Introduction

Tilapia (genus Oreochromis) are a group of fish known for their fast growth, year-round reproduction (with parental care), and sexual maturity size reached in a short time. These characteristics make them efficient in establishing and proliferating in almost any type of aquatic ecosystem (^{Küçük et al., 2013}; ^{Al-Wan & Mohamed 2019}). Tilapia have been introduced into water bodies (ponds, rivers, lakes, reservoirs, etc.) almost worldwide, they are widely cultivated in the tropics and subtropical zones (^{Norato, 2005}; ^{Gómez-Ponce et al., 2011}). They have a high reproductive rate and are therefore fast-growing and easily marketed, and are therefore considered low-cost and easy to acquire (^{FAO, 2009}; ^{Gómez-Ponce et al., 2011}).

In Mexico, this nonnative organism was introduced in the 1960s (^{Cantor, 2007}). Since then, most of the artificial reservoirs in Mexico and in particular, Sinaloa state, have allowed the establishment of important fisheries based on the exploitation of the Oreochromis genus (tilapia). This situation has improved the living standards in rural communities surrounding these water bodies, thus making freshwater fishery one of the most important (ranking 5th in fisheries and aquaculture) in Mexico (^{Beltrán-Álvarez et al., 2009}; ^{Gómez-Ponce et al., 2011}; ^{Vázquez-Vera & Chávez-Carreño, 2022}). Regionally, the state of Sinaloa is positioned as one of the main producing entities in the country, with more than 6,000 tons (t) annually (^{Beltrán-Álvarez et al., 2009}; ^{Vázquez-Vera & Chávez-Carreño, 2022}).

In the north of Sinaloa, particularly in the municipality of El Fuerte, the Josefa Ortiz de Domínguez reservoir (El Sabino) is located, where the average annual production per tilapia fishery is 500 t (^{Beltrán-Álvarez et al., 2015}). In this reservoir, the capture and commercialization of tilapia is the main activity carried out by the surrounding communities (301 fishermen and 299 boats), contributing to maintaining life quality.

Some reservoirs (in Sinaloa only the Luis Donaldo Colosio dam "Huites") operate under an Official Mexican Norm (NOM) published for the regulation of these reservoirs, which protects reproductive cycles of the main commercial species, establishes closed seasons, fishing gear, etc. Despite this, only two (Ignacio Allende reservoir, San Miguel de Allende, Guanajuato, and Cebolletas reservoir, Coroneo, Guanajuato) have an integrated management plan, based on technical aspects of the biological-fishing, limnological and socioeconomic fields, whose purpose is to provide an instrument to regulate fishing activity in the reservoirs (^{INAPESCA, 2021}).

Among the technical parameters of the biological-fishery field, growth estimation is one of the main aspects of population evaluations (population biomass is related to individual growth) (^{Curiel-Bernal et al., 2021}). Currently, several studies have estimated tilapia growth in various freshwater bodies in Mexico, based on direct methods such as the interpretation of layers in the hard parts of the fish (scales and otoliths) (^{Jiménez-Badillo, 2006}; ^{Ramírez, 2007}; ^{Valdez-Leyva, 2008}; ^{Beltrán-Álvarez et al, 2009}; ^{Ortega-Lizárraga, 2010}; ^{Gómez-Ponce et al., 2011}), or through indirect methods such as size frequency population analysis (^{Ramos-Cruz, 1995}; ^{Hernández-Montaño, 2006}; ^{Peña-Messina et al., 2010}; ^{Arellano-Torres et al., 2013}). However, in most of the aforementioned studies, growth estimates have been obtained by a single method or model, without a quantification of the uncertainty associated with these estimates.

Hence, the present work aimed to determine size structure, length-weight relationship, sexual maturity, and growth modeling of the blue tilapia Oreochromis aureus (Steindachner, 1864) population in the Josefa Ortiz de Domínguez reservoir in El Fuerte, Sinaloa state, to provide information on these population parameters and including the uncertainty associated with the estimation, thus contributing to better evaluation for the exploited population.

Material and Methods

Results

From October 2011 to April 2012, 1,689 O. aureus specimens were analyzed, of which 1,044 were males and 645 were females (Figure 1a). The length-weight relationship for both sexes throughout the study generally showed a high degree of association (r = 0.98, p < 0.001, Table 1 and Figure 1b). The slope value (b) for both sexes during the whole study, expresses an isometric type growth (p > 0.05, Table 1 and Figure 1b). Similarly, the length-weight relationship for separate sexes (females and males) during the whole study showed a high degree of association (r > 0.98, p < 0.001, Table 1). The value of slope (b) for males expressed isometric growth (p > 0.05, Table 1), while for females the value of slope (b) was different from 3 (p < 0.05, Table 1).

The length-weight relationship by month for female tilapia O. aureus, showed a high association degree (r > 0.94, p < 0.001), with the highest correlation values in February and March (r = 0.99, p < 0.001) and lowest values in October (r = 0.94, p < 0.001) and April (r = 0.95, p < 0.001, Table 1). Likewise, values of slope (b) for females by month showed isometric-type growth in October, November, January, March, and April (p > 0.05, Table 1); during February the value of slope (b) was different from 3 (p < 0.05, Table 1).

The length-weight relationship by month for male tilapia O. aureus, showed a high association degree (r > 0.94, p < 0.001), with the highest correlation values in February and March (r = 0.98, p < 0.001) and lowest values in January (r = 0.97, p < 0.001) and October (r = 0.94, p < 0.001). The values of slope (b) for males by month showed isometric-type growth in November, January, February, March, and April (p > 0.05, Table 1); the value of slope (b) was different from 3 during October (p < 0.05, Table 1).

Figure 1 Monthly length structure (a) for females, males and both sexes and length-weight relationship (b) for Oreochromis aureus in the Josefa Ortiz de Domínguez reservoir, El Fuerte, Sinaloa, Mexico. 

The weight frequency distribution was measured by separate sexes of O. aureus tilapia, showing a range from 44 to 896 g in males (X̅ 129 ± 99.7) and for females from 50 to 626 g (X̅ 124 ± 74.4). No significant differences were found in the weight of both sexes, even though males weighed more than females (Table 2). In females, the length ranged from 125 to 305 mm TL (X̅ 186.7 ± 28.5), and in males from 125 and 370 mm TL (X̅ 188.3 ± 33.7) (Table 2 and Figure 1a). No significant differences were found when comparing size distribution between males and females (Kolmogorov-Smirnov p = 0.673). The comparison between months of frequency distribution for females with respect to males showed that only in October there were significant differences (p = 0.009).

A multinomial analysis was applied to size structures in female tilapia O. aureus, showing modal groups from one to three per month and four groups in March 2012 (Figure 2). For males, a multimodal behavior was observed with two and four groups per month and five modal groups in March 2012. Modal progression identified four cohorts for females and six cohorts for males (Figure 2).

The best models for growth estimation parameters of O. aureus tilapia (as indicated by the quality estimators estimators AIC _c , ∆ _i y ω _i ) with the additive error were: cases 2 and 5 for both sexes (Table 3). In females, case 2 was estimated at L _∞ = 310.7 mm of TL and a value of parameter a = 1.7; with case 5, we estimated a L _∞ = 328.8 mm of TL and a value of a = 1.2. In males, with case 2, a = 362.9 mm TL and a value of a = 1.2 were estimated. L _∞ = 362.9 mm of TL and a value of the parameter a = 2.2; with case 5, a = 410.6 mm of TL and a value of a = 1.2 were estimated. L _∞ = 410.6 mm of TL and the value of parameter a = 1.2. Table 3 shows the values of each case for females and males with their respective confidence intervals.

Figure 2 Monthly length structure (bars), modal groups (white circles centered on each curve) and modal progression of the individual cohorts (dotted line labeled numerically in chronological order of occurrence) for females (a) and males (b) of Oreochromis aureus in the Josefa Ortiz de Domínguez reservoir, El Fuerte, Sinaloa, Mexico. 

The growth modeling (growth curves) for both female and male O. aureus tilapias can be seen in figure 3 for both cases and confidence intervals of the best models are shown in figure 4. L _∞ and a of the best models are shown in Figure 4. An average model was estimated since the two best cases did not reach a ω _i = 0.90, so it cannot be declared as the best model.

Figure 3 Growth curves for females (a) and males (b) adjusted with cases 2, 5 and average of the Schnute model, in Oreochromis aureus from the Josefa Ortiz de Domínguez reservoir, El Fuerte, Sinaloa, Mexico. 

The overall sex ratio for O. aureus tilapia was 1.6 M:1 H, showing significant differences (p < 0.05), with male dominance. Monthly sex ratio behavior only in March 2012 showed no significant differences (X² = 1.6 and p > 0.05, Table 4).

The estimated mature length or L₅₀ for female O. aureus tilapia was 197.2 mm TL (Figure 5a). Confidence intervals estimated using likelihood profiles indicate that female O. aureus tilapia can mature between 191.8-203 mm TL (Figure 5b).

Figure 4 Confidence intervals of L _∞ and a estimated by means of likelihood profiles for cases 2 and 5. Females case 2 (a-b) and case 5 (c-d), males case 2 (e-f) and case 5 (g-h).  

Figure 5 Size at maturity or L_50% (a), likelihood values, and confidence intervals of size at maturity (b) for females of Oreochromis aureus in the Josefa Ortiz de Domínguez reservoir, El Fuerte, Sinaloa, Mexico. 

The size at which 50 % of the organisms were caught was estimated at 175 mm TL. It was also determined that more than 75 % of the total catches were smaller than 200 mm TL, as a consequence of the selectivity of the nets used in the commercial catch (Figure 6).

Figure 6 Probability of capture (selectivity curve) of the sizes of Oreochromis aureus in the Josefa Ortiz de Domínguez reservoir, El Fuerte, Sinaloa, Mexico. 

Discussion

The primary use of water from the Josefa Ortiz de Domínguez reseroir is for agricultural irrigation in the valleys of El Fuerte and El Carrizo, Sinaloa, and to a lesser degree, for drinking water supply for the populations downstream of the dam. The original water use in this reservoir did not prevent the establishment of fisheries such as catfish, carp, bass, and tilapia, the latter of which is one of the most important, with an average production per fishery of 500 t (^{Beltrán-Álvarez et al., 2015}). Tilapia fish capture (from January to April and from August to December) and its commercialization is the main activity carried out in the communities on the shores of the reservoir, helping to maintain quality of life standards, providing a source of food and employment for more than 300 fishermen and their families, settled in communities on the shores of this reservoir (^{Álvarez-Anaya, 2008}).

In this study, the size range for both sexes of tilapia O. aureus was from 125 to 370 mm TL, similar to that reported by some authors for this same species in different reservoirs in Sinaloa: ^{Sánchez (2000}) in the Luis Donaldo Colosio reservoir (170-320 mm TL), ^{Beltrán-Alvarez et al. (2006}) at Gustavo Díaz Ordaz reservoir (120-350 mm TL), ^{Álvarez-Anaya (2008}) at Josefa Ortiz de Domínguez reservoir (87-336 mm TL), Beltrán-Álvarez et al. (2009), at Sanalona reservoir (125-345 mm TL), and Beltrán-Álvarez et al. (2014), at Eustaquio Buelna reservoir (90-272 mm TL). Despite the above, and based on the selectivity analysis performed (Figure 6) of the total organisms in this study, it was observed 75 % at sizes between 125 to 194 mm TL. The same was observed by Álvarez-Anaya (2008), reporting that more than 75 % of the O. aureus tilapia organisms captured with trawls of different mesh sizes (21/2, 23/4, 3, 31/8, 31/4, 31/2 inches) and trawls, corresponded to sizes less than 225 mm TL.

Although there is a recommendation for a minimum catch size of 260 mm TL and the use of a 3-inch mesh size for catching tilapia in this reservoir (^{Beltrán-Álvarez et al., 2015}), compliance with these recommendations is not always respected. As documented by Beltrán-Álvarez et al. (2015) and evidenced in this study, commercial catches are carried out with different mesh sizes of 21/2, 2 3/4, 27/8, 31/8, 31/4, and 31/2 inches. Likewise, ^{Álvarez-Anaya (2008}) and the present study determined that, due to the selectivity of the fishing gear used, more than 75% of the catches are smaller than 225 mm TL (smaller than the minimum recommended size), which may be the cause of this decrease in the size of the organisms caught each fishing season and, thus, the decrease in the volume of catches of tilapia O. aureus in this reservoir.

The size at maturity or L₅₀ estimated for female tilapia O. aureus in this work was 197.2 (191.8-203) mm TL, which is reached at one year of age, similar to and within the range of that estimated by some authors for this same species in different reservoirs in Sinaloa: 197 mm TL (139.4 g) by ^{Belmont (2003}) at Aurelio Benassini Vizcaíno reservoir "El Salto", 195 mm TL (124.2 g) by ^{Guardado (2006}) at José López Portillo reservoir "El Comedero" and 195 mm TL (147 g) by ^{Álvarez-Anaya (2008}) at Josefa Ortiz de Domínguez reservoir. Other studies carried out in different reservoirs in Mexico for this same species, recorded mature sizes greater than those estimated in the present study: 235 mm TL by ^{Ramos-Cruz (1995}), in the Benito Juárez reservoir (Oaxaca), 236.7 mm by ^{Hernández-Montaño & Orbe (2002}), in the "Zimapán", Hidalgo-Querétaro, and 251 mm TL by ^{Orbe et al. (2002)}, in the Aguamilpa reservoir, Nayarit.

A selectivity analysis was carried out for the total number of organisms analyzed in this study, and an average catch size was estimated (the size at which 50 % of the organisms were caught) of 175 mm TL. When comparing the present results with the mature size for female tilapia O. aureus of 197.2 (192-203) mm TL, it can be inferred that more than 50 % of the organisms (females) are being captured below their first maturity size. This, together with the fact that more than 75 % of the total catches are smaller than 200 mm TL (as a consequence of the selectivity of the small mesh size nets used in commercial catches), would be directly impacting the reproductive and juvenile population, which would harm the population and, therefore, on the sustainability of the fishery of this resource.

Despite these negative impacts observed in this work and which are caused by fishing, we must take into account the tilapia fry planting programs that are carried out on an annual-biannual or tri-annual basis in the reservoirs of the state of Sinaloa. This type of restocking program (planting of fingerlings) carried out by federal and state authorities provides a respite from the fishing pressure that is exerted season after season on commercial species in these reservoirs (^{Beltrán-Álvarez et al., 2015}). However, to date in this reservoir there is no formal evaluation of the status of the tilapia resource, nor improvements or population increases due to restocking programs.

Other parameters that could be counteracting the negative impacts observed (mainly caused by fishing) are the rapid growth, year-round reproduction (with parental care), and sexual maturity size reached in a short time, of O. aureus tilapia. These characteristics make this species successful to establish and proliferate in almost any type of aquatic ecosystem (^{Küçük et al., 2013}; ^{Beltrán-Álvarez et al., 2015}; ^{Al-Wan & Mohamed 2019}).

Obtaining the best possible estimates of individual growth parameters is essential in fisheries management and aquaculture studies, as growth is a key component of population dynamics. Population biomass is related to individual growth because fish grow in response to seasonal and local environmental conditions at a time or location (^{Curiel-Bernal et al., 2021}). The importance is reflected in a large amount of scientific literature on individual growth in fisheries and aquaculture.

With the multinomial analysis carried out in this study, 2 to 6 modal groups (cohorts) were estimated in the monthly size frequencies obtained from commercial catches of tilapia O. aureus in the Josefa Ortiz de Domínguez reservoir (Figure 2). ^{Jiménez-Badillo (2006}) found 3 to 6 cohorts of tilapia O. aureus in Infiernillo reservoir, Michoacán. ^{Leonce-Valencia & Defeo (1997}), and ^{Jiménez-Badillo (2006)} mention that in fish populations (such as tilapia), it is common to observe a mixture of cohorts, as a consequence of the multiple spawning and continuous recruitments that this species presents throughout the year. Therefore, it is of utmost importance to determine the influence that each group of monthly data has on the estimation of growth parameters.

The Schnute growth model used for growth estimation in the present research consists of a differential equation that forms eight families of curves as a function of the parameter values. It is a general four-parameter growth model whose alternative solutions contain the preceding models as special cases. Maximum likelihood was used as a criterion since its use provides a better solution to adequately estimate growth parameters, as it is a more robust test than traditional methods (^{Katsanevakis, 2006}). In addition, the selection of the most appropriate model or case, based on information theory has been recommended as a better and more robust alternative than traditional approaches (Katsanevakis, 2006; ^{Cerdenares-Ladrón de Guevara et al., 2011}). The advantage of using model quality estimators (AIC _c , ∆ _i y ωi) is that tested cases (models) can be hierarchically ordered according to their fit to the data and the average parameters for a growth model can be obtained.

The range of the estimated value of L _∞ in the present study, both for females and males of tilapia O. aureus, is similar or with slight differences to that reported by ^{Beltrán-Álvarez et al. (2014}), in Eustaquio Buelna reservoir, Sinaloa, where they estimated a value of. L _∞ = 357 for females and 294 mm TL for males and to that reported by ^{Beltrán-Álvarez et al. (2009)}, at the Sanalona reservoir, Sinaloa, where they estimated a value of L _∞ = 428 for females and 414 mm TL for males.

The variation in growth parameters that may occur is mainly due to the size range (as a consequence of the selectivity of the nets used in the commercial catch), the sample size used, and the reliability of the sampling. The different methods and criteria for determining growth can also affect the results of each study (^{Álvarez-Anaya, 2008}; ^{Beltrán-Álvarez et al., 2009}; Beltrán-Álvarez et al., 2014; ^{Curiel-Bernal et al., 2021}). The growth curves estimated with cases 2 and 5 indicate that males, compared to females of O. aureus tilapia, reach a size close to their theoretical maximum length in a shorter time.

Similarly, when comparing the slopes in the length-weight relationship of females and males, significant differences were found. The same was recorded for tilapia O. aureus by ^{Sánchez (2000}) at Huites reservoir, ^{Ramírez (2007}) at Varejonal reservoir, and ^{Valdez-Leyva (2008}) at Sanalona reservoir, where males were significantly larger than females. In contrast, ^{Beltrán-Álvarez et al. (2009}), and Beltrán-Álvarez et al. (2014), at Sanalona and Eustaquio Buelna reservoirs, found that females reached a length close to their theoretical maximum length in a shorter time. The possible causes of the difference in the growth of O. aureus tilapia could be the availability of food, water temperature, dissolved oxygen, pH, and transparency of the different reservoirs, in addition to the intrinsic variables of the species, such as the genetic capacity to support or adapt to changes in the environment or gene pool, physiology, reproductive stage, etc.

As determined in the present study, male tilapia O. aureus reaches a size close to their theoretical maximum length in a shorter time, a sex ratio of 1.6 M:1 H was also estimated, which is statistically different from the theoretical ratio of 1:1. ^{Meza et al. (1998}), ^{Álvarez-Anaya (2008}), and ^{Valdez-Leyva (2008}) in the Bacurato, Josefa Ortiz de Domínguez and Sanalona reservoirs, respectively, mention that males dominated over females. ^{Peña-Messina et al. (2010}) mention that the females of some fish such as tilapia, after fertilization tend to move to deeper sites and places with vegetation for incubation and protection of offspring, while males move to shallower feeding areas, thus increasing the possibility of being captured.

Conclusions

According to the tests performed in the present study, (selectivity, size at first maturity, and growth), it is suggested that the commercial catch of O. aureus during the study was composed of a high percentage (>75 %) of juveniles and spawners, which could harm the population and, therefore, on the sustainability of the resource. Despite these negative impacts observed on the population, there are restocking programs (fry planting) in this reservoir, which provide a respite from fishing pressure. In addition, the features of O. aureus, such as rapid growth, year-round reproduction, and sexual maturity size reached in a short time, make this species very successful and prolific.

Even though the information used for the present work is not recent, it provides biological-fishery information on tilapia in this reservoir, where there is no formal evaluation of the exploited population, much less a management plan that defines technical aspects of the biological-fishery, limnological and socioeconomic fields, which allows regulating the fishing activity, which is of great importance for the livelihood of the communities surrounding this reservoir.