Growth and Development Dynamic of the Lena Population Siberian Sturgeon (Acipenser baerii Brandt, 1869) Bred in a Recirculating Aquaculture System

TL;DR

This study tracks the growth of Siberian sturgeon in a controlled aquaculture system to improve breeding practices and sustainability.

Contribution

The study identifies key morphological predictors for body weight and optimal breeding selection timing in Siberian sturgeon.

Findings

Growth rates decline with maturity, shifting focus to reproductive readiness.

Body weight can be reliably predicted using morphological measurements like body height and thickness.

Optimal breeding selection occurs at 2 years and 2 months or older.

Abstract

Siberian sturgeon is a highly promising fish for commercial farming due to its quick weight gain and strong ability to survive in controlled environments. We explored how these fish grow and develop over time in a closed-loop water system to refine breeding strategies. The results showed that growth rates decreased as the fish matured, shifting focus from rapid expansion to reproductive readiness. Body weight varied more widely than other physical traits, but the fish’s size and shape were strongly linked to weight, allowing reliable predictions through simple formulas. Certain traits, like body height and thickness, show promise as predictors for future development of contactless weight assessment systems using technologies such as computer vision. The findings also suggest the timing for selecting the healthiest individuals for breeding. Overall, this information can help optimize farming practices, making sturgeon production more efficient and sustainable for food industries.

Siberian sturgeon (Acipenser baerii Brandt, 1869), characterized by its rapid mass accumulation and high survival rate under industrial breeding conditions, is one of the most promising aquacultural species. This research aimed to study the growth and development of farmed Siberian sturgeon (Acipenser baerii Brandt, 1869) to improve breeding programs. This research was conducted at the Federal Research Center for Animal Husbandry named after Academy Member L.K. Ernst and focused on the Lena population broodstock of Siberian sturgeon of the April 2022 generation (n = 98), grown in a recirculating aquaculture system (RAS). The experiment took into account body weight (W, g) and eleven morphological measurements: L—absolute length (cm); LR—fish body length increase (cm/day); l—commercial length (cm); L2—fork length (cm); HL—head length (cm); PV—pectoventral distance (cm); VA—ventroanal distance (cm); pl1—peduncle length (cm); H—body height (cm); h—peduncle height (cm); SC—body thickness (cm); GC—body circumference (cm); and Cc—peduncle circumference (cm). These measurements were taken from the same sample of fish at five different time points, all belonging to the same generation and approximately the same age. Measurements were taken every 3 to 9 months: 1 y (group G1), 1 y. 5 m. (group G2), 2 y. 2 m. (group G3), 2 y. 5 m. (group G4), 3 y. 2 m. (group G5), and 3 y. 5 m. (group G6). To evaluate the rate of growth and development, relative speed of growth (SGR) and relative speed of lengthening (SLR) during the observation period were determined. To characterize the fish’s exterior, we evaluated Fulton’s condition factor (KF) and the leanness index (Q). With increasing age, there was a significant (p < 0.01) decline in both SGR (from 0.454 to 0.065 g%/day) and SLR (from 0.132 to 0.028 cm%/day), which reflects changes in the fish’s physiological processes tied to the transition from the growth phase to the puberty phase. Relatively large variability was observed in body weight (Cv = 19.7–30.4%) compared to morphological measurements (Cv = 5.7–14.9%). Correlations between morphological measurements and the body weight of the fish varied from low to high (r = 0.22–0.97). Equations that allow for very precise (coefficient of determination R2 = 0.800–0.933) estimation of the fish’s body weight based on morphological measurements were developed. The most preferable predictors were measurements of H (R2 = 0.931), SC (R2 = 0.933), and L2 (R2 = 0.930). These morphological measurements are promising candidates for future development of contactless live weight detection using computer vision and machine learning algorithms. The study of live weight conjugacy at different ages showed that the best time to use this measurement to select fish for reproduction is at the age of 2 y. 2 m. or older. Acquired data can be used for the development and improvement of programs for the selection and breeding of Siberian sturgeon grown in a recirculating aquaculture system.

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1. Introduction

Species of the Acipenseridae family, possessing qualities favored by consumers of meat and caviar, are considered one of the most valuable resources for providing high-quality, healthy, and safe food products for human consumption [1,2]. However, many of these species inhabiting their natural waters are currently at risk of extinction, making aquaculture especially important in providing food and serving as a means to preserve biodiversity [3]. The current state of sturgeon farming in Russia is characterized by positive development dynamics, facilitated by favorable economic conditions and increasing production profitability [4]. However, the effectiveness of the commercial farming of sturgeon is highly dependent on correctly choosing the production object, which is determined by a species’ biological characteristics [5]. It is known that the biological characteristics of different sturgeon species, such as growth rate, puberty timing, productive traits, and farming conditions, differ significantly [6,7].

Siberian sturgeon (Acipenser baerii Brandt, 1869) is particularly suitable for aquaculture because of its rapid mass accumulation and high survivability rate under industrial breeding conditions [8]. Determining the correlation between live weight and morphological measurements is of great importance for sturgeon selection and genetics, as this allows us to assess how closely quantitative traits are related at the phenotype level (observable characteristics) and understand how changes in one trait can influence others [9]. Furthermore, morphological parameters are also being considered as potential predictors for fish sex determination. It has been shown that characterization of head size and shape using geometric morphometrics can be used as a non-invasive method for sex determination in sturgeon [10]. However, the literature contains limited information regarding the growth and development of the Lena population of Siberian sturgeon under aquaculture conditions.

This study contributes novel insights into the growth dynamics of the Lena population of Siberian sturgeon (Acipenser baerii Brandt) in a recirculating aquaculture system (RAS), including age-dependent declines in relative growth rates, correlations between morphometric traits and body weight, and recommendations for selection timing in breeding and management. Unlike broader studies on Siberian sturgeon hybrids or other populations (Dediu L. et al. [11]), our research focuses on the Lena population, offering equations for non-contact weight estimation, which can enhance sustainable aquaculture practices.

Mass accumulation is one of the key characteristics of a biological object used in agriculture, underlying the profitability of production. The relativity of weight change to the increase in body size is uneven at different periods of postembryonic development but tends to stabilize with age, especially when reaching sexual maturity [12]. A characteristic feature of fish is their ability to grow throughout their whole life; however, this is limited by factors related to water quality, such as temperature [13] and the total volume of the tank [14].

According to the square-cube law, discovered and demonstrated by Galileo, an increase in the linear dimensions of an object leads to an increase in its surface area proportional to the same value squared and its volume cubed, which can be expressed as

$$[eqn]$$

where l—object’s linear size, S—object’s surface area, and V—object volume, changing proportionally to the value of x in periods from 0 to 1.

Volume is a fundamental quantity for calculating the mass of an object while maintaining a constant density:

$$[eqn]$$

where W—mass, and ρ—density.

Or, if we assume that the object has the shape of a rectangular parallelepiped with equal sides (cube), then the formula is as follows:

$$[eqn]$$

The allometric growth formula based on the research of Huxley J.S. et al. [15] is as follows:

$$[eqn]$$

where W—live mass, L—body length, α—constant that, according to Huxley, has no biological meaning, and b—constant reflecting the ratio of the increment of W to the increment of L.

However, it is worth noting that α takes the place of ρ in the general form of the mass formula. From this, one can conclude that, in relation to the object of study, the meaning of the allometric growth formula can be literally interpreted as “The live mass of a fish, if its body had a constant uniform density and the shape of a cube”, which, despite the apparent absurdity of such a simplification, can be used as a metric of the uniformity of the variability ratio of the live mass and total body length. Thus, if the condition b = 3 is met, it can be assumed that the relationship between body length and live weight is fully consistent with the square-cube law, meaning that changes in live weight are independent of any variable other than body length. A coefficient in the range of values < 3 thus indicates a body weight deficit relative to the population’s body length, while a coefficient > 3 indicates an excess. It follows that any deviation can be interpreted as the presence of a significant dependence of live weight on another linear measurement such as height or body girth. The growth and development of an organism cannot be reduced to just an increase in length, and therefore minor deviations from the equality of 3 can be considered as variants within the normal range.

Monitoring the mass accumulation of fish during the rearing process is crucial for optimizing aquaculture conditions and feeding rations [16]. Accurate and reliable determination of fish weight reduces the likelihood of over- and underfeeding, which can have a negative impact on both weight accumulation and the health status of fish [17,18]. In recent years, to reduce the operator’s labor costs for measuring and determining the weight of fish, machine vision and machine learning algorithms for predicting fish weight based on measurements of morphological parameters have been increasingly utilized in aquaculture [16,19]. The first step in developing such algorithms is the selection of morphological measurements that are the most accurate predictors of fish mass at different age periods.

It should also be noted that obtaining data on the growth characteristics of fish at different age periods and the relationship between growth and morphological indicators is of particular relevance in terms of developing breeding programs based on the use of DNA markers [20,21] and genomic methods for assessing breeding value [22].

This research aimed to study the growth and development of the farmed Lena population of Siberian sturgeon (Acipenser baerii Brandt, 1869), grown in a recirculating aquaculture system, and improve breeding programs.

2. Materials and Methods

The research was conducted at the Federal Research Center for Animal Husbandry named after Academy Member L.K. Ernst and focused on the Lena population broodstock of Siberian sturgeon of the April 2022 generation (n = 98), grown in a recirculating aquaculture system (RAS). Research was conducted only on live fish, so mortality was not taken into account. Thus, the sample size was the same across all time periods. The fish were kept in a 3.14 m^2^ tank with a stocking density of 20–25 kg/m^2^, which corresponds to generally accepted farming standards for growing fish in RAS. The water temperature was maintained at a stable level of 21 ± 1 °C. The concentration of dissolved oxygen averaged 10.8 mg/L and did not fall below 9 mg/L throughout the entire period of the individuals’ growth. The water’s hydrochemical parameters (concentrations of ammonium, nitrites, nitrates, and pH level) throughout the entire growing period did not exceed the established maximum permissible values for growing sturgeon fish. On average, the hydrochemical parameters were as follows: nitrites (NO_2_)—0.05 mg/L, nitrates (NO_3_)—20 mg/L, ammonium nitrogen (NH_3_/NH_4_)—0.0 mg/L, and hydrogen index (pH)—7.5 units [23]. The sample was not divided by gender at any stage of the study. Feeding took place year-round with DIBAQ ESTURIOM HMD compound feed in accordance with the manufacturer’s standards for each size and weight group (Table 1).

To study the growth and development of Siberian sturgeon during the growing process, live weight (W, g) was determined with an accuracy of ±2.5 g using electronic scales (M-ER 326 AFU-32.1, Mertech, South Korea) and eleven morphological measurements using a generally accepted method [24] (Figure 1). In total, six gradings were carried out based on the above-mentioned indicators. Gradings were carried out on the following dates: 16 January 2023 (G1), 7 June 2023 (G2), 11 March 2024 (G3), 25 June 2024 (G4), 31 March 2025 (G5), 25 June 2025 (G6). Measurements of morphometric parameters were carried out by one operator using a caliper IIIЦ-II–250–0.02 (state standard 166-89, Chelyabinsk Tool Plant, Chelyabinsk, Russia) and a measuring tape measuring 150 × 2 cm with a centimeter scale and millimeter divisions with an error of ±2 mm. All measurements were conducted on the same sample of 98 live fish without anesthesia to minimize stress, with the operator ensuring consistent positioning as per the scheme in Figure 1. Data was collected during routine gradings to avoid additional handling, with body weight recorded first using electronic scales, followed by linear measurements in sequence (L, l, L2, HL, PV, VA, pl1, H, h, SC, GC, Cc).

To characterize the growth rate of fish, the average daily growth rate (GR) and average daily body length increase (LR) were determined:

$$[eqn]$$

where

W_n_—body weight in current period, g;

W(n−1)—body weight in previous period, g;

t—period length, days.

$$[eqn]$$

where

L_n_—absolute body length in current period, cm;

L(n−1)—absolute body length in previous period, cm;

t—period length, days.

Relative speed of growth (SGR) and relative speed of lengthening (SLR) were calculated for comparable values obtained according to Prokeš M. et al., 2011 [6]:

$$[eqn]$$

where

W_n_—body weight at current period, g;

W_n_−1—body weight in previous period, g;

t—period length, days.

$$[eqn]$$

where

L_n_—absolute body length in current period, cm;

L_n_−1—absolute body length in previous period, cm;

t—period length, days.

Exterior traits of fish in general were described using various ratios [25].

Fulton’s condition factor (KF):

$$[eqn]$$

where

W—body weight, g;

l—commercial length, cm.

Leanness ratio (Q):

$$[eqn]$$

where

l—commercial length, cm;

H—body height, cm.

Higher Q values indicate a more elongated (“lean”) body in the fish.

To characterize the variability of the studied parameters, the coefficient of variation was calculated as the ratio of the standard deviation to the mean value of the parameter, expressed as a percentage.

To characterize the relationship between body length and height, the isometric growth formula was used [16]:

$$[eqn]$$

where

W—body length, g;

L—body length, cm;

a—allometric constant;

b—allometric ratio.

At b ≈ 3, growth is considered isometric, with a proportional increase in live weight and body length. Values of b > 3 indicate positive allometric growth, in which the proportion is shifted toward a greater increase in live weight, while values of b < 3 indicate negative allometric growth, characterized by a greater increase in length than in live weight [26].

The allometric growth model was selected because it is a standard approach for evaluating the relationship between body length and weight in fish, allowing assessment of isometric versus allometric growth patterns [16]. Assumptions include logarithmic transformation to linearize the relationship and the use of least squares regression:

$$[eqn]$$ $$[eqn]$$

where W—body weight, L—body length, and e—residuals

The coefficients loga and b were thus found using the least squares method; the initial representation of the dependence in matrix form has the general form:

$$[eqn]$$

where y—observable values vector (logarithm of body weight logW), X—predictors design matrix (constant is represented by vector of ones and predictor is represented by vector of logarithmically transformed body length values logL), and β—predictor estimates vector.

In general, the solution algorithm (LS) is represented as

$$[eqn]$$ $$[eqn]$$

where $[eqn]$ —transposed X, and $[eqn]$ —vector of estimates β.

The difference in allometric ratios was considered significant according to Wald’s pairwise tests:

$$[eqn]$$

where $[eqn]$ , $[eqn]$ —pair of ratios tested, and $[eqn]$   $[eqn]$ —squared standard errors:

$$[eqn]$$

The calculations were carried out in a script written as part of the study in Python 3.13 using the libraries pandas, numpy, scikit-learn (sklearn.linear_model module, LinearRegression method), and scipy (stats module, t, norm methods).

The statistical methods mentioned were selected to address specific research objectives. Student’s t-test was used for pairwise group comparisons of means (e.g., growth rates across ages, verified in the data).

Pearson correlation analysis quantified relationships between body weight and morphometric traits to partially indicate interest points in terms of prediction ability. Consequently, linear regression models, fitted via least squares, predicted weight from morphometrics, assuming linearity supported by R^2^ values.

Allometric growth modeling followed Huxley’s standard approach for fish to evaluate isometric versus allometric patterns. Wald Z-tests compared allometric coefficients to assess changes in growth patterns over time.

3. Results

Data on the growth and development of the Lena population of Siberian sturgeon bred in a closed aquaculture system are presented in Table 2.

As shown in Table 2, during the growing process, a progressive increase in both live weight and the values of morphological measurements characterizing the size and shape of the fish body was observed. The growth rate was the highest at an earlier age (groups G1 and G2), after which it gradually decreased as the fish aged (groups G3 and G4). The values of body length increased progressively with age. In aquaculture, the leanness index (Q) biologically quantifies body elongation, with higher values indicating a more slender form due to greater linear growth relative to depth, often seen in early ontogeny. Significantly higher Q values (b < 3), where the increase in length outpaces weight, were found. Stabilization of Q post-G3 corresponds to positive allometry (b > 3), reflecting intensified muscle mass accumulation relative to skeletal elongation.

In group G1, significantly lower values of the condition factor were observed compared to other groups. It can be assumed that at this age, the formation of the axial skeleton mainly occurred with a relatively smaller increase in muscle mass. In group G2, the condition factor increased and then remained at a similar level in groups G3 and G4, which indicates a similar pattern of mass accumulation and increase in body length from 2 y. 2 m. to 3 y. 2 m. Significantly higher values of the leanness index were observed (p < 0.01) in group G1 compared to the other groups. It is likely that during this age period, the spinal column primarily lengthened, with relatively less rib growth. In other age periods, no significant differences in the values of the leanness index were found, which indicates a proportional increase in body length and height.

Data on the growth rate of the Lena population of Siberian sturgeon estimated by the indicators of relative growth speed and relative body lengthening speed at different age periods are presented in Figure 2.

As shown in Figure 2, with increasing fish age, a significant (p < 0.01) decrease in both the SGR and SLR was observed, which likely reflects the physiological restructuring in the fish’s body during the transition from the growth stage to sexual maturity.

It should be noted that live fish weight showed relatively greater variability (C_v_ = 19.7–30.4%) compared to morphometric parameters (C_v_ = 5.7–14.9%), indicating a greater influence of environmental conditions on body weight gain than parameters characterizing fish size and shape. A trend was the increase in C_v_ values for most parameters with increasing fish age (Figure 3).

We analyzed the correspondence between the rates of increase in live weight and body length according to the square-cube law, expressed in the observed allometric coefficient b of the function W = aL^b^. The results are presented in Table 3 and Table 4 and in Figure 4, showing the differences in the relationship between growth and body size observed across different age periods. At an earlier age (1 y., 1 y. 5 m.), the growth pattern demonstrated a negative isometric character, approaching isometry in the second time interval (b = 2.28 and 2.91, respectively). Starting from the age of 2 y. 2 m. and up to 3 y. 5 m., positive allometric growth was observed (b = 3.23–3.33), in which a relatively greater increase in body weight occurred compared to the increase in length. It follows that there is a predominant accumulation of body mass at an older age. The overall positive allometric growth observed throughout the experiment (b = 3.51) suggests that the fish were reared under optimal conditions in the RAS.

Significant differences were found for all pairwise comparisons of the allometric coefficient of morphometric measurements dated 16 January 2023 (G1). The data from the second grading (G2) did not demonstrate statistically significant differences compared to the values from the third (G3) and fourth (G4) gradings. The data from the third (G3) and fourth (G4) gradings differed significantly only from the generalized allometric coefficient (obtained on all data) and first (G1) grading. The dependences of live weight on length in the fifth (G5) and sixth (G6) gradings were significantly different from those in the first and second gradings.

Thus, starting from the third grading, the sample, on average, demonstrated no statistically significant differences in the dependence of live weight on body length.

Analysis of the data presented in Table 5 allowed us to draw the following conclusion: for both the leanness index (Q) and Fulton’s condition factor (KF), a trend similar to allometry was observed, with values stabilizing by the third grading. Thus, the leanness index at early life stages (gradings 1–2) demonstrated high length-to-thickness ratios (4.87–10.68), along with a comparatively low condition factor (0.30–0.32). The allometric coefficient during these periods was characterized by values below 3 (2.29–2.91), indicating a deficit in live weight relative to the observed body length in the population; this yielded a correlation between allometric growth, elongation, and the condition factor of individuals during the considered periods.

The results of the correlation calculations between fish weight and morphometric parameters in groups of Siberian sturgeon are presented in Table 6.

As shown in Table 6, the morphometric measurements had a low to high correlation with fish weight (r = 0.22–0.97). Lower correlation coefficient values at different age periods were noted for head length (r = 0.22–0.82), ventroanal distance (r = 0.40–0.70), and caudal peduncle length (r = 0.36–0.61), making them less preferable predictors of fish live weight. The lowest correlation of morphometric measurements was observed during the second grading (r = 0.32–0.55), which may be due to the ontogenetic features of Siberian sturgeon during this developmental period. After G2, the correlation increased with each subsequent grading and reached medium-high positive values during G4–G6 (r = 0.58–0.97).

As shown in Table 7 and Figure 5, using the two parameters characterized by the highest values of the determination coefficient, the equations we developed allowed us to determine fish weight based on morphometric measurements with high accuracy (R^2^ = 0.8003–0.9333). The most preferred predictors are fork length (R^2^ = 0.9302), body height (R^2^ = 0.9308), and body thickness (R^2^ = 0.9333). These morphological measurements are promising candidates for future development of contactless live weight detection using computer vision and machine learning algorithms.

The effectiveness of breeding efforts is largely determined by the ability to select individuals with improved commercial qualities as early as possible. As noted above, live weight is the most important breeding trait for Siberian sturgeon. To determine the earliest age for predicting mature Siberian sturgeon weight, we calculated correlation coefficients for weight at different ages and the closely related standard body length (r = 0.80–0.92, p < 0.01) (Table 8).

As shown in Table 8, at the beginning of the experiment, the live weight and standard body length of Siberian sturgeon (group G1, age 1 year) were, on average, positively correlated with the same parameters in group G2 at the age of 1 year and 5 months (r = 0.44—0.46). Subsequently, the correlation between the values of adjacent gradings increased, ranging from medium-high between G2 and G3-G6 (r = 0.57–0.73) to high between G3, G4, G5, and G6 (r = 0.57–0.73). The correlation between G1 and G3-G6 tended to decrease to very low levels (r = 0.23–0.08). Moreover, the standard fish length indicator was slightly higher than the live fish weight indicator (r = 0.16–0.23 and r = 0.08–0.12).

4. Discussion

The reported coefficients of variation highlight greater variability in body weight (C_v_ = 19.7–30.4%) than morphometric traits (C_v_ = 5.7–14.9%), likely due to environmental factors such as feeding. This variability could reduce the robustness of predictive models in variable conditions, but the high determination coefficients (R^2^ = 0.800–0.933) for traits like body height and thickness suggest they remain effective for breeding selection and computer vision monitoring, as these traits show lower variability and strong correlations with weight.

The study revealed important patterns in the growth and development of the Lena population of Siberian sturgeon (Acipenser baerii Brandt, 1869) reared in aquaculture. It was shown that with age, the SGR and SLR significantly decreased (from 0.454 to 0.065 g%/day and 0.132 to 0.028 cm%/day, respectively) due to the changes in physiological mechanisms as the organism transitions from active growth to sexual maturity. Similar age-related decreases in growth rates have been reported in captive Siberian sturgeon juveniles, where environmental factors like temperature and density influence growth indices [27,28]. Interestingly, sterlet of the Volga population (A. ruthenus), studied under comparable RAS conditions, also exhibited a significant decrease in SGR from 0.370 to 0.042 g%/day between the ages of 1 year 7 months to 3 years 2 months [29]. However, the absolute values of the specific growth rate in Siberian sturgeon during similar age periods were higher, reflecting its well-known potential as a fast-growing species in aquaculture.

A significant positive relationship (r = 0.22–0.97) was established between fish weight and morphometric measurements, which indicates the possibility of accurately predicting live weight based on external characteristics. Comparable positive correlations between morphometric traits (e.g., length and height) and body weight have been observed in juvenile lake sturgeon, supporting the use of these parameters for predictive models [30].

Among the morphometric traits studied, the best indicators of mass were body height (H), body thickness (SC), and fork length (L2), providing accurate mass prediction (R^2^ = 0.931, 0.933, and 0.930, respectively). In sterlet under similar experimental conditions, the most accurate predictors were also parameters related to body height (H, R^2^ = 0.941) and fork length (L2, R^2^ = 0.903), although the second most significant trait was peduncle height (h, R^2^ = 0.916) [31]. This similarity in key predictors, despite species differences in body shape (sterlet having a more streamlined body), indicates the universality of body height and circumference parameters as reliable weight indicators in sturgeons under RAS conditions.

Notably, similar high correlations between morphometric measurements and body weight have been reported for stellate sturgeon (Acipenser stellatus), another commercially important sturgeon species. In four-year-old stellate sturgeon reared under artificial conditions, negative allometric growth (b < 3) was observed in both larger (b = 2.83) and smaller (b = 2.59) individuals, with the deviation from isometry being more pronounced in the smaller fish group [32]. This suggests that monitoring allometric growth patterns can be valuable for identifying underdeveloped individuals among same-age groups.

The application of morphometric measurements for weight prediction has been successfully demonstrated in other fish species using computer vision and machine learning approaches. In rainbow trout (Oncorhynchus mykiss), correlations between body surface area and weight achieved R^2^ values of 0.97–0.99 using linear, power, and polynomial regression models [33,34]. Similarly, recent studies on Nile tilapia (Oreochromis niloticus) fingerlings demonstrated that computer vision-based weight prediction models using segmented image features (area, major and minor axes) achieved R^2^ = 0.99 with a mean absolute error of only 1.57 g [35]. Advanced discrete event system simulation combined with machine learning modeling has also been applied to predict weight dispersion in European seabass (Dicentrarchus labrax) aquaculture, achieving R^2^ = 99.9% for mean final weight prediction and R^2^ = 90.3% for standard deviation of final weight [36]. These findings support the potential applicability of our derived equations for developing automated, non-invasive weight estimation systems for Siberian sturgeon in aquaculture settings.

The mathematical modeling of fish growth has evolved from simple empirical models to more comprehensive nutrient-based approaches. As noted in reviews of growth modeling in fish nutrition, simple growth models often lack biological interpretation and overlook fundamental properties of fish such as ectothermy and indeterminate growth [37]. A characteristic feature of fish is their ability to grow throughout their whole life, which is limited by environmental factors. While we did not test any ML models here, our regression equations, characterized by high determination ratios, provide a foundation for integrating image-based data in future studies, as demonstrated in recent aquaculture applications [31].

It was determined that the selection of individuals based on mass for subsequent breeding is optimally performed starting at the age of 2 years and 2 months, since this is the period during which maximum stability of morphometric characteristics is achieved. This aligns with breeding guidelines for sturgeons, where selection is recommended after early maturity indicators stabilize, often around 2–5 years depending on species [32]. For sterlet, similar conclusions were drawn based on the analysis of individual variability and correlations between age groups: effective selection by mass also becomes possible from approximately 2 years of age [29]. Furthermore, studies on the allometry of natural mortality have demonstrated that the relative survival advantage of stocking larger fish increases with the level of mortality at reference length, with mortality being inversely proportional to body length [38]. This has important implications for the timing of selection and release in sturgeon restocking programs, as optimal release size depends on maximizing survival to the fishable stock.

The observed transition to positive allometric growth (b = 3.23–3.33) after approximately 2 years reflects shifts in energy allocation from somatic growth to gonadal development as fish approach puberty, consistent with reduced growth rates. This may involve endocrine regulation, such as increased growth hormone (GH) expression post-hatching to support early growth, which later modulates during maturation. Similar patterns in sturgeons link this to metabolic adjustments, where energy is prioritized for reproduction over linear growth [39,40]. Eagderi et al. (2017) showed that early larval development is characterized by distinct allometric phases, with an inflection point occurring around 11–13 days past hatching corresponding to the transition from endogenous to exogenous feeding [41]. Our results suggest that this pattern of phase-dependent allometry may persist into later life stages. The shift from negative allometry (b = 2.28–2.91) at 1–1.5 years to positive allometry (b = 3.23–3.33) at 2.2–3.5 years indicates that developmental priorities continue to change throughout ontogeny, with a clear inflection zone occurring between these age intervals [41]. Interestingly, in sterlet, the pattern of allometric growth during ontogeny was more variable: after a phase close to isometry (b ≈ 2.9) at approximately 1.5 years, there was a period of negative allometry (b = 2.49) at 2 years 2 months, followed by a transition to positive allometry (b > 3.2) at older ages [29]. In Siberian sturgeon, such a pronounced phase of negative allometry at the 2+ age was not observed, which may indicate an earlier or smoother redistribution of resources toward mass accumulation in this species.

The dynamics of allometric growth observed in our study are consistent with patterns reported for other fish species during early development. In Eurasian perch (Perca fluviatilis), developmental phases during early ontogeny were characterized by distinct allometric growth patterns, with most body segments showing positive allometry (fast growth) throughout the larval period before transitioning toward isometry [42]. Studies on meager (Argyrosomus regius) larvae identified three distinct growth stages marked by functional transitions, with principal component analysis revealing inflection points at specific body lengths (3.21 mm and 5.35 mm SL) that marked developmental transitions from cranial growth to locomotor enhancement and onset of juvenile traits [43]. These morpho-functional transitions highlight critical windows for aquaculture management.

Similar stage-specific allometric patterns have been documented in other commercially important species. In yellowtail kingfish (Seriola lalandi) larvae, five developmental stages were characterized from hatching to the juvenile stage, with growth and development of structures associated with vital functions such as feeding, sensorial, and breathing systems being more critical during early development (prior to 23 dph), reflected by positive allometric growth of head and eyes [44]. In the long-snout seahorse (Hippocampus reidi), three developmental stages were identified with different growth rates (0.89 mm/d, 0.30 mm/d, and 1.03 mm/d for stages I, II, and III, respectively), emphasizing the significance of snout and tail growth in younger individuals [45]. In South Pacific bonito (Sarda chiliensis chiliensis), six post-embryonic stages were described with allometric growth patterns showing that eyes, mouth, and head developed faster than other bodily characters, indicating prioritization for a fully functional mouth when larvae enter the exogenous feeding stage [46]. These comparative studies underscore the universality of stage-dependent allometric growth patterns across diverse fish taxa, while also highlighting species-specific variations that reflect ecological and phylogenetic adaptations.

Furthermore, allometric growth patterns can vary between sexes in some fish species. Studies on red porgy (Pagrus pagrus), a protogynous hermaphrodite, revealed significant sexual dimorphism in cranial morphometric characters, with males showing isometric growth patterns for head height while females exhibited negative allometry [47]. Although sex was not differentiated in our study, future research on sex-specific allometric patterns in Siberian sturgeon could provide additional insights for breeding program optimization, particularly given the importance of identifying females for caviar production.

The condition factor (KF) and leanness index (Q) showed trends similar to allometry, namely stabilization of values by the third grading. The leanness index at early life stages (gradings 1–2) demonstrated high length-to-height ratios (10.68–10.72), along with a comparatively low condition factor (0.30–0.32). Studies on landlocked ayu (Plecoglossus altivelis altivelis) have similarly demonstrated that condition factors vary significantly among developmental stages, with Fulton’s condition factor (KF) showing significant correlations with both total length and body weight, making it a good indicator for assessing fish wellbeing [48]. Allometric studies on the bivalve Anadara inaequivalvis from the Kerch Strait have demonstrated the importance of understanding relative growth patterns for assessing adaptation and production potential in aquaculture species, with the relationship between shell length and wet weight following the standard allometric model W = aL^b^ [49]. Thus, the utility of condition factors and allometric relationships as physiological indicators appears to be conserved across diverse aquatic taxa.

Comprehensive numerical models of fish growth dynamics, such as those developed for southern one-finned sculpin (Pleurogrammus azonus), have demonstrated that the dynamics of length, weight, and food bolus weight can be represented as a hierarchical system of interacting elements formalized through ordinary differential equations [50]. The model showed that weight dynamics are determined by food bolus weight and body weight itself, with a negative coefficient reflecting the organism’s metabolic expenditures. Length dynamics have a cumulative character (only positive increments), while weight dynamics are determined by accumulation and losses for vital activity (positive and negative increments). Such an approach provides a mechanistic understanding of the relationship between feeding, metabolism, and growth that could complement our morphometric-based predictive models.

The data obtained represents a valuable contribution to the development of non-invasive fish health monitoring methods based on computer technologies and machine learning algorithms. Such approaches are supported by recent developments in non-invasive methods for sturgeon weight estimation and stress classification using machine learning and computer vision [31]. Recent advances in automated fish weight estimation have demonstrated the feasibility of instance segmentation models for extracting morphometric features from images with high precision [35]. The morphometric measurements identified in our study as the most reliable predictors of body weight (H, SC, L2) are well-suited for extraction from two-dimensional images, making them promising candidates for integration into computer vision systems. These methods could serve as the basis for improving the effectiveness of selection and breeding programs aimed at improving the productivity and sustainability of Siberian sturgeon populations raised in recirculating aquaculture systems.

5. Conclusions

This study opens up prospects for optimizing the management of industrial sturgeon production, ensuring improved product quality and sustainable development of the aquaculture industry.