year fishing ban and the extension of the Yangtze River Estuary Fishing Ban Zone provided greater protection space for the population restoration of endangered species such as <italic>C. nasus</italic>. An objective evaluation of the impact of the 10-year fishing ban in the Yangtze River on the recovery of the <italic>C. nasus</italic> resources is crucial for further optimizing management measures. However, due to the high similarity in phenotypes and mixed habitat of <italic>Coilia brachygnathus</italic> and <italic>C. nasus</italic>, accurately assessing the resource status of <italic>C. nasus</italic> presents a significant challenge. Therefore, it is very important to select a reasonable research area and apply appropriate assessment methods.</p>
<p>The scientific and accurate assessment of fishery resources is crucial for formulating fishery management policies. Traditional fishery assessment methods, such as the Beverton&#x2013;Holt method, often require multiple life-history parameters and age data (<xref ref-type="bibr" rid="B53">Ralston et&#xa0;al., 2011</xref>; <xref ref-type="bibr" rid="B26">Hordyk et&#xa0;al., 2015</xref>). However, since more than 90% of global fishery populations lack sufficient data, making scientific assessments with traditional methods challenging (<xref ref-type="bibr" rid="B31">Kindong et&#xa0;al., 2020</xref>). Over the past decade, several fishery resource assessment methods based on limited data have been developed and implemented. To some extent, these methods have alleviated the pressure on fishery resource assessment due to the lack of data to some extent (<xref ref-type="bibr" rid="B21">Goodwin et&#xa0;al., 2006</xref>; <xref ref-type="bibr" rid="B9">Cope and Punt, 2009</xref>; <xref ref-type="bibr" rid="B51">Punt et&#xa0;al., 2011</xref>; <xref ref-type="bibr" rid="B50">Phillips et&#xa0;al., 2015</xref>; <xref ref-type="bibr" rid="B2">Armelloni et&#xa0;al., 2021</xref>). Among these, the electronic length&#x2013;frequency analysis (ELEFAN) and length-based Bayesian biomass estimation method (LBB) are the simplest in terms of data requirements, requiring only representative length-frequency data (LFD) to estimate biological parameters and population resource status (<xref ref-type="bibr" rid="B17">Froese et&#xa0;al., 2018</xref>; <xref ref-type="bibr" rid="B3">Barman et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B80">Zhang et&#xa0;al., 2021a</xref>; <xref ref-type="bibr" rid="B1">Al-Mamun et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B33">Kumar et&#xa0;al., 2022</xref>). These methods offer a rational basis for the sustainable development of commercial fisheries and effective fishery management (<xref ref-type="bibr" rid="B10">Cui et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B30">Ju et&#xa0;al., 2020</xref>). In China, the ELEFAN method and LBB method have been widely applied to assess the resources of various fish populations in different maritime areas (<xref ref-type="bibr" rid="B10">Cui et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B65">Wang L. et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B61">Wang Y. et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B78">Zhai et&#xa0;al., 2020</xref>). For an endangered species such as <italic>C. nasus</italic>, traditional methods requiring extensive catch data are not suitable, whereas the ELEFAN method and LBB method can assess the resource status with limited data. At the same time, by leveraging the life history characteristics of <italic>C. nasus</italic>, the resource assessment in the Yangtze River Estuary and its adjacent sea areas can fundamentally exclude the influence of <italic>Coilia brachygnathus</italic>, thereby enabling a scientifically rigorous and effective reflection of the resource status of <italic>C. nasus</italic>, while also evaluating the impact of the 10-year fishing ban in the Yangtze River. In addition, following implementation of the 10-year fishing ban in the Yangtze River, no reference catch production monitoring data are available for the basin. Therefore, the supplement of marine fishing data is very important for a complete understanding of the impact of the fishing ban.</p>
<p>The purpose of this study is to objectively evaluate the effect of the policy by analyzing the recovery of anadromous <italic>C. nasus</italic> population from the perspective of the ocean outside the Yangtze River estuary after the implementation of the 10-year fishing ban policy in the Yangtze River, and to provide basic data for future research on <italic>C. nasus</italic> population. The technical route is shown in <xref ref-type="fig" rid="f1">
<bold>Figure&#xa0;1</bold>
</xref>.</p>
<fig id="f1" position="float">
<label>Figure&#xa0;1</label>
<caption>
<p>The technical route of this study. The black bold arrows indicate the introduction of data sources or the introduction of formulas here. The red dotted arrow indicates that the output result is fed into the new model as initial data. The red bold arrows indicate the output result. F represents the formula used in the fitting. Such as, F (6) denotes the calculation according to <xref ref-type="disp-formula" rid="eq6">Formula 6</xref>.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-11-1474996-g001.tif"/>
</fig>
</sec>
<sec id="s2" sec-type="materials|methods">
<label>2</label>
<title>Materials and methods</title>
<sec id="s2_1">
<label>2.1</label>
<title>Survey area</title>
<p>The Yangtze River Estuary (<xref ref-type="fig" rid="f2">
<bold>Figure&#xa0;2</bold>
</xref>), extending inward, is connected to the Yangtze River and its tributaries, as well as the lakes and rivers that flow into it. Outward, it communicates with the waters of the East China and Yellow Seas to form an area where land runoff and seawater converge. Moreover, the estuary represents a junction of various marine current systems, including the Subei coastal current, the Taiwan warm current, and the Yellow Sea cold water masses. Sea areas are rich in nutrients and bait organisms that integrate the functions of spawning grounds, feeding grounds, and nurseries (<xref ref-type="bibr" rid="B34">Li et&#xa0;al., 2015</xref>). The unique natural environment of the Yangtze River Estuary fosters rich diversity of fishery biological resources, including estuarine, marine, freshwater, and migratory fishes (<xref ref-type="bibr" rid="B8">Chen Y. et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B6">Chen et&#xa0;al., 2021</xref>). As a vital migration corridor for diadromous species in the Yangtze River basin, the estuary is bifurcated by islands like Chongming Island into distinct northern and southern branches. These branches show notable variations in topography, hydrological features, and environmental factors, which substantially affect the distribution and abundance of fishery resources (<xref ref-type="bibr" rid="B77">Zhai et&#xa0;al., 2023</xref>).</p>
<fig id="f2" position="float">
<label>Figure&#xa0;2</label>
<caption>
<p>Map of the survey area. Grid delineates the survey area. The red area designates the core zone of the <italic>C. nasus</italic> reserve; the pink area signifies the experimental zone of the same reserve. The area bounded by the red line and to the left of the red line shows the Yangtze River Estuary Fishing Ban Zone; the area to the right of the red line shows the allowable fishing area.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-11-1474996-g002.tif"/>
</fig>
</sec>
<sec id="s2_2">
<label>2.2</label>
<title>Data sources</title>
<p>The body length data for this study were collected from sample collections and scientific papers. Sample collection areas A and B utilized stow nets for fishing. The length of the opening rope was 26 m and 22 m, the length of the side rope was 24 m and 5.5 m, the total stretched length of the net was 60 m and 32 m, and the mesh size was 20 mm and 25 mm for areas A and B, respectively. The nets were secured by a stake that was firmly wedged into the seabed, and they were equipped with two bamboo beams to regulate the horizontal expansion of the net mouth. The vertical expansion of the net mouth was sustained by the buoyancy of the top beam and the adhesive force of the bottom beam (<xref ref-type="bibr" rid="B66">Xiong et&#xa0;al., 2017a</xref>; <xref ref-type="bibr" rid="B52">Qin et&#xa0;al., 2024</xref>). The data for area C were read off from scientific papers (<xref ref-type="bibr" rid="B40">Ma et&#xa0;al., 2022</xref>). The sampling gear used were gillnets, consisting of multiple rectangular nets linked together and typically set up in fish migratory channels, which catch fish by winding around or piercing (<xref ref-type="bibr" rid="B35">Li et&#xa0;al., 2009</xref>; <xref ref-type="bibr" rid="B67">Xiong et&#xa0;al., 2017b</xref>). The gillnet used in this study had a mesh size of 40 mm, a length of 150 m, and a height of 12 m (<xref ref-type="bibr" rid="B40">Ma et&#xa0;al., 2022</xref>).</p>
<p>
<italic>C. nasus</italic> samples were collected in accordance with the Technical Specifications for Marine Fishery Resources Survey. The collected samples were cryogenically preserved and transported to the laboratory for biological analyses, which included measuring body length and body weight, determining sex, and assessing gonadal development stages (I-VI). Body length and weight measurements accurate to 1 mm and 0.1 g, respectively. A total of 4,994 samples of <italic>C. nasus</italic> were collected. And the specific data sources and body length data were recorded in detail in <xref ref-type="table" rid="T1">
<bold>Table&#xa0;1</bold>
</xref> and <xref ref-type="supplementary-material" rid="SM1">
<bold>Supplementary Material S1</bold>
</xref>. In addition, we also collected catch production monitoring records from the same commercial fishing vessel in area B in April each year from 2020 to 2022, and extracted the relevant data of <italic>C. nasus</italic>. Details of the catch production monitoring data can be found in <xref ref-type="supplementary-material" rid="SM1">
<bold>Supplementary Material S2</bold>
</xref>.</p>
<table-wrap id="T1" position="float">
<label>Table&#xa0;1</label>
<caption>
<p>Basic data information of <italic>C. nasus</italic> in survey areas.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="top" align="left">Survey area</th>
<th valign="top" align="left">Year</th>
<th valign="top" align="left">Survey period</th>
<th valign="top" align="left">Individual number</th>
<th valign="top" align="left">Length range<break/>(mm)</th>
<th valign="top" align="left">Analytical way</th>
<th valign="top" align="left">Use of nets</th>
<th valign="top" align="left">Source</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left" rowspan="2">A</td>
<td valign="top" align="left">2021</td>
<td valign="top" align="left">March&#x2013;April &amp; December</td>
<td valign="top" align="left">2,417</td>
<td valign="top" align="left">13&#x2013;361</td>
<td valign="top" align="left">ELEFAN, LBB</td>
<td valign="top" align="left">stow net</td>
<td valign="top" align="left">Original survey data</td>
</tr>
<tr>
<td valign="top" align="left">2022</td>
<td valign="top" align="left">February&#x2013;May &amp; November&#x2013;December</td>
<td valign="top" align="left">2,217</td>
<td valign="top" align="left">51&#x2013;347</td>
<td valign="top" align="left">ELEFAN, LBB</td>
<td valign="top" align="left">stow net</td>
<td valign="top" align="left">Original survey data</td>
</tr>
<tr>
<td valign="top" align="left">B</td>
<td valign="top" align="left">2023</td>
<td valign="top" align="left">March&#x2013;April &amp; September&#x2013;December</td>
<td valign="top" align="left">360</td>
<td valign="top" align="left">95&#x2013;410</td>
<td valign="top" align="left">ELEFAN, LBB</td>
<td valign="top" align="left">stow net</td>
<td valign="top" align="left">Original survey data</td>
</tr>
<tr>
<td valign="top" align="left">C</td>
<td valign="top" align="left">2019&#x2013;2020</td>
<td valign="top" align="left">March&#x2013;June</td>
<td valign="top" align="left">3,210</td>
<td valign="top" align="left">113&#x2013;406</td>
<td valign="top" align="left">LBB</td>
<td valign="top" align="left">gillnet</td>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B40">Ma et&#xa0;al. (2022</xref>, <xref ref-type="fig" rid="f2">
<bold>Figure&#xa0;2</bold>
</xref> therein)</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The length&#x2013;frequency data of <italic>C. nasus</italic> used in area C are from <xref ref-type="bibr" rid="B40">Ma et&#xa0;al. (2022)</xref>.</p>
</fn>
<fn>
<p>ELEFAN, electronic length&#x2013;frequency-frequency analysis; LBB, length-based Bayesian biomass estimation.</p>
</fn>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="s2_3">
<label>2.3</label>
<title>Data analysis</title>
<sec id="s2_3_1">
<label>2.3.1</label>
<title>Catch production monitoring data analysis</title>
<p>The number percentage, weight percentage, and occurrence frequency of <italic>C. nasus</italic> captured from 2020 to 2022 were calculated as follows:</p>
<disp-formula id="eq1">
<label>(1)</label>
<mml:math display="block" id="M1">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi>N</mml:mi>
<mml:mo>%</mml:mo>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>T</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>100</mml:mn>
<mml:mo>%</mml:mo>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<disp-formula id="eq2">
<label>(2)</label>
<mml:math display="block" id="M2">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi>W</mml:mi>
<mml:mo>%</mml:mo>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mi>T</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>100</mml:mn>
<mml:mo>%</mml:mo>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<disp-formula id="eq3">
<label>(3)</label>
<mml:math display="block" id="M3">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi>F</mml:mi>
<mml:mo>%</mml:mo>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mi>T</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>100</mml:mn>
<mml:mo>%</mml:mo>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <italic>N%</italic> is the percentage of the total number of <italic>C. nasus</italic> in relation to the total number of fish species caught, <italic>W%</italic> is the percentage of the total weight of <italic>C. nasus</italic> in relation to the total weight of all fish species caught, and <italic>F%</italic> is the percentage of occurrences of <italic>C. nasus</italic> in relation to the total number of fishing trips.</p>
</sec>
<sec id="s2_3_2">
<label>2.3.2</label>
<title>Marine investigation data analysis</title>
<p>The body length&#x2013;weight relationship of <italic>C. nasus</italic> was calculated using the following formula:</p>
<disp-formula id="eq4">
<label>(4)</label>
<mml:math display="block" id="M4">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi>W</mml:mi>
<mml:mo>=</mml:mo>
<mml:mi>a</mml:mi>
<mml:msup>
<mml:mi>L</mml:mi>
<mml:mi>b</mml:mi>
</mml:msup>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <italic>W</italic> is the body weight of <italic>C. nasus</italic>, <italic>L</italic> is the body length of <italic>C. nasus</italic>, <italic>a</italic> is the growth condition factor, and <italic>b</italic> is the power exponent.</p>
</sec>
<sec id="s2_3_3">
<label>2.3.3</label>
<title>Electronic length&#x2013;frequency analysis</title>
<p>ELEFAN is a method for deriving von Bertalanffy growth function parameters from the LFD (<xref ref-type="bibr" rid="B44">Mildenberger et&#xa0;al., 2017</xref>). ELEFAN has been integrated with R statistical computing software to create the TropFishR package, which offers both traditional and updated versions of ELEFAN, as well as new optimization techniques. In this study, two optimized ELEFAN algorithms were used to fit the seasonally oscillating von Bertalanffy growth function: &#x201c;Simulated Annealing&#x201d; (ELEFAN-SA), and &#x201c;Genetic Algorithm&#x201d; (ELEFAN-GA). The best fit method (<italic>Rn_max</italic>) was used for further analyses:</p>
<disp-formula id="eq5">
<label>(5)</label>
<mml:math display="block" id="M5">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mi>n</mml:mi>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mi>E</mml:mi>
<mml:mi>S</mml:mi>
<mml:mi>P</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>A</mml:mi>
<mml:mi>S</mml:mi>
<mml:mi>P</mml:mi>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <italic>ESP</italic> is the sum of the explainable peaks, <italic>ASP</italic> is the sum of the available peaks, and <inline-formula>
<mml:math display="inline" id="im1">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>x</mml:mi>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the best fit (<xref ref-type="bibr" rid="B48">Pauly, 1985</xref>).</p>
<p>The optimal bin size (<italic>OBS</italic>), which can effectively reduce the estimation bias, was determined using the following formula (<xref ref-type="bibr" rid="B60">Wang K. et&#xa0;al., 2020</xref>):</p>
<disp-formula id="eq6">
<label>(6)</label>
<mml:math display="block" id="M6">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi>O</mml:mi>
<mml:mi>B</mml:mi>
<mml:mi>S</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0.23</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msubsup>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>x</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0.6</mml:mn>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <italic>OBS</italic> is the optimal bin size, and <inline-formula>
<mml:math display="inline" id="im2">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the maximum body length of the fish.</p>
<p>The ELEFAN-SA and ELEFAN-GA methods use restructured data in combination with the seasonally oscillating von Bertalanffy growth function for analysis (<xref ref-type="bibr" rid="B49">Pauly and Morgan, 1987</xref>):</p>
<disp-formula id="eq7">
<label>(7)</label>
<mml:math display="block" id="M7">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:msup>
</mml:mrow>
<mml:mo>}</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im3">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>K</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>&#x3a0;</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mi>s</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>&#x3a0;</mml:mi>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>T</mml:mi>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula>
<mml:math display="inline" id="im4">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>K</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>&#x3a0;</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mi>s</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>&#x3a0;</mml:mi>
<mml:mo>(</mml:mo>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>T</mml:mi>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>. <italic>C</italic> is the constant for the amplitude of the oscillation (with a value range of 0&#x2013;1), and <italic>TS</italic> is the phase that regulates the seasonal oscillation (with a value range of 0&#x2013;1).</p>
<p>The total mortality rate (<italic>Z</italic>) was estimated based on the length-converted catch curve, and the natural mortality coefficient (<italic>M</italic>) was determined using Pauly&#x2019;s empirical formula (<xref ref-type="bibr" rid="B47">Pauly, 1980</xref>):</p>
<disp-formula id="eq8">
<label>(8)</label>
<mml:math display="block" id="M8">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>g</mml:mi>
<mml:mi>M</mml:mi>
<mml:mo>=</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>0.0066</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>0.279</mml:mn>
<mml:mi>l</mml:mi>
<mml:mi>g</mml:mi>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>+</mml:mo>
<mml:mn>0.6434</mml:mn>
<mml:mi>l</mml:mi>
<mml:mi>g</mml:mi>
<mml:mi>K</mml:mi>
<mml:mo>+</mml:mo>
<mml:mn>0.4634</mml:mn>
<mml:mi>l</mml:mi>
<mml:mi>g</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <italic>L<sub>inf</sub>
</italic> is the asymptotic body length, <italic>K</italic> is the growth parameter, and <italic>T</italic> is the annual average temperature of the habitat for <italic>C. nasus</italic>. The average habitat temperature for <italic>C. nasus</italic> in 2021 and 2022 was 14.2&#xb0;C. The average habitat temperature was obtained from <xref ref-type="bibr" rid="B45">National Oceanic and Atmospheric Administration (2022)</xref> Ocean Watch, with a spatial resolution of 1&#xb0; and a temporal resolution of months (<ext-link ext-link-type="uri" xlink:href="https://oceanwatch.pifsc.noaa.gov">https://oceanwatch.pifsc.noaa.gov</ext-link>).</p>
<p>The fishing mortality coefficient (<italic>F</italic>) was calculated as follows (<xref ref-type="bibr" rid="B59">Wang et&#xa0;al., 2021</xref>):</p>
<disp-formula id="eq9">
<label>(9)</label>
<mml:math display="block" id="M9">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi>F</mml:mi>
<mml:mo>=</mml:mo>
<mml:mi>Z</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>M</mml:mi>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>The fishery development rate (<italic>E</italic>)was calculated as follows (<xref ref-type="bibr" rid="B59">Wang et&#xa0;al., 2021</xref>):</p>
<disp-formula id="eq10">
<label>(10)</label>
<mml:math display="block" id="M10">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mo>=</mml:mo>
<mml:mi>F</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>Z</mml:mi>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
</sec>
<sec id="s2_3_4">
<label>2.3.4</label>
<title>Length-based Bayesian biomass estimation</title>
<p>Compared to ELEFAN, the LBB method is more accurate, using the ratios of total mortality and fishing mortality to growth rate in the estimation process instead of fixed values for <italic>K</italic>, <italic>M</italic>, and <italic>Z</italic>. Here, we only list the main reference formulas; the R code was downloaded from <ext-link ext-link-type="uri" xlink:href="http://oceanrep.gemar.de/44832/">http://oceanrep.gemar.de/44832/</ext-link>. Similar to ELEFAN, we assumed that fish growth followed the von Bertalanffy growth equation (<xref ref-type="bibr" rid="B58">von Bertalanffy, 1938</xref>; <xref ref-type="bibr" rid="B4">Beverton and Holt, 1957</xref>), as follows:</p>
<disp-formula id="eq11">
<label>(11)</label>
<mml:math display="block" id="M11">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>k</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:msup>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im5">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the asymptotic length at which the fish reaches maturity, <italic>K</italic> is the growth coefficient, <italic>t</italic> is the age of the fish, and <italic>t<sub>0</sub>
</italic> is the theoretical age at which the fish would be at zero length.</p>
<p>When the commercial catch is fully selected by a specific fishing gear, the length&#x2013;frequency curve of the catch can be described as a function of <italic>Z</italic> in relation to the length growth rate:</p>
<disp-formula id="eq12">
<label>(12)</label>
<mml:math display="block" id="M12">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>s</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mi>Z</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>K</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im6">
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the number of fish surviving at length <italic>L</italic>, <inline-formula>
<mml:math display="inline" id="im7">
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>s</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the number of fish fully selected at length <inline-formula>
<mml:math display="inline" id="im8">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, with all individuals entering the net being retained, and <italic>Z/K</italic> is the ratio of <italic>Z</italic> to the growth parameter.</p>
<p>Here, assuming that fish were caught in a stow net, the selectivity can be expressed by the following functions:</p>
<disp-formula id="eq13">
<label>(13)</label>
<mml:math display="block" id="M13">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>a</mml:mi>
<mml:mo>(</mml:mo>
<mml:mi>L</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <italic>S<sub>L</sub>
</italic> is the proportion of individuals of length <italic>L</italic> captured by the fishing gear, <italic>L<sub>c</sub>
</italic> is the length at first capture, and <italic>a</italic> indicates the steepness of the net&#x2019;s selectivity curve.</p>
<p>The parameters <inline-formula>
<mml:math display="inline" id="im9">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula>
<mml:math display="inline" id="im10">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <italic>a</italic>, <italic>M/K</italic>, and <italic>F/K</italic> were estimated using the following equations (<xref ref-type="bibr" rid="B17">Froese et&#xa0;al., 2018</xref>):</p>
<disp-formula id="eq14">
<label>(14)</label>
<mml:math display="block" id="M14">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mi>F</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mfrac>
<mml:mi>M</mml:mi>
<mml:mi>K</mml:mi>
</mml:mfrac>
<mml:mo>+</mml:mo>
<mml:mfrac>
<mml:mi>F</mml:mi>
<mml:mi>K</mml:mi>
</mml:mfrac>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<disp-formula id="eq15">
<label>(15)</label>
<mml:math display="block" id="M15">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im11">
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the number of individuals in the length group <inline-formula>
<mml:math display="inline" id="im12">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula>
<mml:math display="inline" id="im13">
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the number of individuals in the previous length group, and <inline-formula>
<mml:math display="inline" id="im14">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the number of individuals caught in the length group <inline-formula>
<mml:math display="inline" id="im15">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<p>The length distribution <inline-formula>
<mml:math display="inline" id="im16">
<mml:mrow>
<mml:msub>
<mml:mover accent="true">
<mml:mi>P</mml:mi>
<mml:mo>^</mml:mo>
</mml:mover>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> predicted by the LBB model was expressed by the following equation:</p>
<disp-formula id="eq16">
<label>(16)</label>
<mml:math display="block" id="M16">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mover accent="true">
<mml:mi>P</mml:mi>
<mml:mo>^</mml:mo>
</mml:mover>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msup>
<mml:mo>&#x2211;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
</mml:msup>
<mml:msub>
<mml:mover accent="true">
<mml:mi>N</mml:mi>
<mml:mo>^</mml:mo>
</mml:mover>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im17">
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is a function of the estimable population dynamic determents <inline-formula>
<mml:math display="inline" id="im18">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<p>By substituting <inline-formula>
<mml:math display="inline" id="im19">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <italic>M/k</italic>, and <italic>M/F</italic> into <xref ref-type="disp-formula" rid="eq17">Equations 17</xref>, <xref ref-type="disp-formula" rid="eq18">18</xref>, we obtained the optimal length <inline-formula>
<mml:math display="inline" id="im20">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>p</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for unexploited generations with maximum biomass, as well as the optimal catch length <inline-formula>
<mml:math display="inline" id="im21">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>p</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>:</p>
<disp-formula id="eq17">
<label>(17)</label>
<mml:math display="block" id="M17">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>p</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>(</mml:mo>
<mml:mfrac>
<mml:mn>3</mml:mn>
<mml:mrow>
<mml:mn>3</mml:mn>
<mml:mo>+</mml:mo>
<mml:mfrac>
<mml:mi>M</mml:mi>
<mml:mi>k</mml:mi>
</mml:mfrac>
</mml:mrow>
</mml:mfrac>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<disp-formula id="eq18">
<label>(18)</label>
<mml:math display="block" id="M18">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>p</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>(</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>+</mml:mo>
<mml:mn>3</mml:mn>
<mml:mfrac>
<mml:mi>F</mml:mi>
<mml:mi>M</mml:mi>
</mml:mfrac>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:mfrac>
<mml:mi>F</mml:mi>
<mml:mi>M</mml:mi>
</mml:mfrac>
<mml:mo>)</mml:mo>
<mml:mo>(</mml:mo>
<mml:mn>3</mml:mn>
<mml:mo>+</mml:mo>
<mml:mfrac>
<mml:mi>M</mml:mi>
<mml:mi>F</mml:mi>
</mml:mfrac>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>The relative unit supplement yield <italic>Y&#x2019;/R</italic> was given by the following equation:</p>
<disp-formula id="eq19">
<label>(19)</label>
<mml:math display="block" id="M19">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mfrac>
<mml:msup>
<mml:mi>Y</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
<mml:mi>R</mml:mi>
</mml:mfrac>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>F</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:mi>F</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>M</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
<mml:mo stretchy="false">/</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>K</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo stretchy="false">[</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>3</mml:mn>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
<mml:mo stretchy="false">/</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo stretchy="false">/</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>K</mml:mi>
<mml:mo>+</mml:mo>
<mml:mi>F</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo>+</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>3</mml:mn>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
<mml:mo stretchy="false">/</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo stretchy="false">/</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>K</mml:mi>
<mml:mo>+</mml:mo>
<mml:mi>F</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2212;</mml:mo>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
<mml:mo stretchy="false">/</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mn>3</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:mn>3</mml:mn>
<mml:mo stretchy="false">/</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>K</mml:mi>
<mml:mo>+</mml:mo>
<mml:mi>F</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>Assuming that the catch per unit of fishing effort was proportional to the population biomass, and that fishing mortality was directly proportional to fishing effort, dividing both sides of <xref ref-type="disp-formula" rid="eq19">Equation 19</xref> by <italic>F/M</italic> resulted in the following equation:</p>
<disp-formula id="eq20">
<label>(20)</label>
<mml:math display="block" id="M20">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>P</mml:mi>
<mml:mi>U</mml:mi>
<mml:msup>
<mml:mi>E</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
</mml:mrow>
<mml:mi>R</mml:mi>
</mml:mfrac>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mfrac>
<mml:msup>
<mml:mi>Y</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
<mml:mi>R</mml:mi>
</mml:mfrac>
</mml:mrow>
<mml:mrow>
<mml:mfrac>
<mml:mi>F</mml:mi>
<mml:mi>M</mml:mi>
</mml:mfrac>
</mml:mrow>
</mml:mfrac>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:mi>F</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>M</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
<mml:mo stretchy="false">/</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>K</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo stretchy="false">[</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>3</mml:mn>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
<mml:mo stretchy="false">/</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo stretchy="false">/</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>K</mml:mi>
<mml:mo>+</mml:mo>
<mml:mi>F</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo>+</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>3</mml:mn>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
<mml:mo stretchy="false">/</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo stretchy="false">/</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>K</mml:mi>
<mml:mo>+</mml:mo>
<mml:mi>F</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2212;</mml:mo>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
<mml:mo stretchy="false">/</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mn>3</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:mn>3</mml:mn>
<mml:mo stretchy="false">/</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>K</mml:mi>
<mml:mo>+</mml:mo>
<mml:mi>F</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>When <italic>F</italic>=0, the relative biomass expression is:</p>
<disp-formula id="eq21">
<label>(21)</label>
<mml:math display="block" id="M21">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>B</mml:mi>
<mml:msub>
<mml:mo>'</mml:mo>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>&gt;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mi>R</mml:mi>
</mml:mfrac>
<mml:mo>=</mml:mo>
<mml:msup>
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<mml:mo stretchy="false">(</mml:mo>
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</mml:msub>
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</mml:msub>
</mml:mrow>
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<mml:mi>M</mml:mi>
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</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mi>M</mml:mi>
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<mml:mi>K</mml:mi>
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<mml:mo>+</mml:mo>
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<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:mfrac>
<mml:mn>2</mml:mn>
<mml:mrow>
<mml:mi>M</mml:mi>
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<mml:mi>K</mml:mi>
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<mml:mo>&#x2212;</mml:mo>
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<mml:mrow>
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<mml:mo stretchy="false">(</mml:mo>
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<mml:mo>&#x2212;</mml:mo>
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<mml:mi>L</mml:mi>
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</mml:msub>
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<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
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</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mn>3</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:mfrac>
<mml:mn>3</mml:mn>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mo stretchy="false">/</mml:mo>
<mml:mi>K</mml:mi>
</mml:mrow>
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</mml:mrow>
<mml:mo>]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <italic>B<sub>0</sub>
</italic> is the initial biomass. The biological reference point <italic>B/B<sub>0</sub>
</italic> of the developed stock can be expressed as follows:</p>
<disp-formula id="eq22">
<label>(22)</label>
<mml:math display="block" id="M22">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mfrac>
<mml:mi>B</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>B</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>P</mml:mi>
<mml:mi>U</mml:mi>
<mml:mi>E</mml:mi>
<mml:mo>'</mml:mo>
</mml:mrow>
<mml:mi>R</mml:mi>
</mml:mfrac>
</mml:mrow>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>B</mml:mi>
<mml:msub>
<mml:mo>'</mml:mo>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>&gt;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mi>R</mml:mi>
</mml:mfrac>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <italic>B</italic> is the current biomass. When <italic>F</italic>, <italic>M</italic>, <italic>L<sub>c</sub>
</italic>, and <inline-formula>
<mml:math display="inline" id="im22">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>p</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are equal, the ratio of the biomass corresponding to the maximum sustainable yield to the initial biomass can be obtained by recalculating <xref ref-type="disp-formula" rid="eq19">Equations 19</xref>&#x2013;<xref ref-type="disp-formula" rid="eq22">22</xref>.</p>
</sec>
</sec>
</sec>
<sec id="s3" sec-type="results">
<label>3</label>
<title>Results</title>
<sec id="s3_1">
<label>3.1</label>
<title>Statistical results</title>
<sec id="s3_1_1">
<label>3.1.1</label>
<title>Resource proportion of <italic>C. nasus</italic>
</title>
<p>According to the survey data in April from the Yangtze River Estuary and adjacent sea areas, the number percentage, weight percentage, and occurrence frequency of <italic>C. nasus</italic> showed a continuous upward trend from 2020 to 2022, indicating recovery of <italic>C. nasus</italic> resources (<xref ref-type="table" rid="T2">
<bold>Table&#xa0;2</bold>
</xref>).</p>
<table-wrap id="T2" position="float">
<label>Table&#xa0;2</label>
<caption>
<p>The proportion of <italic>C. nasus</italic> caught during the fishing season (April) outside the Yangtze River Estuary Fishing Ban Zone from 2020&#x2013;2022.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="top" align="left">Year</th>
<th valign="top" align="left">
<italic>N</italic>%</th>
<th valign="top" align="left">
<italic>W</italic>%</th>
<th valign="top" align="left">
<italic>F</italic>%</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">2020</td>
<td valign="top" align="left">0.36</td>
<td valign="top" align="left">0.37</td>
<td valign="top" align="left">25</td>
</tr>
<tr>
<td valign="top" align="left">2021</td>
<td valign="top" align="left">1.85</td>
<td valign="top" align="left">1.50</td>
<td valign="top" align="left">42</td>
</tr>
<tr>
<td valign="top" align="left">2022</td>
<td valign="top" align="left">5.23</td>
<td valign="top" align="left">5.54</td>
<td valign="top" align="left">100</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>
<italic>N</italic>%: percentage of the total number of <italic>C. nasus</italic> in relation to the total number of fish species caught; <italic>W%</italic>: percentage of the total weight of <italic>C. nasus</italic> in relation to the total weight of all fish species caught; <italic>F%:</italic> percentage of occurrences of <italic>C. nasus</italic> in relation to the total number of fishing trips.</p>
</fn>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="s3_1_2">
<label>3.1.2</label>
<title>Body length and weight characteristics of <italic>C. nasus</italic>
</title>
<p>Based on measure body length and weight data, fitting was performed to derive the length&#x2013;weight relationship curves of <italic>C. nasus</italic> for 2021&#x2013;2023. The regression parameter <italic>b</italic> for the length&#x2013;weight relationship was consistently greater than 3, indicating a positive allometric growth pattern. All fitting degrees of determination were greater than 0.89, suggesting a strong correlation and a good fit (<xref ref-type="fig" rid="f3">
<bold>Figure&#xa0;3</bold>
</xref>). During the three-year period, the average body length and weight of <italic>C. nasus</italic> increased annually (<xref ref-type="table" rid="T3">
<bold>Table&#xa0;3</bold>
</xref>). The gonadal development stage was mainly in stage II, and the proportion of stage II individuals in 2021, 2022, and 2023 was 83.7%, 86.1%, and 79.5%, respectively. The ratio of female to male was 1:1.28, 1:1.14, and 1.87:1, respectively.</p>
<fig id="f3" position="float">
<label>Figure&#xa0;3</label>
<caption>
<p>Length&#x2013;weight relationship of <italic>C. nasus</italic> from 2021&#x2013;2023.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-11-1474996-g003.tif"/>
</fig>
<table-wrap id="T3" position="float">
<label>Table&#xa0;3</label>
<caption>
<p>Composition of body length and weight of <italic>C. nasus</italic> from 2021 to 2023.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="top" align="left">Year</th>
<th valign="top" align="left">Body length range (mm)</th>
<th valign="top" align="left">Weight range (g)</th>
<th valign="top" align="left">Average body length (mm)</th>
<th valign="top" align="left">Average weight (g)</th>
<th valign="top" align="left">Dominant length group (mm) and percentage (%)</th>
<th valign="top" align="left">Dominant weight group (mm) and percentage (%)</th>
<th valign="top" align="left">Number</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">2021</td>
<td valign="top" align="left">13&#x2013;361</td>
<td valign="top" align="left">0.9&#x2013;176.6</td>
<td valign="top" align="left">165.68 &#xb1; 59.61</td>
<td valign="top" align="left">16.79 &#xb1; 22.51</td>
<td valign="top" align="left">91&#x2013;225 (79.31%)</td>
<td valign="top" align="left">0&#x2013;30 (83.08%)</td>
<td valign="top" align="left">2,417</td>
</tr>
<tr>
<td valign="top" align="left">2022</td>
<td valign="top" align="left">51&#x2013;347</td>
<td valign="top" align="left">0.3&#x2013;143.0</td>
<td valign="top" align="left">163.26 &#xb1; 61.43</td>
<td valign="top" align="left">19.30 &#xb1; 20.98</td>
<td valign="top" align="left">76&#x2013;240 (88.90%)</td>
<td valign="top" align="left">0&#x2013;40 (84.08%)</td>
<td valign="top" align="left">2,217</td>
</tr>
<tr>
<td valign="top" align="left">2023</td>
<td valign="top" align="left">95&#x2013;410</td>
<td valign="top" align="left">1.7&#x2013;181.3</td>
<td valign="top" align="left">231.84 &#xb1; 73.95</td>
<td valign="top" align="left">39.27 &#xb1; 36.35</td>
<td valign="top" align="left">151&#x2013;315 (74.44%)</td>
<td valign="top" align="left">0&#x2013;70 (82.22%)</td>
<td valign="top" align="left">360</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="s3_2">
<label>3.2</label>
<title>Model Evaluation</title>
<sec id="s3_2_1">
<label>3.2.1</label>
<title>Population parameters estimated based on ELEFAN</title>
<p>According to the calculation results of <xref ref-type="disp-formula" rid="eq6">Equation 6</xref>, the <italic>OBS</italic> for the LFD of <italic>C. nasus</italic> was determined to be 1 cm. After setting the moving average to 11 (<xref ref-type="fig" rid="f4">
<bold>Figure&#xa0;4</bold>
</xref>), and applying both methods, the ELEFAN-GA (<inline-formula>
<mml:math display="inline" id="im23">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>x</mml:mi>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> =0.32) fitting outcome was superior (<xref ref-type="fig" rid="f5">
<bold>Figure&#xa0;5</bold>
</xref>). The ELEFAN-GA results from 2021&#x2013;2023 indicated that <inline-formula>
<mml:math display="inline" id="im24">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was 42.92 cm, <italic>K</italic> was 0.43 year<sup>-1</sup>, and the theoretical age at length zero (<italic>t<sub>0</sub>
</italic>) for 2021&#x2013;2022 was -0.31 year. Additionally, <italic>Z</italic> from 2021&#x2013;2022 was 1.47 year<sup>-1</sup>, <italic>F</italic> was 0.79 year<sup>-1</sup>, <italic>E</italic> was 0.54.</p>
<fig id="f4" position="float">
<label>Figure&#xa0;4</label>
<caption>
<p>Visualization of <italic>C. nasus</italic> length&#x2013;frequency data. <bold>(A)</bold> Originally measured body length frequency data <bold>(B)</bold> Recombined body length frequency data for <italic>MA</italic> = 11.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-11-1474996-g004.tif"/>
</fig>
<fig id="f5" position="float">
<label>Figure&#xa0;5</label>
<caption>
<p>The seasonal VBGF fitted to length frequency distribution of <italic>C. nasus</italic> using ELEFAN-SA and ELEFAN-GA algorithms.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-11-1474996-g005.tif"/>
</fig>
</sec>
<sec id="s3_2_2">
<label>3.2.2</label>
<title>Population parameters estimated based on LBB</title>
<p>We then combined the <inline-formula>
<mml:math display="inline" id="im25">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> = 42.92 cm and <italic>M/K</italic> = 1.57 values obtained by the ELEFAN method, as prior information, with the LBB method, and estimated that the asymptotic length (<inline-formula>
<mml:math display="inline" id="im26">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) of <italic>C.&#xa0;nasus</italic> captured from 2019&#x2013;2023 was 38.7&#x2013;43.3 cm, and <inline-formula>
<mml:math display="inline" id="im27">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mi>p</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> were 19&#x2013;26 cm (<xref ref-type="table" rid="T4">
<bold>Table&#xa0;4</bold>
</xref>; <xref ref-type="fig" rid="f6">
<bold>Figure&#xa0;6</bold>
</xref>). <italic>Z/K</italic>, <italic>F/K</italic> and <italic>M/K</italic> generally declined, indicating a decreasing impact of fishing pressures. The relative biomass (<italic>B/B<sub>0</sub>
</italic>) of the <italic>C. nasus</italic> population gradually increased, indicating a recovery trend. The ratio of biomass at maximum sustainable yield to initial biomass (<italic>B/B<sub>MSY</sub>
</italic>) increased from 0.5 in 2019 to 2.4 in 2023, indicating that the <italic>C. nasus</italic> population gradually recovered from an overfished state to healthy (<xref ref-type="table" rid="T4">
<bold>Table&#xa0;4</bold>
</xref>; <xref ref-type="fig" rid="f7">
<bold>Figure&#xa0;7</bold>
</xref>).</p>
<table-wrap id="T4" position="float">
<label>Table&#xa0;4</label>
<caption>
<p>Parameter estimates and 95% confidence intervals for each year were obtained using the LBB method in this study.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="top" align="left"/>
<th valign="top" align="left">2019</th>
<th valign="top" align="left">2020</th>
<th valign="top" align="left">2021</th>
<th valign="top" align="left">2022</th>
<th valign="top" align="left">2023</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">
<italic>L<sub>max</sub>
</italic> (cm)</td>
<td valign="top" align="left">40.6</td>
<td valign="top" align="left">39.7</td>
<td valign="top" align="left">36.1</td>
<td valign="top" align="left">34.7</td>
<td valign="top" align="left">41.0</td>
</tr>
<tr>
<td valign="top" align="left">
<italic>L<sub>Copt</sub>
</italic> (cm)</td>
<td valign="top" align="left">26</td>
<td valign="top" align="left">26</td>
<td valign="top" align="left">23</td>
<td valign="top" align="left">19</td>
<td valign="top" align="left">19</td>
</tr>
<tr>
<td valign="top" align="left">
<italic>L<sub>inf</sub>
</italic> (cm)</td>
<td valign="top" align="left">42.9 (42.2&#x2013;43.7)</td>
<td valign="top" align="left">43.0 (42.1&#x2013;43.9)</td>
<td valign="top" align="left">43.3 (42.2&#x2013;44.1)</td>
<td valign="top" align="left">38.7 (38.0&#x2013;39.8)</td>
<td valign="top" align="left">39.8 (39.1&#x2013;40.4)</td>
</tr>
<tr>
<td valign="top" align="left">
<italic>F/K</italic>
</td>
<td valign="top" align="left">4.71 (4.06&#x2013;5.49)</td>
<td valign="top" align="left">10.1 (7.77&#x2013;11.50)</td>
<td valign="top" align="left">1.35 (1.12&#x2013;1.56)</td>
<td valign="top" align="left">0.43 (0.28&#x2013;0.74)</td>
<td valign="top" align="left">0.08 (0.04&#x2013;0.15)</td>
</tr>
<tr>
<td valign="top" align="left">
<italic>Z/K</italic>
</td>
<td valign="top" align="left">6.28 (5.67&#x2013;7.09)</td>
<td valign="top" align="left">11.80 (9.36&#x2013;13.20)</td>
<td valign="top" align="left">2.94 (2.76&#x2013;3.10)</td>
<td valign="top" align="left">2.05 (1.95&#x2013;2.23)</td>
<td valign="top" align="left">1.33 (1.21&#x2013;1.44)</td>
</tr>
<tr>
<td valign="top" align="left">
<italic>F/M</italic>
</td>
<td valign="top" align="left">3.03 (2.55&#x2013;3.62)</td>
<td valign="top" align="left">5.95 (4.56&#x2013;6.99)</td>
<td valign="top" align="left">0.85 (0.63&#x2013;1.07)</td>
<td valign="top" align="left">0.27 (0.16&#x2013;0.53)</td>
<td valign="top" align="left">0.06 (0.03&#x2013;0.13)</td>
</tr>
<tr>
<td valign="top" align="left">
<italic>Y&#x2019;/R</italic> (gr)</td>
<td valign="top" align="left">0.04 (0.027&#x2013;0.045)</td>
<td valign="top" align="left">0.02 (0.014&#x2013;0.025)</td>
<td valign="top" align="left">0.03 (0.021&#x2013;0.041)</td>
<td valign="top" align="left">0.02 (0.010&#x2013;0.048)</td>
<td valign="top" align="left">0.01 (0.004&#x2013;0.025)</td>
</tr>
<tr>
<td valign="top" align="left">
<italic>B/B<sub>0</sub>
</italic>
</td>
<td valign="top" align="left">0.18 (0.141&#x2013;0.233)</td>
<td valign="top" align="left">0.12 (0.080&#x2013;0.148)</td>
<td valign="top" align="left">0.26 (0.176&#x2013;0.345)</td>
<td valign="top" align="left">0.59 (0.266&#x2013;1.310)</td>
<td valign="top" align="left">0.90 (0.302&#x2013;2.160)</td>
</tr>
<tr>
<td valign="top" align="left">
<italic>B/B<sub>MSY</sub>
</italic>
</td>
<td valign="top" align="left">0.50 (0.39&#x2013;0.64)</td>
<td valign="top" align="left">0.33 (0.22&#x2013;0.41)</td>
<td valign="top" align="left">0.71 (0.49&#x2013;0.95)</td>
<td valign="top" align="left">1.60 (0.73&#x2013;3.59)</td>
<td valign="top" align="left">2.40 (0.80&#x2013;5.74)</td>
</tr>
<tr>
<td valign="top" align="left">Stock status</td>
<td valign="top" align="left">Fully/overfished stocks</td>
<td valign="top" align="left">Stocks outside of safe biological limits</td>
<td valign="top" align="left">Recovering stocks</td>
<td valign="top" align="left">Healthy</td>
<td valign="top" align="left">Healthy</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Refer to <xref ref-type="bibr" rid="B17">Froese et&#xa0;al. (2018)</xref> and <xref ref-type="bibr" rid="B76">Zhai et&#xa0;al. (2022)</xref> for the definition of fish stock status. <italic>L<sub>max</sub>
</italic>: maximum body length; <italic>L<sub>c</sub>
</italic>: length at first capture; <italic>L<sub>Copt</sub>
</italic>: optimal catch length; <italic>L<sub>inf</sub>
</italic>: asymptotic body length; <italic>F/K</italic>: ratio of fishing mortality coefficient to growth parameter; <italic>Z/K</italic>: ratio of total mortality rate to growth parameter; <italic>F/M:</italic> ratio of fishing mortality coefficient to natural mortality coefficient; <italic>Y&#x2019;/R</italic>: relative unit supplement yield; <italic>B/B<sub>0</sub>
</italic>: relative biomass; <italic>B/B<sub>MSY</sub>
</italic>: ratio of biomass at maximum sustainable yield to initial biomass.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<fig id="f6" position="float">
<label>Figure&#xa0;6</label>
<caption>
<p>Estimation results of the length-based Bayesian biomass estimation (LBB) method for <italic>C. nasus</italic> from 2019&#x2013;2023 <bold>(A&#x2013;E)</bold>. Left figure shows the LFD, <italic>a priori</italic> asymptotic body length (<italic>L<sub>inf</sub>
</italic>), and ratio of total mortality to growth rate (<italic>Z/K</italic>) estimated from LFD. Right figure shows the results of fitting the LBB master equation to LFD.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-11-1474996-g006.tif"/>
</fig>
<fig id="f7" position="float">
<label>Figure&#xa0;7</label>
<caption>
<p>Continuous estimation results of <italic>C. nasus</italic> from 2019&#x2013;2023 using the LBB method. <bold>(A)</bold> Average capture length/optimal length for unexploited generations with maximum biomass (<italic>L<sub>mean</sub>/L<sub>opt</sub>
</italic>; solid black line) and length at first capture/optimal catch length (<italic>L<sub>c</sub>/L<sub>Copt</sub>
</italic>; dashed black line). <bold>(B)</bold> Fishing mortality coefficient/natural mortality coefficient (<italic>F/M</italic>; solid black line) and its 95% confidence interval (dashed black line), with a reference line (solid green line) indicating the point where <italic>F = M</italic>. <bold>(C)</bold> Relative biomass of the <italic>C. nasus</italic> population (<italic>B/B<sub>0</sub>
</italic>; solid black line) and its 95% confidence interval (dashed black line). Biomass (<italic>B</italic>) value for <italic>F</italic> = <italic>M</italic> and optimal <italic>L<sub>c</sub>
</italic> is shown by the dashed green line, whereas that for an alternative ratio of biomass at maximum sustainable yield to initial biomass of 0.5 is shown by the dashed blue line.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-11-1474996-g007.tif"/>
</fig>
</sec>
</sec>
</sec>
<sec id="s4" sec-type="discussion">
<label>4</label>
<title>Discussion</title>
<p>Both the ELEFAN and LBB methods are advantageous in that they minimize data requirements (<xref ref-type="bibr" rid="B54">Shi et&#xa0;al., 2022</xref>), enabling a reasonable assessment of the population status of <italic>C. nasus</italic>. The ELEFAN method is a technique for inferring the stock status of a population by analyzing the length&#x2013;frequency distribution of captured fish. Since its development, FiSAT II software has become the preferred tool for conducting ELEFAN analyses and has been widely applied across various fisheries worldwide (<xref ref-type="bibr" rid="B73">Ye et al., 2014</xref>; <xref ref-type="bibr" rid="B46">Osei et&#xa0;al., 2021</xref>). After the development of the TropFishR package, fixed applications within the FiSAT II software were optimized, leading to the formation of a comprehensive suite of methods for fishery analysis using LFD, such as: ELEFAN-SA and ELEFAN-GA (<xref ref-type="bibr" rid="B32">Korkmaz et&#xa0;al., 2023</xref>). Similar to the ELEFAN method, the LBB method use LFD as the initial input for population assessment (<xref ref-type="bibr" rid="B81">Zhang et&#xa0;al., 2021b</xref>). Moreover, the ELEFAN method can offer effective prior information for the LBB method, thereby improving the precision of its estimation outcomes (<xref ref-type="bibr" rid="B83">Ziegler et&#xa0;al., 2011</xref>). In the LBB method, the default <italic>M/K</italic> values can be replaced by alternative values according to different life histories among populations. Choosing <italic>M/K</italic> values within the range of 0.3&#x2013;3.0 has a minimal impact on relative biomass estimates (<xref ref-type="bibr" rid="B17">Froese et&#xa0;al., 2018</xref>). Therefore, we applied the management reference points <inline-formula>
<mml:math display="inline" id="im28">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (42.92 cm), <italic>M</italic> (0.68 year<sup>-1</sup>), and <italic>K</italic> (0.432 year<sup>-1</sup>) estimated using the ELEFAN method as prior information for LBB estimation, thereby correcting the fixed default value of <italic>M/K</italic> and enhancing the accuracy and credibility of the LBB estimation results. In this study, we measured the whole length data of 4,494 individuals of <italic>C. nasus</italic> over a period of 3 years, representing the recent population composition of this species. Consequently, the collected data meet the requirements of both methods. In addition, the estimation results are suitable for fishery management and can be used directly as prior information for other assessment methods.</p>
<p>Fishery production data reflect the growth conditions of organisms to a certain extent (<xref ref-type="bibr" rid="B20">Geng et&#xa0;al., 2019</xref>). The data collected during April over three consecutive years (2020&#x2013;2022) indicate that, after implementation of the 10-year fishing ban on the Yangtze River, the relative proportion of <italic>C. nasus</italic> in the catch increased. Both its weight proportion and number of individuals increased considerably, from less than 1% to over 5%. The average body length and weight also showed a consistent annual increase, indicating a clear resource recovery trend (<xref ref-type="table" rid="T2">
<bold>Table&#xa0;2</bold>
</xref>). Fish growth parameters indicate not only their growth and survival status but also habitat suitability to a certain degree (<xref ref-type="bibr" rid="B24">Han et&#xa0;al., 2017</xref>). The biological data of <italic>C. nasus</italic> from 2021&#x2013;2023 also revealed consistent outcomes: the distribution of body length and weight became more uniform. An increase in the number of larger-sized individuals was also observed, alongside an increase in both the average body length and average weight of the population. <italic>C. nasus</italic> has a relatively short life cycle and is highly sensitive to fishing pressure, necessitating a lengthy recovery period following resource depletion (<xref ref-type="bibr" rid="B82">Zhang et&#xa0;al., 2005</xref>). However, following implementation of the 10-year fishing ban and the expansion of the Yangtze River Estuary Fishing Ban Zone, the high-pressure fishing activities that previously threatened the resources of <italic>C. nasus</italic> in the Yangtze River Basin have completely ceased. This has greatly reduced fishing pressure on <italic>C. nasus</italic>, allowing breeding adults to smoothly enter the spawning grounds, thereby increasing the recruitment of the population. Concurrently, the mortality rate of young fish attributed to bycatch in eel fry nets has decreased considerably. Furthermore, we observed the fish season of <italic>C. nasus</italic>, which was not observed during overfishing. In the study, the <italic>C. nasus</italic> had an obvious fishing season, which began at the end of February and extended through May. This finding aligns with historical data on the timing of the fishing season (<xref ref-type="bibr" rid="B75">Yuan et&#xa0;al., 1980</xref>; <xref ref-type="bibr" rid="B37">Liu et&#xa0;al., 2012</xref>). The reappearance of migratory <italic>C. nasus</italic> in the Xiangjiang River of Hunan Province in 2023 substantiates the profound impact of the decade-long fishing moratorium on the conservation of this species.</p>
<p>In this study, sample data of <italic>C. nasus</italic>, collected following implementation of the fishing ban, were used to estimate the population status via the ELEFAN method. With the fishery development rate of 0.54, indicating that the effects of historical overfishing are still present. Although the early phase of the Yangtze River&#x2019;s 10-year fishing moratorium demonstrated a nascent recovery in the number and resource status of <italic>C. nasus</italic>, a prolonged period of recovery is still essential (<xref ref-type="bibr" rid="B29">Jiang et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B40">Ma et&#xa0;al., 2022</xref>). Moreover, the estimation results of the LBB method provided further details. Between 2019 and 2023, <italic>C. nasus</italic> resources exhibited a fluctuating upward trend. Except for a minor decline in 2020, the relative biomass of <italic>C. nasus</italic> has increased annually, demonstrating a positive recovery trend. Although the issuance of special fishing licenses for <italic>C. nasus</italic> ended in the Yangtze River Basin in 2019, the resource volume did not significantly increase in the subsequent period, which may be attributed to the high-intensity fishing activities that still persist in the Yangtze River Basin. Fishing activities, such as eel fry fishing, may impede the recovery of <italic>C. nasus</italic> populations (<xref ref-type="bibr" rid="B82">Zhang et&#xa0;al., 2005</xref>). In China, the period in which eel fry are usually caught, between January and April, significantly overlaps with the migration of young <italic>C. nasus</italic> for feeding (<xref ref-type="bibr" rid="B18">Ge et&#xa0;al., 2013</xref>). The Yangtze River Estuary is the main migration channel and primary area for eel fry fishing (<xref ref-type="bibr" rid="B63">Wang S. et&#xa0;al., 2023</xref>). During the eel fry fishing season, numerous eel fry nets are deployed in the Yangtze River Estuary area, where young <italic>C. nasus</italic> enter the nets with the tide, resulting in a large number of deaths (<xref ref-type="bibr" rid="B82">Zhang et&#xa0;al., 2005</xref>). Multiple studies have indicated that young <italic>C. nasus</italic> often become a dominant bycatch species during eel fry fishing (<xref ref-type="bibr" rid="B18">Ge et&#xa0;al., 2013</xref>; <xref ref-type="bibr" rid="B13">Deng et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B70">Yan et&#xa0;al., 2024</xref>). Consequently, despite the cessation of specialized fishing for <italic>C. nasus</italic>, eel fry fishing activities may still affect the recovery of the <italic>C. nasus</italic> population to some extent. After the full implementation of the 10-year fishing ban in the Yangtze River in 2021, eel fry fishing was prohibited within the Yangtze River Estuary Fishing Ban Zone, allowing the early recruits of <italic>C. nasus</italic> to pass through the area smoothly improving its survival rate and increasing the amount of <italic>C.&#xa0;nasus</italic> resources.</p>
<p>Fish resources are affected by many factors, such as fish adaptability, germplasm characteristics and habitat environment (<xref ref-type="bibr" rid="B41">Meffe, 1986</xref>; <xref ref-type="bibr" rid="B72">Yang et al., 2014</xref>; <xref ref-type="bibr" rid="B16">Duarte et&#xa0;al., 2020</xref>). The population of <italic>C. nasus</italic> is primarily affected by its own reproductive capacity and environmental factors (<xref ref-type="bibr" rid="B82">Zhang et&#xa0;al., 2005</xref>). <italic>C. nasus</italic> individuals can reach sexual maturity at two years of age and have a strong reproductive capacity, allowing rapid population increases and demonstrating significant potential for resource recovery (<xref ref-type="bibr" rid="B56">Song et&#xa0;al., 2022</xref>). Since the Yangtze River Protection Strategy was proposed in 2016, there has been a strengthening of river management along the Yangtze River and water source management, which collectively contributed to a significant and comprehensive improvement in the ecological environment of the Yangtze River Basin (<xref ref-type="bibr" rid="B15">Dong et&#xa0;al., 2024</xref>). The spawning and hatching habitats of <italic>C. nasus</italic> are located within the Poyang Lake and Dongting Lake (<xref ref-type="bibr" rid="B69">Xuan et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B29">Jiang et&#xa0;al., 2022</xref>). The improved habitat not only boosts the survival rate of <italic>C. nasus</italic> eggs but also provides an excellent feeding environment for larvae and juveniles, thereby increasing the resources of the early supplementary population of <italic>C. nasus</italic>. Moreover, as a high trophic level consumer in the Yangtze River, the trophic level of <italic>C. nasus</italic> increases with body length (<xref ref-type="bibr" rid="B12">Deng, 2023</xref>; <xref ref-type="bibr" rid="B38">Liu et&#xa0;al., 2023</xref>). There are fewer fish that prey on <italic>C. nasus</italic> in the river, and the resources for adult <italic>C. nasus</italic> are well protected. These factors contribute to the possibility of maintaining a stable population structure and a continuous increase in resources as showed in this study. The relative biomass of <italic>C. nasus</italic> in 2022 doubled from that in 2021, likely because of the accumulation of population resources prior to this period. Additionally, the expansion policy implemented in the Yangtze River Estuary Fishing Ban Zone on November 20, 2021, provided a wider range of protection for young <italic>C. nasus</italic> that year. In 2022 and 2023, the relative biomass increased by 3.3 times and 4 times than in 2021, respectively, and the population assessment results of <italic>C. nasus</italic> were in a healthy state. However, the proportion of young <italic>C. nasus</italic> below age 1 caught during 2022 and 2023 was low, so the lack of assessment of young <italic>C.&#xa0;nasus</italic> possibly cause an overestimation of the population state in our study. In the future, it is necessary to increase the survey frequency of young <italic>C. nasus</italic> as they return from the spawning grounds to the sea, in order to better assess the population dynamics.</p>
<p>
<xref ref-type="table" rid="T5">
<bold>Table&#xa0;5</bold>
</xref> illustrates that <xref ref-type="bibr" rid="B76">Zhai et&#xa0;al. (2022)</xref> used the LBB method to evaluate the historical resource status of <italic>C. nasus</italic>. In contrast, the results of this study on the population status of <italic>C. nasus</italic> in 2021 are similar to those of 2011 (<xref ref-type="table" rid="T4">
<bold>Tables&#xa0;4</bold>
</xref>, <xref ref-type="table" rid="T5">
<bold>5</bold>
</xref>), which reflects that the utilization intensity of <italic>C. nasus</italic> resources has decreased and its resource sustainability has increased. However, the <italic>F/M</italic> in 2011 was significantly higher than that in 2021, suggesting that the excessive fishing pressure during 2011 was the primary cause for the population decline, a factor closely tied to the geographical locations of the two study areas. Numerous studies have shown that the distribution of <italic>C.&#xa0;nasus</italic> is significantly influenced by environmental factors such as temperature, water depth, and salinity. Specifically, in the Yangtze River Estuary, <italic>C. nasus</italic> is predominantly found in areas with water depths exceeding 10 meters, where the temperature is relatively high and salinity fluctuations are minimal (<xref ref-type="bibr" rid="B23">Guo et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B57">Tong et&#xa0;al., 2018</xref>). The northern branch of the Yangtze River Estuary is characterized by shallow water depths and significant salinity changes. Therefore, the resources of <italic>C. nasus</italic> in the southern branch of the Yangtze River Estuary are usually significantly higher than those in the northern branch, and fishing vessels are more inclined to catch <italic>C. nasus</italic> in the southern branch of the Yangtze River Estuary. The survey area in 2011 of <xref ref-type="bibr" rid="B76">Zhai et&#xa0;al. (2022)</xref> for <italic>C. nasus</italic> was situated in the southern branch of the Yangtze River Estuary, where fishing pressure is higher. This aligns with our research findings. Moreover, the study also indicates that the implementation of the 10-year fishing ban along the Yangtze River and the expansion of the Fishing Ban Zone in the Yangtze Estuary have had a positive impact on the recovery of diadromous fish species, including <italic>C. nasus</italic>. Currently, in the early stages of the fishing ban, aquatic biological resources have been effectively protected and have shown notable recovery. The index of aquatic biological integrity has improved markedly from pre-ban levels (<xref ref-type="bibr" rid="B43">Meng et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B64">Wang Y. et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B39">Luo, 2024</xref>; <xref ref-type="bibr" rid="B71">Yang et&#xa0;al., 2024</xref>). Therefore, the study advocates for the implementation of long-term monitoring and research on diadromous fish populations with a particular emphasis on important migration channels as the adjacent marine areas of Yangtze River Estuary Fishing Ban Zone. It will enable a scientific assessment of resource changes and facilitate the timely adjustment of management measures in ocean, especially for <italic>C. nasus</italic>, and help to accelerate the recovery of <italic>C. nasus</italic> from its endangered status.</p>
<table-wrap id="T5" position="float">
<label>Table&#xa0;5</label>
<caption>
<p>Parameter estimates and 95% confidence intervals obtained using the length-based Bayesian biomass estimation (LBB) method in previous studies.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="top" align="left"/>
<th valign="top" align="left">2006</th>
<th valign="top" align="left">2011</th>
<th valign="top" align="left">2019&#x2013;2020</th>
<th valign="top" align="left">2021</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">
<italic>L<sub>max</sub>
</italic> (cm)</td>
<td valign="top" align="left">35.0</td>
<td valign="top" align="left">33.4</td>
<td valign="top" align="left">16.2</td>
<td valign="top" align="left">36.1</td>
</tr>
<tr>
<td valign="top" align="left">
<italic>L<sub>inf</sub>
</italic> (cm)</td>
<td valign="top" align="left">38.2</td>
<td valign="top" align="left">38.7</td>
<td valign="top" align="left">17.1</td>
<td valign="top" align="left">43.3</td>
</tr>
<tr>
<td valign="top" align="left">
<italic>F/K</italic>
</td>
<td valign="top" align="left">0.44 (0.23&#x2013;0.72)</td>
<td valign="top" align="left">2.28 (1.76&#x2013;2.64)</td>
<td valign="top" align="left">1.5 (1.16&#x2013;2.19)</td>
<td valign="top" align="left">1.35 (1.12&#x2013;1.56)</td>
</tr>
<tr>
<td valign="top" align="left">
<italic>Z/K</italic>
</td>
<td valign="top" align="left">1.67 (1.53&#x2013;1.79)</td>
<td valign="top" align="left">3.68 (3.43&#x2013;3.95)</td>
<td valign="top" align="left">2.21 (2.00&#x2013;2.53)</td>
<td valign="top" align="left">2.94 (2.76&#x2013;3.10)</td>
</tr>
<tr>
<td valign="top" align="left">
<italic>F/M</italic>
</td>
<td valign="top" align="left">0.36 (0.17&#x2013;0.76)</td>
<td valign="top" align="left">1.62 (0.93&#x2013;2.11)</td>
<td valign="top" align="left">0.55 (0.35&#x2013;0.90)</td>
<td valign="top" align="left">0.85 (0.63&#x2013;1.07)</td>
</tr>
<tr>
<td valign="top" align="left">
<italic>Y&#x2019;/R</italic> (gr)</td>
<td valign="top" align="left">0.04 (0.01&#x2013;0.09)</td>
<td valign="top" align="left">0.057 (0.028&#x2013;0.084)</td>
<td valign="top" align="left">0.110 (&#x2212;0.460 to 1.200)</td>
<td valign="top" align="left">0.03 (0.021&#x2013;0.041)</td>
</tr>
<tr>
<td valign="top" align="left">
<italic>B/B<sub>0</sub>
</italic>
</td>
<td valign="top" align="left">0.63 (0.16&#x2013;1.40)</td>
<td valign="top" align="left">0.26 (0.13&#x2013;0.39)</td>
<td valign="top" align="left">0.08 (&#x2013;0.33 to 0.86)</td>
<td valign="top" align="left">0.26 (0.176&#x2013;0.345)</td>
</tr>
<tr>
<td valign="top" align="left">
<italic>B/B<sub>MSY</sub>
</italic>
</td>
<td valign="top" align="left">1.7 (0.42&#x2013;3.80)</td>
<td valign="top" align="left">0.71 (0.35&#x2013;1.10)</td>
<td valign="top" align="left">0.17(&#x2013;0.72 to 1.90)</td>
<td valign="top" align="left">0.71 (0.49&#x2013;0.95)</td>
</tr>
<tr>
<td valign="top" align="left">Stock status</td>
<td valign="top" align="left">Healthy</td>
<td valign="top" align="left">Fully/overfished stocks</td>
<td valign="top" align="left">Stocks outside of safe biological limits</td>
<td valign="top" align="left">Recovering stocks</td>
</tr>
<tr>
<td valign="top" align="left">Source</td>
<td valign="top" align="left">Zhai et&#xa0;al.</td>
<td valign="top" align="left">Zhai et&#xa0;al.</td>
<td valign="top" align="left">Zhai et&#xa0;al.</td>
<td valign="top" align="left">This study</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Refer to the LBB estimation results of <xref ref-type="bibr" rid="B76">Zhai et&#xa0;al. (2022)</xref>. <italic>L<sub>max</sub>
</italic>: maximum body length; <italic>L<sub>inf</sub>
</italic>: asymptotic body length; <italic>F/K</italic>: ratio of fishing mortality coefficient to growth parameter; <italic>Z/K</italic>: ratio of total mortality rate to growth parameter; <italic>F/M:</italic> ratio of fishing mortality coefficient to natural mortality coefficient; <italic>Y&#x2019;/R</italic>: relative unit supplement yield; <italic>B/B<sub>0</sub>
</italic>: relative biomass; <italic>B/B<sub>MSY</sub>
</italic>: ratio of biomass at maximum sustainable yield to initial biomass.</p>
</fn>
</table-wrap-foot>
</table-wrap>
</sec>
</body>
<back>
<sec id="s5" sec-type="data-availability">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/<xref ref-type="supplementary-material" rid="SM1">
<bold>Supplementary Material</bold>
</xref>. Further inquiries can be directed to the corresponding author/s.</p>
</sec>
<sec id="s6" sec-type="ethics-statement">
<title>Ethics statement</title>
<p>The animal study was reviewed and approved by Marine Fisheries Research Institute of Jiangsu Province.</p>
</sec>
<sec id="s7" sec-type="author-contributions">
<title>Author contributions</title>
<p>SW: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Writing &#x2013; original draft, Writing &#x2013; review &amp; editing. YX: Conceptualization, Funding acquisition, Resources, Writing &#x2013; review &amp; editing. HZ: Formal analysis, Investigation, Visualization, Writing &#x2013; review &amp; editing. DS: Formal analysis, Visualization, Writing &#x2013; review &amp; editing. YW: Data curation, Investigation, Resources, Writing &#x2013; review &amp; editing. HG: Data curation, Investigation, Resources, Writing &#x2013; review &amp; editing. CZ: Formal analysis, Visualization, Writing &#x2013; review &amp; editing. LL: Conceptualization, Funding acquisition, Methodology, Writing &#x2013; review &amp; editing. XZ: Conceptualization, Funding acquisition, Methodology, Writing &#x2013; review &amp; editing.</p>
</sec>
<sec id="s8" sec-type="funding-information">
<title>Funding</title>
<p>The author(s) declare financial support was received for the research, authorship, and/or publication of this article. This work was supported by the National Nature Science Foundation of China (Grant No. 32473169) and the Fisheries Ecology and Resources Monitoring Projects of Agricultural Ecological Protection and Resource Utilization in Jiangsu Province (2021&#x2013;SJ&#x2013;110&#x2013;02 and 2022&#x2013;SJ&#x2013;061&#x2013;01).</p>
</sec>
<sec id="s9" sec-type="COI-statement">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec id="s10" sec-type="disclaimer">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<sec id="s11" sec-type="supplementary-material">
<title>Supplementary material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/fmars.2024.1474996/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/fmars.2024.1474996/full#supplementary-material</ext-link>
</p>
<supplementary-material xlink:href="Table1.docx" id="SM1" mimetype="application/vnd.openxmlformats-officedocument.wordprocessingml.document"/>
</sec>
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