Comparative Population Dynamics of Schizothorax wangchiachii (Cyprinidae: Schizothoracinae) in the Middle Reaches of the Yalong River and the Upper Reaches of the Jinsha River, China

Simple Summary Ecological characteristics of the two economically important Schizothorax wangchiachii populations from the upper Yangtze River were compared. Their age structures were similar, but the growth coefficient, initial sexual maturity age and age at first capture were significantly different between the two populations. Both populations were in an overfishing state due to the current fishing intensity. These results can provide information for planning additional resource protection for Schizothorax wangchiachii. Abstract To explore the differences in the growth characteristics and population dynamics of Schizothorax wangchiachii populations in the Jinsha River (JSR) and the Yalong River (YLR), samples were collected in the upper reaches of the JSR (n = 230) from 2019 to 2020 and the middle reaches of the YLR (n = 187) from 2017 to 2018. In the JSR and YLR populations, the age range was 11 and 12 years old, respectively, and the best growth equation was the Von Bertalanffy equation. The comparative analysis of the two populations showed that the growth coefficient, initial sexual maturity age and age at first capture of the YLR population were greater than those of the JSR population. Comparing the mortality rates of the two groups, we found that the YLR population had the higher female mortality rate (0.658 years−1) and the lower male mortality rate (0.453 years−1). Our assessment of the three natural mortality rates showed that the Fcur of both male and female populations was greater than F25%, indicating that both populations were in an overexploited state. Therefore, we suggest considering the two groups as separate protection units and implementing management measures such as ecological regulation, restoration of tributary habitat and strengthening of fishing ban monitoring to protect their resources.


Introduction
Determining the age of fish is the basis for fish population dynamic assessments. Based on age data and a population dynamic assessment, parameters such as fish growth parameters, yield per recruit and exploitation rate can be calculated [1]; the results could clarify the development status of the population and the trends in resource decline, providing a basis for formulating relevant protection measures [2][3][4]. Studies has shown that the growth characteristics of fish were not uniform, and there were spatial and temporal

Sample Collection
The JSR and the YLR (the largest branch of the Jinsha River) are near the Qinghai-Tibet Plateau and are both typical mountain rivers [16,17]. The spatial distribution of multi-year average precipitation in the upper reaches of the JSR is in the range of 30 to 1000 mm, and the water vapor content over the basin is less than 15 mm, which is relatively scarce [18,19]. The lowest annual average water temperature in the upper reaches of the JSR is 0.3 • C, with a short ice cover period. However, the middle reaches of the YLR have a long winter ice cover period, with a water temperature of 0 • C [19,20]. The average annual flow of the Shigu section is approximately 2300 m 3 /s [21].
From April 2017 to May 2018, in the middle reaches of the YLR and its tributary Xianshui River, and from September 2019 to October 2019 and from June 2020 to July 2020, in the upper reaches of the JSR (Benda-Shigu), S. wangchiachii was collected by means of purchase from fishermen and self-fishing using gill nets (2-5 cm mesh), ground cage fishing nets (length, width and height: 15 m, 0.3 m and 0.3 m, respectively), as well as via identification in the ichthyofaunal monographs in China [22,23]. Random sampling was performed within the sampling section, gill nets and ground cage fishing nets were placed at 8 am every day and catches were collected at 8 am the next day.
The fish were euthanized with MS-222 (98%), and then the body length (BL, accurate to 0.1 cm), body weight (BW, accurate to 0.1 g) and other basic biological data were measured and recorded. On-site dissection was conducted to determine the sex and gonad stage, and the lapillus was extracted, stored in a 1.5 mL centrifuge tube filled with ethanol (95%), and brought back to the laboratory for treatment ( Figure 1). stage, and the lapillus was extracted, stored in a 1.5 mL centrifuge tube filled with ethanol (95%), and brought back to the laboratory for treatment, (Figure 1).

Sample Preparation
Neutral resin was used to fix the concave surface of the microotolith on the slide. After natural air drying, 800 # to 3000 # abrasive paper and water were used to polish it, and the slide was observed under the microscope until the growth center of the otolith could be clearly observed. Then, the otolith grinding plate was washed with water. It was polished with polishing paper until the wheel pattern was completely clear. Finally, the resin was dissolved, turned over, dried, and fixed again, and the other side of the otolith was polished using the same method. Once the wheel pattern was clear, observations were made and photographs were taken with the Leica Dc500 digital photography system, and the pictures were saved. In the identification of annual rings, the dividing line between the dense belts formed in autumn and winter and the sparse belts formed in spring and summer of the following year were used to determine the age mark.

Age Assessment and Verification
Age was calculated as follows. When the number of annual rings on the otolith was n, n was recorded as the age. If a new ring outside the nth ring had not yet fully formed but a few dense bands appeared, the age was recorded as (n + 1) [24]. Age was determined without knowledge of the basic biological information of S. wangchiachii. Two annual ring counts were carried out; if the results were different, counting was performed a third time. Age estimates were compared by calculating the index of average percentage error (IAPE) between researchers and between pairs of aging materials [25,26]. To calculate the IAPE, the formula of Beamish and Fournier was used as follows:

Sample Preparation
Neutral resin was used to fix the concave surface of the microotolith on the slide. After natural air drying, 800 # to 3000 # abrasive paper and water were used to polish it, and the slide was observed under the microscope until the growth center of the otolith could be clearly observed. Then, the otolith grinding plate was washed with water. It was polished with polishing paper until the wheel pattern was completely clear. Finally, the resin was dissolved, turned over, dried, and fixed again, and the other side of the otolith was polished using the same method. Once the wheel pattern was clear, observations were made and photographs were taken with the Leica Dc500 digital photography system, and the pictures were saved. In the identification of annual rings, the dividing line between the dense belts formed in autumn and winter and the sparse belts formed in spring and summer of the following year were used to determine the age mark.

Age Assessment and Verification
Age was calculated as follows. When the number of annual rings on the otolith was n, n was recorded as the age. If a new ring outside the nth ring had not yet fully formed but a few dense bands appeared, the age was recorded as (n + 1) [24]. Age was determined without knowledge of the basic biological information of S. wangchiachii. Two annual ring counts were carried out; if the results were different, counting was performed a third time. Age estimates were compared by calculating the index of average percentage error (IAPE) between researchers and between pairs of aging materials [25,26]. To calculate the IAPE, the formula of Beamish and Fournier was used as follows: where x ij is the ith age determination of the jth fish, x j is the average age calculated for the jth fish, and R is the number of times the age of each fish was determined.

Modeling the Length-Weight Relationship and Growth
The power function W = aL b was used to fit the relationship between body weight and body length of S. wangchiachii [27]. Analysis of covariance (ANOVA) was used to analyze the difference in the body length-weight relationship between male and female individuals [28]. A t test was used to compare the allometric growth index (b) and 3 to determine whether S. wangchiachii was growing at a uniform speed [27,29].
Three equations were used to describe the relationship between fish age and growth, including the von Bertalanffy equation (VBGF), logistic equation (LGF) and Gompertz equation (GGF). The minimum residual sum of squares (RRS) and Akaike information criterion (AIC) were used to determine the optimal growth equation, for which the fitting degree was determined using the determination coefficient R 2 . The formulas are as follows [30][31][32]: LGF : where L t is the expected total length at age t years, L ∞ is the asymptotic total length, k is the growth parameter indicating the rate at which S. wangchiachii grows toward L ∞ , and t 0 is the theoretical age at zero total length. The AIC was used to determine the optimal growth model. The formula is as follows [33]: where m is the model parameter; LnL (p1, . . . , pm, σ 2 ) is the residual sum of squares; and the optimal model is the one with the minimum AIC value.

The Ages at First Sexual Maturity
The body length was divided into different sections with a group distance of 20 mm, and then the sexual maturity (gonad development reached stage III to VI) ratio of female and male populations in the section was counted. Then, the median body length group distance and sexual maturity ratio of each section were fitted using logistic regression, and the formula is as follows [34]: where P is the sexual maturity ratio of each body length section; L mid is the median body length group spacing (20 mm); L 50 is the body length of the first sexual maturity; and k is the slope. The proportion of sexually mature individuals in each age group was counted by sex, and logistic regression was performed with each age group. The formula is as follows [35]: where G: sexual maturity ratio of each age group; T: age; T 50 : age of first sexual maturity; and k: slope.

Estimation of Mortality
The Chapman-Robson (CR) method was used to estimate the total mortality rate (Z) of S. wangchiachii, and the formula is as follows [36]: where t c is the starting age; T is the average age of the sample when it is greater than t c ; and N is the number of samples when it is greater than t c . The following two empirical equations were applied to estimate the natural mortality rate (M) [37]: where the parameters are as follows: M T , natural mortality calculated according to growth parameters; M G , natural mortality estimated by the limit age method; k, the growth parameter; M R , the median of the M G and M T was selected as the reference natural mortality; t 0 , the age at zero length; and L ∞ , the asymptotic length. In addition, t max is the longevity of S. wangchiachii, which was estimated using the following formula [38]: The fishing mortality rate (F) was calculated as F = Z − M. The estimates of M and F were assumed to be constant throughout the fish lifespan.

Per-Recruit Analysis
Yield per recruit (YPR) and spawning stock biomass per-recruit (SSB/R) models were developed for the pooled data. The YPR and SSB/R were calculated using the following formulas [39]: where Y is the total catch; R is the total supplementary population; SSB is the total number of parent fish in the breeding population; SPR is the spawning potential ratio, defined as the value of dividing the unit supplementary amount of parental quantity by the unit supplementary amount of parental quantity without the fishing mortality rate under a certain fishing mortality coefficient; SSBR is the unit supplementary amount of parent fish; F is the fishing mortality rate; M is the natural mortality rate; t max is the maximum observed age; t r is the age at recruitment, which was the youngest age in the catch; t c is the age at first capture (t max , t r and t c are obtained from age frequency distribution analysis); k is the growth parameter; t 0 is the hypothetical age at zero length; L ∞ is the asymptotic length in the von Bertalanffy growth function; a and b are parameters in the weight-length relationship; G t is the proportion of mature fish at age t (S. wangchiachii spawns just once each year), which was modeled by a previously published logistic function [40]; and S t is the gear selectivity coefficient for fish of age t and was set to 'knife edge' selectivity as follows:

Biological Reference Points
To determine the fishery status of the S. wangchiachii stock downstream of the JSR, the current fishing mortality (F cur ) was compared with four F-based BRPs: F max , where the fishing mortality rate produces the maximum YPR; F 0.1 , which refers to fishing mortality where the slope of the YPR curve was 10% of the slope at the origin [41]; and F 25% and F 40% , which were fishing mortality rates at which the SPR was 25% and 40%, respectively [42].

Statistical Analysis
Data are expressed as the mean ± standard error. SPSS 20.0, GraphPad Prism 8.0 and Excel 2018 were used to process and analyze the data. When p < 0.05, the difference was considered significant. Images in this paper were processed with CorelDRAW 2019, Adobe Illustrator 2023 and ArcGIS10.4.1.

Sample Characteristics
The BL of S. wangchiachii in YLR and JSR ranged from 101.0 to 401.0 mm and 88.0 to 334.0 mm, and the BW ranged from 20.6 to 1011.2 g and 10.6 to 640.3 g, respectively ( Table 1). The mean weights of YLR and JSR S. wangchiachii were 232.6 ± 167.3 and 131.6 ± 99.15 g, respectively. The average body length and body weight of the YLR population were significantly greater than those of the JSR population (p < 0.05).

Age Structure and Verification
There was an approximately circular nucleus in the center of the otolith, and the transparent and opaque zones on the otolith were arranged in an irregular concentric circle. The transparent band was narrow and transparent, while the dark band was opaque, allowing for clear growth blockages. The junction of the bright and dark bands was the annulus. The ring spacing on the otolith shows a regular decreasing trend, with larger ring spacing near the central nucleus, while ring spacing away from the central nucleus gradually decreases ( Figure 2B).
We considered the dividing line between the dense zone formed in autumn and winter and the sparse zone formed in spring and summer of the following year to be the annual ring. In transmitted light, the annual rings appeared as dark bands, so counting the dark bands as ages and calculating the average percentage error three times ensured the accuracy of identification. In the YLR and JSR groups, the reliability of the age estimates had a low IAPE (1.51% and 1.68%), indicating high accuracy. There were certain differences in the age composition of the two populations. The age range of the population in the YLR was 2 to 13 years, and the dominant age group was 5 to 9 years, representing 65.77% of the total. The age range of the population in the JSR was 1 to 11 years, and the dominant age group was 4 to 7 years, representing 77.39% of the total (Figure 2A).

Growth Modeling
The analysis of covariance (ANOVA) showed that there was no significant difference in the relationship between body length and body weight of the fitted male and female individuals in the YLR population (F = 0.109, P = 0.741, p > 0.05). This indicated that regression analysis of the relationship between body length and body weight could be carried out for male and female individuals combined. The same was true for the JSR population (F = 0.035, P = 0.852, p > 0.05). There was no significant difference between the b value and 3 (YLR: t = 1.2177 ≤ t0.01 = 2.602; JSR: t = 2.4230 ≤ t0.01 = 2.598), indicating that the growth of the fish in the YLR and JSR populations was uniform ( Table 2).
Compared with other models, the growth model based on the von Bertalanffy equation had a lower AIC value (YLR 66.49/JSR 80.10) ( Table 2), and the results of the χ 2 test indicated that the difference between the theoretical value and the actual value was not significant for the von Bertalanffy equation (p > 0.05). These results suggested that the von Bertalanffy equation can better reflect the growth of S. wangchiachii.  Note: YLR, Yalong River; JSR, Jinsha River; W, body weight; L, body length; Lt, total length at age t years; L∞, asymptotic total length; t0, theoretical age at zero total length; a, growth condition factor; b, allometric growth index; k, growth parameter; AIC, Akaike information criterion.

Growth Modeling
The analysis of covariance (ANOVA) showed that there was no significant difference in the relationship between body length and body weight of the fitted male and female individuals in the YLR population (F = 0.109, P = 0.741, p > 0.05). This indicated that regression analysis of the relationship between body length and body weight could be carried out for male and female individuals combined. The same was true for the JSR population (F = 0.035, P = 0.852, p > 0.05). There was no significant difference between the b value and 3 (YLR: t = 1.2177 ≤ t 0.01 = 2.602; JSR: t = 2.4230 ≤ t 0.01 = 2.598), indicating that the growth of the fish in the YLR and JSR populations was uniform ( Table 2). Table 2. Comparison of three functions of two Schizothorax wangchiachii populations from the Jinsha River Basin. Note: YLR, Yalong River; JSR, Jinsha River; W, body weight; L, body length; L t , total length at age t years; L ∞ , asymptotic total length; t 0 , theoretical age at zero total length; a, growth condition factor; b, allometric growth index; k, growth parameter; AIC, Akaike information criterion.

Models
Compared with other models, the growth model based on the von Bertalanffy equation had a lower AIC value (YLR 66.49/JSR 80.10) ( Table 2), and the results of the χ 2 test indicated that the difference between the theoretical value and the actual value was not significant for the von Bertalanffy equation (p > 0.05). These results suggested that the von Bertalanffy equation can better reflect the growth of S. wangchiachii. Tables 3 and 4 show the biological parameters of the two populations of S. wangchiachii. In the YLR population, the ages at first sexual maturity of female and male S. wangchiachii were 7.09 and 5.41 years, respectively, and the ages at first capture (t c ) were 6.82 and 7.10 years, respectively. The total mortality (Z) of females and males was 0.658 and 0.453 year −1 , respectively. According to the growth parameters, the natural mortality (M G ) of female and male fish was 0.06 and 0.07 year −1 , respectively, and the corresponding fishing mortality (F cur ) was 0.59 and 0.38 year −1 , respectively. The natural mortality (M T ) of female and male fish estimated by the limit age method was 0.13 and 0.15 year −1 , and the corresponding F cur was 0.52 and 0.30 year −1 , respectively. The median of the M G and M T was selected as the reference natural mortality (M R ), the M R of female and male fish were 0.09 and 0.11 year −1 , and the corresponding F cur was 0.56 and 0.34 year −1 , respectively. Note: YLR, Yalong River; JSR, Jinsha River; k, growth parameter; t 0 , theoretical age at zero total length; L ∞ , asymptotic total length; t c , the ages at first capture; Z, total mortality; M T , natural mortality calculated according to growth parameters; M G , natural mortality estimated by the limit age method; M R , the reference natural mortality calculated from the medians of M T and M G ; F cur , current fishing mortality; t r , age at recruitment; a, growth condition factor; b, allometric growth index; T 50 , ages at first sexual maturity.

Growth Parameters
In the JSR population, the ages at first sexual maturity of female and male S. wangchiachii were 6.09 and 5.19 years, and the t c values were 5.49 and 5.36 years, respectively. The Z values of females and males were 0.504 and 0.532 year −1 , respectively. According to the growth parameters, the M G of female and male fish were 0.06 and 0.06 year −1 , and the corresponding F cur values were 0.44 and 0.47 year −1 , respectively. The M T of female and male fish obtained by the limit age method were 0.14 and 0.12 year −1 , and the corresponding The growth parameter k, the age at initial sexual maturity and the age at initial catch of the YLR population were greater than those of the JSR population. The total mortality rate of female individuals in the YLR population was the highest, and the total mortality rate of male individuals was the lowest. The male age at first capture of the YLR population was the largest and that of the JSR population was the smallest.

Per-Recruit Analysis
Per-recruit analysis was conducted with the biological parameters. In the YLR population, the three natural mortality rates (M G , M R , M T ) were used to fit the change trend of the spawning potential ratio (SPR) and yield per recruit (YPR) of female and male fish under different fishing intensities ( Figures 3A,B and 4A,B). The range of the spawning potential ratio (SPR) for females was 2.92 to 11.25%, while that for males was 5.91 to 18.57% (Table 4).
Under the three natural mortality rates, the F cur of both female and male populations was greater than F 25% , indicating that the population was in an overdeveloped state. Table 4. Estimates of fishing mortality (F) and YPR and SPR reference points for female and male Schizothorax wangchiachii in the upper Jinsha River and in the middle reaches of the Yalong River.

Group
M (year −1 )     Three natural mortality values were used to simulate the effects of different fishing intensities and starting ages on the YPR and SPR of female and male fish. The YPR value first increased rapidly and then decreased with increasing fishing intensity and maintained a relatively stable state ( Figure 3A,B). Similarly, the YPR value also first increased and then decreased with increasing fishing age and natural mortality ( Figure 5). The SPR value increased with increasing fishing age, decreased rapidly with increasing fishing intensity, and then remained stable ( Figures 4A,B and 6).
The catch per unit supplement curve (X axis: fishing death coefficient, Y axis: age at first capture (tc)) was drawn ( Figures 5 and 6). The optimal yield area in the figure was the area between Line A (optimal tc point connection) and Line B (optimal F point connection). In 2017-2018, the corresponding catch per unit supplementary number of females (F = 0.52-0.59, tc = 6.82 a) and males (F = 0.30-0.38, tc = 7.10 a) in the current fishery site did not fall within the range of the optimal yield area, indicating that the current population resources of S. wangchiachii in the middle reaches of the YLR are in an overdeveloped state (Figures 5 and 6). Three natural mortality values were used to simulate the effects of different fishing intensities and starting ages on the YPR and SPR of female and male fish. The YPR value first increased rapidly and then decreased with increasing fishing intensity and maintained a relatively stable state ( Figure 3A,B). Similarly, the YPR value also first increased and then decreased with increasing fishing age and natural mortality ( Figure 5). The SPR value increased with increasing fishing age, decreased rapidly with increasing fishing intensity, and then remained stable ( Figures 4A,B and 6).
The catch per unit supplement curve (X axis: fishing death coefficient, Y axis: age at first capture (t c )) was drawn (Figures 5 and 6). The optimal yield area in the figure was the area between Line A (optimal t c point connection) and Line B (optimal F point connection). In 2017-2018, the corresponding catch per unit supplementary number of females (F = 0.52-0.59, t c = 6.82 a) and males (F = 0.30-0.38, t c = 7.10 a) in the current fishery site did not fall within the range of the optimal yield area, indicating that the current population resources of S. wangchiachii in the middle reaches of the YLR are in an overdeveloped state (Figures 5 and 6).
In the JSR populations, the range of the spawning potential ratio (SPR) for females was 2.38 to 7.59%, while that for males was 1.85 to 6.50% (Table 4). Based on the three natural mortality rates, the F cur of both female and male populations was greater than F 25% , indicating that the population was in an overdeveloped state ( Figures 3C,D and 4C,D).
Three natural mortality values were used to simulate the effects of different fishing intensities and starting ages on the YPR and SPR of female and male fish. The YPR value first increased rapidly and then decreased with increasing fishing intensity and maintained a relatively stable state ( Figure 3C,D). Similarly, the YPR value first increased and then decreased with increasing fishing age and natural mortality (Figure 7). The SPR value increased with increasing fishing age, decreased rapidly with increasing fishing intensity, and then remained stable ( Figures 4C,D and 6).
The catch per unit supplementary amount curve (X axis: fishing death coefficient F; Y axis: age at first capture (t c ) was drawn (Figures 7 and 8), and the optimal yield area in the figure was the area between Line A (the best t-point connection) and Line B (the best F-point connection). In the period from 2019 to 2020, the catch per unit supplementary amount corresponding to females (F = 0.36-0.44, t c = 5.49 a) and males (F = 0.41-0.47, t c = 5.36 a) in the current fishery area did not fall within the range of the optimal yield area, which implies that the utilization of the population resources of S. wangchiachii in the upper reaches of the JSR was in an overexploitation state (Figures 7 and 8). The "P" point shows the current average fishing conditions. The optimal yield area in the figure is the area between Line A (optimal t c point line) and Line B (optimal F point line). M T , natural mortality was calculated according to growth parameters; M G , natural mortality was estimated by the limit age method; M R , the reference natural mortality was calculated from the medians of M T and M G . Animals 2023, 13, x FOR PEER REVIEW Figure 6. Isopleths of the spawning potential ratio (SPR) for Schizothorax wangchiachii in th reaches of the YLR. (a,c,e) The response of SPR to age at first capture (tc) and fishing mo under different natural mortalities in female S. wangchiachii; (b,d,f) the response of SPR t under different natural mortalities in male S. wangchiachii. The "P" point represents th estimated SPR; MT, natural mortality was calculated according to growth parameters; M mortality was estimated by the limit age method; MR, the reference natural mortality was c from the medians of MT and MG.
In the JSR populations, the range of the spawning potential ratio (SPR) for was 2.38 to 7.59%, while that for males was 1.85 to 6.50% (Table 4). Based on t natural mortality rates, the Fcur of both female and male populations was greater t indicating that the population was in an overdeveloped state ( Figures 3C,D and Three natural mortality values were used to simulate the effects of differen intensities and starting ages on the YPR and SPR of female and male fish. The YP first increased rapidly and then decreased with increasing fishing intens maintained a relatively stable state ( Figure 3C,D). Similarly, the YPR value first i and then decreased with increasing fishing age and natural mortality (Figure 7). value increased with increasing fishing age, decreased rapidly with increasing intensity, and then remained stable ( Figures 4C,D and 6). which implies that the utilization of the population resources of S. wangchiachi upper reaches of the JSR was in an overexploitation state (Figures 7 and 8). The "P" point is the average fishing conditions. The optimal yield area in the figure is the area between Line A ( tc point line) and Line B (optimal F point line). MT, natural mortality was calculated acco growth parameters; MG, natural mortality was estimated by the limit age method; MR, the r natural mortality was calculated from the medians of MT and MG.

Discussion
The results of this study indicated that both the upper reaches middle reaches of the YLR were in an overdeveloped state, which overfishing and population recovery ability. Due to overfishing an catch of main fishing objects such as S. wangchiachii has decreased, wit of which did not reach the age of sexual maturity, and the fish reso declining trend [10]. Phenomena such as excessive fishing and e observed in the JSR Basin, leading to a sharp decrease in fish resources led to a sharp decrease in the number of larger breeding individuals in

Discussion
The results of this study indicated that both the upper reaches of the JSR and the middle reaches of the YLR were in an overdeveloped state, which may be related to overfishing and population recovery ability. Due to overfishing and other factors, the catch of main fishing objects such as S. wangchiachii has decreased, with younger fish, most of which did not reach the age of sexual maturity, and the fish resources have shown a declining trend [10]. Phenomena such as excessive fishing and electric fishing were observed in the JSR Basin, leading to a sharp decrease in fish resources [43,44]. Overfishing led to a sharp decrease in the number of larger breeding individuals in the fish population, which would have a greater impact on the slow-growing and late sexual maturity schizothoracids [11,43].
The findings of this study showed that the growth parameter k value can be used to analyze life history strategies. The growth parameter k value depicted a slow-growing population at 0.05 to 0.10/year, an intermediately growing population at 0.10 to 0.20/year, and a fastgrowing population at 0.20 to 0.50/year [45]. In this study, the growth parameter k value of the population in the middle reaches of the YLR was 0.0500, and the growth parameter k value of the population in the upper reaches of the JSR was 0.0608, indicating that the two populations of S. wangchiachii were slow-growing, and the resources were damaged and recovery would be difficult. Comparing the growth characteristics of different populations of schizothoracids (Table 4), the value of the growth parameter k of S. wangchiachii was less than 0.1, the asymptotic body length was greater, and the apparent growth index was between 4 and 5. The values of the parameters indicated that S. wangchiachii had slow growth and a long lifespan, and its growth characteristics conformed to the growth law of most schizothoracids.
The growth characteristic parameters of the same fish differed in various river sections [46,47]. In this study, by calculating the growth coefficient of the two populations, we concluded that the population of S. wangchiachii in the upper reaches of the JSR grows faster than that in the middle reaches of the YLR. There were many factors that contributed to these differences, including habitat differences among river sections (such as food abundance and water temperature), differences in the number and composition of samples, and differences in individual metabolic levels [47,48]. The larger the size of individuals obtained during sampling was, the larger their progressive body length and weight, the wider the range of body length or age, and the closer the growth characteristic parameters [47,49]. In addition, we also found a significant difference in the total mortality rate between male and female individuals in the YLR population, with females having a higher total mortality rate than males. However, the difference in total mortality rate between male and female individuals in the JSR population was relatively small, and females had a lower total mortality rate than males. In this study, compared with the YLR population, the JSR upstream population was represented by more samples, but its age range and size were smaller. This may be an important reason for the difference in growth parameters between the two populations.
In addition, fish are temperature-changing animals, and their feeding and growth will be affected by water temperature. Some scholars have noted that the different growth characteristics of different populations of schizothoracids were closely related to the environment; specifically, they were positively related to water temperature and food and negatively related to altitude and flow rate [50]. In this study, based on the growth coefficients of the two populations, we concluded that the population in the upper reaches of the JSR grows faster than the population in the middle reaches of the YLR. According to relevant research reports, the lowest annual average water temperature in the upper reaches of the JSR was 0.3 • C, with a short ice cover period. However, the middle reaches of the YLR had a long winter ice cover period, with a minimum water temperature of 0 • C [51]. In addition, the abundance of bait organisms in the middle reaches of the YLR was low [51,52]. In this study, the elevation of the sampling section in the middle reaches of the YLR was 2572 to 3230 m, the elevation of the sampling section in the upper reaches of the JSR was 1818 to 3408 m, and there was a significant relationship between river water temperature and altitude. This suggests that the regional differences in altitude and water temperature may be the main reasons for the growth differences between distinct geographic populations of S. wangchiachii. Similar results were also confirmed in a study of Gymnodiptychus dybowskii in different geographical groups of the Ili River [50].
To better develop fisheries management strategies, many scholars have advocated the use of biological reference points such as F Max , F 25% and F 40% [53][54][55]. The analysis results of S. wangchiachi in this study show that under the current three natural mortality rates, the F cur of the male and female populations was greater than F 25% , which indicates that the population was overexploited. Thus, corresponding protection measures are needed. For example, the capture age of the female and male populations of S. o'connori increased to no less than 17 and 14 years old, respectively, ensuring that the reproductive potential ratio was always higher than F 25% [4]. However, there were differences in population parameters such as catch per unit recruitment, reproductive potential, and age of first sexual maturity between the JSR and YLR. If management was carried out according to the same population, the spatial heterogeneity of the population was ignored, which would lead to overfishing of fishery resources [56,57]. Therefore, the JSR and YLR groups should be treated as two protection units, and different protection measures should be formulated according to the resource status of each group.
Due to the current fishing intensity, the JSR population and the YLR population of S. wangchiachii were in an overexploitation state, the female starting age was lower than the age of first sexual maturity, and the male starting age was higher than the age of sexual maturity. The proportion of males and females and the number of breeding groups were bound to be threatened. Reducing fishing mortality and increasing fishing age could reduce fishing intensity and maintain high catches, which is a reasonable measure for resource management [1,4]. Combined with the variation trend of the spawning potential ratio and yield per recruit with the fishing intensity in this study, it was recommended to increase the starting age of the female and male populations of S. wangchiachii in the YLR to 15 and 11 years and the starting age of the female and male populations in the JSR to 12 and 13 years, respectively.
At the same time, the proportion of natural river sections in the main stream of the JSR was only 48.49%, mainly concentrated in the upper reaches of the JSR. The natural section of the middle reaches of the YLR accounted for only 25.37%, mainly distributed in the section from Yajiang County to the dam site of Yangfanggou Hydropower Station. Changes in the natural river environment had a negative impact on the completion of the life history of S. wangchiachii [1,51]. Therefore, we recommend strictly controlling the intensity of hydropower development, reasonably carrying out ecological dispatching, and ensuring sufficient ecological discharge; some inefficient and ecologically harmful small-scale hydropower infrastructure should be demolished to restore the natural habitat of the river, select representative tributaries to implement systematic ecological restoration, and restore river connectivity.
In addition, the biological and ecological information of S. wangchiachii is incomplete, which makes it impossible to accurately assess its population status and is not conducive to the development of related protection work such as artificial reproduction. Therefore, we suggest carrying out a comprehensive survey on the number of species, geographical distribution, population status and threat level, strengthen diversified scientific research, and provide more basic data for its protection [58,59].
Finally, given the comprehensive fishing ban in the Yangtze River Basin, it is necessary to strengthen the management of fishing bans in each survey area, establish a fishing ban management team for the mainstream and important tributaries, invest in more regulatory equipment, improve the regulatory reward and punishment system, and severely crack down on illegal fishing to ensure that the important waters of the mainstream and tributaries can be monitored in real time throughout the year [60].

Conclusions
Our study analyzed the growth characteristics and population dynamics of two different S. wangchiachii populations, including those from the upper reaches of the JSR and the middle reaches of the YLR. The initial sexual maturity age and the ages at first capture of the YLR population were higher than those of the JSR population, while the growth parameter k was lower than that of the JSR population. Under the current fishing intensity, the reproductive potential ratio of male and female fish in the upper reaches of the JSR and the middle reaches of the YLR was lower than the lower limit reference point F 25% , and both populations were overfished. It is recommended to raise the age of arrest and implement arrest monitoring. Our study helps to reveal the growth characteristics and population dynamics of S. wangchiachii in the upper reaches of the Jinsha River and the middle reaches of the YLR and provides a basic reference for the formulation of biological protection measures.