Assessment of Exploited Stock and Management Implications of Tiger Tooth Croaker (Otolithes ruber) in Coastal Waters of Makran, Pakistan

Abstract

Pakistan’s marine fishing industry is crucial to the country’s economy, generating employment opportunities and foreign revenue. It produces 80% of the country’s total fish production. Otolithes ruber is a commercially important fish on the Makran coast of Pakistan, contributing significantly to the region’s croaker fisheries. This study is the first to apply three length-based approaches for assessing the stock status of O. ruber in the Makran coast: (1) TropFishR to estimate the mortality, growth parameters, and current exploitation status, reference points based on the yield per recruitment model, (2) the length-based Bayesian biomass method (LBB) to calculate stock biomass, and (3) the length-based spawning potential ratio (LBSPR) to estimate the spawning potential ratio. The length–weight relationship of Otolithes ruber was a positive allometric pattern (b = 3.28; R² = 0.94). Growth parameters for Otolithes ruber were L_∞ = 55.47 cm, K = 0.50 year⁻¹. The calculated total mortality rate (Z), natural mortality (M), and fishing mortality (F) were 2.27 year⁻¹, 0.67 year⁻¹, and 1.6 year⁻¹, respectively. The exploitation rate (E) was 0.70, indicating severe overexploitation. The current length at first capture (Lc₅₀) = 27.37 cm was lower than that at first maturity (Lm₅₀) = 30.75 cm, indicating growth overfishing. The current spawning potential ratio (8%) was lower than the optimal value (40%), indicating recruitment overfishing. The current biomass, concerning virgin biomass B/B_o, was also 8%, resulting in a 92% stock decline. We recommend reducing the exploitation pressure by limiting the commercial catch to an optimum length range of 34.5–42.2 cm and reducing fishing pressure by 40% to ensure sustainable fishery management.

1. Introduction

Otolithes ruber (Bloch & Schneider, 1801) is a member of the Sciaenidae family, known as croakers or drums [1]. Sciaenidae is one of the most prominent families of the order Perciformes, consisting of 293 species belonging to 69 genera. Otolithes ruber is a demersal fish [2]. They can be found in sandy and muddy bottoms and near river mouths. They typically reside at depths between 10 and 40 m [3,4]. They inhabit marine and brackish waters with warmer temperatures ranging from 26 °C to 29 °C. They are distributed along the Indian Ocean, the east coast of Africa, and the western Pacific Ocean [1]. Their worldwide distribution is recorded in tropical and subtropical coastal waters and estuarine waters of the Atlantic, Indian, and Pacific oceans [5].

The Makran coast of Pakistan is part of the larger Makran region, known for its arid coastal landscapes. It stretches along the Gulf of Oman, encompassing parts of both Pakistan and Iran. The Arabian Sea borders it to the south, the Siāhān Range to the north, and the Kech River Valley to the east [6]. The marine capture fisheries in Pakistan play a vital role in the country’s economy by generating employment opportunities and earning foreign exchange. They contribute approximately 80% of the country’s total fish production [7]. The marine fisheries of Pakistan have experienced significant impacts in recent years, primarily due to excessive fishing pressure, unsustainable fishing methods, and marine contamination [8].

Population dynamics and stock assessment are important aspects of fisheries management, as they provide information about the fish stock [9]. Length-frequency data are more accessible than length-at-age data because fish can be measured without needing to purchase. This makes length-frequency data a valuable tool for fisheries managers. The studies of growth, mortality, exploitation, and age are essential components of fish stock assessment [10]. Managers use stock assessments as their primary tool to understand fish stocks’ status and future trends [11]. To conduct fish stock assessments, it is necessary to utilize a range of qualitative analyses, including studies on fish behavior, biological factors, statistical models, and methodological approaches [12]. A regulatory measure, such as implementing closure periods, restricted fishing areas, and reducing the number of vessels and catches, should be taken when fish stock assessment studies indicate a stock decline [12].

The length-based spawning potential ratio (LBSPR) was created by [13] and is widely used to assess the status of fish stocks in tropical oceans. It utilizes length-frequency data and population parameters as input to predict the stock status, considering the percentage of the reproductive population that remains in the exploited stock. Length-based Bayesian biomass (LBB) is a novel method that utilizes the Bayesian approach and length data to assess the stock status of fisheries [14]. It estimates the growth and mortality rates, the level of exploitation, and the stock size relative to their natural values [15]. It also provides essential management indicators, such as the optimal length for first capture (Lc_{_opt}) and the optimal length for maximum yield per recruit (L_opt) [14].

Moreover, the length-based Bayesian method provides estimates of relative biomass (B/B₀ and B/B_MSY), which indicate the stock’s health [14]. The TropFishR package is a valuable tool for fisheries analysis with length-frequency data. It contains a collection of fish stock assessment methods suitable for data-poor fisheries [16]. The package is based on the FAO manual “Introduction to tropical fish stock assessment” by [11], and other more recent methods. Using length-frequency data, the package allows users to estimate growth and mortality parameters, exploitation levels, stock size, and management indicators for fish stocks [16].

Stock assessment and population dynamics of Otolithes ruber have been conducted in Iran [4,17], Mozambique [18], Iraq [19], Kenya [20], Bangladesh [21], and India [22,23]. These studies consistently indicate that O. ruber stocks are under pressure, with signs of overexploitation. For instance, assessments from Iran, Kenya, and Mozambique have reported clear evidence of overfishing due to a high exploitation rate. Similarly, research conducted in Bangladesh and India has shown low biomass levels, also suggesting an overexploited status. Taken together, these findings highlight that O. ruber stocks are overexploited in many parts of their distribution range.

There has also been a study on the Otolithes ruber population dynamics in Pakistan [24]. However, that study only estimated the growth and mortality parameters and did not consider the spawning potential ratio or stock biomass. In our research on the Makran coast of Pakistan, we applied three of the most widely used methods for estimating fish stock status using length frequency data: TropFishR [16], length-based spawning potential ratio [13], and length-based Bayesian Biomass method [14]. These methods can provide more comprehensive information about the stock status.

Along the Makran coast of Pakistan, limited studies have been conducted on fish population dynamics and stock assessment. For better management of the fish population, it is necessary to perform more stock assessments and population dynamics studies. This study aims to assess the stock status of Otolithes ruber along the Makran coast by estimating key population dynamics and stock assessment parameters, such as the growth coefficient (K), asymptotic length (L_∞), fishing mortality (F), natural mortality (M), total mortality (Z), yield per recruit (Y/R), selectivity parameters, maturity parameters, spawning potential ratio (SPR), and current biomass. These parameters were used to assess the stock status. This study will provide management recommendations to assist fisheries managers in ensuring the sustainable management of Otolithes ruber along the Makran coast of Pakistan.

2. Materials and Methods

2.1. Study Area and Data Collection

To estimate the stock status of the Otolithes ruber in the coastal water of Makran, Pakistan, length–weight data were collected from the commercial catches from the three different fish harbors of Jiwani (25°2′44.57″ N, 61°44′26.49″ E), Gwadar (25°6′50.81″ N, 62°20′0.77″ E), and Pasni (25°15′45.08″ N, 63°28′30.54″ E) (Figure 1). The samples were collected from the commercial catch with the help of local fishermen, and mechanised fishing boats and gill nets were used to catch the tiger tooth croaker. Both sexes’ length and weight data of 1359 Otolithes ruber were collected monthly from September 2020 to September 2021. The total length was measured to the nearest 0.1 cm from the tip of the mouth to the tip of the tail, while the total weight was measured to the nearest 1 g.

2.2. Assessment Models

2.2.1. Length–Weight Relationship

The length–weight relationship of Otolithes ruber was estimated by the following power equation [25].

W = aL^b

where W = weight of the fish in g, L = total length of the fish in cm, “a” is the intercept, and “b” is the slope or relative growth coefficient, which describes the variation in weight with respect to the length.

2.2.2. Growth Pattern

Population parameters such as asymptotic length (L_∞) and growth coefficient (K) were estimated from length-frequency data using the von Bertalanffy growth function (VBGF) in the TropFishR package [16], based on the following equation:

• L_t = L_∞ (1 − e^−K(t−t0)) [11],
  where L_t = length at age t, L_∞ = asymptotic length, K = growth coefficient, t_o = theoretical age of a fish at length zero. Electronic length frequency analysis (ELEFAN-GA) [26] was used in the TropFishR to fit the function. The initial value for L_∞ was obtained using the formula as L_∞ = L_max/0.95 [27], where L_max is the maximum observed length of the fish in the sample. The initial seed value of the L_∞ was set as L_∞ ± 20%, and the K range was between 0.01 and 2. A suitable moving average (MA = 7) was adjusted based on the rule of thumb suggested by [28]. The growth performance index (Φ’) was estimated using the formula of [29], Φ’ = log₁₀ K + 2 log₁₀ L_∞, and the theoretical age of a fish at zero length (t₀) was calculated using the following equation:
• log(−t₀) = −0.3922 − 0.275 log(L_∞) − 1.038 log(K) [27].

2.2.3. Fishing Mortality and Exploitation

Total mortality (Z) was estimated using the length-converted catch curve method through the TropFishR package. Natural mortality (M) was calculated using the formula by [30].

M = 4.118 × K^0.73 × L_∞ ^−0.33

Then fishing mortality was estimated as F = Z − M. The exploitation rate (E) was calculated as E = F/Z [11].

2.2.4. Yield per Recruitment

Thompson and Bell model length-based yield per recruit analysis (YPR) was performed using the TropFishR package [16] to assess the stock status of the Otolithes ruber and identify reference points for sustainable management. This analysis incorporated data on fish mortality rates, growth patterns (von Bertalanffy growth parameters), size distribution (length frequency data), and the relationship between fish length and weight (length–weight coefficients). The fishing mortality rate was then compared against these established reference points to evaluate potential impacts on the fish stock. Fishing mortality rate corresponds to 10% of the slope of the yield-per-recruit curve at the origin (F_0.1). The fishing mortality rate reduces the spawning biomass to 50% of its unexploited level (F_0.5). The fishing mortality rate at which the spawning potential ratio is about 40% (F_0.4). Fishing mortality rate that maximises the yield per recruit (F_max).

2.2.5. Length-Based Spawning Potential Ratio (LBSPR)

The length-based spawning potential ratio (LBSPR) is a commonly used approach for evaluating fish stocks, particularly in situations with limited data. It determines the spawning potential ratio (SPR), which serves as a key reference point for assessing the health and status of a stock [13]. In an unfished population, SPR is 1, indicating maximum egg production, while an SPR of 0 means no reproductive capacity remains [13]. An SPR of 0.4 is often linked to maximum sustainable yield, while values below 0.2 indicate insufficient recruitment to maintain the population, leading to recruitment overfishing [31]. The length-based spawning potential ratio model requires several input parameters, such as asymptotic length (L_∞), M/K ratio, length and weight parameters (a and b), and maturity parameters, length at 50% maturity (Lm₅₀) and length at 95% maturity (Lm₉₅) [32]. Lm₅₀ and Lm₉₅ of the Otolithes rubber were calculated by using the following equations.

• Log Lm₅₀ = 0.8979 × Log L∞ – 0.0782 [33].
• Lm₉₅ = 1.1 × Lm₅₀ [31].

The LB-SPR R package [34], available at https://CRAN.Rproject.org/package=LB-SPR and accessed on 15 August 2024, was used to estimate SPR.

2.2.6. Length-Based Bayesian Biomass (LBB)

The length-based Bayesian Biomass (LBB) method [14] evaluates stock status based on three primary indicators: the biomass required to reach maximum sustainable yield (B/B_MSY), the ratio of current biomass to unexploited biomass (B/B₀), and the ratio of fishing mortality to natural mortality (F/M). If B/B_MSY is greater than 1, the stock is considered underexploited. If it falls between 0.8 and 1.0, it is fully exploited. However, if B/B_MSY is less than 0.8, the stock is over-exploited [14,35]. Additionally, if the ratio of current biomass to unexploited biomass (B/B₀) is less than 0.5, the stock is considered overexploited. Similarly, a ratio of fishing mortality to natural mortality (F/M) greater than 1 also suggests overexploitation [14]. The ideal values for the ratios L_mean/L_opt (mean length of harvested fish to optimal harvesting length) and L_c/L_{c_opt} (length at first capture to optimal length at first capture) are 1. Values below 1 for these ratios indicate the presence of excessive juvenile fishing or growth overfishing.

The LBB analysis was conducted using the LBB R package [14], available at https://www.Cran.R-project.org/package=LBB, and accessed on 15 August 2024. Several key input parameters were used in this LBB analysis, such as the asymptotic length (L_∞), M/K, Lc₅₀, and Lm₅₀. The length-converted catch curve analysis method with the “calc_ogive” function in the TropFishR package was used to estimate the length at 50% capture (Lc₅₀).

$${\mathrm{L}}_{\mathrm{opt}}(\mathrm{length} \mathrm{at} \mathrm{optimal} \mathrm{yield}) \mathrm{was} \mathrm{estimated} \mathrm{as} {\mathrm{L}}_{\mathrm{opt}}=L_{\mathrm{\infty }} ({\displaystyle \frac{3}{3+\frac{M}{k}}})$$

The range of L_opt was calculated as ± 10% of L_opt, and the number of fish above the L_opt range was considered mega spawners [36].

3. Results

3.1. Length–Weight Relationship

The minimum total length (TL) was recorded as about 17.5 cm, whereas the largest size was about 51.5 cm, and most individuals were from 26 to 31 cm in total length (TL). The length–weight relationship model of Otolithes ruber was as W 0.0036L^3.28, R² =0.94 (Figure 2), and the relative growth coefficient (b) was 3.28, which indicates positive allometric growth for Otolithes ruber in the study area.

3.2. Growth Pattern

ELEFAN-GA method in TropFishR package was used to estimate von Bertalanffy growth parameters (VBGFs) as asymptotic length (L_∞) = 55.47 cm in total length and growth coefficient (K) = 0.50 year⁻¹ (Figure 3); the calculated t_o was −0.27 (

Table 1. Summary of the population parameters of the Otolithes ruber.

Parameters	Calculated Value
Asymptotic length (L∞ cm)	55.47
Growth coefficient (K year−1)	0.50
Growth performance index (Φ’)	3.18
Hypothetical age (t0 year)	−0.27
Total mortality (Z year−1)	2.27
Natural mortality (M year−1)	0.67
Fishing mortality (F year−1)	1.6
Exploitation rate (E year−1)	0.70
Length at first capture (Lc50 cm)	27.37
Length at 50% maturity (Lm50 cm)	30.75
Length at 95% maturity (Lm95 cm)	33.82
Sample size (n)	1359
Intercept of LWR (a)	0.0034
Relative growth coefficient (b)	3.28
Rnvalue	0.18

).

The response surface (Rn) for the goodness of fit model VBGF was 0.189. The growth performance index (Φ’) was estimated using VBGF growth parameters at 3.18.

3.3. Mortality and Exploitation Rate

The total mortality rate (Z) was calculated at 2.27 year⁻¹ based on the length-converted catch curve (Figure 4), natural mortality (M) was estimated at 0.67 year⁻¹, and fishing mortality was obtained at 1.6 year⁻¹. The exploitation rate (E) was calculated at 0.70 year⁻¹, higher than the optimum value of 0.50, indicating 40% overexploitation of the Otolithes ruber on the Makran coast, Pakistan.

3.4. Length at First Capture and Length at Maturity

Length at first capture (Lc_50%) was found to be 27.37 cm, while age at first capture (t₅₀) was 1.15 years, respectively (Figure 5). The length at 50% capture (Lc₅₀) of 27.37 cm was lower than the length at 50% maturity (Lm₅₀) of 30.75 cm (Figure 6), indicating growth overfishing for the Otolithes ruber on the Makran coast of Pakistan.

3.5. Yield per Recruitment

Biological reference points for Otolithes ruber on the Makran coast were obtained through the yield per recruitment model: F_max (fishing mortality which gives maximum yield per recruit) = 2.42 year⁻¹, F_0.5 (fishing mortality when spawning biomass is 50%) = 0.82 year⁻¹, and F_0.1 (fishing mortality rate where the yield-per-recruit curve slope is 10% of the initial slope) = 1.40 year⁻¹ (Figure 7 and

Table 2. Reference points and current fishing mortality against yield per recruit.

Fishing Mortality (Year−1)	Yield per Recruit (g/Recruit)
F0.1 = 1.40	148.77
F0.5 = 0.82	124.06
Fmax = 2.42	157.93
Fcurrent = 1.60	151.59

). These results show that the current fishing mortality of 1.6 is higher than the biological reference points F_0.5 and F_0.1, indicating growth overfishing for Otolithes ruber on the Makran coast, Pakistan. The current yield per recruit for Otolithes ruber was 151.59g/recruit (Figure 8), slightly higher than the yield per recruit of F_0.5.

3.6. Length-Based Spawning Potential Ratio (LBSPR)

The results of the length-based spawning potential ratio (LBSPR) are shown in Figure 9 and

Table 3. Outputs of the LBSPR.

Parameters	Value
Spawning potential ratio	0.08 (8%)
SL50%	28.32 cm
SL95%	35.09 cm
F/M	4.31

. The outputs of the LBSPR were as follows: total length at 50% and 95% selectivity (SL₅₀ and SL₉₅) were 28.32 and 35.09 cm, respectively. The length at 50% selectivity SL₅₀ (28.32 cm) from LBSPR was also lower than that at first maturity (30.75 cm), indicating growth overfishing.

The relative F/M was 4.31, which is higher than the reference point of 1, indicating high fishing pressure, while the current spawning potential ratio was 8%, which is well below the limit point of 20%.

3.7. Length-Based Biomass (LBB)

The output of the LBB method is shown in Figure 10 and

Table 4. Summary of the results of the length-based Bayesian biomass model.

Variables	Value
L∞ (CI)	54.4 (53.6–55.3) cm
Lopt	38.34
Lopt range	34.5–42.2 cm
Lopt/L∞	0.7
Lc_opt	36 cm
Lc_opt/L∞	0.66
Lmean	36.3 cm
M/K (CI)	1.29 (1.17–1.41)
F/M	4.74 (3.96–5.46)
F/K	6.06 (5.53–6.6)
Z/K	7.35 (6.92–7.89)
B/Bo (CI)	0.08 (0.06–0.09)
Lc50 (CI)	29.3 (29–29.7)
Lc95 (CI)	38 (37.8–38.4)
Alpha (CI)	0.34 (0.33–0.35)
Lmean/Lopt	0.88
Lc/Lc_opt	0.82
L95th/L∞	0.94
B/Bmsy (CI)	0.21 (0.17–0.26)
Stock status	Collapsed

. The results indicate that the current biomass of Otolithes ruber is at 0.08 of its unfished biomass (B/B₀), which is significantly lower than the reference point of 0.5. This suggests that the stock has declined by 92%. The high value of F/M (4.74) also indicates a high fishing mortality level for this species on the Makran coast, Pakistan. The current length at first capture (Lc₅₀), 29.3 cm, was lower than the optimum length at first capture (Lc__opt), 36 cm, indicating growth overfishing. The values of L_mean/L_opt (Mean Length/optimal Length ratio) and L_c/L_opt (length at first capture/optimal Length ratio) were 0.88 and 0.82 both values are lower than the reference points of 1, indicating a high proportion of small catches in the samples resulting in growth overfishing (Figure 10).

4. Discussion

4.1. Length–Weight Relationship

The length–weight relationship (LWR) is considered the fundamental parameter for fish stock assessment, and the value of ‘b’ can vary from 2.5 to 3.5 [37]. If the slope ‘b’ is equal to 3, it indicates isometric growth; if the ‘b’ value is less than 3, it means that it is negative allometric growth. If the b value is greater than 3, it indicates positive allometric growth. Additionally, since the length–weight parameters ‘a and ‘b’ are the input parameters for the YPR analysis, they were calculated before running TropFishR [38]. In the current study, the ‘b’ value was 3.28, indicating that Otolithes ruber exhibits positive allometric growth along the Makran coast of Pakistan. The ‘b’ value was compared with values from different locations (

Table 5. Comparison of length–weight parameters of Otolithes ruber from different sources with the current study.

Study Area	b	a	R2	Source
Makran Coast, Pakistan	3.28	0.0036	0.94	[current study]
Taiwan	2.63	0.0300	0.83	[40]
Philippines	2.73	0.0150	0.91	[42]
South Africa	3.13	0.00049	-	[39]
India	2.83	0.018	0.88	[43]
Persian Gulf, Iran	2.70	0.032	0.86	[41]
Northern Makran, Sea Iran	2.94	0.012	0.91	[4]
Persian Gulf, Iran	3.19	0.005	0.99	[3]
Iraq	2.75	0.023	0.99	[19]

). It varied from 2.63 to 3.28 in various places. Studies from South Africa [39], the Persian Gulf, Iran [3], and the Makran coast, Pakistan (present study) showed positive allometric growth, i.e., b value is greater than 3. In contrast, the other studies [4,19,40,41,42,43] showed negative allometric growth, i.e., b value is less than 3. The highest ‘b’ value was found in the current study (Makran coast), i.e., 3.28, while the lowest ‘b’ value was found in Taiwan at 2.63 [40]. These variations in the growth pattern may be attributed to climate change, variations in the timing of sample collection, differences in food availability, and variations in geographical locations [44].

4.2. Growth Parameters

Studies on population parameters, such as the growth coefficient (K), asymptotic length (L_∞), mortalities (fishing, natural, and total mortality rate), and exploitation level (E), are very important for the management of marine resources [45]. These studies with statistical analysis are beneficial for determining the status of the fish stocks [46]. Data from otoliths are hard to get, so length-frequency data from most locations are used to estimate the growth parameters [11].

The estimated von Bertalanffy growth function (VBGF) parameters, L_∞ and K, were calculated as 55.47 cm and 0.50 year⁻¹, respectively, and were compared with findings from other studies conducted in various countries (

Table 6. Growth parameters of Otolithes ruber from different geographical locations and the current study.

Study Area	K year−1	L∞ (cm)	Φ’	Source
Makran coast, Pakistan	0.50	55. 47	3.18	[current study]
Sofala Bank, Mozambique	0.32	45.9	2.84	[18]
KwaZulu-Natal, South Africa	0.31	41.9	2.73	[1]
India, Tamil Nadu	0.27	37.28	2.57	[23]
Iran, Gulf of Oman	0.41	65.0	1.85	[4]
Iran, Persian Gulf	0.27	67.57	3.09	[3]
Balochistan, Pakistan	0.83	34.65	2.99	[24]
Northwest Arabian Gulf, Iraq	0.36	68.5	3.22	[19]
Malindi-Ungwana Bay, Kenya	0.70	41.7	3.08	[20]

). The lowest value of the growth coefficient (K) was recorded in Tamil Nadu, India [23] and the Persian Gulf, Iran [3]. In contrast, the highest value was recorded on the Balochistan coast of Pakistan [24]. The highest recorded value of asymptotic length (L_∞) was recorded at 68.5 cm in the Northwest Arabian Gulf, Iraq [19], while the lowest value was recorded in the Balochistan coast, Pakistan [24]. The differences between these values may be due to changes in environmental patterns, different fishing methods, different areas, sample numbers, and timing [47].

It is known that the species with higher asymptotic length (L_∞) tend to have lower growth coefficients (K) and lower natural mortality rates [48]. The estimated value of the current study’s growth performance index (Φ’) was close to those conducted in the Northwest Arabian Gulf, Iraq, and the Persian Gulf [3,19].

4.3. Mortality and Exploitation

Mortality is an essential parameter in fish population dynamics and can be attributed to various factors, such as parasites, diseases, ageing [49], fishing activities, and environmental factors [50]. Mortality rates of O. ruber are compared with studies from different locations, as shown in

Table 7. Comparison of different mortalities and exploitation levels of Otolithes ruber from various countries.

Study Area	F	M	Z	E	Source
Makran coast, Pakistan	1.6	0.67	2.27	0.70	[current study]
Iran, Persian Gulf	1.25	0.7	1.95	0.64	[17]
SofalaBank, Mozambique	1.25	0.7	1.95	0.64	[18]
Balochistan, Pakistan	2.17	1.46	3.18	0.68	[24]
Northwest Arabian Gulf, Iraq	0.41	0.69	1.10	0.38	[19]
Malindi-Ungwana Bay, Kenya	2.30	0.93	3.23	0.71	[20]

. The mortality parameters of Otolithes ruber from the Makran coast were found to be fishing mortality 1.6 year⁻¹, natural mortality 0.67 year⁻¹, and total mortality 2.27 year⁻¹. The values were closer to those of the Persian Gulf, Iran, and Sofala Bank, Mozambique [17,18]. However, the high values of fishing mortality, 1.6 year⁻¹, and the exploitation rate, 0.70 year⁻¹, suggest that the Otolithes ruber on the Makran coast is overexploited.

4.4. Length at First Maturity

The length at first maturity of Otolithes ruber is compared between our study and various studies conducted worldwide (

Table 8. Comparison of the length at first maturity of Otolithes ruber with different studies.

Area	Lm 50 (cm)	Source
Makran coast, Pakistan	30.75	[current study]
Oman Sea	40.0	[52]
Makran Sea, Iran	43.3	[4]
Persian Gulf	28.0	[3]
Kwazulu-Natal coast, South Africa	23.70	[39]
San Miguel Bay, Philippines	13.95	[51]

). Length at first maturity in the current study was approximately 30.75 cm, higher than at first capture, 27.37 cm. This shows that fish are being captured before maturity, resulting in overfishing. The highest Lm₅₀ was recorded on the Makran Sea, Iran [4], while the lowest was in San Miguel Bay, Philippines [51]. Our current study’s length at first maturity was closer to that recorded in the Persian Gulf [3].

4.5. Yield per Recruitment

Fisheries scientists use the yield per recruit model to estimate various biological reference points. F_0.1 is the reference point for harvesting the stock sustainably, and F_max = fishing mortality, which produces the maximum yield per recruit. The reference points F_0.1 and F_max can be used to determine growth overfishing [53]. Yield per recruit increases with an increase in fishing mortality until it reaches the maximum sustainable yield point, beyond which the yield declines, potentially leading to population collapse [54]. In our study, the current fishing mortality rate (F_current) of 1.60 year⁻¹ is higher than the reference points of F_0.5 =0.82 year⁻¹ and F_0.1 = 1.40 year⁻¹, indicating overfishing for the Otolithes ruber (Figure 7). To achieve sustainable fishing, the current mortality rate must be reduced by approximately 48.75% to reach F_0.5, and by 12.5% to reach F_0.1.

4.6. Length-Based Spawning Potential Ratio (LBSPR)

The LBSPR method relies on equilibrium conditions and several key assumptions [13], such as a single growth curve shared by both sexes, constant recruitment and natural mortality over time, normal distribution of length-at-age, stable cohort growth rates, accurate modeling of growth through the von Bertalanffy equation, and asymptotic selectivity favoring larger fish [13]. One way to assess the impact of fishing on a fish population is by using the length-based spawning potential ratio (LBSPR) [55]. LBSPR measures how much fishing reduces the reproductive potential of the population. Excessive fishing can lead to both growth overfishing and recruitment overfishing. Growth overfishing occurs when fish are harvested before they reach their optimal size for maximum yield. In contrast, recruitment overfishing occurs when the spawning stock biomass is so low that it cannot sustain the population through reproduction [56]. Our study found that O. ruber along the Makran coast had a very low spawning potential ratio of 0.08 (8%), indicating severe overfishing. This is well below the target reference point of 40% and the limit of 20%, indicating recruitment overfishing. As the SPR decreases, the catch tends to consist of a higher proportion of smaller fish, further highlighting stock overfishing. Achieving the target SPR of 40% is often challenging in many commercially exploited fish stocks [57].

4.7. Length-Based Bayesian Biomass (LBB)

The LBB method serves as a practical and efficient approach for assessing fish stock status, particularly in data-poor situations [14]. In contrast to other length-based methods used in this study, such as LBSPR and TropFishR, the LBB model is more streamlined and quicker to apply, as it depends exclusively on length-frequency (LF) data and does not require supplementary inputs like age structure, mortality rates, growth parameters, or recruitment information [14]. We used the length-based Bayesian biomass (LBB) method to evaluate the biomass status of O. ruber on the Makran coast of Pakistan. This model is suitable for data-limited fisheries and has been applied to many significant fish stocks in different countries. This model provides the current biomass in relation to the unfished biomass [14]. Many studies have employed this approach to assess the current biomass of fish stocks worldwide [21,22,58,59,60]. The LBB method was applied in the northeastern Arabian Sea, India, to determine the stock status of the Otolithes ruber, which was found to be over-exploited (B/B_o = 0.35) [22]. Similarly, in the Bay of Bengal, Bangladesh, the stock status assessment of Otolithes ruber using the LBB method also indicated over-exploitation, as reported by [21] (

Table 9. Comparison of the stock status of Otolithes ruber in different studies based on the length-based Bayesian biomass approach.

Study Area	B/B0	B/BMSY	F/M	F/K	Lmean/Lopt	Reference
Makran coast, Pakistan	0.08	0.21	4.74	6.06	0.88	[current study]
Northwest coast of India	0.35	0.97	1.10	1.70	0.99	[22]
Bay of Bengal, Bangladesh	0.17	0.47	2.1	2.1	0.86	[21]

).

Our results showed that O. ruber was overexploited on the Makran coast, as indicated by its low current biomass, which was only 8% of its virgin biomass (B/B₀) and 21% of its optimal biomass (B/B_msy). This result was consistent with the stock status derived from the TrophFishR and spawning potential ratio models. Therefore, it is suggested that management measures be implemented to increase Otolithes ruber’s biomass on the Makran coast.

5. Conclusions

This study assessed the stock status of Otolithes ruber on the Makran coast of Pakistan using three length-based approaches: TropFishR, LBSPR, and LBB. The consistent findings across all three methods indicate that the population is in a state of overfishing and overexploitation. The key evidence supporting this conclusion includes the following:

• The current exploitation rate (E = 0.70) exceeds the optimum level (E = 0.50), suggesting excessive fishing pressure.
• The observed length at first capture (L_c = 27.37 cm) is lower than both the optimal length (L_opt = 38.34 cm) estimated from the LBB model and the length at first maturity (L_m = 30.75 cm), indicating the harvest of immature individuals.
• Current biomass is only 8% of the virgin (unfished) biomass (B/B₀ = 0.08), highlighting severe stock depletion.
• The spawning potential ratio (SPR = 0.08) is far below the recommended threshold (>0.4), indicating serious recruitment overfishing.

These findings point to an urgent need for management interventions to ensure the recovery and sustainability of Otolithes ruber on the Makran coast.

Policy Recommendations

Based on the assessment results, the following policy and fisheries management measures are recommended:

Implement size-based harvest regulations: Fishers should target individuals between 34.5 cm and 42.2 cm in total length to avoid growth and recruitment overfishing.

Establish routine fishery monitoring and data collection programs: A standardized fishery data collection system should be implemented to regularly gather length-frequency, biological, and catch-effort data, which are critical for future stock assessments. The collection of age-based and sex-specific biological data is particularly essential for refining length-based estimates.

Introduce a fishery observer program: Observers should monitor fishing activity, gear types, bycatch, and compliance with regulations, contributing to more effective management.

Conduct broader stock assessments: Additional studies should assess the status of other commercially important fish species along the Makran coast, using both length-based and age-based methods to inform regional fisheries policy. This includes integrating environmental variables and habitat factors to better understand their influence on stock dynamics.

Enforce seasonal or spatial closures: Where feasible, temporal or spatial closures could be introduced to protect spawning aggregations and juvenile habitats of Otolithes ruber.

Although the length-based methods applied—TropFishR, LBSPR, and LBB—are valuable tools in data-limited contexts, their reliability depends heavily on several assumptions and the quality of input data. In this study, limitations such as the absence of sex-specific growth parameters, age-structured data, and environmental drivers may introduce uncertainty in the estimates. Therefore, future research efforts should prioritise collecting comprehensive biological data, including age and sex information, to validate and improve the accuracy of stock assessments. This can be complemented by integrating environmental and ecological factors to account for their potential influence on stock dynamics, thus providing a more complete understanding of the factors affecting the sustainability of the species.