Size at onset of sexual maturity in Macrobrachium amazonicum (Heller, 1862) phenotypes: an integrative approach.

The size at the onset of sexual maturity (SOM) was determined in four hololimnetic populations of Macrobrachium amazonicum using morphometric, physiological and functional criteria. Male prawns from two populations analyzed had hypertrophied chelipeds and large body proportions, showing the presence of four morphotypes, i.e. large-size phenotype (LS). However, the other two populations showed smaller males without morphotypes, i.e. small-size phenotype (SS). The development of sexual weapons in males modulated the mating system and SOM in this species. It was verified that there is a synchrony between physiological and functional maturities in SS males. On the other hand, functional maturity in LS males occurred after physiological and morphological maturities. In females, we verified synchronization between morphological and functional maturities. The results obtained indicated that, in both sexes, physiological maturity anticipates the others criteria. There were no differences between the sequential scheme of sexual maturity for female phenotypes, being: physiological → functional morphological. However, the evaluation of sexual maturity in males must take into account the phenotype of population, since that was modulated by functional maturity. The sequential scheme for LS males is: physiological → morphological → functional, while for SS males it is: physiological = functional → morphological.


INTRODUCTION
Some prawn species of the genus Macrobrachium Spence Bate, 1868 can inhabit coastal and inland waters (without marine influence), as is the case of the Amazon River prawn Macrobrachium amazonicum (Heller, 1862). This species displays a great environmental adaptability and wide intraspecific variability, with populations showing significant differences in morphological and reproductive traits (Odinetz-Collart & Rabelo 1996, Vergamini et al. 2011, Hayd & Anger 2013, Augusto & Valenti 2016, Paschoal et al. 2019. The Amazon River prawn has a wide distribution in the Americas, occurring from Costa Rica to Argentina. In Brazilian basins, it occurs in estuarine and/or freshwater ecosystems from the state of Roraima to Paraná (Vergamini et al. 2011, Pileggi et al. 2013. In estuaries, M. amazonicum has an amphidromous life history, where adults live and reproduce in freshwater environments, while their larvae develop in estuarine environments, returning to freshwater when juveniles (Bauer 2013). In these environments, individuals of this species have higher dimensions (body size) than those recorded for animals of inland populations. Furthermore, amphidromous females show high fecundity values (maximum fecundity range : 1,344 -7,417 eggs) when compared to females of inland populations (maximum fecundity range: 315 -4,264 eggs) (Maciel & Valenti 2009, Hayd & Anger 2013, Pantaleão et al. 2018, Paschoal et al. 2019). In addition, amphidromous populations have a social hierarchy, where males with dominant morphotypes (GC1 and GC2) have selective advantages over submissive morphotypes (TC and CC) (Moraes-Valenti & Valenti 2010, Ibrahim 2011. However, some populations with such characteristics were recently recorded in lentic environments of the Paraná Basin (southeastern Brazil) (Pantaleão et al. 2014, Paschoal & Zara 2017, Paschoal et al. 2019, indicating the shift of amphidromy by the entirely freshwater life cycle (i.e. hololimnia), due to the biological and physical impossibility of migrations to estuaries (Anger 2013).
The knowledge of the life history for different populations of M. amazonicum is fragmented and has gaps to be filled as reproductive and morphological aspects, since it is focused on studies dealing with amphidromous populations (Anger et al. 2009). In addition, the phenotypic plasticity of M. amazonicum populations is not yet fully understood (Anger 2013). Three types of phenotypes are recorded for the species: (a) large-size amphidromous populations, and (b) large-size and (c) small-size hololimnetic populations (Moraes-Riodades & Valenti 2004, Vergamini et al. 2011, Pantaleão et al. 2012, Paschoal & Zara 2017, Paschoal et al. 2019). These phenotypic differences recorded for this species are attributed to intrinsic factors (i.e. physiological and behavioral differences) (Moraes- Riodades & Valenti 2004, Augusto & Valenti 2016 and/or the availability of nutritional resources in different areas (Pantaleão et al. 2012(Pantaleão et al. , 2014.
The wide phenotypic and physiological plasticity of M. amazonicum makes the size at the onset of sexual maturity (SOM) of the species being variable between populations (Pantaleão et al. 2012). Thus, it is necessary to use several criteria to estimate the SOM, since this information is crucial for the maintenance and improvement of the Amazon River prawn stocks (Moraes-Valenti & Valenti 2010). This species is very important in artisanal fisheries and is highly consumed in northern and northeastern Brazil (Odinetz-Collart & Moreira 1993, Maciel & Valenti 2009), and considered a species with great potential for world aquaculture (New 2005). Consequently, several studies have been conducted in recent years in order to improve, maintain and increase the quality of stocks, larviculture and sustainable farming (Preto et al. 2010, Henares et al. 2013, Maciel & Valenti 2014, Dutra et al. 2016, Henry-Silva et al. 2015, Santos et al. 2016. Despite its importance, information about sexual maturity in M. amazonicum is limited to morphometric relationships (relative growth) and the determination of morphometric maturity (see Odinetz-Collart & Rabelo 1996, Moraes-Riodades & Valenti 2004, Maciel & Valenti 2009, Pantaleão et al. 2012. Thus, there is a gap related to physiological maturity (i.e. maturation of the reproductive systems) for the species. Also, there were no studies analyzing functional maturity (i.e. ♂: capability to mate and copulate, ♀: to carry eggs) in M. amazonicum. In this context, the present study analyzes the morphometric differences of four hololimnetic populations of M. amazonicum showing distinct phenotypes and determines the SOM in these populations, correlating morphometric, physiological and functional criteria.
Prawns were collected by active sampling, a sieve (60 cm in diameter and 1.25 mm mesh) was swept through marginal vegetation and macrophyte banks for 30 minutes by one person; and passive collection, where six baited-traps (85 cm length x 35 cm width/height) were placed near the margin (0.5 -2 m), baited with small pieces of beef liver and removed after four hours. Immediately after capture, the animals were anesthetized by chilling (ten minutes in ice) and preserved in 70% ethanol (except for animals used in histological analysis that were kept alive). After that, they were placed in properly labeled bottles and transported to the laboratory.
All animals collected during the monthly samplings were counted, and subsamples were obtained following Wenner et al. (1991): if N ≤ 80 individuals were collected, all animals were analyzed; when 80 < N < 160 individuals were collected, 80 individuals were randomly selected to be sexed and measured. If 160 < N < 320 were collected, 50% of the specimens were checked; and in the case of samples with N ≥ 321 individuals, 25% of the animals were selected. Individuals randomly selected from the subsamples were sexed by the (a) verification of the secondary sexual characters: absence (♀) or presence (♂) of the appendix masculina on the endopodites of the second pair of pleopods, (b) verification of the positions of the gonopores: openings in the coxopodites of the 3° (♀) or 5° (♂) pair of pereiopods, and (c) dissection of the reproductive organs: ovaries (♀) and testes (♂) (Paschoal & Zara 2017).
Male prawns were visually divided into four morphotypes: translucid claw (cheliped) (TC), cinnamon claw (CC), green claw 1 (GC1) and green claw 2 (GC2). These morphotypes were classified according to Moraes-Riodades & Valenti (2004) and Pantaleão et al. (2014), based on size and color of the chelipeds, angles of the spines on the carpus and propodus and the pubescence on dactyls. Subsequently, principal component analyses (PCA's) were performed to separate different morphological groups (morphotypes) in males for each population, using all body dimensions measured (log 10 ) in these animals (Sampedro et al. 1999).
The morphometric maturity was estimated by the relative growth patterns of the species, which was determined by allometric equations Y = aX b (Huxley 1950). These equations were adjusted, having as independent variable (X) the CL and relating it to the other body dimensions of the animal (dependent variables, Y). Values of the allometric constant (b) were tested using the t-test, as H 0 :b = 1 (or 3 in the case of weight), and used to determine the growth patterns of a specific body part in relation to CL. Equations were subsequently linearized (log y = log a * log x -b). The morphometric relationships that presented differences in the growth patterns were submitted to a non-hierarchical analysis of K-means clustering, minimizing the variability within the groups and maximizing the variation between them. The result of this analysis was refined by applying a discriminant analysis. The inflection point between the groups identified by the discriminant analysis was considered as the morphometric SOM, i.e. the smallest adult in population (Sampedro et al. 1999, Pantaleão et al. 2012. After the determination of groups, differences between slopes (b) and intercepts (a) of lines at each development stage were compared using Covariance analysis (ANCOVA) (α = 0.05). All calculations and statistical analyzes were performed with the software R version 3.3.1. (R CORE TEAM 2016).

Histology and physiological maturity
For the determination of the physiological maturity, all males and females of the subsamples of each population had their reproductive systems dissected. The macroscopic morphology of the reproductive systems was analyzed under stereomicroscope. The physiological SOM in the different populations was established by the smallest CL recorded for the animals that reached the following criteria: (a) males with spermatozoa in their testes and vasa deferentia (VD), and (b) females with oocytes in exogenous or secondary vitellogenesis (with yolk granules) (Viau et al. 2006, Poljaroen et al. 2010, Soonklang et al. 2012, Zara et al. 2012, Nascimento & Zara 2013. The presence of spermatozoa in the testes and VD, as well as that of vitellogenic oocytes in the ovarian lobes, was verified by smears of these structures (obtained from animals preserved in ethanol) under light microscope (Cuzin-Roudy & Amsler 1991, Paschoal & Zara 2017. In order to confirm  Pantaleão et al. 2014). 2° pl, width of the second abdominal pleura. al, abdomen length. cl, carapace length. dcl, dactyl length. mcl, major cheliped length. ppl, propodus length. tl, total length. the smears results, ten recently-collected individuals of both sexes from each population showing different macroscopical stages of sexual development were anesthetized by chilling (-20 °C / 5 min.) and dissected. After the dissection, the animals had fragments of their reproductive systems fixed in 4% buffered-paraformaldehyde (24 hours). Subsequently, they were washed twice in the same 0.2 M sodium phosphate buffer (pH 7.2), dehydrated in an increasing series of ethanol (70 to 95%), and embedded and included in glycol-methacrylate historesin Leica ® . Blocks were cut in 4-5 μm sections with a rotary microtome. After the microtomy, the slides were stained with hematoxylin and eosin (H&E) for general histological description (Zara et al. 2012.

Functional maturity
For M. amazonicum females, functional maturity was determined by the smallest CL recorded for ovigerous females captured in the field for each population (Viau et al. 2006). In males, functional maturity was considered as the ability to copulate and transmit ejaculate (Elner & Beninger 1995). For this purpose, animals of the SJB and CRC populations were analyzed by ad libitum sampling in the laboratory (one set per population), in order to verify the mating behavior and copulation. Due to the gregarious behavior of these SS populations (L.R.P. Paschoal & F.J. Zara personal data), 90 prawns of each population (N: 180) were kept for a month in six aquariums with dark bottoms (45 cm x 25 cm x 30 cm), with basalt gravel as substrate and macrophytes and fragments of rocks for shelter. Each aquarium contained 15 females and 15 males. Male prawns had their cephalothorax marked with a mixture of fast-drying glue gel (Super Bonder Power Flex Gel ® ) and silver purpurin powder. Prawns were acclimated and conditioned to a 12 hour photoperiod and 26 °C (± 0.5). For CAS and SBG populations, showing the presence of males with submissive and dominant morphotypes (see below), and nocturnal and cryptic habits (L.R.P. Paschoal & F.J. Zara personal data), the LS prawns were observed in the field for six hours (18:00 to 0:00 h) at each monthly sample, for observation of pair formation and copulation. For nocturnal observations, LED spotlights (up to 5 m in range) were positioned near to the margins of the aquatic environments. When the copulation success was verified, the pairs were immediately captured with a hand net (0.13 mm mesh). All four morphotypes were examined with regard to mating behavior and reproductive probabilities. After the evaluation of the mating behavior in the populations, the functional SOM in males was established by the smallest CL recorded for the individual captured, showing the necessary characteristics for the successful copulation. The types of mating systems observed in M. amazonicum were analyzed and classified according to Correa & Thiel (2003).
For males of LS populations, the relationship that best demonstrated a clear difference between juveniles and adults, and separated the morphotypes was MCL vs. CL. The morphometric SOM in LS males was estimated at 8.40 mm CL for CAS population, and at 7.40 mm CL for SBG population (Fig. 2 and Table II). The ANCOVA results showed that there were significant differences for the intercepts (a) in all morphotypes of LS populations. However, only the morphotypes CC vs. GC1 in both populations showed differences in slopes (b) indicating that the other morphotypes have similar relative growth rates when compared to each other (Appendix II). Additionally, it was possible to demonstrate that only the GC1 morphotype showed positive allometry for MCL vs. CL relationship (Appendix III). Both LS populations showed similar relative growth parameters and allometric levels, demonstrating the investment in sexual weapons (chelipeds and their articles) (Appendices II and III). On the other hand, in SS males without morphotypes, the TL vs. CL relationship demonstrated the morphometric SOM at 5.30 mm CL in SJB population, and at 6.30 mm CL in CRC population ( Fig. 2 and Table  II). The results of ANCOVA's show that in SJB population, immature and mature SS males have different relative growth rates for almost all morphometric relationships, whereas in CRC population these rates are quite similar (Appendix II). The allometric levels of these populations are similar, showing that adult animals tend to invest less energy for body growth than juveniles (Appendix III).
Similar to LS males, LS females also invested energy on growth of the chelipeds. The relationship that best demonstrated the differences between juveniles and adults was MCL vs. CL. The morphometric SOM was recorded at 10.50 mm CL in CAS population, and at 10.30 mm CL in SBG population ( Fig. 3 and Table II). The results of the ANCOVA's showed that for the SBG females, the growth rates for chelipeds and their articles are divergent along maturation, whereas for CAS females the allometric coefficient rates are similar (Appendix IV). Adult females of both LS populations showed positive allometry for chelipeds and their articles (Appendix V). In females of SS populations, the relationship that best demonstrated the sexual maturity was 2° PL vs. CL. The morphometric SOM was recorded at 7.30 mm CL in SJB population, and at 8.30 mm CL in CRC population ( Fig. 3 and Table II). In both populations, the body growth (TL) is similar between immature and mature females, however they exhibit differences in abdominal pleura width (2° PL) growth rates during the maturation (Appendix IV). Adult females of the SS populations presented positive allometry for the width of the second abdominal pleura (2° PL), while in the LS populations, this condition was registered only in females of the SBG population. In CAS population, females showed negative allometry for this relationship (Appendix V).

Physiological maturity
The smallest size at the onset of physiological (histological) maturity recorded in LS males was 5.70 mm CL in CAS population, and 4.60 mm CL in SBG population, whereas for the SS males it was 3.70 mm CL in SJB population, and 4.00 mm CL in CRC population (Table II).
No anatomical or histological differences were observed in the male reproductive system for studied populations or between the four morphotypes, except for CC males that show a very low concentration of spermatozoa in their   Material -Fig. S2). In M. amazonicum, the reproductive system consists of a pair of testes and vasa deferentia (VD) connected to the gonopores of the coxopodites of the fifth pair of pereiopods ( Fig. 4a-b). The testes exhibit thick anterior lobes arranged over the hepatopancreas or perigastric organ (Fig. 4a), while the posterior lobes are thinner, located below the heart. These organs are connected to the VD, which are arranged laterally in the cephalothorax, connecting to the gonopores of the fifth pair of pereiopods (Fig. 4b). In mature animals, the testes and VD are whitish and quickly identified macroscopically ( Fig. 4a-b). These organs in immature animals are thin, colorless and cannot be distinguished macroscopically. Testes smears from immature animals showed only spermatogonia and the spermatozoa were absent in VD. In physiologically mature males, it is noted by histology that the testes are formed by several seminiferous tubules grouped in lobules with cells in spermatogenesis and spermiogenesis ( Fig. 4c-d), and the VD are filled by secretion and spermatozoa ( Fig. 4e-f). Testes smears and histology in mature animals show typical tack-shaped spermatozoa with a very prominent spike filling the seminiferous tubules, whereas only a small peripheral area of the tubules shows spermatogonia (Fig. 4cd). The seminiferous tubules are surrounded by accessory (Sertoli) cells and involved by connective tissue (Fig. 4d). The VD is divided into three regions: proximal, medial and distal, these regions are differentiated only by the increase of the vessel caliber. All regions show the same histological aspect, vary from squamous to cubic epithelium with basal nuclei enveloped laying on the musculature (Fig. 4e-f). Inside the lumen of VD in physiologically mature animals, a large amount of centrally compacted spermatozoa is surrounded by secretion forming a single sperm mass involved by acidophilic secretion, easily noted in the distal region of the VD, the ejaculatory ducts (ED) (Fig. 4e-f ). This final portion of VD is much dilated (i.e. bulbs of the ED), which have thicker musculature than the other regions (Fig. 4e-f ) and the androgenic glands are arranged perpendicularly to the muscular layer on ED (Fig. 4e). These glands are well-developed in mature animals, whereas in immature animals they are extremely reduced or absent.

testes (Supplementary
The smallest size at the onset of physiological maturity recorded for females of the two LS populations was 6.70 mm CL, while for the two SS populations it was 5.00 mm CL (Table  II). The physiological maturity is marked by the colorimetric and volumetric transformation of the ovaries throughout their development and progressive accumulation of yolk granules in the cytoplasm of oocytes (Fig. 5a-i). The immature ovaries are colorless or translucent before reaching physiological maturity (Fig. 5a). These organs are characterized by the presence of many oogonia, previtellogenic oocytes (meiosis) and oocytes in primary vitellogenesis without mature yolk granules (Fig. 5b-c). At this stage, the oocytes in primary vitellogenesis show a large rounded nucleus with few blocks of heterochromatin dispersed and one or two well evident nucleoli. The cytoplasm is strongly basophilic and may have small vesicles or acidophilic dilatations that characterize the endogenous yolk (Fig. 5b-c). When females attain the physiological maturity, they show for the first time the greenish coloration of the mature ovaries, a macroscopic evidence of sexual maturity in this species (Fig. 5d). This color is due to the presence of oocytes in exogenous (secondary) vitellogenesis, with mature yolk granules accumulated in the cytoplasm (Fig. 5ef). At the beginning of this stage, large follicular cells surround the secondary vitellogenic oocytes. The nucleus becomes smaller, due to the process of compaction promoted by the yolk granules. These granules are acidophilic and few lipid droplets are detected at this stage. The previtellogenic oocytes are still easy to find in the ovary (Fig. 5e). At the end of maturation, the ovaries occupy a large area of the coelomic cavity in the cephalothorax and exhibit an intense greenish coloration (Fig. 5g). At this stage, the oocytes are well-developed and have a larger diameter when compared to the previous stages ( Fig. 5h-i). The main feature of these oocytes is the cytoplasm filled with acidophilic mature yolk granules and many lipid droplets. In this ovarian stage, the oocytes are surrounded by flattened follicular cells and are well adhered to each other, producing a more compact appearance ( Fig. 5h-i).

Functional maturity
In all studied populations, ovigerous females were captured during the 15 months of study, indicating a pattern of continuous reproductive activity. The smallest size recorded for ovigerous females in SS populations was 7.10 mm CL in SJB and 7.40 mm CL in CRC, whereas for LS females the smallest ovigerous had 9.40 mm CL in both populations. It is noteworthy that these females carrying eggs with eye pigmentation, i.e. fertilized eggs. Functional maturity was close to the morphometric maturity, with few ovigerous females captured under to the size estimated for morphological maturity (Table II). Laboratory mating (copulation) experiments carried out with SS populations were characterized by the "pure search" pattern (sensu Correa & Thiel 2003), with no signs of agonistic behavior among males. The animals tended to concentrate in one area and there were no pair formation. Males of this phenotype had functional maturity simultaneously to histological maturity (Table II). Besides that, males with small sizes (CL ≥ 3.70 mm) had a welldeveloped and functional appendix masculina, corroborating the functional maturity. On the other hand, copulations in LS populations were observed only after the pair formation in field. Thirty couples were captured and evaluated in CAS population, while in SBG population 20 couples were analyzed. It was possible to verify that only males with dominant morphotypes (GC1 and GC2) were able to copulate, although submissive males (TC and CC) were more abundant in both populations (morphotypes ratio: 4 TC: 3 CC: 2 GC1: 1 CG2). GC1 and GC2 males were observed near to the margin (up to 2 m) in aquatic environments with sandy sediment, and placed themselves behind or beside (in parallel) of receptive females. Dominant males protected and guarded females before and after copulation, and it was common to observe agonistic behaviors (fights) between males with hypertrophied chelipeds. During these fights, the male elevated its pereiopods and the anterior portion of the body, and attacked its opponent with the dactyls of the second pair of chelipeds. Commonly, this event was short ranging from three to fifteen seconds ( -X : 12 ± 3 seconds). Sneak copulation strategy was not observed in the LS populations during the 15 months of sampling. The mating system of these populations has the "neighborhoods of dominance" pattern (sensu Correa & Thiel 2003). The smallest size of males in LS populations captured after the observed copulation was 14.40 and 15.20 mm CL for CAS and SBG, respectively (Table II).

DISCUSSION
The populations of Macrobrachium amazonicum analyzed in this study showed very distinct morphological and reproductive characteristics, indicating the great environmental adaptability and wide phenotypic plasticity of the species. Intraspecific variation of the reproductive strategy and SOM maximizes the reproductive success of the species in different aquatic environments (Odinetz-Collart 1991).
In two of the four populations analyzed, both adult males and females exhibited large body proportions, and these animals spent energy for the growth of chelipeds (i.e. largesize phenotype). In addition, the presence of morphotypes in males of these populations was verified through the analysis of this morphometric variable (MCL). In general, males of the genus Macrobrachium have higher body proportions than females, since they tend to invest more energy for somatic growth and the development of robust chelipeds (i.e. sexual weapons), increasing the success in intra/interspecific competitions (Correa & Thiel 2003, Moraes-Riodades & Valenti 2004, Paschoal & Zara 2018. The pronounced sexual dimorphism in M. amazonicum with the presence of social hierarchy confers adaptive advantages for dominant males (GC1 and GC2), such as: more success at obtaining food resources and dominating territories (Correa & Thiel 2003, Ibrahim 2011, and access to females available for mating, as observed in the present study. Thus, animals with larger sizes and robust sexual weapons would have greater reproductive success, explaining the positive allometric growth for MCL registered only for the GC1 morphotype. Since the morphotype development is sequential, it could be raised that animals with GC1 morphotype will concentrate more energy for the acquisition of sexual weapons during the passage to the morphotype GC2, and after entering in this final morphotype they cease the somatic growth, allocating energy only for the maintenance of metabolic processes (Moraes- Riodades & Valenti 2004, Augusto & Valenti 2016. On the other hand, the increase of chelipeds size in females from LS populations would be related to the optimization of the reproductive events, as mating choices, protection and maternal care for hatching and spawning (Viau et al. 2006).
Currently, only the study of Pantaleão et al. (2014) found morphotypes in males of M. amazonicum from inland populations (Tietê River Basin, São Paulo -southeastern Brazil), being the present work the second record of this condition. These same authors estimated the morphometric SOM in males with morphotypes at 8.8 mm CL, a higher value than recorded here. However, the functional maturity analyzed here in populations with morphotypes was recorded with significantly higher values, showing that neither the physiological nor the morphological maturities actually express the moment when the LS males are able to copulate and transfer their gametes and/or defend females and territories. Regarding females, there are no studies evaluating morphometric maturity in populations with dominant morphotypes from inland waters or using the same methodology used here, which hinders comparison with other populations. However, the morphometric SOM in LS females is similar among the studied populations.
The absence of morphotypes, the lower energy investment for somatic growth and, consequently, the smaller body sizes were the main characteristics of males from the other two studied populations (i.e. small-size phenotype). However, the females of these populations invest energy for the growth of the second abdominal pleura. This pattern is typical in caridean shrimps that adopted the "pure search" mating system, where males that do not protect or defend females invest energy for the production of gametes by shifting the energy that would be used for body growth, while females accumulate energy for the growth of the brood chamber (abdomen and pleuras) optimizing the fecundity and protection of embryos (Bauer 2004, Paschoal et al. 2013. Pantaleão et al. (2012) also analyzed the morphometric aspects of small-size phenotype of the Amazon River prawn from inland environments (Tietê River Basin, São Paulo -southeastern Brazil). As recorded here, these authors did not register morphotypes in males, correlating the absence of morphotypes in SS populations to the fish predation and/ or to the adoption of "pure search" mating system. Pantaleão et al. (2012) estimated the morphometric SOM for this species at 4.26 mm CL for males and 5.39 mm CL for females. These values are lower than those recorded in the present study. It can be verified that the morphometric maturity estimated here, when compared to the other criteria of maturity (physiological and functional) shows higher values, overestimating the SOM in M. amazonicum. Males of SS populations are mature and functional even with small sizes, thus the analysis of sexual maturity in M. amazonicum should take into account the general phenotype of the population. The wide variability of SOM values would justify the use of the physiological maturity in populations without morphotypes, because this is similar to functional maturity.
The male and female reproductive systems of M. amazonicum show the anatomical organization similar to that commonly described for gonochoric caridean shrimps (Sandifer & Lynn 1980, Bauer 2004). Histologically, it is possible to verify that the reproductive systems of the Amazon River prawn are similar to the other species of the genus Macrobrachium (Chow et al. 1982, Sagi et al. 1988, Mossolin & Bueno 2002, Poljaroen et al. 2010, Soonklang et al. 2012. In both sexes of M. amazonicum, the physiological maturity anticipates the others maturities and is attained at small sizes (CL) within the analyzed populations. This shows that in these animals the physiological and morphological maturities are not synchronized, and they need their reproductive systems fully functional before the pubertal molt. This pattern is similar to that of other species of the genus Macrobrachium (Chow et al. 1982, Sagi et al. 1988, Mossolin & Bueno 2002, Poljaroen et al. 2010, Soonklang et al. 2012) and some brachyurans (Zara et al. 2012, Nascimento & Zara 2013. However, it is the opposite of that recorded for some aeglids (Viau et al. 2006) and penaeid shrimps (Heckler et al. 2013), where the morphological maturity anticipates the physiological maturity. In M. amazonicum, males become physiologically mature before females, and this may be associated with the short lifespan of male prawns. Gavio et al. (2006) and Paschoal et al. (2016) suggested that the caridean males reach their optimal reproductive condition at small sizes and are capable to copulate with larger females, but they disappear from the population due to the low longevity, while females with longer life spans remain in the population and continue to grow.
Only males with GC1 and GC2 morphotypes were able to copulate. Also, the sneak copulation was not observed in the LS populations of M. amazonicum. Ra'anan & Sagi (1985) suggested that the high frequency of large prawns in populations favors small sneaking males, since dominant males will be occupied with fights and territorial protection, which consumes a large amount of energy and time. However, if the frequency of dominant males is low (as observed in the present study), their relative reproduction advantage over the submissive males increases, promoting a reproductive-dominance hierarchy (i.e. only dominant males are capable to mate and copulate). The mating system that best fits the LS populations of M. amazonicum would be the "neighborhoods of dominance" (sensu Correa & Thiel 2003), which would explain the high values of functional maturity recorded for males of these populations. Dominant males (GC1 and GC2 morphotypes) of these populations have hypertrophied chelipeds and it is possible to observe that these animals protect and guard females during the mating period. Moreover, these males destined a smaller portion of energy to sperm production, while a greater portion is directed to somatic growth and the production and maintenance of sexual weapons, increasing the fitness and improving the success of males in intraspecific competitions (Moraes-Riodades & Valenti 2004, Paschoal & Zara 2018. In contrast, males from the SS populations invest much less energy for somatic growth leading to absence of sexual weapons. However, they attain physiological and functional maturities at smaller sizes when compared to animals of LS populations, indicating that the energy that would be spent on growth is better used in reproductive events, such as sperm production (Paschoal et al. 2016, Paschoal & Zara 2018. Additionally, SS males are gregarious, without display both agonistic behavior and female guard. Thus, the mating system of SS populations has the "pure search" pattern (sensu Correa & Thiel 2003). In all populations of M. amazonicum analyzed, few ovigerous females (i.e. functionally mature) were captured under to the size estimated for morphometric maturity, indicating that there is synchronization between morphological and functional maturities in females. Thus, the use of relative growth or the evaluation of the smallest ovigerous female is indicated to estimate the SOM in female palaemonid shrimps, as suggested by Paschoal et al. (2013Paschoal et al. ( , 2016.

CONCLUSIONS
The use of morphometric data showed to be a useful tool for the determination of distinct phenotypes and population stocks in M. amazonicum. The three criteria used for the evaluation of sexual maturity showed that, in both sexes, physiological maturity anticipates the others and that males reach sexual maturity in smaller sizes than females in all criteria, except for functional maturity in males of LS populations. The development of chelipeds (sexual weapons) in males, in addition to change the mating strategies in M. amazonicum, modulated the SOM in this species, since LS prawns needed robust chelipeds for pairing and copulation success. Thus, the sequential scheme of sexual maturity in M. amazonicum may be summarized as: ♀ -physiological → functional ≅ morphological, ♂ LS -physiological → morphological → functional, and ♂ SSphysiological = functional → morphological. The sexual maturity in M. amazonicum varies from one criterion to another, as well as between the two evaluated phenotypes, so we suggest that the best criterion used to estimate the SOM for the maintenance and preservation of the Amazon River prawn stocks is that registered with the highest value of CL. The information presented here may also be used in the evaluation and maintenance of farmed specimens and breeders, improvement of stocks, assessment of temporal series of breeders, as well as may be used in studies involving the population biology of the species in freshwater environments.