Multi-model assessment and management of data-limited fish stocks in the Bohai Sea, China

Abstract

Similar to small-scale fisheries elsewhere in the world, the Bohai Sea fishery in China operates under data-limited conditions. This study employed five length-based data-limited assessment methods to evaluate the sustainability of 19 important exploited fish stocks, which are core components supporting the provisioning, regulating and cultural ecosystem services of the Bohai Sea ecosystem. Results indicate that 26% of the assessed species are in a sustainable state with no risk; 37% are in an acceptable condition but require targeted management measures; and the remaining 37% necessitate comprehensive enhanced management (16% are overfished, while 21% face high risks). The findings provide management recommendations tailored to each species’ status: (1) regulate fishing effort and catch quotas; (2) increase minimum landing sizes; and (3) enlarge minimum mesh sizes. Global experience demonstrates that scientifically assessed and managed fish stocks are showing biomass recovery. Therefore, adopting these management recommendations is crucial for securing sustainable food production and maintaining the integrity of ecosystem services from the Bohai Sea fishery ecosystem.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-56613-3.

Introduction

Small-scale fisheries (SSF) are regarded as a vital economic and social driver for global food and nutritional security, accounting for two-thirds of seafood consumption and nearly half of global reported catches¹. They also are critical carriers of marine ecosystem services. They underpin provisioning services (sustainable seafood supply), regulating services (habitat maintenance and biodiversity conservation), and cultural services (livelihood support for coastal communities). Ensuring their sustainability requires science-based management, which in turn depends on understanding fish stock status and exploitation levels. Stock assessment provides the necessary scientific and quantitative foundation for this understanding and for guiding effective management². By providing quantitative indicators of stock status, fisheries assessment allows comparisons among species and offers an important basis for evaluating broader ecosystem condition. The recovery of many depleted stocks under science-based management further highlights the value of such assessment frameworks^3,4.

Globally, only about 50% of exploited fish stocks have been formally assessed, largely because traditional (conventional data-intensive) stock assessment methods require substantial data inputs^5,6. This challenge is particularly pronounced in small-scale fisheries, which are often characterized by highly diverse catch compositions—sometimes involving hundreds of species—and a general lack of key species-specific data, such as detailed catch records, age composition, or abundance indices. As a result, the management of many species in these data-limited fisheries operates without the support of robust stock assessments^7–9.

Insufficient data has led to the characterization of many small-scale fisheries as data-limited. In response to the growing need for managing data-limited fisheries, methods for estimating stock status and exploitation rates have advanced rapidly in recent years^10–12. These methods can be broadly categorized into six types based on their input requirements: (1) risk or vulnerability assessment, (2) indicator-based, (3) life history-based, (4) catch-only, (5) length-based, and (6) model-based approaches¹³. Although all six fall under the umbrella of data-limited stock assessment methods, they differ in various aspects—such as the suitability of their model outputs for informing effort or catch regulations.

Length-frequency data, whether obtained from fishery-dependent catch sampling or fishery-independent scientific surveys, often constitute the most accessible primary data type for many small-scale fisheries. Consequently, length-based assessment methods have been widely applied as part of the data-limited assessment toolkit to support the management of these fisheries. Notable examples include: Length-Based Pseudo-Cohort Analysis (LBPA; Canales and Mardones, 2021); Length-Based Spawning Potential Ratio Model (LBSPR;¹⁴); Length-Based Integrated Mixed Effects Model (LIME;¹⁵); Length-Based Bayesian Biomass Approach (LBB;¹⁶); and Length-Based Indicators (LBI;¹⁷,¹⁸). These length-based methods, which require only length composition of catches along with life-history parameters, are becoming increasingly prevalent for assessing data-limited fish stocks^14,19. They hold significant potential for application in assessing fish species where catch statistics are unavailable.

The Bohai Sea, a vital component of the Northwest Pacific’s Yellow Sea Large Marine Ecosystem (YSLME), serves as a critical spawning, feeding, and fishing ground for dozens of fish species and plays a significant role in recruitment of fish stocks across the Yellow and Bohai Seas^20–22. Those fish stocks are core components supporting the provisioning, regulating and cultural ecosystem services of the Bohai Sea ecosystem. Currently, fisheries in the Bohai Sea are predominantly small-scale, livelihood-oriented operations run by individual households. Since the 1960s, the dominant fish species in these fisheries have undergone multiple successive shifts^23,24,22. Consequently, studying the status and potential of Bohai Sea fish resources and proposing science-based management recommendations are of great significance for safeguarding fishers’ livelihoods and the health of the YSLME. Existing catch statistics make it difficult to disaggregate species-specific fishery yields for the Bohai Sea from the broader YSLME, hindering the application of traditional models to assess the status of Bohai Sea fish stocks. Consequently, the unknown status of most fish stocks makes it challenging for managers to comprehensively evaluate the effectiveness of the numerous existing Bohai Sea fishery management measures, such as seasonal fishing moratoria, gear restrictions, minimum mesh-size regulations, and stock enhancement programs, and to make timely, science-informed adjustments.

The primary objective of this study is to conduct a scientific assessment of the current multi-species fisheries in the Bohai Sea using data of key fish species obtained from scientific surveys. Specifically, the study aims to: (1) evaluate the stock status of major fish species in the Bohai Sea using five length-based methods (LBPA, LBSPR, LIME, LBB, and LBI); (2) analyse the relationship between stock status and population characteristics; and (3) assess the effectiveness of current fisheries management strategies in population recovery and propose species-specific management recommendations.

Materials and methods

Data used

Fish length-frequency data were collected from trawl surveys in the Bohai Sea conducted by the Yellow Sea Fisheries Research Institute, Chinese Academy of Fishery Sciences. The 34 fixed monitoring stations, forming a semi-regular spatially representative pattern, from where length-frequency data were repeatedly collected are shown in Fig. 1, with surveys taking place during May–June, August–September, October, and December–January from 2021 to 2024. The survey vessel used was the fisheries research vessel Zhongyuke 102. Based on data availability, 19 major fish species (7 pelagic and 12 demersal) were selected as the study subjects. Population characteristics (Table 1) of these species were compiled from the FishBase database, market prices statistics, and scientific literature^25,26. Specifically, trophic level, habitat layer, and lifespan-related traits were derived from FishBase and published studies; unit price was obtained from market price statistics; unit price classification was assigned according to the corresponding unit price values (High > 15, Low < 7, and Medium ≥ 7 and ≤ 15); and commercial level was determined based on Cheng et al.,²⁵. These variables spanned a broad range of trophic levels, life spans, commercial values, and market price categories, thereby ensuring broad representativeness of the selected stocks.

Fig. 1.

Stations for the scientific survey of fishery resources in the Bohai Sea during 2021—2024.

Table 1.

Major fish stocks and their characteristics in the Bohai Sea in this study.

Species name	Code	Lifespan	Lifespan level	Habitat Layer	Trophic Level	Trophic Level classification	Commercial Level	Unit Price	Unit Price classification
Engraulis japonicus	EJA	4	Medium	pelagic	3.1	Low	High	3.49	Low
Setipinna taty	STA	4	Medium	pelagic	3.5	Low	Medium	12	Medium
Thryssa kammalensis	TKA	3	Low	pelagic	3.3	Low	Low	3.1	Low
Sardinella zunasi	SZU	6	Medium	pelagic	3.2	Low	High	10	Medium
Pampus argenteus	PAR	6	Medium	pelagic	3.3	Low	High	85.86	High
Konosirus punctatus	KPU	6	Medium	pelagic	2.9	Low	Medium	8	Medium
Coilia mystus	CMY	6	Medium	pelagic	3.2	Low	Low	15	Medium
Trichiurus lepturus	TLE	10	High	demersal	4.4	High	High	77.14	High
Larimichthys polyactis	LPO	7	High	demersal	4	Medium	High	36.57	High
Cynoglossus joyneri	CJO	6	Medium	demersal	3.3	Low	High	40	Medium
Ammodytes personatus	APE	3	Low	demersal	3.1	Low	High	5.98	Low
Eupleurogrammus muticus	EMU	3	Low	demersal	3.6	Medium	High	70	High
Pholis fangi	PFA	4	Medium	demersal	3.2	Low	Low	5	Low
Chaeturichthys stigmatias	CST	1	Low	demersal	3.6	Medium	High	15	Medium
Amblychaeturichthys hexanema	AHE	2	Low	demersal	3.7	Medium	Medium	4	Low
Argyrosomus argentatus	AAR	10	High	demersal	4.4	High	High	16.71	High
Liparis tanakae	LTA	7	High	demersal	4.4	High	Low	4	Low
Johnius belangerii	JBE	4	Medium	demersal	4.1	High	Medium	12	Medium
Zoarces elongatus	ZEL	4	Medium	demersal	3.5	Medium	Low	8	Medium

Life history and fishery parameters (See Table 2 and Supplementary Table 1) required for the length-based models were sourced from: (1) local studies on life history parameters^{27,28,20,23,21,29,30}; (2) the FishBase database and the R package “FishLife”³¹; (3) the natural mortality estimation procedure in the Barefoot Ecologist’s Toolbox³²; and (4) the length-transformed catch curve procedure for estimating selectivity in the R package “TropFishR”³³.

Table 2.

Summary of input, assumptions, and output of the length-based models.

Method	Inputs	Assumptions	Outputs
LBPA	(1) Length-frequency data	(1) Natural mortality is constant	(1) Current F
	(2) von Bertalanffy growth function (L∞; K; t0)	(2) Selectivity and maturity follow logistic curve	(2) SPR
	(3) Length–weight relationship (a and b)		(3)F/Ftar
	(4)M
	(5) Length at 50% and 95% maturity (L50 and L95)
	(6) Spawn time
LBSPR	(1) Length-frequency data	(1) Stock is in equilibrium	(1)F/M (used to calculate F)
	(2) Asymptotic length (L∞)	(2) Natural mortality and growth rates are constant	(2) Length at 50% and 95% selectivity (Ls50 and Ls95)
	(3) Coefficient of variation (CVL∞)	(3) Selectivity and maturity follow logistic curve	(3)SPR
	(4) M/K; steepness (h)	(4) Both sexes have the same growth curve and the sex ratio is equal	(4)F
	(5) Length–weight relationship (a and b)	(5) The lengths at each age are normally distributed around a mean length-at-age value.
	(6) L50 and L95
LIME	(1) Length-frequency data	(1) Natural mortality is constant	(1) SPR
	(2) L∞; K; t0; CVL∞	(2) Selectivity and maturity follow logistic curve	(2) Recruitment
	(3) Length–weight relationship		(3) Spawning biomass
	(4)M; steepness (h)		(4)Mean length
	(5) Ls50 and Ls95		(5) Ls50 and Ls95
	(6) Length at 50% maturity (L50)		(5)Current F; F/M
	(7) maturity ogive
LBB	(1) Length-frequency data	(1) Growth, mortality and recruitment rates are constant	(1)Lmean/Lopt
	(2) L∞	(2) Selectivity follow logistic curve	(2)Lc/Lopt
	(3) M/K		(3)F/M
	(4) Lc		(4)B/B0
	(5) Length at 50% maturity (L50)		(5)B/BMSY
LBI	(1) Length-frequency data	(1) Stock is in equilibrium	(1)Lc/Lmat
	(2) L∞	(2) Selectivity follow logistic curve	(2)L25%/Lmat
	(3) M/K	(3)A length-based proxy for MSY is LF=M=0.75Lc+0.25 L∞	(3)Lmax5%/L∞
	(4) Length–weight relationship	(4) Lopt is derived under the Beverton–Holt framework as L∞ × 3/(3 + M/K)	(4)Pmega
	(5) Length at 50% maturity (L50)	(5) Constant M/K	(5)Lmean/Lopt
			(6)Lmean/LF=M

Length-based methods

This study employed five length-based methods—LBPA, LBSPR, LIME, LBB, and LBI—to fit data from 19 representative fish stocks in the Bohai Sea. Table 2 summarizes the model inputs, assumptions, and outputs. These models, grounded in both non-equilibrium and equilibrium principles, are commonly used in contemporary stock assessment. All require at least one year of length-composition data along with assumptions about growth, natural mortality, and sexual maturity to estimate stock status reference points^34–37,15. Models were deemed converged when the final gradient for all parameters fell below 0.001.

The Length-Based Pseudo-Cohort Analysis (LBPA) model estimates parameters using multiple length-frequency samples and penalized maximum likelihood. The use of multiple length-frequency samples from different time periods is intended to reduce sensitivity to the equilibrium assumption inherent in the model³⁸. The model fits length-frequency data via a per-recruit pseudo-cohort analysis framework to estimate selectivity parameters, fishing mortality (F), and the biological reference point Spawning Potential Ratio (SPR). Spawning Potential Ratio is defined as the ratio of the reproductive potential under a given fishing pressure to the reproductive potential in an unfished state^39,14,15. Because SPR can be directly linked to biological reference points, SPR-based targets have been widely used in data-limited fisheries management to evaluate stock status and guide exploitation levels. The modeling results can inform fishing strategies aimed at achieving a fishing mortality rate at which the spawning potential ratio is reduced to 40% of its unfished value (termed “SPR₄₀_%”). This level is considered a risk-averse boundary for many low-resilience stocks⁴⁰ and serves as a target reference point. Conversely, SPR₂₀_% is regarded as a threshold or limit reference point, below which a stock is considered overfished⁴¹. The LBPA model is implemented using the R package LBPA_r³⁸.

The Length-Based Spawning Potential Ratio (LB-SPR) model is one of the primary methods for estimating reference points in data-limited fisheries, enabling rapid assessment of stock status relative to an unfished condition. This model assumes equilibrium conditions—constant recruitment and mortality—by employing a static, equilibrium-based length-structured model in which age structure is incorporated implicitly through the growth equation¹⁴,⁴². LB-SPR estimates SPR independently for each year based solely on that year’s length composition. To account for interannual variability, SPR values were smoothed across the study period followed the procedure recommended by Hordyk et al.,¹⁴. This step was intended to reduce short-term interannual variability in the annual estimates. The value from the final smoothed year was then used, as it represents the most recent stock status estimate while retaining information from preceding years. Inputs for LB-SPR include the ratio of natural mortality to the von Bertalanffy growth coefficient (M/K), annual length composition data, the von Bertalanffy asymptotic length parameter (L_∞), and the lengths at 50% and 95% maturity (L₅₀ and L₉₅). The model estimates the ratio of fishing mortality to natural mortality (F/M) and the lengths at 50% and 95% gear selectivity (S₅₀ and S₉₅) by fitting predicted to observed length composition data, from which SPR is derived¹⁴. The LB-SPR model is implemented using the R package LBSPR⁴³. In addition, the variability in length-at-age (CVL_∞) was represented using the default/internal setting in the LB-SPR implementation, following the original framework.

The Length-based Integrated Mixed Effects (LIME) model is an age-structured population dynamics model that reconstructs age structure from length-composition data and life-history parameters, while allowing for variable fishing mortality and recruitment, without requiring direct age observations. Required life history inputs include the length-age relationship, von Bertalanffy growth parameters, length-weight parameters, natural mortality, and the length at 50% maturity (L₅₀)¹⁵. In addition to length-composition data and life-history parameters, the LIME framework also requires steepness (h), the coefficient of variation in length at age, and the maturity ogive; in the present analysis, these followed the settings used in the model implementation. The model can also integrate multiple years and types of data—such as length frequency, abundance indices, and catch data—to improve the estimation of time-varying fishing mortality¹⁵. LIME estimates the lengths at 50% and 95% gear selectivity (LS₅₀ and LS₉₅), Dirichlet-multinomial parameters (which govern the effective sample-size weighting of the length-composition likelihood), recruitment standard deviation, and fishing mortality as fixed effects, and annual recruitment as a random effect. Unlike LB-SPR, LIME relaxes the equilibrium assumption for recruitment and fishing mortality when multiple years of data are available. The LIME model is implemented using the R package LIME¹⁵.

The Length-Based Bayesian Biomass (LBB) model represents a distinct approach to analyzing length-frequency data, differing significantly from the three length-based models mentioned above¹⁶. It estimates the asymptotic length (L_∞) under an informative prior, together with length at first capture (L_c, equivalent to LS₅₀), the ratio M/K, and the ratio F/M across the size range represented in the length-frequency data. In this study, the prior for L_∞ was specified directly rather than being derived from the maximum observed length (L_max). Using these parameters as inputs, the method applies standard fisheries equations to estimate stock depletion (B/B₀, i.e., the ratio of current relative biomass to that in the unfished state). Furthermore, these parameters allow for the estimation of the optimal length at first capture (L_{c_opt}) that maximizes yield and biomass under a given fishing effort, as well as a proxy indicator for the relative biomass that would produce maximum sustainable yield (B_MSY/B₀). The relative biomass estimates from LBB show no significant difference from the “true” values in simulated data and are consistent with independent estimates from full stock assessments¹⁶. However, the estimated relative fishing mortality (F/F_MSY) tends to be higher than independent assessments suggest, making it unsuitable as a reliable indicator of current fishing pressure¹⁶. The LBB method is implemented using the R code LBB_33a⁴⁴.

The Length-Based Indicators (LBI) method^17,18, is a model-free, indicator-based approach that relies on theoretical optima derived from life-history theory and uses length-composition data and life-history parameters to calculate several indicator ratios. These ratios provide references for stock status in terms of conservation/sustainability, yield optimization, and maximum sustainable yield. The core parameters include: L_c (length at first capture), Lmat (L₅₀, length at 50% maturity), L₂₅_% (the first quartile of the length distribution), L_max₅_% (mean length of the largest 5% of individuals), L∞ (asymptotic length from von Bertalanffy growth function), L_opt (length providing optimal yield under the Beverton–Holt framework, calculated as L_∞ × 3/(3 + M/K) and assuming a constant M/K ratio), and L_F=M (the mean length expected in the catch when fishing mortality equals natural mortality, i.e., F = M, calculated as 0.75L_c + 0.25 L∞, and used as a proxy for MSY conditions). The derived indicator ratios are categorized as follows: (1) conservation attributes: L_max₅_%/L_∞, Pmega (proportion of mature megaspawners), L₂₅_%/L_mat, L_c/L_mat; (2) yield optimization attributes: L_mean/L_opt; (3) maximum sustainable yield attributes: L_mean/L_F=M. The LBI method is implemented using the R code LBI_Indicators.R (ICES¹⁸.

Length-frequency data in this study were collected across multiple years and seasons. Because the models used here differ in their assumptions and temporal data requirements, the input data were organized in a method-specific manner rather than being treated uniformly. For the LBPA model, analyses were conducted on a yearly basis, and seasonal length-frequency data within each year were not collapsed into a single annual distribution; instead, they were retained as multiple seasonal datasets and fitted simultaneously in the model³⁸. For LBSPR, LBB, and LBI, a year-specific strategy was used, in which seasonal data within each year were combined into a single annual length-frequency dataset, and each annual dataset was then used for year-specific analysis¹⁴. For LIME, seasonal data within each year were likewise pooled into a single annual length-frequency dataset after standardization, but these annual datasets were further used as a time series of year-specific inputs across the study period for interannual model fitting¹⁵. To avoid bias caused by unequal seasonal sample sizes, each seasonal dataset was first resampled to 300 individuals prior to annual pooling or model fitting¹⁵. This procedure ensured balanced seasonal contribution and improved comparability among years. A summary of the data treatment used for each method is provided in Supplementary Table 2.

Although several of the length-based methods applied here were originally developed for fishery-dependent length compositions, we used standardized survey-derived length-frequency data because comparable commercial catch-at-length data were not consistently available across species, years, and regions. The survey gear had a mesh size similar to that prevalent among commercial fishing nets, and the survey stations covered the main fishing grounds of the target species, providing a fishery-independent but broadly relevant source of size composition data. Nevertheless, we do not assume that survey selectivity is identical to fishery selectivity, and the resulting estimates are therefore interpreted as survey-based proxies rather than direct fishery-dependent estimates.

Comprehensive analysis of fish stocks status in the Bohai Sea

This study applied z-score normalization to standardize the stock status estimates (SPR or B/B_MSY) from each model, transforming the data to a mean of 0 and a standard deviation of 1. Boxplots of stock status categorized by different population characteristics were generated. Mixed effects models⁴⁵ were applied to further analyse the factors influencing the patterns of fish stock status:

1

where StockStatus_ij represents the stock status (response variable) estimated by the j-th model for species i; β₀ denotes the global fixed intercept (baseline value shared by all species); β₁–β₅ are fixed-effect coefficients (representing the global influence of predictors on stock status); TrophicLevel_ij, HabitatLayer_ij, CommercialValue_ij, UnitPrice_ij, and Model_ij are fixed-effect predictors; u_i represents the random intercept for species i (species-specific deviation); ϵ_ij is the random error, assumed to be normally distributed as ϵij∼N(0,σ²_u). Because the five assessment methods do not produce an identical stock status metric, the stock status indicator used in the comparison was method-specific. Specifically, SPR was used for LBPA, LIME, and LBSPR, and B/B_MSY for LBB. These indicators were then normalized before comparative analysis.

The model was implemented using the R package “lme4”⁴⁵. The “glmm.hp” package⁴⁶ was employed to perform hierarchical partitioning of the marginal strength of association (R²), calculating the independent contributions of each predictor to the marginal R².

Results

Status of fish stocks in the Bohai Sea based on different length-based approaches

Firstly, we have depicted the output results of the LBPA, LBSPR, LIME, and LBB models using anchovy as an example (Fig. 2). Subsequently, we have presented the distribution of stock status and fishing pressure for 19 fish species of the Bohai Sea using Kobe-style diagrams (Figs. 3, 4, 5 and 6).

Fig. 2.

Illustrative application of four length-based models for fish resource assessment in the Bohai Sea using anchovy as an example (a, b: LBPA, c, d: LBSPR and LIME, e, f: LBB). In panel (a), the green and red curves represent the modeled relationships of yield and biomass/SPR-related reference response to fishing mortality, and the black point indicates the estimated current status relative to the reference point. In panel (b), the black and green curves represent the estimated selectivity and maturity ogive, respectively. In panel (c), colored points and connecting lines show annual SPR estimates from the two models (purple = LBSPR; green = LIME); vertical bars indicate the corresponding uncertainty range / variability estimate, and horizontal dashed lines indicate reference SPR levels. In panel (d), the purple and green curves show the estimated selectivity-at-length relationships from LBSPR and LIME, respectively. In panel (e), black points represent the observed relative length-frequency data, the red curve represents the fitted LBB curve, and the vertical green lines indicate the reference lengths estimated by the model (e.g., Lopt and L∞, where applicable). In panel (f), the black line shows the annual trajectory of the estimated relative biomass indicator, while the horizontal reference lines indicate the corresponding biomass benchmarks used for interpretation.

Fig. 3.

The status of 19 fish stocks (SPR) and fishing pressure (F/M) exerted on each in the Bohai Sea based on LBPA assessment (The code for each stock is shown in Table 1); (a) Kobe-style plot of stock status and fishing pressure for all assessed stocks. Each point represents one stock, positioned according to its estimated SPR (x-axis) and F/M (y-axis). The colored background indicates stock-status categories: red = overfished and depleted, amber = subject to overfishing but not depleted, yellow = depleted but rebuilding, and green = sustainable; and (b) Enlarged uncertainty display for the LBPA estimate, showing the model-based uncertainty in SPR and fishing mortality. The upper inset shows the joint uncertainty in SPR and fishing mortality, with grey points representing posterior draws / simulated estimates and contour lines indicating the joint density. Dashed lines indicate the corresponding reference values. The lower inset shows the marginal distribution of fishing mortality.

Fig. 4.

The status of fish stocks (SPR) and fishing pressure (F/M) on them in the Bohai Sea based on LBSPR assessment (The code for each stock is shown in Table 1); (a) Kobe-style plot of stock status and fishing pressure for all assessed stocks. Each point represents one stock, positioned according to its estimated SPR (x-axis) and F/M (y-axis). The colored background indicates stock-status categories: red = overfished and depleted, amber = subject to overfishing but not depleted, yellow = depleted but rebuilding, and green = sustainable; and (b) Reference curves from the LBSPR model showing the expected relationships among SPR (red), relative spawning biomass (SSB/SSB₀, green), and relative yield (blue) across increasing levels of relative fishing mortality (F/M).

Fig. 5.

The status of fish stocks (SPR) and fishing pressure (F/M) on them in the Bohai Sea based on LIME assessment (The code for each stock is shown in Table 1). The red zone = overfished depleted stock, amber = overfishing but not depleted, yellow = depleted but rebuilding, and green = sustainable.

Fig. 6.

The status of fish stocks (B/B_MSY) and fishing pressure (F/M) on them in the Bohai Sea, based on the LBB assessment (The code identifying each stock is listed in Table 1.). The red zone = overfished depleted stock, amber = overfishing but not depleted, yellow = depleted but rebuilding, and green = sustainable.

Results based on the LBPA model (Fig. 3a) indicate that the stock status of all fish species, except for Zoarces elongatus (ZEL), was within an acceptable state (SPR > SPR_limit). Regarding fishing pressure, F/M was less than 1 for 11 species and greater than 1 for eight species. A higher F/M value does not necessarily indicate that fishing pressure exceeds sustainable limits. For instance, for Konosirus punctatus (KPU), which had an F/M of 1.50, the probability that its current fishing mortality (F = 1.30) is below the target fishing mortality (F_tar=1.41) was 63% (Fig. 3b).

Results based on the LBSPR model (Fig. 4a) indicate that the stock status of all fish species, except for Zoarces elongatus (ZEL) and Argyrosomus argentatus (AAR), was found to be within an acceptable range (SPR > SPR_limit). Regarding fishing pressure, the F/M was less than 1 for six species and greater than 1 for 13 species. For species with relatively good stock status, a higher F/M value should be interpreted cautiously as only a preliminary indicator of potential fishing pressure. Taking Pampus argenteus (PAR) as an example, its F/M ratio of 1.20 was below the level corresponding to optimal yield (Yield, Fig. 4b), indicating that the current fishing pressure remained within sustainable limits.

Results based on the LIME model (Fig. 5) indicated that, with the exception of Johnius belangerii (JBE), all other fish stocks were in an acceptable state (SPR > SPR_limit). In terms of fishing pressure, nine fish species exhibited F/M < 1, while ten fish species showed F/M > 1. Among the ten fish species with F/M > 1, nine (90%) exhibited SPR > SPR_limit, and four (40%) showed SPR > SPRtar.

Results based on the LBB model (Fig. 6), six fish stocks were identified as overfished (B < B_MSY), while 13 stocks maintained good status, among which seven species showed an F/M ratio less than 1. Table 3 summarizes the optimal length at first capture (L_{c_opt}), the ratio of current length at first capture to the optimal length (L_c/L_{c_opt}), and the ratio of mean length to the optimal mean length (L_mean/L_opt) for each species. Seven of the 19 species exhibited both L_c/L_{c_op} and L_mean/L_opt ratios below 1, indicating truncated length structures and a prevalence of smaller individuals in the catches. The LBB results further revealed that although Johnius belangerii (JBE) is currently overfished, its current L_{c_opt} remains close to the optimal value.

Table 3.

Summary of length-based reference points of the LBB.

Scientific name	Code	Lc_opt	Lc/Lc_opt	Lmean/Lopt
Engraulis japonicus	EJA	9.1	1.3	1.19
Setipinna taty	STA	8.3	1.2	1.1
Thryssa kammalensis	TKA	6.1	1.4	1.2
Sardinella zunasi	SZU	8.6	1.5	1.18
Pampus argenteus	PAR	13	0.88	0.96
Konosirus punctatus	KPU	9.8	1.3	1.1
Coilia mystus	CMY	10	1.2	1
Trichiurus lepturus	TLE	32	0.51	0.79
Larimichthys polyactis	LPO	8.8	1.32	1.3
Cynoglossus joyneri	CJO	13	1	1
Ammodytes personatus	APE	7.7	1.4	1.6
Eupleurogrammus muticus	EMU	8.8	1.1	1
Pholis fangi	PFA	7.3	1.6	1.5
Chaeturichthys stigmatias	CST	19	0.42	0.79
Amblychaeturichthys hexanema	AHE	7.6	0.48	0.85
Argyrosomus argentatus	AAR	9.3	0.43	0.5
Liparis tanakae	LTA	21	0.59	0.62
Johnius belangerii	JBE	6.2	1.1	1.1
Zoarces elongatus	ZEL	29	0.63	0.75

Results based on the LBI method (Table 4) indicate that L_c/L_mat and L_25%/L_mat ratios for 11 fish species fall below the reference points recommended by ICES¹⁸, indicating that undersized (immature) individuals of these species are vulnerable to capture and require further protection. Three species exhibited both L_max5%/ L_∞ and Pmega values below the reference points, suggesting an insufficient presence of large spawning individuals within their populations. The L_mean/L_opt ratio indicated that three species deviated from the optimal yield level. Furthermore, the L_mean/L_F=M ratio revealed that seven species were being exploited beyond the MSY-based sustainable level.

Table 4.

Summary of length-based metrics relative to the corresponding ICES reference values in the LBI framework. Bold cells indicate values below the relevant ICES reference values, whereas Italic cells indicate values satisfying those reference criteria.

	Conservation				Optimizing	MSY
	Lc/Lmat	L25%/Lmat	Lmax5%/L∞	Pmega	Lmean/Lopt	Lmean/LF=M
Code	> 1	> 1	> 0.8	> 0.3	~ 1 (> 0.9)	≥ 1
EJA	0.83	0.83	0.81	0.28	0.92	1.04
STA	0.72	0.83	0.84	0.52	1.19	1.1
TKA	1.02	1.02	0.99	1	1.66	1.04
SZU	1.05	1.05	0.81	1	1.42	0.93
PAR	0.46	0.88	0.66	0.82	1.36	1.08
KPU	1.07	1.07	0.63	0.58	1.13	0.88
CMY	1.24	1.59	0.95	0.78	1.22	1.13
TLE	1.61	1.68	0.49	0.9	1.26	0.78
LPO	1.05	1.05	0.69	0.88	1.27	1
CJO	0.61	0.96	0.69	0.54	1.15	1.12
APE	1.28	1.28	0.78	0.79	1.24	1
EMU	0.6	0.87	0.71	0.94	1.32	1.09
PFA	1.04	1.04	0.8	1	1.72	1
CST	0.64	0.72	0.58	0.03	0.77	0.92
AHE	0.83	0.83	0.91	0.26	1.11	1.03
AAR	0.46	0.71	0.575	0.01	0.54	0.92
LTA	0.5	0.61	0.81	0.11	0.73	1.01
JBE	0.9	0.9	0.67	0.24	1.04	0.86
ZEL	0.77	0.77	0.8	0.1	0.90	0.87

Comprehensive analysis of the fish stocks status in the Bohai Sea

When species were grouped by population characteristics (Fig. 7), the results revealed substantial distributional differences in stock status across categories. The most pronounced disparities were observed among trophic levels, market price categories, and life span groups. Species characterized by higher trophic levels, greater market value, and longer life spans generally exhibited lower stock status estimates. Demersal fish stocks showed greater variability in status compared to pelagic species. In contrast, differences in stock status distributions across assessment models were relatively minor, with LBB and LBPA producing similar distribution ranges, as did LBSPR and LIME.

Fig. 7.

The distribution of stock status for different stock characteristics and model classes. Different colours are used to distinguish categories visually. In each box-plot, the central horizontal line represents the median, the box represents the interquartile range (IQR, 25th–75th percentiles), the whiskers extend to 1.5 × IQR, and points beyond the whiskers indicate outliers.

The mixed effects model results (Fig. 8) provided a more direct assessment of trait–status relationships and showed similar overall tendencies: species with higher trophic levels and greater economic value tended to exhibit lower stock status estimates, although none of the fixed effects were statistically significant. The factors with relatively higher contributions (Fig. 9a) were, in descending order: trophic level, market price, and life span. Random effects revealed systematically lower stock status for Zoarces elongatus, and systematically higher stock status for Pholis fangi, Chaeturichthys stigmatias, and Coilia mystus.

Fig. 8.

Summary of the output of the mixed effect model.

Fig. 9.

Hierarchical Partitioning of Marginal R² (a) for the mixed effect model and (b) for the mixed effect model with interaction effect.

The model itself showed no significant effect on estimates for species with similar population characteristics (Figs. 8 and 9a), but significant model-population characteristic interaction effects were detected (Fig. 9b). For example, considering the model-life span interaction, the inclusion of interaction terms increased the marginal R² of the model by 7% compared to the original model (Fig. 9b).

Management recommendations for fish stocks in the Bohai Sea

Based on the stock status results derived from five length-based models for the 19 fish species of the Bohai Sea in this study, the following management recommendations (Fig. 10) are proposed, categorized by the required level of intervention:

Fig. 10.

Summary of recommended management measures for Bohai Sea stocks based on current stock status. Recommendations: the decreasing trends (red arrows) indicate catches should be reduced, potentially through stricter output controls such as reduced total allowable catch (TAC) or quotas; the stable trends (black arrows) indicate catches should be maintained; the net with fish icon indicates that a minimum net size should be applied; the vessel icon indicates that fishing effort should be reduced; the vernier caliper icon indicates that a minimum landing size should be applied or increased.

Category 1: Maintain Current Management.

Thryssa kammalensis (TKA), Coilia mystus (CMY), Ammodytes personatus (APE), Pholis fangi (PFA), and Liparis tanakae (LTA) stocks are in very good (healthy) status, and can sustain current fishing practices.

Category 2: Moderate Technical or Input Measures.

Stocks in this category generally require moderate technical or input-based management measures, although the specific recommendation differs among species. Engraulis japonicus (EJA) and Setipinna taty (STA) can sustain current yield levels, but it is recommended to appropriately increase the mesh size of the primary fishing gear to enhance juvenile protection. Sardinella zunasi (SZU) is in good stock status, but a reduction in fishing effort is recommended. Larimichthys polyactis (LPO) is in good stock status and its sustainable use can be further promoted by implementing or increasing controls on the minimum landing size.

Pampus argenteus (PAR) and Amblychaeturichthys hexanema (AHE) are in good stock status. However, it is recommended to appropriately increase the mesh size of the primary fishing gear and implement or increase controls on the minimum landing size. Konosirus punctatus (KPU) is in good stock status, but fishing effort and yield should be reduced, and minimum landing size controls should be implemented or increased.

Category 3: Stringent Multi-faceted Management (High Risk).

This category includes stocks that require stronger precautionary management to prevent further decline. Trichiurus lepturus (TLE) has acceptable stock status. However, it is recommended to reduce fishing effort and yield, appropriately increase the mesh size of the primary fishing gear, and implement or increase controls on the minimum landing size.

Cynoglossus joyneri (CJO), Eupleurogrammus muticus (EMU), and Chaeturichthys stigmatias (CST) have acceptable but high-risk stock status. Management should be strengthened to prevent further deterioration by reducing fishing effort and yield, appropriately increasing the mesh size of the primary fishing gear, and implementing or increasing controls on the minimum landing size.

Category 4: Stringent Multi-faceted Management and Rebuilding Stock (Overfished).

This category includes stocks that require rebuilding-oriented management to promote recovery. Argyrosomus argentatus (AAR), Johnius belangerii (JBE), and Zoarces elongatus (ZEL) are either overfished or experiencing overfishing. Management for this category should focus on stock rebuilding through stricter reductions in fishing effort and yield (via output controls such as total allowable catches or vessel catch caps), stronger controls on gear selectivity and minimum landing size, and rebuilding actions such as extended spatial closures, and stock enhancement via strategic release of cultured fish where appropriate.

Discussion

Stock assessment provides critical information on fish population and fishery status, serving as the foundation for science-based fisheries management. This study demonstrates that length-based assessment models/methods—LBPA, LB-SPR, LIME, LBB, and LBI—provide valuable tools for evaluating fish stocks in the Bohai Sea with limited data. These tools offer a comprehensive understanding of the current status of 19 important fish stocks within the Bohai Sea fishery ecosystem, establish a solid foundation for sustaining resource productivity, and can assist in formulating targeted management measures to strategically prevent overfishing and rebuild overexploited stocks.

The data-limited length-based assessment methods applied in this study are widely applicable to most fisheries worldwide. Their utility is well-documented in the literature and has been extensively validated through simulation testing^{34,35,47,36,37,15}. Among these methods, LBI, LBSPR, and LBB operate under equilibrium assumptions, presuming constant recruitment parameters, whereas LIME and LBPA incorporate different mechanisms to relax these equilibrium assumptions.

Differences in model structures lead to variations in assessment outcomes, meaning the stock status estimated for specific fish species can differ significantly across models. For instance, this study revealed that while the LBPA and LIME models indicated the Pampus argenteus stock was in a healthy status above the target reference point, the LBB model classified it as overfished, and the LBSPR model assessed it as acceptable, above the limit reference point but below the target. Such discrepancies have also been widely reported in other model comparison studies, confirming their common occurrence^47,36,15. Rational design of management strategies must account for uncertainties in model outputs⁴⁸. Researchers and fishery managers need to address situations where different models yield highly divergent stock status estimates. In this study, the overall stock status was determined based on the proportion of results from the five methods indicating a “healthy” status, with targeted management recommendations provided according to the status indicated by various metrics. For example, Johnius belangerii stock was assessed by two models (LBSPR and LBPA) as being in an acceptable state—above the limit but below the target reference point—while three models (LIME, LBB, and LBI) classified it as overfished. Based on this majority outcome, the stock was assessed to be overfished.

This study examined six population characteristics—trophic level, habitat layer, lifespan, market price, and commercial value—revealing associations between these traits and interspecific differences in stock status. These linkages may stem from selective resource utilization and variations in population resilience. In other words, population characteristics partially determine or influence both the resource use strategy and population resilience, ultimately leading to differences in stock status among species^49,50. Empirical evidence suggests that longevity and late maturation are key traits associated with low resilience and high collapse risk in populations of larger-bodied fish⁵¹. Consistent with this, our study also demonstrated that longer-lived species generally exhibited poorer stock status compared to short-lived species. Fish resource utilization patterns are often driven by multiple interacting factors. Our results support the conclusion that population characteristics—such as economic value and trophic level— influence resource use strategies, thereby helping to explain observed differences in stock status among species. Specifically, high market price combined with high catchability can increase fishing effort, potentially leading to overexploitation and stock collapse. Conversely, low market prices tend to reduce fishing pressure, making sustainable management more achievable⁵⁰.

This study categorized the stock status and corresponding management recommendations for 19 representative fish species in the Bohai Sea into four distinct groups:

(1) Sustainable and Healthy Stocks.

Thryssa kammalensis (TKA), Coilia mystus (CMY), Ammodytes personatus (APE), Pholis fangi (PFA), and Liparis tanakae (LTA) are currently in a healthy status and capable of sustaining current exploitation levels.

(2) Relatively Good Status Requiring Targeted Management.

Engraulis japonicus (EJA), Setipinna taty (STA), Sardinella zunasi (SZU), Larimichthys polyactis (LPO), Pampus argenteus (PAR), Amblychaeturichthys hexanema (AHE), and Konosirus punctatus (KPU) are in relatively good stock status but require specific targeted management interventions to maintain sustainability.

(3) Acceptable Status Requiring Comprehensive Strengthened Management.

Trichiurus lepturus (TLE), Cynoglossus joyneri (CJO), Eupleurogrammus muticus (EMU), and Chaeturichthys stigmatias (CST) are in marginally acceptable status but at high risk of overfishing, necessitating comprehensive enhanced controls.

(4) Overfished or Overfishing Requiring Stringent Management.

Argyrosomus argentatus (AAR), Johnius belangerii (JBE), and Zoarces elongatus (ZEL) are overfished or overfishing, requiring comprehensive intensified management measures and rebuilding-oriented actions to facilitate stock recovery. The unsustainable status of the stocks not only threatens the provision of fishery products (a key food source for coastal communities) but also impairs the ecosystem’s capacity to deliver biodiversity conservation, habitat maintenance and carbon sequestration services.

Engraulis japonicus was once the most abundant fish species in the Bohai and Yellow Seas^29,52 and one of the most widespread and commercially valuable pelagic species in the western North Pacific, used primarily for fishmeal production⁵³. Due to intensive exploitation and a sharp increase in fishing pressure, Engraulis japonicus experienced a severe decline in stock abundance during the late 1990s and early 2000s^54,52. Larimichthys polyactis is another iconic fish species in the Bohai Sea. Since the 1980s, Larimichthys polyactis stocks and other commercially valuable demersal fish species (such as Trichiurus lepturus and Cynoglossus joyneri) have severely declined^21,20. Both Setipinna taty and Pampus argenteus are important commercial species²⁰. Since the beginning of the 21st century, they have become primary targets and now hold a prominent position in the fisheries of the Bohai and Yellow Seas^54,23. The stock status of these four species is indicative of the current productive capacity (food production function) of the Bohai Sea fishery ecosystem. While the system shows some signs of recovery compared to the period of severe resource decline, continued strategic management aimed at rebuilding stocks remains essential. Traditional commercial species like Trichiurus lepturus and Cynoglossus joyneri continue to recover slowly, necessitating strong regulatory management of targeted recovery measures.

This study reveals that it is low quality fish species with low commercial value which are currently in a sustainable healthy state within the Bohai Sea. Among them, Liparis tanakae, which occupies a high trophic level, has partially replaced the ecological role of traditional high-trophic-level species like Trichiurus lepturus, potentially triggering trophic cascades through interspecific interactions. Previous research indicates that under scenarios with minimal climate change, the synergistic effects of fishing pressure and predator dynamics (food web cascades) are the primary drivers of population dynamics⁵⁵. This point requires further investigation to clarify the impact of species alternations on the food production capacity of the Bohai Sea fishery ecosystem.

Notwithstanding these summative species assessments and management recommendations, a key limitation of this study is that the length-based models were fitted to survey-derived rather than commercial catch-derived length compositions. Although the survey gear had a mesh size similar to that of the dominant fishing gear and the survey stations covered the main fishing grounds, some mismatch between survey selectivity and fishery selectivity may still exist. In particular, commercial fleets may preferentially target areas containing larger individuals, whereas fishery-independent surveys are designed to sample the stock more systematically. Accordingly, the resulting estimates should be interpreted as standardized survey-based indicators or proxies of stock status, rather than fishery-based estimates of exploitation.

A further source of uncertainty in this study arises from both temporal variability in observed length-frequency data and uncertainty in fixed biological input parameters (see Supplementary Tables 3, 4). As shown in the supplementary material, the interannual variation in model outputs for the two representative species was generally moderate, suggesting that the estimates were not excessively unstable through time. Sensitivity analyses further indicated that changes in key biological parameters, particularly L_inf and M/K, could affect the magnitude of the estimated stock indicators, with the extent of response differing among methods and species. These results indicate that the outputs of the length-based models should be interpreted as conditional on both the observed length structure and the biological assumptions used. In addition, because the main analyses were based primarily on year-specific pooled annual length-frequency data, seasonal variability was not fully propagated and may represent an additional source of uncertainty.

Although some methods (e.g., LBPA) provide uncertainty information directly, uncertainty could not be incorporated uniformly into all main figures because the five methods differ in both output structure and uncertainty formulation. Standardizing each seasonal dataset to 300 individuals improved the stability of the length-frequency inputs¹⁵, but did not eliminate all sources of uncertainty. We therefore addressed uncertainty mainly through supplementary analyses of interannual variability and parameter sensitivity, and note that full bootstrap propagation across methods remains a topic for future work.

Nevertheless, this study contributes to understanding the status of the Bohai Sea fishery ecosystem: 26% of the assessed species are in a sustainable status with no risk; 37% require comprehensive and enhanced management (16% are overfished, and 21% are at high risk); and the remaining 37% are in an acceptable status but need targeted management measures. Figure 10 outlines the management measures we strongly recommend implementing in accordance with stock status. As noted by Hilborn et al.⁷, scientifically assessed and managed fish stocks globally are either increasing in biomass or have already reached or exceeded biomass levels capable of providing long-term sustainable yields (B_MSY). Therefore, adopting management recommendations based on scientific assessments, such as those in this study, is crucial for sustaining multiple ecosystem services of marine systems. Looking ahead, future research developing ensemble modeling approaches would improve upon our study by reconciling discrepancies among stock-status estimates produced by different models⁵⁶. Indeed, expanding on this further, Han et al.⁴⁷ suggested that ensemble modeling can help overcome some of the limitations of individual length-based models to reduce uncertainty arising from multiple model outputs. Ultimately, this will improve identification of the most reasonable parameter estimates, thereby producing more reliable scientific advice supporting strategic management decisions.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Qingpeng Han made substantial contributions to conceptualization, methodology, software, validation, formal analysis, data curation, writing – original draft, and visualization. Xiujuan Shan made substantial contributions to conceptualization, methodology, software, validation, formal analysis, writing – review & editing, visualization. Harry Gorfine and Xianshi Jin made substantial contribution to methodology, software, writing – review & editing. Yongqiang Shi and Chengbin Liu made substantial contributions to writing – review & editing.

Funding

This work was supported in part by National Natural Science Foundation of China [32403027]; National Key Research and Development Program [2024YFD2400400]; Central Public-interest Scientific Institution Basal Research Fund, YSFRI, CAFS [NO. 20603022024008]; Qingdao Postdoctoral Innovation Program [QDBSH20240102033]; the Special Fund of Taishan Scholar; Innovation team of fishery resources and ecology in Yellow and Bohai Seas [2023TD01].

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Article impact statement

The multi-model approach supports the Bohai sea fish stock assessment and conservation in data- limited situations.