Population Dynamics of the Common Carp ( Cyprinus carpio L. 1758) Stock in Lake Arekit, Ethiopia: Implications for Management and Conservation

Cyprinus carpio is a widely distributed and commercially important fsh species in Ethiopia. Efective management is essential to sustain fsheries and provide benefts to local communities. Tis study aims to estimate the growth, mortality, and exploitation rate of C . carpio using length-frequency data. A total of 194 C . carpio specimens (117 females and 77 males) were collected between June 2022 and May 2023. Te population parameters were determined using FISAT (ELEFAN I) software. Te Von Bertalanfy growth function estimations were L ∞ � 51.45cm total length, K � 1.1year − 1 ; t 0 � − 0.124year, and growth performance index ( Φ′ ) � 3.464. Te total mortality rate ( Z ), natural mortality rate ( M ), and fshing mortality rate ( F ) were 2.55 year − 1 , 1.58year − 1 , and 0.97year − 1 , respectively. Te estimated potential longevity ( t max ) and average age at which C . carpio attains length at the optimum cohort biomass or yield per recruit ( L opt � 34.79) in Lake Arekit were calculated as 2.60years and 1.29years, respectively. Te Z / K ratio (2.32), exploitation rate ( E � F / Z � 0.38), and highest permissible yield per recruit for C . carpio ( E max � 0.421) suggest enhancing fshery production by increasing the exploitation rate of the underexploited C . carpio in Lake Arekit. Te results of this study provide information on the stock of C . carpio , which can be used to guide management eforts. Te fsh catch in Lake Arkeit is currently far lower than it could be. Terefore, the fsh harvest should be boosted through the use of permitted nets, the establishment of groups of fshermen who can catch fsh efectively, and the linking of the benefts of fsh farming’s supply chain to the potential of fsheries.


Introduction
Te common carp (Cyprinus carpio, Linnaeus 1758) is frequently cultivated and has a signifcant commercial value as a food fsh in its natural range and in the areas where it has been introduced [1].Cyprinus carpio was initially brought to Ethiopian waterways in 1936 for aquaculture [2,3].
Small-scale fsheries require the most immediate action, particularly regarding rules and policies governing food security and nutrition [4].Small-scale fsheries, which also provide many local people in developing countries with a source of employment and food security, employ over 90% of all catch fshers [4,5].Nearly half of the fsh caught worldwide in developing countries are caught in small-scale fsheries.Furthermore, 90-95% of small-scale landings are made to be used by local people [4,6,7].Small-scale fsheries are therefore essential for immediately increasing the supply of nutrient-dense foods for local, national, and international markets while acting as a sizable source of income for those who work in the sector both directly and indirectly [4].Despite their signifcance and potential, numerous smallscale fshing communities such as Lake Arkeit, the focus of this study remains marginalized, and their impact on nutrition and food security is still neglected [8].Proper assessment and management are essential for maintaining fsheries and the advantages they provide to society [5][6][7].Understanding species life histories, population dynamics, and the sustainability of fsheries depends on understanding fsh growth.Growth is correlated with several life-history features, such as the natural mortality rate [9], which are known to afect how a fsh species reacts to exploitation [10].Te maximum sustainable yield (MSY) and fshing efort in lakes have also been determined through stock assessments.
Although numerous studies on C. carpio population characteristics, including growth parameters, reproductive biology, age determination, and population dynamics, have been carried out in various water bodies in Ethiopia [3,4,11,12], there have been no studies on the population growth parameters, mortality, and exploitation rate in Lake Arekit.Te fshing of C. carpio in this lake has been managed in accordance with data on other carp populations in the same area, including Lake Langano and the Koka Reservoir.Te management of the fsheries in these bodies of water generally includes establishing fshery cooperatives, raising awareness, providing of-farm opportunities, implementing integrated conservation eforts, reducing wetland farming, and becoming familiar with social networks.
Te general state of the Lake Arekit fshery is unknown.However, the study's preliminary assessment did show that the fshing potential in the lake is poor.Te biological characteristics of C. carpio and their stocks in Lake Arekit should be studied and frequently evaluated for efcient fshery management.Terefore, the C. carpio population in Lake Arekit was examined for various population features, including the length-weight relationship, growth parameters, death rates, the exploitation rate, and stock analysis.

Study Area.
Tis study was carried out in Lake Arekit (Ethiopia).Te lake is situated between 38 °04′30″ and 38 °05′0″ E latitude and 7 °57′0″ and 7 °58′0″ N longitude at an elevation of approximately 2870 m above sea level (Figure 1).It is 2.5 km long (from north to south) and 1.1 km wide (from east to west), respectively.Te lake's maximum depth was determined to be 3.2 m.Lake Arekit is a shallow freshwater ecosystem, with an average depth of 2.5 m, in Ethiopia's rift valley basin.It is a lake that is rather small in size, with a surface area of approximately 150 hectares.Tis lake is located in the Southern Nation Nationality People Regional State (SNNPRS), 220 km from Addis Ababa, the capital city of Ethiopia.Te lake does not have an outlet and receives its water from adjacent watersheds and direct rainfall.Lake Arekit is a productive lacustrine ecosystem that is alkaline, turbid, and rich in nutrients (phosphate and nitrate) [13].Te watershed of the lake is signifcantly impacted by anthropogenic efects, and eutrophication is brought on by nutrient infuxes.Te lake also provides irrigation services to the community.During the study's reconnaissance survey, it was found that the common carp (Cyprinus carpio) was the only species of fsh habiting Lake Arekit.

Data Collection.
Fish samples from Lake Arekit were collected using gill nets with stretched mesh sizes of 6 cm, 8 cm, and 10 cm between June 2022 and May 2023 from 3 diferent sites (Figure 1).Troughout the sampling periods, 194 Cyprinus carpio samples (117 females and 77 males) were gathered.Data for the examination of the lengthweight relationship of fsh were generated from the captures by measuring the length and weight of fsh.Individual fsh were weighed to a precision of 1 g, and their total length was measured using a measuring board to a precision of 0.1 cm.

Data Analysis
2.3.1.Length-Weight Relationships.Te relationship between length and weight of the fsh was examined by using correlation analysis and simple linear regression.Te fsh's length-weight relationships were computed using the methods presented by Ricker [10] to determine whether their growth pattern was isometric (b � 3) or allometric (b ≠ 3).Te relationships between the length and weight of Cyprinus carpio in each sex category were calculated using the following equation: where TW � total weight of fsh (g), TL � total length (cm), and a and b � constants.Te log transformed relationship (TW � aTL b ) gives the regression equation; Log W � log a + b log L. "a" and "b" values and linear representations of the graphs were carried out using MS Excel 2010.
Using the Student's t test at a 95% confdence level, the equation's constant value, b, was checked for accuracy against a value of b � 3. Te fsh growth pattern was isometric if the test results did not deviate from the constant value of b � 3, while when the test results produced b values other than 3, the fsh had an allometric growth pattern.

Growth Parameters.
A length frequency analysis was used to estimate the growth parameters (L ∞ , k, t 0 ) using Von Bertalanfy's growth function model [14] are described as follows: where Lt � length of the fsh at age t, L ∞ � asymptotic length (maximum length of the average), K � coefcient of growth, and t 0 � theoretical age at length 0 cm.Te asymptotic length (L ∞ ) and growth coefcient (K) were calculated using FISAT [8].Te theoretical age at length zero (t 0 ) was estimated using Pauly's [15] empirical equation shown as follows: Also, the reliability of these growth parameters was tested by applying the growth performance index (Φ′, phiprime), which was computed from the Munro and Pauly [16] equation, as indicated in the following equation: Te longevity (also called maximum age) (t max ) was obtained from the Pauly [17] equation, as indicated in the following equation: (5)

Mortality and Exploitation
Rates.Te total mortality (Z) was calculated using the length-converted catch curve analysis [10] from the FISAT II software suite (equation ( 6)), and natural mortality (M) was estimated in accordance with Pauly [18] and Pauly [17] empirical formula (equation ( 7)).
Te rate of fshing mortality (F) was calculated by the following Gulland [19] equation: where Z is the total mortality, F is the fshing mortality, and M is the natural mortality.Te exploitation level (E) of the study fsh was obtained from an equation proposed by Pauly [18].
where E is the exploitation rate; F is the fshing mortality, and Z is the total mortality.
If the exploitation rate values are under 0.5, the fsh stocks are easily exploited, while if the E values are between 0.5 and 1, the stocks are overexploited.
Te Jackknife approach was used to determine the bestft growth curves using mean growth parameters.Tis method enabled us to measure the impact of fuctuations in the input data and the degree of uncertainty in the growth parameter approximations.

Yield per Recruit (Y′/R) and Biomass per Recruit (B′/R).
Te model of Beverton and Holt [20], as updated by Pauly and Soriano [21], was used to forecast the species' relative yield per recruit (Y′/R) using the knife-edge analysis incorporated into the FISAT software.E 0.1 (the exploitation point at which the related increase in yield per recruit reached 1/10 of the related increase computed at a very Journal of Applied Ichthyology devalued value of E), E 0.5 (the exploitation rate corresponding to 50% of the unexploited relative biomass per recruit (B/R)), and E max (the exploitation point that gives the maximum relative yield per recruit) were estimated using L c / L and M/K values.Te stock status was indicated by the biological target reference points (E 0.1 and E max ) and the current exploitation rate (E) [22].
Te length at optimum cohort biomass or yield per recruit (L opt ) was calculated by Beverton and Iles [23] as follows: where L ∞ and K are as defned above and M is the natural mortality coefcient.
Te average age of the parents at the time of birth of young fsh was calculated as the generation time (tg).It was estimated as the fsh's average age at L opt , since this is when fsh produce the most eggs on average, according to Beverton and Iles [23].

Virtual Population Analysis (VPA).
VPA allows for reconstruction of population from total catch data by length.Te initial step was to estimate the terminal population (N t ), followed by the successive estimation of F values, and fnally, the population sizes are computed for each length class (midpoint).Tis length-structured virtual population analysis (VPA) was carried out using relevant information and cohort analysis [8].Te input parameters used were L ∞ , K, M, and F and constants of length-weight relationship (a and b) were used as inputs to VPA analysis for the species.Te initial step is to estimate the terminal population (N t ) given the inputs, from the following equation: where C t is the terminal catch (i.e., the catch taken from the largest length class).Ten, starting from N t , successive values of F are estimated, by iteratively solving: where and where population sizes (N i ) are computed from the following equation: Te last two equations are used alternatively, until the population sizes and fshing mortality for all length groups have been computed [8].An F-array representing the fshing mortality for each length group, the reconstructed population (in numbers), and the mean stock biomass by length class were made using FiSAT II.Te results of the VPA analysis were the biomass (tons), the yield (tons), total and fshing mortality, and exploitation ratios.

3.2.
Growth Parameters (L ∞ , K, t 0 , Φ, and t max ).Te Von Bertalanfy growth parameters for C. carpio were L ∞ � 51.45 cm and K � 1.1 year −1 (Table 2, Figures 3 and 4).Furthermore, the age at length 0 cm (t 0 ) value obtained from the Von Bertalanfy parameters was found to be −0.124years.Te maximum age (t max ) was calculated to be 2.60 years, and the values of the growth performance index were equal to Φ′ � 3.464 for C. carpio in Lake Arekit (Table 2).Te equation of the Von Bertalanfy growth model for C. carpio in Lake Arekit was L t � 51.45 * (1 − e −1.1(t + 0.124) ) (Table 2).
Figure 4 shows the length frequency distributions for C. carpio in Lake Arekit and the best-ft growth curves using the mean growth parameters obtained from the jackknife approach.According to the length frequency statistics, the 34-38 cm total length range dominated the C. carpio population, with a frequency of 34.02%, followed by the 29-33 cm total length, with a frequency of 26.23% (Figure 4).

Mortality and Exploitation Rates.
In comparison to the estimated fshing mortality (F) of 0.97 year −1 and the natural mortality (M) of 1.58 year −1 , C. carpio had a total mortality coefcient (Z) of 2.55 year −1 in Lake Arekit (Table 3, Figure 5).Te exploitation rate (E) of 0.38 year −1 for C. carpio appeared to be less than the anticipated level of exploitation (E � 0.50) (Figure 5).Te length class of the maximum biomass was determined to be 34.79 cm (Table 3, Figure 6).In Lake Arekit, the age at which C. carpio reaches its maximum cohort biomass or yield per recruit (L opt ) was calculated to be 1.29 years age, on average (Table 3).

Virtual Population Analysis (VPA).
Te results of the virtual population analysis (VPA) of C. carpio in terms of natural losses, survival, and fshing mortality are shown in Figure 6.With an increase in length and fshing mortality, the natural losses and survivorship of the fsh population declined.Te highest number of C. carpio harvested ranged between 34 and 38 cm TL (Figure 6), indicating that the fshing mortality value of the species was inconsistent.Te VPA results showed there were diferences in fshing mortality rates with regards to the mean length.At midlength (34.79 cm TL), the fshing mortality rate peaked (F � 2.53 year −1 ).F t � 0.97 year −1 was the terminal fshing mortality rate (Figure 6, Table 4).

Yield per Recruit (Y′/R) and Biomass per Recruit (B′/R).
Te relative Y′/R and B′/R analyses of C. carpio are shown in Figure 7. Te maximum allowable limit of the exploitation level (E max ), which yields the maximum relative yield per recruit, was estimated to be 0.421 (Figure 7).Te marginal gain in the relative yield per recruit at E 0.1 , the level of exploitation at 10% of the marginal increase estimated for a very low value of E, was 0.355.Te relative biomass per recruit at the exploitation level (E 0.5 ), or 50% of the relative biomass of the unexploited stock, was 0.278 (Figure 7).

Discussion
4.1.Length-Weight Relationship.Table 5 presents the growth coefcient (b) values for C. carpio in several geographic locations and shows various growth types.Some studies [24,26,27,30] revealed negative allometric patterns.Tis is in agreement with the present study.Te negative allometric growth of C. carpio in the Lake Arekit showed that the fsh were not developing properly, presumably as a result of the inappropriate environmental conditions as well as overfishing.However, other studies [25,28,31] indicated positive allometric growth patterns (Table 5).Te variations in the growth pattern of the same species in diferent geographical localities may be due to various factors, such as the number and size of specimens examined, stomach fullness, sex    6).For the same species, the growth parameter values vary across diferent geographic regions.Te asymptotic length (L ∞ ) of C. carpio in the current study was higher than that of the species in some waters [25] but lower than that of the species in other waters [34][35][36][37][38] (Table 6).Diferent environmental circumstances, food availability, metabolic activity, reproductive activity, fsh size, survey technique, and fshing pressure are a few variables that may have an impact on how diferently the same species grows in different places [32,42].A fsh's ability to grow is infuenced by three factors: its genetic makeup, the growth-restraining abiotic environment it encounters, and the biotic   environment [43].Moreover, the development rates of related species can vary depending on habitat [32,44].Fish lifespan has been linked to the Von Bertalanfy curvature parameter K [45] and longevity has been linked to mortality [46].Fish species with high K values also had high M values, whereas the opposite was true for fsh species with low K values.If natural mortality is high, a slow-growing species (low K) will soon become extinct [47].Te variations in the growth coefcients (K) for C. carpio in various geographical locations are shown in Table 6.Te varying growth coefcients of the same fsh species residing in various waterways are mainly related to the fuctuating water characteristics and ecological circumstances of the aquatic environment.In comparison to C. carpio populations in other research locations, the growth coefcient (K) value of the C. carpio in the present study represents a faster growth rate (Table 6), owing to high growth rates and short asymptotic lengths [47].According to Sparre and Venema [47], K > 1.0 indicates rapid growth, K � 0.5 indicates medium growth, and K < 1 indicates slow growth.Given that C.  Journal of Applied Ichthyology carpio in Lake Arekit has a high life span and a high growth coefcient, it is clear that this species grows quickly (Table 6).
Te study's age at zero length, t 0 (−0.124),verifed that the C. carpio from Lake Arekit quickly reached its maximum size.Te age at zero length, t 0 in the current study seems to be comparable to that discovered by Stroe et al. [34] in the Danube Delta (t 0 � −0.077).Te lowest value (t 0 � −2.423) was obtained from Keban Dam Lake, Turkey [41], AlMassira Dam (t 0 � −1.27) [40], and Almus Dam (t 0 � −1.922) [25].Tis variance could be caused by several developmental   In the fsh stock assessment, which is based on K and L ∞ , the use of "Φ" is a more precise estimator [16].Tis index is the most accurate technique for determining the average growth parameters of a particular species and should produce results comparable to those for other groups of the same species [47].Te estimates for C. carpio in the Southern Caspian Sea (Φ = 2.97) [35] and Koka Reservoir (Φ = 3.19) [4] were both lower than those in the current study.Tis shows that our estimations of growth parameters were accurate.Te results from Lake Karamık (Φ = 7.15) [36] and Almus Dam (Φ = 5.80) [25]were both greater than those of the current study (Φ = 3.464).Tis diference in the phi prime index between the same species may be due to differences in the size of the largest individuals sampled [36] and various exogenous and endogenous factors afecting fsh growth performance and longevity [48].
Fish exhibit a wide range of life stages.Te maximum lifespan (t max ) of C. carpio in Lake Arekit difers from the 5.49 years reported in Lake Naivasha by Oyugi [49]; as well as those in Lake Karamık (10 years) [36], Damsa Dam Lake (8 years) [29], and Lake Gariep (7 years) [39].It does, however, slightly exceed the maximum age determined by Ferraj et al. [40] in the Merdja Sidi Abed Dam (2 years), Algeria (Table 6).Te diferences in the lifespan of the same fsh species in varied geographical location may be related to the habitat quality of the fsh.

Mortality Parameters (Z, M, and F).
It has been noted that C. carpio populations in various locations exhibit variability in their fsh mortality rates (Table 6).Te mortality rate in fsh populations is infuenced by age, abiotic conditions, parasitic diseases, carnivorous fshes, food shortages, and hunting [35].For the carp population sampled from Lake Arekit, total mortality (Z) was signifcantly higher than that found at other locations such as Koka Lake (0.83 yr −1 ) [4], Danube Delta (1.47 yr −1 ) [34], and Lake Paniai (1.17 yr −1 ) [38].Tese fndings suggest that the C. carpio population in Lake Arekit was not properly managed.
Te value obtained for the same species in other bodies of water [34,37,38,40] is less than the value hypothesized for C. carpio in Lake Arekit (Table 6).Te fshing mortality (F) for C. carpio in Lake Arekit is greater than for Lake Paniai [38] and the Danube Delta (Stroe et al. [34]; where it was 0.52 yr −1 and 0.65 yr −1 , respectively).It was evident from comparing the estimated values for M and F that natural mortality accounted for the majority of C. carpio deaths in Lake Arekit.Te total, natural, and fshing mortalities for C. carpio in Lake Arekit were high.Fish physiological circumstances and fshing pressure may be responsible for these results.
Te M/K ratio in this study is within the range for most species and indicates that the M for C. carpio in Lake Arekit was accurately computed.A Z/K ratio calculated in this study likewise pointed to a population with a high mortality rate.Tis is consistent with the general [45] criteria: if Z/K is less than one, the population is dominated by growth; if it is greater than one, the population is dominated by mortality; and if it is equal to one, the population is in an equilibrium condition where growth and mortality are equal.If the Z/K ratio in a mortality-dominated population is 2, it indicates that the population is being lightly exploited [45].Terefore, our Z/K results indicate that there may be an unexploited stock in Lake Arekit.Tis is further supported by the predicted low exploitation rate, which indicates limited exploitation stock.Terefore, our Z/K value indicates underexploited stock.

Virtual Population Analysis (VPA) and Exploitation Rate at MSY. Te present exploitation ratio (E) value found in
this study is less than the optimal level of E � 0.5 [19].Sustainable yield is optimal when F � M, and the stock is often underexploited when E < 0.5 [19].As a result, the C. carpio stock in Lake Arekit is likely to be underutilized.Te current study's exploitation rate (E) estimate is greater than those of Lake Koka (0.34) [4], Lake Mangla (0.27) [37], Lake Gariep (0.14) [39], and Merdja Sidi Abed Dam (0.24) [40].However, the E estimated for C. carpio stock in Lake Karamık [25] and the Southern Caspian Sea  [35] reported slight overexploitation of the fsh, with values of 0.60 and 0.59, respectively (Table 6).Fishing mortality rates varied signifcantly throughout the course of these specimens' lives, with F varying in response to variations in mean lengths.Te minimum yield for this fshery was achieved at F MSY (fsh mortality at maximum sustainable yield), and it dropped with F values higher than F MSY .With the current fshing mortality for this species, F cur is lower than F msy (but somewhat higher than F 0.5 , the optimum reference point); therefore, the stock may be considered sustainable.E � 0.38 was the rate of exploitation.Te relative yield and biomass per recruit were used to calculate this rate, which was > E 0.1 � 0.355, E 0.5 � 0.0.278, and E max � 0.421 (Figure 7).A midlength of 34.79 cm and an average age of 1.29 years were the length and age ranges for the largest peak in fshing mortality (F � 2.53 year −1 ) and the optimal cohort biomass or yield per recruit (L opt ) (Figure 6, Tables 3 and 4).Te relative yield per recruit (Y/R) and biomass per recruit were calculated as functions of L c /L ∞ and M/K, respectively.M/K's computed value was 1.44, whereas L c /L ∞ remained at 0.59.Te fndings indicated that, in comparison to the current exploitation rate of 0.38, the highest values for yield per recruit for C. carpio were at the exploitation level of 0.421.Based on these data, the C. carpio stock in Lake Arekit was clearly within sustainable limits.In fact, increasing fatality rates in fshing can increase the level of exploitation.Our research indicates that raising the rate at which Lake Arekit's underutilized C. carpio is harvested could boost fshery production.

Conclusions and Recommendations
Knowledge of fsh population dynamics is essential for making up-to-date decisions and implementing efective management strategies.In this study, we assessed for the frst time the growth parameters, mortality rates, rate of exploitation, fshing efort, and maximum sustainable yield (MSY) of C. carpio collected from Lake Arekit.Our fndings revealed the exploitation rate of C. carpio in Lake Arekit is below the ideal value, indicating that the fshery stock is underexploited.It is advised to implement the following fsheries management strategies in order to increase fshing in the study lake: setting up a regular monitoring programme to determine and record the C. carpio population, creating more fshermen's associations (at the moment, there is only one with 15 members), creating a social network and raising awareness for fsheries, involving numerous stakeholders, and creating chain values for fsheries, among other things.

Figure 1 :
Figure 1: Map of the study area (Lake Arekit) and the sampling sites.

Figure 3 :Figure 4 :
Figure 3: Estimation of L ∞ by the ELEFAN I method for C. carpio in Lake Arekit.

Figure 5 :
Figure 5: Length converted catch curve of C. carpio in Lake Arekit.Yellow and black dots are calculated points.Black dots are used to ft regression line (length-group that are fully recruited into the stock and used in the analysis to calculate mortality).Yellow dots indicate small size fshes and those that were excluded from estimation.Black outlines circles are the extrapolated points to estimate the probability of capture.

Figure 6 :
Figure 6: C. carpio population estimation in Lake Arekit using the VPA from the FiSAT output.

Figure 7 :
Figure 7: Relative yield per recruit and biomass per recruit (selection ogive) for C. carpio in Lake Arekit.E 0.1 � 0.355, E 0.5 � 0.278, and E max � 0.421 (yellow dotted line).Current E � 0.38.(Note.Te red line represents E 0.1 and yellow line represents E-ma.Black lines are either yield per recruit (Y/R), maximum sustainable yield points (MSY), or biomass per recruit (B/R)).

Table 1 :
Length-weight relationship of C. carpio from Lake Arekit from June 2022 to May 2023.

Table 2 :
Growth parameters of C. carpio from Lake Arekit.
4.2.Growth Parameters (L ∞ , K, t 0 , Φ, and t max ).Te growth parameters (L ∞ and K) for C. carpio obtained in this study are compared with those obtained from other studies (Table

Table 4 :
FISAT II output of virtual population analysis of C. carpio in Lake Arekit.

Table 5 :
Length-weight relationship for C. carpio of the previous studies.

Table 6 :
Comparison of on Von Bertalanfy growth parameters, mortality, and exploitation rates for C. carpio from diferent areas of the world.