The study was undertaken in the Northern Iran marine waters within the Southeast Caspian Sea, and the Southeast Caspian Sea is one of the most important areas in the sea- Northern Iran ( Figure 1 ). The Caspian Sea area is divided into three, approximately equal, parts: Northern, Middle, and Southern (Aladin and Plotnikov, 2004). The volumes are extremely different. The Southern Caspian has the largest volume - some 64% of the total volume, and its area is 35% of the total sea area. It is the deepest part of the sea with the maximum depth reaching 1025 m. According to I.S. Zonn (2000), the area is from 144690 up to 151018 km², and the average volume - 48300 km³. The average depth is 300 m.

Sampling was carried out using a small beach seine (30 m long, 2 m depth, and mesh size of 3 mm knot to knot), a total of 956 specimens were collected in the southeast Caspian Sea from March 2022 until February 2023. It was set out in such a way that the dragline of one wing remained fastened to the beach, while one wing, the net bag, and then the other wing with its dragline were taken out in a wide arc and then brought back to the beach. In the laboratory, total length (TL) was measured to the nearest 1 mm for all fish sampled. Total weight, the weight of gonads, and their subsamples were recorded with an electronic analytical balance to the nearest 0.01 g. For the age determination scales and opercula were used.

Sex was determined by examination of the gonads. Maturity stages were estimated according to the Nikolsky (1963) scale. Gonadosomatic index (GSI %) = (gonad weight/total body weight) - 100 was calculated for each fish and all values were averaged for each sampling date. A. boyeri is a batch spawner, its spawning takes place over a long period of 2-3 months (Creech, 1992). Therefore, to decrease the error due to multiple spawning, we used ovaries of 126 ripe specimens with IV maturity stage, from females caught in March to estimate absolute and relative fecundities. The gonads were removed, weighed, and then placed in Gilson’s fluid for 3-4 weeks to harden eggs and dissolve ovarian membranes. The peritoneum was removed and individual eggs were released from the egg mass. The number of eggs was estimated by gravimetric method, using three pieces removed from the ovary. The relative fecundity index was calculated as RF = AF/TW, where AF is absolute fecundity and TW is total weight (Bagenal and Tesch, 1978). Egg diameter was examined by measuring 20-30 eggs taken randomly from pieces of the ovary of 254 ripe females caught in March 2022-February 2023. Measurements were made to the nearest 0.05 mm with an ocular micrometer microscope. Comparison of GSI between months was carried out by analysis of variance (ANOVA). An analysis of covariance (ANCOVA) was performed to test significant differences in weight-length relationships and GSI values between the sexes. The overall sex ratio was assessed using the Chi-square test (Zar, 1984). Statistical analyses were performed with SPSS-26 software package and a significant level of 0.05 was accepted.

The overall sex ratio was 1:1.34 (M: F; 569 females, 387 males). The sex ratio of the population was significantly different from the ideal Mendel ratio [X² (1, N= 956) = 34.65, p < 0.001], yet sex ratio changes were found to be significant within age classes. Males were significantly dominant in the 1 and 2 age groups, whereas females were significantly dominant in 2 and older age groups [X² age1 (1, N = 141) = 3.32, p > 0.05; X² age2 (1, N = 112) = 6.00, p> 0.05; X² age2 (1, N = 176) = 4.64, p > 0.05; X² age3 (1, N = 147) = 12.62, p > 0.05; X² age4 (1, N = 144) = 11.26, p > 0.05); X² age5 (1, N = 6) = 13.01, p > 0.05]. All the specimens were found to be sexually mature in the first spring after hatching.

During the study period, A. boyeri showed a minimum length of 60 mm and a maximum length of 125 mm. The total weight fluctuated between a minimum of 1.2 g and a maximum of 12.51 g. The fishes within the length group of 70 to 90 mm were found to be most abundant in the catch. The values of an a (intercept) and b (slope) of the length-weight relationship equation were reported to be 0.0058 and 3.0643 for the population, 0.0055 and 3.0774 for males, and 0.0083 and 2.9185 for females respectively ( Figure 2 ). The highest relative condition factor (K_n ) in June was reported to be 0.92 and 0.75 for the males and females respectively ( Figure 3 ).

The frequency of occurrence of adult female specimens was plotted against length class and fitted to a logistic function to determine the mean fish length at first sexual maturity (L_m ). In the case of A. boyeri the length at first sexual maturity was reported to be 70 and 75 mm for both males and females. The various biometric and population parameters of A. boyeri are depicted in Figure 4 .

The growth constant (K) in the population, males and females were reported to be 0.28, 0.34, and 0.35 year^-1, and the asymptotic length (L_∞ ) was reported to be 131.0, 126.5, and 131.3 mm respectively. The length frequency of males and females in Figure 5 is presented, indicating the highest abundance in the length classes of 7.5-8 and 8-8.5. The von Bertalanffy growth curve and the length-frequency histograms are presented in Figure 6 . The growth performance index of the A. boyeri was reported to be 1.68, 1.74, and 1.78 and the age at zero length (t₀) was reported to be -0.28, -0.31, and -0.31 years for Population, males, and females respectively.

The mortality parameters i.e., the total mortality, the fishing mortality, the natural mortality, and the exploitation ratio for A. boyeri were reported to be 0.79 year^-1, 0.78 year^-1, 0.01 year^-1, and 0.02 for the population, 1.73 year^-1, 0.35 year^-1, 1.38 year^-1 and 0.21 for males and 0.20 year^-1, 0.31 year^-1, 0.90 year^-1 and 0.26 for females respectively ( Figure 7 ).

The A. boyeri population from the southeast Caspian Sea exhibits recruitment peaks during late winter, spring, and summer months (March to September) for the entire population; in males, this occurs in spring and early summer (April to July), and in females, it is seen in spring and summer (June to September), collectively contributing approximately 70-85% to total recruitment ( Figure 8 ). The fishing mortality rate (F) for the overall population remains steady beyond a length of 95 mm. However, in males, this rate initially rises after 95 mm until reaching 120 mm, where it then stabilizes. Conversely, in females, this rate also shows a marked increase up to 120 mm in length, as revealed by VPA ( Figure 9 ). The yield per recruit model by Beverton and Holt estimates an exploitation rate at 50% of the unexploited relative biomass per recruit (E_0.5) as 0.38, a maximum yield exploitation rate (E_max) of 0.94, and an exploitation rate for which the marginal increase in relative yield per recruit is 10% (E_0.1) as 0.80 for the population. The values for males are 0.37, 0.90, and 0.76, and for females, 0.38, 0.80, and 0.67, respectively ( Figure 10 ). The length at first capture (L_c) for both males and females of A. boyeri was found to be 60 mm. The summary of the growth parameters of the Atherina boyeri is presented in Figure 11 .

According to the overall sex ratio of the population, females were dominant. This indicates that the sex ratio of the Atherina boyeri population in the Southeast Caspian Sea is not close to the ideal Mendelian ratio. The sex ratio significantly differed within age classes, with females being dominant in age classes 2 and 3, suggesting that male A. boyeri have a shorter lifespan compared to females. In many fish species, females live longer than males, a trend observed in A. boyeri both in sea, brackish waters, and inland waters (Creech, 1992; Sezen, 2005; Gaygusuz, 2006; Tarkan et al., 2007; Ozeren, 2009; Patimar et al., 2008). Our study aligns with several recent studies examining the sex ratio of A. boyeri, which consistently show a female-biased sex ratio across different populations and timeframes. For instance, Bartulović et al. (2004) reported a male-to-female ratio of 1:1.30, with females outnumbering males throughout the year. Similarly, Manzo (2020) found a ratio of 1:1.38, with females predominating, and noted that the sex ratio fluctuated by age group, with females being more dominant in younger populations. Our study also showed female dominance across the year, without significant variation by age. In a study by Yılmaz et al. (2021), the male-to-female ratio was even more skewed at 1:1.75, particularly in June, further confirming the trend of female-biased sex ratios in A. boyeri populations. Likewise, Kovačić et al. (2022) reported a ratio of 1:1.46, reinforcing the general trend of female dominance observed in other studies. These findings suggest that A. boyeri populations tend to exhibit a female-dominant sex ratio across various environments and seasons. The consistent dominance of females in multiple studies indicates that ecological, biological, and environmental factors likely play a significant role in shaping the sex ratio, warranting further research to better understand the underlying causes. In conclusion, our study confirms the female-biased sex ratio in A. boyeri and emphasizes the need for more in-depth investigations into the factors contributing to these patterns.

The growth pattern of a fish population, exploitation intensity, recruitment potential, and mortality are the most vital factors in fish population dynamics. Utilizing the length-frequency data, the current study provides inferences on the population of A. boyeri in the Southeast Caspian Sea. The species, albeit not having the status of a food fish shows strong potential as a native fish as such the study of the various aspects of its population tends to be imperative, which forms the backdrop for the current research problem (Nissar et al., 2024). Length-weight relationship (LWR) is a fundamental concept in fish population studies that facilitates the estimation of the weight of a species using its length data and vice versa. This vital bioecological tool yields data on the general condition of a fish population and has practical applications in fisheries management and assessment of stocks (Ricker, 1975; Arafat and Bakhtiyar, 2022). Analyzing the length and weight data of A. boyeri from the Southeast Caspian Sea revealed that the fish exhibited a length range of 60 to 125 mm and 60 to 113.3 mm and a weight range of 6.0 to 12.50 g and 6.5 to 12.50 g in males and females respectively. The value of LWR growth coefficient b in males and females was found to be 3.0774 and 2.9185 indicating positive and negative allometric growth patterns respectively.

The length at first sexual maturity (Lm) for Atherina boyeri has been reported to range between 70 and 75 mm for both males and females. In marine and lagoon habitats, where this species tends to reach sexual maturity at smaller sizes, environmental factors such as salinity and temperature are believed to play a significant role in determining L_m . However, studies focusing on the length at first maturity of A. boyeri are limited. Reported L_m values vary widely depending on habitat and study: 27 mm in the Suez Canal (Fouda, 1994), 34 mm in the Mesolongi-Etolikon Lagoon (Leonardos and Sinis, 2000), 38 mm in the Southern France Lagoon (Tomasini and Laugier, 2002), 52 mm in the Mala Neretva River (Bartulović et al., 2004), and 45.93 mm in Lake Eğirdir (Küçük et al., 2012). Additionally, Bartulović et al. (2006) reported an L_m of 77.52 mm for females in the Mala Neretva River, while Gaygusuz (2006) found values of 40-44 mm for males and 35-39 mm for females in İznik Lake. Comparing these findings with our results, we observed similarities with Bartulović et al. (2004, 2006), where A. boyeri in Mala Neretva River exhibited L_m values close to our findings. However, significant differences are noted with other studies, particularly those by Küçük et al., 2012 and Gaygusuz (2006). The lower L_m values reported by others may reflect differences in habitat conditions, such as temperature and food availability, in the Mala Neretva River. Conversely, the lower L_m values observed by Gaygusuz (2006) in İznik Lake could be attributed to methodological variations, including sampling size or age structure of the studied populations. These discrepancies highlight three key factors influencing L_m : (i) habitat variability, (ii) differences in methodologies used to assess data, and (iii) variations in sample size and the length ranges examined. Saborido-Rey (2016) proposed that in short-lived species with high mortality rates, maturity curves (ogives) are often best described by a logistic function. These species typically mature over a narrow size range, after which all individuals become sexually mature. Our results align with this framework, showing that A. boyeri completes maturation within a 20 mm length interval (35-55 mm fork length, Figure 4 ) for both males and females. Accurate estimation of L_m -the length at which 50% of individuals in a population are sexually mature—is vital for sustainable fishery management. As Fontoura et al. (2009) highlighted, L_m forms the scientific foundation for implementing Minimum Landing Sizes (MLS), ensuring that each fish has the opportunity to reproduce at least once before capture. This approach is essential for maintaining the sustainability of fish stocks and supporting ecological balance.

The asymptotic length was reported to be 129.6 and 131.3 mm in both males and females and happens to be a vital factor for demarcating the mesh size limits of fishing gears (Gebremedhin et al., 2021). In males and females, the von Bertalanffy curvature parameter (growth constant) for A. boyeri of the Southeast Caspian Sea was reported to be 0.34 year^–1 and 0.35 year^–1 respectively, indicative of a moderate growth rate as per Sparre and Venema (1998). The size distribution of a fish stock can be altered by various external factors, especially the fishing technique and the ambient temperature (Tu et al., 2018). These factors alongside the data models utilized can eventually alter the growth rates and asymptotic lengths of a stock (Etim et al., 1998). Gençoğlu and Ekmekçi (2016) analyzed the population status of A. boyeri from the Hirfanlı Reservoir in Turkey and reported a lower rate of growth (K_male = 0.15 year^–1, K_female = 0.20 year^–1) than the current study, which was attributed to the Mediterranean conditions of the reservoir. Fish growth in temperate waters is often constrained by lower temperatures. Therefore, it is not surprising that species capable of growing in temperate waters exhibit higher growth rates compared to warmer and Mediterranean regions (Lowe-McConnell, 1987; Henderson, 2005).

The natural mortality of neither sex was found to be higher than the fishing mortality for A. boyeri, indicative of less exploitation of the fish from the Southeast Caspian Sea, since it is not a food fish and the exploitation ratio of 0.20 and 0.26 in males and females respectively, is indicative of the same. The value of K is associated with the longevity of a fish species which in turn is related to mortality (Beverton and Holt, 1959; Saville, 1977). If the natural mortality of a slow-growing fish species is high, it could go extinct (Sparre and Venema, 1998). Mortality and growth rates are connected, with natural mortality showing direct dependence on K and an inverse dependence on asymptotic length (Sparre and Venema, 1998), besides the growth rates also influence the susceptibility of a fish to fishing or predation (Pauly, 1984; Allen and Hightower, 2010). Up to now, there are no published information on the Overall condition and population dynamics of this native species in the southeast Caspian Sea. However, based on the results of this study, natural mortality and fishing mortality significantly differ between the neither sex.

The addition of new individuals to a harvestable stock is denoted by recruitment and happens to be a strong driver of the fish population (Camp et al., 2020). A. boyeri showed recruitment peaks during spring and summer months (April to July), contributing approximately 80% to the total recruitment and coinciding with an increase in the temperature whereas winter months showed the lowest recruitment given a decrease in the temperature (Kindong et al., 2018). The availability of food and favourable weather conditions are the primary factors that could influence the recruitment of fish (Shoji et al., 2011; Okamoto et al., 2012; Tableau et al., 2015; Gebrekiros, 2016; Kripa, 2017). Virtual population analysis provides insights into the proportion of survivors and the losses caused by natural mortality and fishing, which are assessed by plotting various length groups against fishing mortality. In this study, for both males and females, the number of survivors and natural losses decreased with increasing size. Fishing mortality also increased for both sexes after a length of 75 mm. The highest catch rates were observed in the length groups of 65 to 85 mm for males and 70 to 95 mm for females. No previous studies or assessments were available on this parameter in fish stock evaluation, making these findings the first data on the overall status of this species in the study area. The yield per recruit (Y/R) analysis, calculated using the Beverton and Holt model for both sexes, estimated Emax and E_0.1 values of 0.90 and 0.80 for males, and 0.76 and 0.67 for females, respectively. These values are higher than the exploitation ratios of 0.20 for males and 0.26 for females, indicating that A. boyeri remains underexploited in the southeast Caspian Sea.

The GSI values indicated that the reproductive period lasted around 4 months. In the Southeast Caspian Sea, this period was shorter compared to what other studies have reported in different regions ( Table 1 ). Water temperature plays a crucial role in determining the length of the spawning season for fish (Nikolsky, 1978). In the Southeast Caspian Sea, A. boyeri could reproduce within a year, spawning in the spring after hatching, and by the end of the first summer, the sex of the juveniles could be identified through a simple macroscopic examination of their gonads. A longer reproductive season is a key strategy in the life cycle of A. boyeri, contributing to its ability to invade inland waters (Bogutskaya and Naseka, 2002).

Batch spawning has been observed in A. boyeri populations (Rosecchi and Crivelli, 1992). During the spawning period, eggs at various stages of development-immature, maturing, and mature-were present together within the same ovaries of females in the Southeast Caspian Sea, suggesting the occurrence of asynchronous or batch spawning. As depicted in Figure 12 , there is significant variation in the GSI among females throughout the spawning season, indicating that some individuals have already completed spawning, while others are still undergoing maturation. Outside of the spawning period, GSI variation was minimal, with only immature oocytes observed in the ovaries. This further supports the occurrence of batch spawning in A. boyeri in the Southeast Caspian Sea. The diameters of mature eggs in this region were in line with those reported by various studies (Creech, 1992; Rosecchi and Crivelli, 1992; Tomasini et al., 1996).

Fecundity in A. boyeri increased progressively with age. No clear relationship with latitude or environmental conditions emerged from comparing these findings with published data, likely due to differences in the criteria used for assessing fecundity.

A. boyeri, a native species for the inland waters in the Southeast Caspian Sea (Iran), has established abundant populations.

Several features of A. boyeri in the Southeast Caspian Sea, such as their short life-span, rapid growth, extended reproductive period, early sexual maturation, and batch spawning, are typical invasive characteristics ensuring establishment success. However, Bamber and Henderson (1985) stated that many atherinids show a high degree of intraspecific morphological variability, which can be linked to estuarine habitats. Such environments are physically highly variable and this has acted to select for generalist genotypes able to adjust their morphology, physiology, and behavior to a wide range of conditions. Additionally, such plasticity preadapts atherinids to invade and rapidly populate fresh waters containing vacant niches. Our results, obtained from the sand smelt population of the Southeast Caspian Sea, support the hypothesis of Bamber and Henderson (1985).

The limited exploitation of the fishery is attributed to the lack of nutritional value of A. boyeri. Comparable results were observed by Amri Sahebi et al. (2015) regarding A. boyeri. These values are largely determined by fishing intensity, fluctuations in feeding patterns, as well as ecological and physiological factors (Biswas, 1993; Zan-Bi et al., 2022).

Along with refraining from fishing during the spawning season, targeting only mature individuals is essential for sustainable fisheries management. The length at first maturity (L_m ) represents a crucial phase in a fish’s life cycle. At this stage, resources previously allocated for growth and survival are redirected toward reproduction (Wootton, 1998). Although L_m is a species-specific characteristic, it can be influenced by factors such as resource availability, fishing pressure, environmental conditions, and biological interactions (Lappalainen et al., 2016; Souza et al., 2019). For A. boyeri, the length at first sexual maturity has been reported as 60 and 65 mm for males and females, respectively. Despite a thorough literature review, no studies have been found providing data on the length at first maturity for A. boyeri. FishBase, a reliable database for fish species, also highlights the absence of data on this parameter for A. boyeri (Froese and Pauly, 2024). Almeida et al. (2018) emphasized that the first sexual maturation is a key milestone in an animal’s life history, which should be considered for effective fisheries management. In this study, the length at first maturity was determined to be 60 and 65 mm for males and females, whereas the length at first capture was found to be 60 mm, indicating that L_m > L_c . This suggests that the stock stability could be disrupted, making the population vulnerable to capture by current fishing gear before reaching maturity. Similar findings indicating L_m > L_c were observed by Wehye et al. (2017) and Rudi et al. (2018). When L_m < L_c , the individuals will at least breed during their lifespan, ensuring stock replenishment and supporting long-term sustainability (Udoh and Ukpatu, 2017; Panda et al., 2018; Mohamed, 2022).