Introduction

Marine fisheries, as an integral component of natural resources, provide an important source of animal protein for human nutrition and development. Since the late 1980s, the global yield of marine fisheries has consistently provided between 86 and 93 million tons of seafood annually, as reported by the Food and Agriculture Organization1. The sustainability of marine fishery production relies on the implementation of science-based fisheries management, a practice which is essential to preserve marine biodiversity and ensure long-term yield2. Reliable stock assessment is fundamental to the implementation of science-based fisheries management policies. However, approximately 90% of global fish stocks lack the quality and quantity of data necessary for formal stock assessments and3, as a result, a substantial portion of marine fishery production originates from data-limited fisheries have been managed without sound scientific foundations or remain unmanaged. Stock assessment in fisheries is basically the process of collecting necessary data then inferring meaningful indicators of fish stock status, which are essential for formulating effective fisheries management strategies4. Typically, conventional stock assessments require extensive data including catch statistics, relative or absolute abundance indices of fish stocks, and detailed biological information such as age structures5,6. Due to the lack of survey funding and challenges in fishery monitoring, these data are often difficult to obtain. This data limitation is a widespread issue, not unique to developing countries but also prevalent in certain fisheries within developed countries3. As a result, how to conduct stock assessments under data-limited situations and develop relevant theoretical methods is a significant challenge currently faced in fishery research7. To address these challenges, a range of data-limited methods has been proposed and developed, broadly categorized into catch-based methods8,9,10,11,12,13 and length-based methods14,15,16,17,18,19,20. These methods are tailored to meet the need for assessing fish stock status in data-limited contexts. In particular, catch-based methods, which utilize the most readily available data—catch, can provide useful references for fisheries management. For many data-limited fisheries worldwide, such highly aggregated catch statistics may turn out to be the only information available for research to support fisheries management. Consequently, they have gained widespread attention and development13,21,22,23,24,25,26.

Despite the widespread attention and applications catch-based methods have received, the reliability of such methods remains controversial27,28,29, especially when using simple methods to substitute catch statistics for relative abundance trends, such as average catch22, which highlights the necessity of relative abundance indicators for precise and reliable assessments. Previous studies and simulations have demonstrated that incorporating abundance information can greatly improve the accuracy and reliability of catch-based assessments by capturing aspects of stock status that catch data alone may not adequately reflect. Ideally, information on abundance should be derived from fishery-independent surveys, which more accurately reflect the absolute or relative abundance of fish stocks in a specific area. However, in situations where only fishery-dependent data is accessible, such as in commercial fisheries that only catch and effort data are available, Catch-per-unit-effort (CPUE) can serve as an index of relative abundance to assess stock status30. While CPUE is typically assumed that CPUE is directly proportional to stock abundance, the consistency between actual CPUE and abundance can vary due to factors like spatial heterogeneity, environmental variables, and variations in fishing vessel characteristics31,32. As a result, research requires considering these additional factors and adopting algorithms to standardize nominal CPUE data for use as an abundance indicator33. However, taking these influencing factors into account undoubtedly increases data demands, making it an impractical solution for species where data is limited. A recent review34 discussed and explored the potential of data-aggregation methods for deriving CPUE, suggesting a novel approach to tackle these challenges. However, this approach may overlook factors such as vessel characteristics, gear settings, or environmental conditions, which can lead to dynamic variations in the catchability coefficient (q). These temporal and spatial changes in q can disrupt the proportional relationship between nominal CPUE and actual stock abundance, leading to biased estimates of stock size. Therefore, understanding the sensitivity of aggregated CPUE data to the dynamics of q is essential to ensure the reliability of aggregated CPUE as a stock index.

In the present study, we introduced a proxy-CPUE indicator based on the above-mentioned concept of data-aggregation34, calculating the proxy of CPUE from total fishing effort data across entire areas. Given the data availability of our target species, the chub mackerel (Scomber japonicus) in the Yellow Sea, we selected three types of fishing effort data to develop three corresponding proxy-CPUE indicators. We then evaluated the efficiency of catch-based models that rely only on catch data against those integrating proxy-CPUE indicators, both in estimating stock status and in retrospective analyses. Further, we assessed a prevalent issue in both our research species and many other under-monitored fisheries: substantial observation errors may exist in catch statistics due to misreporting. In this context, we compared the performance of catch-based models that rely only on catch data against those integrating proxy-CPUE indicators regarding various levels of observation errors in catch data. Finally, we explored four dynamic scenarios for the coefficient of catchability (q), using GVC-based proxy-CPUE as an example to consider the impact of incorporating dynamic changes in q on the assessment results and whether the uncertainty in proxy-CPUE would affect its performance in addressing observation errors in catch data. The aim of the proposed approach is to enable more effective utilization of available data, thereby enhancing the performance of catch-based methods in assessing stock status. Additionally, this study contributes to understanding how catch-based methods respond to observation errors in catch data, which are prevalent in global fisheries.

Results

Performance of estimates

Table 1 presents the assessment results for the scenario with low observation error (cv = 0.05) in catch data, which serve as the baseline for a comparative analysis of the performance of using different data types in estimating stock status. The types of data analyzed include catch-only data and catch data integrated with three proxy-CPUE indicators (\({CPUE}_{\text{GVC}}\), \({CPUE}_{\text{GVP}}\), \({CPUE}_{\text{TVC}}\)). The robustness of the parameter estimates is evaluated by comparing the relative variation (var) of each parameter; with lower var values indicating more robust estimates. The catch-only method exhibited the lowest relative variation for MSY (Maximum Sustainable Yield) estimates (MSYvar at 23%), indicating greater robustness compared to integrating the proxy-CPUE data, which had var ranging from 27 to 43%. However, proxy-CPUE-based estimates exhibited lower relative variations for the relative biomass ratio B/BMSY (where BMSY represents the biomass level that produces MSY) and fishing pressure F/FMSY (where FMSY represents the fishing mortality that achieves MSY) parameters, with \({CPUE}_{\text{GVP}}\) data showing the most robust estimates for B/BMSYvar at 37% and \({CPUE}_{\text{GVC}}\) data showing the most robust estimates for F/FMSYvar at 62%. In contrast, the catch-only method exhibited the least robustness in estimating the two stock status indicators, with B/BMSYvar at 87% and F/FMSYvar at 122%, significantly higher than in the other three types of CPUE indicators.

Table 1 Performance of using only catch data and integrating three types of proxy-CPUE data.
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Stock status

Similar results are observed in the Kobe plot of these four approaches (Fig. 1). The estimation of catch-only method indicated the stock in the final year 2018 is both overfished and lightly overfishing (B2018/BMSY < 1, F2018/FMSY ≈ 1), with a significant portion in the red zone (55.4%), yet with considerable uncertainty as reflected by the wide joint confidence intervals of B/BMSY and F/FMSY, which indicated that the result lacked robustness and was not reliable. In contrast, all the integrating CPUE methods exhibited concentrated joint confidence intervals, with the \({CPUE}_{\text{GVP}}\) showing the most robust outcomes. The three integrating CPUE methods result indicated the stock in the final year 2018 had high probabilities (70.1% to 96.4%) that the stock is healthy and sustainable (B2018/BMSY > 1, F2018/FMSY < 1).

Fig. 1
figure 1

Kobe plot that reveals the retrospective evaluation of fishing pressure (F/FMSY) against relative biomass (B/BMSY) for different data using methods: Catch Only, three types of methods to calculate proxy-CPUE indicators (Gross Vessel Count, Gross Vessel Power, and Targeting Vessel Count). Each method presents data points over multiple years in the F/FMSY vs. B/BMSY space. Each plot is divided into four zones representing different levels of stock status: green for sustainable (B/BMSY > 1 and F/FMSY < 1), yellow and orange for caution (either B/BMSY < 1 or F/FMSY > 1), and red for unsustainable (B/BMSY < 1 and F/FMSY > 1). The shaded area indicates the joint confidence intervals.

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Retrospective patterns

The retrospective analysis over a span of five years revealed different trends across the four scenarios (Fig. 2). The catch-only method performed well in the retrospective analysis, with minimal change in the estimates of the B/BMSY and F/FMSY after sequentially omitting data year by year, evidenced by nearly overlapping trend lines for different years. In the \({CPUE}_{\text{GVC}}\), retrospective analysis showed that omitting data from each year led to variations in the estimates of the two stock status indicators in the final year, compared to estimates using data from all years. While in the \({CPUE}_{\text{GVP}}\), retrospective analysis showed little change in the estimates of the B/BMSY, but variations in F/FMSY became apparent when omitting more than three years of data, leading to a slight overestimation of fishing pressure in the final year. The retrospective analysis of \({CPUE}_{\text{TVC}}\) presented a clear retrospective pattern. The lines are arranged in a regular sequence, and as data are progressively removed, the model estimates a higher B/BMSY and lower F/FMSY.

Fig. 2
figure 2

Retrospective analysis for different data using scenarios: Catch Only, three types of methods to calculate proxy-CPUE indicators (Gross Vessel Count, Gross Vessel Power, and Targeting Vessel Count).

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Performance encountering observation error

When comparing the performance of four assessment methods at different catch observation error levels, which is measured by coefficients of variation (CV) at base (0.05), low (0.15), medium (0.3), and high (0.5), the following trends were observed (Table 2, Fig. 3):

Table 2 Performance of using only catch data and integrating three types of proxy-CPUE indicators.
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Fig. 3
figure 3

Performance of using only catch data and integrating three types of proxy-CPUE indicators. The solid line represents the estimated values for each parameter under the corresponding observation catch error (CV), and the shaded area indicates its 95% confidence interval.

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The catch-only method showed a significant increase in the variation of Maximum Sustainable Yield (MSY) estimates, with MSYvar rising from 22.79% at base catch error CV to 49.89% at high CV, indicating a strong sensitivity to increased catch observation error. Variations in the B/BMSY estimates also fluctuated across CV levels but remained at a higher range (above 85%), suggesting instability in the catch-only method for B/BMSY estimation regardless of the catch observation error levels. The F/FMSY estimates exhibited considerable variations, with F/FMSYvar varying from 122.06% at base CV to 123.67% at high CV, reflecting the low robustness of catch-only on estimating stock status in any observation error levels.

The \({CPUE}_{\text{GVC}}\) method showed resilience to catch errors in MSY estimates, with variation remaining stable, slightly varying from 42.08% at low CV to 43.79% at high CV. For B/BMSY and F/FMSY estimates, \({CPUE}_{\text{GVC}}\) demonstrated notable stability, with var of these two stock status estimates showing slight change across CV levels, maintaining around 40% and 60%. The variation in the estimations of the two stock status indicators is almost half that of in the catch-only method.

For the \({CPUE}_{\text{GVP}}\) method, variation in MSY estimates at base CV was 40.17%, which slightly decreased to 33.24% at high CV, suggesting not a decreasing trend of stability under larger catch errors. The variation for B/BMSY estimates remained consistent across CV levels, with a slight increase from 36.58% at base CV to 40.71% at high CV. The variations in F/FMSY estimates showed a slight increase from 61.60% at base CV to 66.71% at high CV, also indicating a relatively robust method against observation errors in estimating the stock status.

Lastly, the \({CPUE}_{\text{TVC}}\) method demonstrated robustness in MSY estimates, with variation increasing from 26.78% at base CV to 33.95% at high CV. B/BMSY estimates showed a moderate increase in variation from 59.80% at base CV to 66.97% at high CV, a relatively mild growth compared to other parameters. The variation in F/FMSY estimates rose from 82.11% at base CV to 94.52% at high CV.

In summary, while all methods exhibit a decrease in robustness with increased CV, the \({CPUE}_{\text{GVC}}\) and \({CPUE}_{\text{GVP}}\) methods generally showed the best robustness on estimating stock status. In contrast, the catch-only method demonstrated the most significant variation fluctuations in assessing stock status, highlighting a notable decrease in robustness with increased catch observation errors. The \({CPUE}_{\text{TVC}}\) method exhibits moderate robustness in estimating stock status.

Sensitivity to the dynamic of catchability

Using GCV-based CPUE as an example, we simulated three dynamic scenarios (linearly increased, exponentially increased, and stochastic exponentially increased) for the catchability coefficient (q). After considering the dynamic changes in q, CPUE showed some variation, with the CPUE incorporating q dynamics generally being lower than that obtained from constant q (Fig. 4). This implies that ignoring the dynamics of q may lead to an obviously optimistic stock abundance index based on CPUE.

Fig. 4
figure 4

Trends in catchability coefficient (q) and relative CPUE from 1980 to 2018, showing 4 dynamic scenarios of q: constant, linearly increased, exponentially increased, and stochastic exponentially increased q. The three dynamic q scenarios primarily simulate the potential gradual increase in q as fisheries develop (fishing technology and fisherman experience).

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Assessments were conducted using the CPUE under the four dynamic scenarios for q. Despite these differences in CPUE, the final B/BMSY estimates (reflecting relative biomass) were largely consistent across scenarios with constant q and dynamic q, suggesting that the dynamics of q do not significantly affect the final status assessment of the stock for GCV-based CPUE (indicated by the position of the white triangle). Only a minor portion of the stock’s status in intermediate years is altered in scenarios with exponentially increasing q and stochastic exponentially q (Fig. 5). Furthermore, the uncertainty in CPUE resulting from q dynamics does not compromise this method’s capacity to address uncertainties in catch data. The estimates for MSY, B/BMSY, and F/FMSY remain robust, showing no decline in performance as uncertainty in catch data increases (Fig. 6), consistently outperforming the catch-only approach (Figs. 3 and  6).

Fig. 5
figure 5

Kobe plot that reveals the retrospective evaluation of fishing pressure (F/FMSY) against relative biomass (B/BMSY) for GVC-based CPUE method under different q dynamic: constant, linearly increased, exponentially increased, and stochastic exponentially increased q.

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Fig. 6
figure 6

Performance of GVC-based CPUE method under different q dynamic. The solid line represents the estimated values for each parameter under the corresponding observation catch error (CV), and the shaded area indicates its 95% confidence interval.

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Discussion

The present study focused on the response of catch-based models to the prevalent observation errors in catch data. The results illustrated the advantages of integrating proxy-CPUE, particularly in terms of robustness of assessing stock status and resilience to catch observation errors. Our analysis in the base scenario demonstrated distinct performance differences among the methods evaluated. The catch-only method, though exhibited the low relative variation in Maximum Sustainable Yield (MSY) estimates, showed significantly higher variations in the stock status indicators B/BMSY and F/FMSY compared to integrating three proxy-CPUE indicators (\({CPUE}_{\text{GVC}},\) \({CPUE}_{\text{GVP}},\) \({CPUE}_{\text{TVC}}\)). This result suggests a greater robustness of integrating proxy-CPUE in assessing stock status, with \({CPUE}_{\text{GVC}}\) and \({CPUE}_{\text{GVP}}\) both showing robust estimates for B/BMSY and F/FMSY. The Kobe plot analysis further supported these findings, illustrating the higher uncertainty and lesser reliability of the catch-only method, particularly in its estimation of the stock being overfished and lightly overfishing in 2018, with substantial uncertainty as reflected by the wide joint confidence intervals. In contrast, the proxy-CPUE methods displayed more concentrated joint confidence intervals, indicating a higher robustness of estimation. Under various catch observation error levels, the methods responded differently in sensitivity. The catch-only method was notably affected, with significant increases in variation across all parameters, particularly at high observation error levels. This pattern highlights its vulnerability to data quality and the risk of unreliable estimates in data-limited fisheries, which are usually under-monitored with low catch data quality. In contrast, the \({CPUE}_{\text{GVC}}\) and \({CPUE}_{\text{GVP}}\) methods maintain relative stability across different error levels, affirming their robustness in face of catch observation errors. Furthermore, despite potential data uncertainties arising from factors like dynamic changes in the catchability coefficient q, proxy-CPUE consistently maintains its performance effectively. Overall, the findings indicate that integrating proxy-CPUE indicators leads to more robust stock status estimates, especially considering the observation error on catch, which ensure robust assessments and successful decision-making.

Management implications

Effective fisheries or ecosystem management requires a comprehensive consideration of the uncertainties in model outputs. When developing management strategies, these uncertainties should be incorporated into a risk analysis framework35, to mitigate overexploitation due to model uncertainties. Risk analysis assess the outcomes of different management actions under various uncertainties36,37, helping to identify strategies that minimize negative effects on the target species. For example, when both models give an estimate stock biomass around 1000 (Fig. 7), the robust model (blue line and blue shade area) shows higher robustness in the biomass estimates with a narrower confidence interval. On the contrary, the less robust model (red line and orange shade area) displays higher uncertainty with a wider confidence interval.

Fig. 7
figure 7

Comparison of stock assessment results from robust and less robust models. The solid line represents the estimated values for stock assessment, while the shaded area indicates 95% confidence interval.

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Suppose our management objective is to maintain stock biomass above 500 as a sustainable threshold for formulating fishing harvest strategies. Given the risks brought about by uncertainties38, we should use the lower limit of the confidence interval of estimated biomass by the model as the practical threshold for sustainability judgment. Although both models estimate the stock biomass at around 1000, the less robust model frequently falls below 500 in the lower confidence limit. Therefore, in these years, out of consideration for sustaining stock, it may be necessary to reduce catches or stop fishing to maintain population health, resulting in the loss of potential yield. Conversely, the robust model, with its higher statistical confidence, can reliably inform stock status, potentially avoiding the loss of potential yield. In risk-averse fisheries management system, therefore, model with highly unstable outputs only offer limited guidance for practical management. However, with improved precision, managers can set clearer reference points or harvest control rules. For instance, when lower confidence interval thresholds indicate a potential risk of stock depletion (overfished scenario), more conservative decisions (e.g., reduced catch limits) can be implemented promptly. Conversely, if confidence intervals are stable and centered around healthier biomass levels (lightly overfishing scenario), managers may consider cautiously allowing higher catches while still maintaining precautionary measures.

Retrospective analysis

Retrospective analysis is a method frequently used in fisheries39 and ecology40 to evaluate the stability and reliability of models. This analysis reveals the model’s sensitivity to new data and its temporal stability41,42. Therefore, in retrospective analysis, excessive stability, and the presence of evident bias over time are both considered undesirable characteristics of a model. An optimal model should balance sensitivity to new information with maintaining consistent temporal stability43.

In this study, retrospective analysis results highlighted the catch-only method’s excessive consistency in estimates, but also its inadequate responsiveness to changing data, which could mask underlying stock status trends. One of the possible reasons is that the model might be overly simplified by only fitting catch data, therefore failing to capture the actual complexities and dynamics of the system it aims to represent. Another possibility is that the model is only sensitive to the peak values of catch data. Due to the lack of input from abundance indicators, the model primarily determines the stock size information and carrying capacity K through the maximum values of catch history. In the chub mackerel catch data, the catches in the last five years are not the historical maximums, hence the model might be insensitive to these data inputs. On the contrary, \({CPUE}_{\text{TVC}}\) displayed an obvious retrospective pattern, suggesting the estimation has systematic biases or errors, which is most likely due to issues with the quality or length of the data used. The most possible reason is the length of the \({CPUE}_{\text{TVC}}\) data is shorter than other data, with records in yearbooks beginning only in 2002, whereas other data span back to 1980. The inefficient time-series length of catch (16 years in this case) may lead to the systematic bias of catch-based methods44,45,46.

The integrating \({CPUE}_{\text{GVC}}\) and \({CPUE}_{\text{GVP}}\) methods demonstrated a relative stable pattern in retrospective analyses, which is an ideal situation that keeps a balance between being sensitive to new data and maintaining temporal stability. These results suggest that integrating proxy-CPUE as abundance indicators in catch-based models is more effective than using catch data alone. However, caution is advised in cases with overly short time series.

Why proxy-CPUE helps understand stock status

To better understand and manage a fish stock, we often need indicators across three dimensions: size (scale), status, and productivity5,47. The size or scale dimension refers to the absolute total biomass or abundance of the stock, which is critical for establishing biomass-based management measures such as catch limits. The status dimension involves understanding the stock’s relative abundance in relation to management objectives, such as the its abundance relative to a reference value like target size (BMSY). Productivity reflects the rate at which new numbers or biomass are added to the population. It determines the capacity of a population to recover from reductions due to fishing and other mortality events, which is described by intrinsic growth rates r of the production model used in present study.

The fundamental principle of data-limited methods is to extract as much information as possible from the available data to characterize the stock across these dimensions48,49. Among these three dimensions, stock size is the most closely linked to catch, as catch directly reflects the possible magnitude of a stock, especially in fully exploited stocks. In fully exploited stock, catch history might also provide insights into the stock’s status. For instance, when a stock is over-exploited and the catch begins to decline, it often indicates that the relative abundance of the stock has already started to decrease. Additionally, catch can also give us a trend of fishing pressure, with high catch rates possibly indicating intense fishing mortality.

However, catch data alone cannot provide specific stock status, as many factors other than abundance also influence catch levels, such as fishing effort and fishing technology. Therefore, in the absence of direct stock status information, catch data alone offer only an approximate estimate of stock biomass. These points highlight the advantages of integrating abundance information, such as proxy-CPUE indicators, to address the limitations of catch data and enhance stock assessments.

Conclusion and prospects

In this study, we focused on a typical data-limited situation where catch data are available but subject to misreporting, and explored the effectiveness of using a proxy-CPUE indicator to improve catch-based methods. The performance was evaluated by comparing it to the model that relies only on catch data for assessing the stock status. The results indicate that incorporating this proxy-CPUE indicator not only helps to fully utilize existing data but also compensates for the shortcomings of catch data in reflecting the status information of the stock. The integrating proxy-CPUE approach demonstrated better performance, providing more robust assessment results. It also exhibited the satisfying characteristics, striking a balance between responsiveness to new data and maintaining temporal stability in retrospective analyses. The outcomes of this study are potentially valuable for the prevalent data-limited fisheries of similar nature. In situations where detailed, fine-scale CPUE data is unavailable, the integration of such proxy-CPUE indicators can also provide us with reliable assessment results and inform management decisions.

Although the data-aggregation methods employed in this study have demonstrated considerable potential for stock assessments in data-limited fisheries, there remain aspects that warrant further investigation. For example, aggregated data can introduce statistical modeling complexities that call for appropriate error structures and potentially more flexible analytical frameworks34. Additionally, by combining finer-scale observations into broader temporal or spatial units may obscure important behavioral and environmental variations, potentially limiting our understanding of catch rate dynamics. Future research should focus on identifying additional factors that might influence catchability (q), such as seasonality, fishing patterns, and effort allocation dynamics, combined with advanced modeling approaches to quantify these effects. By addressing these factors, data-aggregation methods can be refined to more effectively capture stock dynamics and guide fisheries management in data-limited contexts.

Furthermore, while our model effectively integrates proxy-CPUE indicators to enhance catch-based assessments, it does not explicitly account for the statistical distribution of observation errors associated with aggregated CPUE data. Addressing the distributional properties of observation errors represents an important area for future research to further refine the robustness of catch-based assessment methods. Moreover, future studies should evaluate the performance of proxy-CPUE methods in data-rich fisheries where valid stock trend data are available. This would help assess whether these methods can improve the accuracy of stock trend estimates, thereby expanding their utility for informing management decisions across broader fisheries contexts.

Methods

Overview

This study focuses on the chub mackerel (Scomber japonicus) in the Yellow Sea as the target species. We adopted two catch-based methods, CMSY and BSM (Bayesian state-space Schaefer surplus production Model)10,50, and examined the efficiency of integrating a proxy-CPUE (Catch Per Unit Effort) indicator as an abundance measures into the models. The CMSY method was contrasted with scenarios using only catch data. The primary aim was to evaluate how the integrating proxy-CPUE may perform in assessing stock status and providing management references. This involved comparing two key aspects: the robustness of model outputs and their retrospective analysis performance. Furthermore, this study evaluated how these catch-based models performed under varying levels of observation errors in the catch data.

Data source

Considering the rapid development of fisheries since the late 1970s of chub mackerel, the study utilized its fishery catch data and effort data from 1980 to 2018. The catch data and fishing vessels information were sourced from Chinese Fisheries Statistical Yearbooks. Given the yearbook does not detail effort data specific to different target species and considering China’s mixed-fisheries nature51, we selected three types of fishing vessel data across the area as effort data alternatives for subsequent CPUE (Catch Per Unit Effort) calculations. These three types of fishing effort data are as follow: the total count of fishing vessels in the research area (Gross Vessel Count), the total power of all fishing vessels in the research area (Gross Vessel Power), and the sum of the number of several types of fishing vessels (trawlers, purse seiners, and gillnetters) that target chub mackerel (Targeting Vessel Count, Fig. 8).

Fig. 8
figure 8

Catch and effort data of chub mackerel (Scomber japonicus) in the Yellow Sea from 1980 to 2018. Catch is measured in tons and power in kilowatts. The Targeting Vessel Count effort data starts from 2002 due to the absence of vessel classification in the yearbook prior to that year.

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Using catch and these effort data, we derived proxy-CPUE indicators, calculated as the total catch of a year divided by the overall effort data for that year. Three types of proxy-CPUE indicators of each year are defined as:

$$CPUE_{{{\text{GVC}}}} = C/E_{{{\text{GVC}}}}$$
(1)
$$CPUE_{{{\text{GVP}}}} = C/E_{{{\text{GVP}}}}$$
(2)
$$CPUE_{{{\text{TVP}}}} = C/E_{{{\text{TVC}}}}$$
(3)

\(C\) is the catch of each year, and \(E_{{{\text{GVT}}}}\) is the effort data based on gross vessel count (GVC, similar to gross vessel power—GVP, and targeting vessel count—TVC). These metrics were chosen because they capture broad changes in fishing effort—such as expansions or reductions in the fleet—and can be obtained without extensive data collection infrastructure. The information behind these metrics differs:

  • GVC Measures the total number of active vessels, offering a straightforward indicator of fleet capacity and overall fishing activity.

  • GVP Incorporates vessel engine power, providing additional insight into the fleet’s harvesting capability and potential changes in technology or efficiency.

  • TVC Focuses on vessels specifically targeting the species of interest, refining the effort metric to account for potential targeting behaviors.

These three proxy-CPUE indicators are subsequently served as the relative abundance data in BSM. The fundamental assumption underlying the consideration of these data as the proxy for standardized CPUE data relates to the mixed fishery nature of the Yellow Sea. Fishing vessels operating in this region are typically regarded as unselective51, harvesting all fish species available for capture. Based on this assumption, it is deduced that the fishing effort of a specific fishery is proportion to the entire fishing effort in the area. As a result, three proposed proxy-CPUE indicators can serve as the alternative for CPUE data.

Catch-based methods

CMSY is a typical data-limited method built upon surplus production models, assuming the population dynamic of stock follows logistic growth curve. Unlike traditional surplus production models, CMSY requires only a series of annual catch data, information on the resilience, and priors on relative biomass. With these inputs, it estimates the Maximum Sustainable Yield (MSY) and two stock status outputs: relative biomass (B/BMSY) and fishing pressure (F/FMSY). B/BMSY indicates the current biomass of the stock relative to the biomass at Maximum Sustainable Yield (BMSY), providing a measure of stock size in relation to the optimal level for MSY. A value of B/BMSY greater than one indicates that the stock biomass is above the level for MSY, suggesting a healthy or underfished stock status. Conversely, a value less than one indicates overfished or a depleted stock status. F/FMSY shows current fishing pressure relative to the fishing pressure at MSY (FMSY), assessing whether the current level of fishing mortality is sustainable. A value of F/FMSY greater than one suggests that the fishing pressure is too high and unsustainable, potentially leading to stock depletion. A value less than one indicates that the fishing pressure is sustainable or below the level that would yield the maximum sustainable harvest.

The Bayesian State-Space Schaefer Surplus Production Model (BSM) builds upon the traditional Schaefer model by incorporating Bayesian statistical methods and a state-space approach. The key features of BSM include employing Bayesian statistics, which allows for the inclusion of prior knowledge or expert opinion in the analysis. This approach provides a probabilistic assessment of stock status, offering a range of possible values and their associated probabilities, which is crucial for the risk analysis in fisheries management. The minimum data input requirements of BSM are a series of annual catch data, abundance indices like CPUE, and prior on production model parameters. Similar to CMSY, BSM also provides Maximum Sustainable Yield (MSY) information and estimates of stock status indicators such as B/BMSY and F/FMSY.

Model configuration

Before running CMSY and BSM, a set of priors for the surplus production model parameters is required. These priors are essential for informing the models and are derived from existing knowledge or expert judgment about the fish stocks and their dynamics. They include estimates of biological and ecological characteristics such as intrinsic growth rates r, carrying capacity k, and historical biomass levels.

According to information from the FishBase (www.fishbase.org) website and the species’ resilience level (Froese and Pauly 2014), the prior distribution of intrinsic growth rate r is set as U ~ [0.32–0.76]. The environmental carrying capacity k is determined based on the following formula as the lower and upper limits for uniform distribution:

$$k_{low} = \left[ {2\max \left( C \right)/r_{high} } \right];k_{high} = \left[ {12\max \left( C \right)/r_{low} } \right]$$
(4)

Here \(k_{low}\) and \(k_{high}\) represent the lower and upper limits of the prior distribution of carrying capacity, \(\max \left( C \right)\) is the maximum yield in the given time series, and \(r_{low}\) and \(r_{high}\) are the lower and upper limits of the uniform distribution of intrinsic growth rate.

For the CMSY method, priors for history biomass need to be set for the beginning year (Bstart/k), middle year, and end year (Bend/k) of the time series. Based on empirical settings for relative biomass by Froese et al. (2017), Bstart/k is set as U ~ [0.8–1], and Bend/k/ as U ~ [0.2–0.6], with B2010/k set as U ~ [0.2–0.6] as an additional middle year biomass setting.

In the BSM method, the standard deviation in log space for r is defined as a uniform distribution between 0.001 * \(irf\) and 0.02 * \(irf\)10:

$$irf = 3/\left( {r_{high} - r_{low} } \right)$$
(5)

where \(irf\) represents the inverse range factor determining the range of r.

In the BSM method, the prior for environmental carrying capacity k follows a log-normal distribution, with the mean as the central value and the standard deviation as a quarter of the distance between the median value and its lower limit50.

Additionally, when abundance indicators are available, the BSM method allows for the estimation of the catchability coefficient \(q\), linking biomass with abundance indicators. Therefore, its prior is defined as:

$$q_{low} = 0.25r_{pgm} CPUE_{mean} /C_{mean} ; q_{high} = 0.5r_{high} /CPUE_{mean}$$
(6)

where \({q}_{low}\) and \({q}_{high}\) are the lower and upper limits of the catchability coefficient; \({r}_{pgm}\) is the geometric mean of the prior range of r; \({CPUE}_{mean}\) is the average CPUE over the past 5 or 10 years; \({C}_{mean}\) is the average catch during the same period. For stock with lower biomass, the coefficient for \({q}_{low}\) is changed to 0.5, and for \({q}_{high}\) to 1.0, respectively.

Performance evaluation

CMSY is applied in catch-only scenarios, while BSM is used when integrating proxy-CPUE indicators. Each of the three types of proxy-CPUE data is used in BSM. Considering the issue of imprecise catch data statistics in many data-limited fisheries worldwide, we also explored the performance of the model with various levels of observation error in catch data. We added an observation error with a coefficient of variation (CV) of 0.05 to the catch data as a base scenario to explore the models’ performance when catch data observation error is almost not considered. Subsequently, we added observation errors with CVs of 0.15, 0.30, and 0.50 to the catch data, representing low, medium, and high levels of observation error scenarios, respectively, to compare the models’ performance under different levels of observation errors. Each model was run 5,000 times in each scenario to ensure sufficient iteration.

The performance under different scenarios was assessed by comparing the estimation of three indicators—MSY, B/BMSY and F/FMSY outputs of CMSY and BSM. The estimated values of these parameters, along with the lower and upper limits of their respective 95% confidence intervals, will be calculated. We defined a performance indicator \({P}_{var}\) to measure the robustness of the parameter estimates based on the relative width of their confidence intervals:

$$P_{var} = (P_{UCI} - P_{LCI} )/P*100\%$$
(7)

where \({P}_{var}\) represents the relative variation of three parameters; P is the estimates of the three parameters (MSY, B/BMSY and F/FMSY); \({P}_{UCI}\) and \({P}_{LCI}\) are the 97.5% and 2.5% quantiles, respectively. The larger this value \(\left( {P_{{var}} } \right),\) the less robust and less precise the estimation of the parameter is, implying higher risks when using this result in management.

Retrospective analyses were also conducted on these scenarios to evaluate model performance39,41. We explored the retrospective patterns in the assessment of relative biomass (B/BMSY) and fishing pressure (F/FMSY) in different scenarios, by omitting data from the last one, two, up to five years, respectively. When the predictions from data of different time-series lengths vary greatly, it indicates a strong retrospective pattern in the model.

Simulation analysis of catchability dynamics

Catch-based models generally assume that the catchability coefficient (q) is constant and remains fixed over time. However, developments in fishing technology, enhanced gear efficiency, and increasing fisherman experience often invalidate this assumption. Prior studies have demonstrated that such advancements significantly boost fishing capacity, resulting in a time-dependent increase in q52. This dynamic alters the conventional proportional relationship between CPUE and abundance (\(I\)) based on a constant q:

$$CPUE_{\left( t \right)} = I_{\left( t \right)} \times {\text{q}}$$

To examine the effects of dynamic q on using proxy-CPUE, we analyzed four scenarios of q dynamics, using GVC-based proxy-CPUE data as an example to illustrate:

  1. 1.

    Constant q: Serves as a control scenario, with q remaining unchanged for baseline comparison against dynamic models.

  2. 2.

    Linear growth q: q increases annually by a fixed increment, amounting to a total growth of 50% from 1980 to 2018.

  3. 3.

    Exponentially increased q: q grows annually by 2% relative to the previous year, following an exponential growth curve. This 2% increase is based on empirical values derived from previous studies52,53.

  4. 4.

    Stochastic exponentially q: Adds a 5% random annual variation to the exponential growth model to simulate unpredictable fluctuations in q due to environmental factors or other process errors.

We conducted BSM assessments using CPUE adjusted for four dynamic q scenarios to evaluate to compare how different dynamics of q influence assessment results. Subsequently, we introduced observation errors with coefficients of variation (CVs) of 0.05, 0.15, 0.30, and 0.50 into the catch data. This was done to investigate whether the uncertainty in CPUE, arising from q dynamics, affects the model’s ability to handle observation errors in catch data.