Fisheries resources play a vital role in achieving sustainable development goals, supporting global food and security, and maintaining the health of marine ecosystems. These resources are not only essential for national economies but also for the livelihoods and cultural heritage of coastal communities (FAO, 2023). In Pakistan, the marine fisheries sector significantly contributes to the national economy by providing employment, ensuring food security, and boosting exports. This sector encompasses a diverse range of species and relies on both artisanal and industrial fishing practices. Pakistan coast spans 1,001 km, stretching from the Indian to the Iranian borders, with a continental shelf up to 350 nautical miles (UN, 2015; Pakistan Navy, 2016). The coastline is divided into two distinct regions: the Sindh and Pakistan coasts. The Sindh coast features sandy and muddy seabed enriched by freshwater inflows from the Indus River, which fosters fertile mangrove ecosystems that serve as critical breeding and nursery grounds for various fishery resources. In contrast, the Balochistan coast comprises a rocky, uneven continental shelf (FAO, 2009). Pakistan marine waters are rich in resources, including large and small pelagic fish, demersal fish, shrimp, crabs, lobsters, and cephalopods (FAO, 2009). The marine fisheries industry in Pakistan accounts for approximately 57% of the country’s total fish and fishery products, contributing about 160.9 million US dollars to the gross domestic production (FAO, 2009). The sector supports the livelihoods of approximately 400,000 fishermen and their families. However, Pakistan’s fisheries have been severely impacted by overfishing in recent decades. Numerous studies highlight concerns about global fish stock depletion due to overexploitation (Hilborn et al., 2020). Nevertheless, research suggests that fish stocks can recover if fishing efforts are reduced to sustainable levels via effective fishery management (Worm et al., 2009).

In recent years, national and regional fisheries regulations have increasingly shifted toward science-based management approaches to ensure the sustainability of both commercial and non-commercial fish stocks (MSA, 2007; CFP, 2013). Several factors contribute to the depletion of fisheries resources, including climate change, habitat destruction, water pollution, and disease outbreak. However, overfishing remains the primary threat (Jackson et al., 2001), exacerbated by the rise of industrial fishing since the last century (McIntyre, 1991). Overfishing has significantly disrupted species interactions within the marine ecosystems (Jackson et al., 2001). Pakistan’s fisheries resources operate under open-access conditions, and recent surveys reveal significant stock depletion (Fanning et al., 2011). Achieving balance in natural ecosystems requires accurately quantifying the status of fisheries, not only for sustainable harvests but also for sustainability of marine ecosystems. However, stock assessments are often hindered by limited data availability. Traditional tools often fail to evaluate sustainability goals for key fish stocks due to inadequate data (Costello et al., 2012). Advanced stock evaluation models require extensive datasets, including fishing effort, time-series catch data, and species life history information (Costello et al., 2012; Methot and Wetzel, 2013). Such datasets are often unavailable in developing countries like Pakistan. As a result, researchers frequently use catch-and length-based models (Froese et al., 2017, 2018, 2019). Data limitations in Pakistan are a significant challenge, with over 90% of global fisheries facing similar constraints (Geromont and Butterworth, 2015). While the fisheries department collects annual data on catches and fishing vessels, this data is insufficient for comprehensive stock assessments. To address this gap, more tailored models that utilize limited datasets are needed to calculate biological reference points (BRPs) for maintaining fish stocks. Several methods have been developed to overcome data deficiencies. The Catch-Based Maximum Sustainable Yield (CMSY) and Bayesian Schaefer Model (BSM) offer promising solutions by using time-series catch and efforts data to estimate biomass, MSY, fishing rate (F/Fmsy) relative biomass size (B/Bmsy) and other related fisheries reference points for given stock (Martell and Froese, 2013; Froese et al., 2017). Just Another Bayesian Biomass Assessment (JABBA) models also requires catch and catch per unit effort (CPUE) data (Froese et al., 2017). These models provide reliable insights into fisheries status using incomplete abundance data, aligning analyses with specific biomass conditions (Wang et al., 2020). Similarly, the LBB technique relies on the ratio of natural mortality to somatic growth (M/K) and fishing mortality to somatic growth (F/K) to analyze the proportion of exploited to stable biomass (B/B₀), stock levels needed for maximum sustainable yield (MSY) (B/B_MSY) (Yue et al., 2021). This length-based approach is particularly effective for estimating species growth throughout their lifespans (Froese et al., 2019). By integrating these methods, fisheries management in data-limited context can be significantly improved. Employing innovative tools such as CMSY, BSM, JABBA, and LBB can provide actionable insights to ensure the sustainability of Pakistan marine fisheries.

In fisheries sciences, a wide range of mathematical and statistical techniques are employed to analyze and interpret the dynamics of commercially important fish populations (Haddon, 2011). Among these, autoregressive integrated moving average (ARIMA) models, introduced by Box and Jenkins (1976), are commonly used for time series analysis. ARIMA models assume a linear relationship within the time series data, where each observation is expressed as a linear function of preceding values, with an added error term. This univariate approach, which focuses on linear associations among variables, offers both strength and limitations, depending on the complexity of the data. ARIMA models share foundational principles with other time-series models, such as moving-average (MA) and autoregressive (AR) models, and are capable of capturing seasonal and cyclical patterns. These features contribute to their broad application across scientific and engineering fields, including fisheries science. Their utility in fisheries sciences is particularly significant for analyzing datasets that are constrained by limitations in size or complexity, such as those from the northern Arabian Sea (Sathianandan and Srinath, 1995; Czerwinski et al., 2007; Prista et al., 2011).

Torpedo scad (Megalaspis cordyla), a small pelagic fish from the Perciformes order, inhabits reef-associated areas at depths of 20-100 m (Al-Sakaff and Esseen, 1999). This species is widely distributed across the Indo-Pacific region, including Pakistan, and is commonly found in schools (Kuiter and Tonozuka, 2001). While it can grow up to 80 cm in length, individuals typically reach around 45 cm. The maximum recorded weight of this species is 4.0 kg, and it has a lifespan of 3-5 years. Sexual maturity is reached at approximately 22 cm, marking a crucial point in its life cycle (Smith-Vaniz, 1984; Smith-Veniz, 2003; Hu et al., 2015; Qamar et al., 2018a). It is commercially significant species, primarily exported in frozen form, contributing substantially to Pakistan economy. Due to its high commercial value, it is classified with the higher price category with high price category (Sumaila et al., 2007). Additionally, it is also highly vulnerable to climate change and fishing pressure (Jones and Cheung, 2017; Qamar and Panhwar, 2018b). Along the coastal regions, it is also widely consumed due to its convenient size. Although the biological aspects and ecological importance of M. cordyla have been well-documented (Zafar et al., 2000; Qamar et al., 2016), there has been limited research on its stock assessment in Pakistani waters (Qamar and Panhwar, 2018b; Razaaq et al., 2019). Given its commercial importance, assessing the current biomass of this fishery is essential. Various modeling approaches, including CMSY, BSM, LBB, JABBA, and ARIMA used in this assessment. CMSY is particularly beneficial in data-limited context, relying solely on catch data to estimate stock status and sustainable yield. BSM and JABBA require both catch and CPUE data, providing a more comprehensive view of population dynamics through Bayesian modeling techniques. LBB, using length-frequency data, offers insights into stock status and growth parameters. ARIMA models, on the other hand, use historical time-series data to forecast future catch trends, making them invaluable for developing predictive management strategies. In Pakistan, where detailed data on fishing effort and biological parameters are often lacking, these models provide complementary information on stock status and future projections. For instance, CMSY can deliver preliminary assessment using only catch data, while LBB offers additional reliability by analyzing size-based data. Comparison across models can strengthens confidence in results, particularly in data-poor context. Understanding the current status of M. cordyla stocks through these methodologies is crucial for informed decision-making and sustainable fisheries management in Pakistan. By integrating these approaches, fisheries managers can develop strategies to ensure the long-term viability of this economically significant species, addressing challenges posed by limited data availability.

Fisheries managers rely on biological reference points, stock assessments, and other key metrics, as essential tools for the sustainable management and optimal utilization of fishery resources. These tools, along with approaches like maximum economic yield and ecosystem-based fisheries management, help ensure ecological balance and socio-economic benefits while reducing risks like overexploitation. However, in Pakistan, many key fishery resources lack such estimates due to data limitations and the absence of reliable methods. The country faces significant challenges in acquiring complex datasets, such as research surveys and time-series age structure data, which complicates the establishment of sustainable fishing practices. Machine learning techniques, including ARIMA, LBB, CMSY, and JABBA models, offer reliable results even with limited datasets. Catch and effort data are available for many fish stocks and can be effectively utilized for sustainable fishery management.

In this study, CMSY, BSM, JABBA, and LBB models were applied to estimate the current status of Torpedo scad, while the ARIMA (2, 0, 1) model was used to predict the future catch trends and assess stock size in Pakistani waters. Biological reference points (B/B_MSY) derived from the LBB, CMSY, and JABBA models were all below 1.0 (LBB 0.76, CMSY 0.798, JABBA 0.68), indicating overfishing as suggested by Froese et al. (2018), and Palomares et al. (2018). Additionally, the estimated values of F/F_MSY were higher than sustainable levels, further confirming overexploitation. Stock evaluations based on frameworks of Froese et al. (2017); Martell and Froese (2013), and Palomares et al. (2018), reinforce these findings ( Tables 3 , 4a, b ). The current fishing mortality (F > F_MSY) exceeds standard thresholds by Froese et al. (2018), and the catch of small-sized individuals, as indicated by L_mean/L_opt and L_c/L_{c_opt} rations, further exacerbates the issue. The length recorded in this study (17 cm) ( Table 1 ; Figure 2 ) is smaller than the optical length indicating the harvesting occurred before fish have reached full maturity at the size of 22 cm (Smith-Veniz, 2003; Hu et al., 2015). Similar findings have been reported for other fish species from Pakistani waters indicating the use of smaller trawl mesh sizes (Raza et al., 2022). This could be one of the factors contributing to stock depletion in Pakistani waters. The LBB model also highlighted that F/M values exceed 1, F/K values exceed 2, and Z/K values are high, all indicative of overfishing ( Table 3 ). Similarly, the LBB model offered detailed stock information, while CMSY and JABBA models provided insights for setting sustainable total allowable catch (TAC) limits. These surplus production models (SPMs), such as CMSY and BSM, are widely recognized for their simplicity and effectiveness in assessing biomass removal from fish populations (Ren and Liu, 2020).

In present study, the ARIMA (2, 0, 1) model was identified as the most appropriate model for forecasting catch data, demonstrating superior predictive performance. These findings underscore the importance of selecting optimal model parameters to enhance forecasting accuracy. Previous studies have reported varying ARIMA model configurations for fishery forecasting, reflecting differences in data characteristics and regional trends. For instance, Paul and Das (2010) applied the ARIMA (1, 2, 1) model for inland fish production in India, while Yadav et al. (2020) found the ARIMA (1, 1, 0) model to be most effective for predicting fish production in Assam. Additionally, Pradeep et al. (2021) identified ARIMA (2, 2, 1) and ARIMA (3, 2, 0) as optimal models for forecasting inland and total fish production in India. The ARIMA (0, 2, 1) model has also been successfully applied in fisheries research (Mahalingaraya et al., 2018; Boruah et al., 2020; Rajani et al., 2024), while Selvaraja et al. (2020) reported that ARIMA (5, 1, 5) was suitable for forecasting for seer fish production and ARIMA (2, 2, 1) for mullet fish production. Koutroumanidis et al. (2006) applied various models to different fish species, using ARIMA (1, 1, 1) and (3, 1, 3) for anchovy, ARIMA (1, 0, 1) and (1, 1, 0) for hake, and ARIMA (1, 0, 0) and (0, 1, 1) for Atlantic bonito landing. The identification of the ARIMA (2, 0, 1) model in this study align with previous research that emphasizes the importance of customizing model parameters based on dataset characteristics. This result highlights the need for careful model selection to improve forecasting prevision in fisheries research. The ARIMA model, employed to forecast landing trends, demonstrated low mean square errors, making it particularly useful for data-poor fisheries characterized by limited datasets (Prista et al., 2011). This model can predict future conditions, highlighting potential risks for catch rates under current trajectories (Scandol, 2003; Mesnil and Petitgas, 2009). However, these predictions suggest that the fisheries may face increasing pressure, underscoring the urgent need for effective management strategies. These analyses provide critical insights into historical trends, projected changes, and the challenges confronting fisheries, providing a solid foundation for data-driven decision-making aimed at ensuring sustainable management.

Numerous studies have been conducted on the biological aspects of Torpedo scad in Pakistani waters (Qamar et al., 2018a, b), stock assessment utilizing traditional methods remain limited (e.g., Qamar et al., 2016; Razzaq et al., 2019). Previous assessments often used outdated catch data, but the present study provides an updated evaluation using modern techniques. Studies on various fish stocks in Pakistan have employed CMSY and LBB models to improve fisheries management and conservation (e.g., Raza et al., 2023; Kalhoro et al., 2024a, b). LBB models have been applied to several species to assess their status and suggest management measures for their conservation (Raza et al., 2022). Previously various surplus production models were used to assess different fish species in Pakistani waters to suggest management measures for sustaining the fish biomass (Afzaal et al., 2016, 2018; Kalhoro et al., 2013, 2014a, b, 2015a, b, 2017, 2018; Nadeem et al., 2017). These studies were conducted using the catch and effort data analysis and a stock production model incorporating covariates packages. Razaaq et al. (2019) indicated overexploitation of the fishery using outdated catch data and traditional methods. However, recent, advances have seen the CMSY and LBB models becoming more prevalent in Asian waters, including Pakistan, to suggest the stock status for better fishery management (Zhu et al., 2020, 2021; Liang et al., 2020; Zhang et al., 2022a, b, Al-Mamun et al., 2022; Raza et al., 2022; Khatun et al., 2023; Barua et al., 2023). Multiple modeling approaches were employed to cross-check and validate the results, ensuring robustness and reliability in the stock assessment. By utilizing various models, the study aims to account for different assumptions and methodological variations, enhancing the consistency and support for the findings. The results across the different models reveal minimal discrepancies in the overall outcomes, particularly with regard to the exploitation status of the stock. Despite the variations in the modeling approaches, all models consistently indicate that fishing mortality and exploitation rates exceed the recommended reference points suggested by Froese et al. (2018), and Palomares et al. (2018). This multi-model approach strengths the credibility of the conclusions, providing a comprehensive understanding of the fishery status and offering a solid basis for making informed management decisions to guide sustainable fisheries practices. Global fisheries assessments indicate a decline in fishery resources, driven by overexploitation and inadequate management practices (FAO, 2018; Palomares et al., 2020). Results from multi-model approach confirm that the stock is overfished, with confidence intervals indicating depletion across various exploitation scenario ( Table 4 ). FAO fisheries data may introduce uncertainty due to potential under-reporting, particularly in small-scale fisheries (Zeller et al., 2016; Pauly and Zeller, 2016). However, CMSY, BSM, and JABBA incorporate prior knowledge and Bayesian approaches, which help adjust for incomplete data and maintain predictive reliability (Froese et al., 2017, 2019; Winker et al., 2018). Comparative analysis confirms their robustness, even in data-limited contexts. Despite uncertainties in catch data, the consistency of results across models strengthens confidence in these findings.

Depletion of inshore resources has forced fishing activities into offshore waters. Major fish stocks, including mackerel, tuna, croakers, and pomfrets, face severe threats (Razaaq et al., 2019; Baloch et al., 2020; Raza et al., 2022, 2023). Similar patterns of decline in fisheries resources is evident in the Indian Ocean and adjacent waters including Pakistan using similar methodologies (Nisar et al., 2021; Kalhoro et al., 2024a, b). Studies conducted in Bangladesh waters using JABBA model also provide robust information for better fishery management (Barua et al., 2023). These declines significantly impacted marine ecosystems and local economics, forcing many fishermen to seek alternative livelihood. This study represents the first comprehensive assessment of Torpedo scad stock and future catch predictions using machine learning methods. All models indicate that the stock is currently overexploited. Future catch predictions indicated that without immediate management intervention, the fishery may face significant risk of collapse. It may be advised to reduce fishing efforts in order to alleviate the fishing pressure on marine resources and promote long-term sustainability. To ensure sustainability, it is crucial to implement management measures such as catch limits, regular monitoring, and the development of tools to monitor small-scale fisheries that have limited data records. The ARIMA model, in particular, offers reliable forecasting technique for limited time-series data, aiding resource managers in effective planning.

Biological reference points are essential for achieving sustainable fisheries management, especially in data-limited context. Techniques like CMSY, LBB, JABBA, and ARIMA offer valuable tool for managing such fisheries, though they are limited by not accounting for environmental interactions between stocks. Integrating these methods with ecosystem-based approaches could provide a more comprehensive assessment. The results of this study showed that the M. cordyla fishery is overexploited, with LBB, CMSY, BSM, and JABBA models consistently indicating overfishing. The ARIMA (2, 0, 1) model predicts that if current catch trends continue, this fishery may face collapse. These findings highlight the effectiveness of using catch-only data for management in the absence of more complex datasets. Pakistani marine waters are open-access, which exacerbates the risk of overexploitation. Multi-model approaches could effectively support sustainable fisheries management to inform strategic decisions. To ensure sustainability, measures such as implementing a fishing ban during the breeding season, increasing trawl mesh sizes, and establishing marine protected areas (MPAs) are essential. Additionally, enforcing vessel monitoring and implementing stricter regulations are necessary to combat the illegal fishing activities. Scientific-based TAC limits should be established for each fishery. The alternative approaches, including aquaculture, could be considered to support recovery of wild stocks while ensuring food security. Collaboration between fishery managers and the scientific community is essential to ensure the sustainable utilization of fisheries resources.