Population biology of Uca mordax ( Smith , 1870 ) ( Crustacea , Decapoda , Ocypodidae ) from the southeastern coast of Brazil [ I ] Biologia populacional de Uca mordax ( Smith , 1870 ) ( Crustacea , Decapoda , Ocypodidae ) do litoral sudeste do Brasil

[a] Biologist, Msc., Departamento de Zoologia, Universidade Estadual Paulista (UNESP), Botucatu, SP Brasil, e-mail: vifransozo@ibb.unesp.br [b] Biologist, Msc., Departamento de Zoologia, Universidade Estadual Paulista (UNESP), Botucatu, SP Brasil, e-mail: rafamortari@hotmail.com [c] Biologist, Doctor, Museu de Zoologia, Universidade de São Paulo (MZUSP), São Paulo, SP Brasil, email: alinebenetti@usp.br


Introduction
Morphological changes in crabs of the genus Uca Leach, 1814 have been reported by many authors (1,2,3,4,5,6,7).According to (8), the variations in the growth pattern of certain organs or their parts relative to others in the same individual, or the differences between sexes within one same species as well as among different species, have biological signifi cance.Such changes can mainly occur in the chelipeds, abdomen and pleopods of crabs and are more evident between sexes and juvenile vs. adult phases (9).
The onset of sexual maturity is a biological event of great importance for crabs since it is marked by a series of morphological and physiological transformations, which lead to habit and/or behavioral changes (10).Thus, such stage should be assessed in populational studies (11), considering the great inter or intraspecifi c variations.
The structural characterization of a population provides basic information about the management of natural resources.In the last twenty years, papers about population biology have been more accepted by the researchers.Learning the biological and ecological aspects of a species (juvenile recruitment, growth rate, and size at onset of sexual maturity) provides more information on its birth rate, mortality, growth, migration, and reproduction (12,13).
Population biology of Uca mordax (Smith, 1870) (Crustacea, Decapoda, Ocypodidae) from the southeastern coast of Brazil 25 The normality of distributions was tested through Shapiro-Wilk test (α = 5%) (19) and the homoscedasticity by means of Levene test (α = 5%) (19).Recruitment was defi ned as the juvenile rate in each season, considering juveniles those specimens of smaller size than that at the fi rst sexual maturity for each sex, which was obtained through the allometric technique.The juvenile rate was compared among seasons by using multinomial proportion test complemented with Tukey's test (MANAP; α = 5%) (23).
Sex ratio was analyzed for each month and size class.A chi-square test for goodness of fi t (X²; α = 5%) (19) was used to evaluate the sex ratio and compare the monthly percentages of males and females.

Results
During the sampling period we obtained 1,085 U. mordax specimens, of which 557 were males and 528 females (14 ovigerous crabs).For relative growth assessment and size determination at the onset of sexual maturity, only 372 males and 280 females were used as they were in intermolt stage and had no defective body parts or appendages.
Total crab size varied from 4.9 to 22.9 mm (15.9 ± 2.7) CW for males and from 4.3 to 20.8 mm (14.6 ± 2.8) CW for females.The smallest ovigerous females were 12.9 mm CW, whereas the largest ones measured 20.8 mm CW.
Males reached larger mean sizes (16.4 mm) than females (15.3 mm) (p < 0.05).The rate of males with greater chelipeds on the right side was 51.75 % (p > 0.05).All the obtained relationships between body parts were tested to determine the size at the onset of sexual maturity and those showing the best adjustment and most clear change from juvenile to adult phase were: CW vs. PL for males and CW vs. AW for females.
Males became sexually mature at 11.9 mm CW and females at 11.5 mm CW (Figure 1).The allometric equations for U. mordax are presented in Table 1.
The frequency distributions by size classes per season are represented in Figure 2. Juveniles were present throughout the year but at higher frequencies during the winter and autumn (Figure 3), indicating a recruitment period in such seasons. of capture per unit effort by 2 collectors for 30 min during low tide periods.
Itamambuca mangrove is characterized by mangle vegetation composed exclusively of Laguncularia racemosa (Linnaeus).According to (17), tree density in Itamambuca reaches 1,250 trees per hectare, with a mean height of 4.8 m and mean diameter at breast height of 6 cm.The substratum is composed of poorly sorted medium sand and the organic matter content in the sediment is higher than that in other sites of the same region (Ubatuba, São Paulo State) (18).
All obtained specimens were separated according to sex and ovigerous conditions.Then, a precision caliper (0.01 mm) was used for the following measures: carapace width (CW), carapace length (CL), abdomen width (AW), propodus length (PL) and propodus height (PH) for both sexes, and gonopod length (GL) for males.In males, we measured the major cheliped and in females, the right one.
The handedness of the major cheliped was also recorded and tested by chi-square test (α = 5%) (19).
The mean size of specimens (CW) was compared between sexes and the mean size of the major cheliped (PL), between right and left sides through Mann-Whitney test (α = 5%) as data was not normally distributed (19).Specimens in preand post-molt stage, with defective carapaces and without some appendages, were not included in this part of the study.
The fi rst maturation of U. mordax was determined through the alometric technique, using the software Mature I and Mature II (20,21).The algometric equation Y = aX b (22) was adjusted to the dispersion points of juvenile and adult crabs.
Carapace width (CW) was adopted as the independent variable (X) and related to other body dimensions (dependent variables -Y): CL, AW, PL, PH, and CG.The allometric coeffi cient (b) represents the allometric degree of the studied body part.The statistical signifi cance of the allometric coeffi cient was verifi ed through Student's t-test at 5% level (H 0 : b = 1).Then, all the obtained equations were linearized.The intercepts and the slopes of the straight lines in each development phase were compared by means of covariance analysis (α = 5%) (19).
The population structure was analyzed by season, grouping the data into 10 CW size classes (2 mm wide) according to demographic categories.values are slightly lower than those obtained in the present study (22.9 mm CW for males and 20.8 mm CW for females).At sexual maturity, males had similar sizes in both places but females from Itamambuca, São Paulo State, were larger (11.5 mm CW) than those from Guaratuba, Paraná State (8.77 mm CW).The size of the smallest ovigerous females from Itamambuca (12.9 mm CW) was similar to that at sexual maturity, according to the mean relative growth (11.5 mm CW), supporting our results.Size differences between these two U. mordax populations may be due to latitude effects, as stated by (26).Such effects could also be caused by the differences in the food availability and habitat features (7,17).
Sex ratio did not differ among months (p > 0.05), except for January 2002 (p < 0.05) (Figure 4).As regards size classes, females predominated in the initial classes, whereas males prevailed in the intermediate and fi nal classes, except in class 20-22 mm CW (Figure 5).

Discussion
Sexual maturity represents an important biological event characterized by morphological and physiological changes that can be caused by environmental or behavioral alterations (10).
As mentioned by ( 24) and ( 25), the relationships CW vs. PL and CW vs. AW for males and females, respectively, best evidenced the morphological sexual maturity of crabs, which can be exemplifi ed by the U. mordax population in Itamambuca mangrove.
Uca mordax population in Guaratuba Bay, studied by (16), reached the maximum sizes of 20.0 mm CW (males) and 18.5 mm CW (females).These   Allometric studies performed by ( 28), ( 29) and (2) demonstrated that throughout the ocypodid life cheliped growth in males has a direct relationship with morphological sexual maturity.This is also observed in U. mordax, which shows a positive allometry concerning the relationship CW vs. PL.
Abdominal width growth is generally used to characterize the sexual dimorphism in representatives of the infraorder Brachyura.Similarly to U. mordax, the relationship CW vs. AW in males has presented negative allometry, since these structures have the function of protecting the gonopods in males (30).A similar pattern was found in U. burgersi by (31), Eriphia gonagra (Fabricius, 1781) by (32) and Goniopsis cruentata (Latreille, 1803) by (33).
When U. mordax mean size is compared between sexes, females show to have a smaller maximum size, probably because they spend a reasonable amount of energy for reproductive purposes (34,35), whereas males invest their energy in somatic growth, consequently reaching higher sizes.Such difference could also be related to cohort and agonistic behavior, as reported by others (36,37).
According to (3), the frequency distribution of cheliped laterality can vary with the population structure.In the present paper, the percentage of right chelipeds was higher but not statistically signifi cant, which was also observed by (38) and (39).
Broad-front fi ddler crabs are known to incubate their eggs inside burrows in order to protect them against extreme environmental conditions, favoring embryonic development and larval hatching synchronically (40).A small number of U. mordax ovigerous females (11) were captured during this study and most of them were found inside burrows, suggesting they keep buried while incubating.
Uca mordax recruitment showed to be continuous throughout the studied period, presenting an elevated frequency of juveniles in the autumn and winter.Such fact was also observed by (27), who mentioned that juveniles become adults during the coldest months of the year in the northern coast of São Paulo State.
The proportion of male and female crabs tends to be very close to 1:1.However, such relation can be infl uenced by a series of factors, such as life span, migration, mortality, differential growth, and sex change (40).Nevertheless, U. mordax sex ratio did not present statistical difference over seasons, except during the summer.

Figure 1 -
Figure 1 -U.mordax.Dispersion points and adjusted curve for the relationship CW vs. PL for males (A) and CW vs. AW for females (B) (closed cycle = juvenile males and females; open cycle = adult males and females; CW = carapace width; PL = cheliped propodus length; AW = abdomen width) Source: Research data.

Table 1 - 27 Figure 2 -
Figure 2 -U.mordax.Frequency distribution histogram by size classes carapace width (mm) in each demographic category Source: Research data.

Figure 3 -
Figure 3 -U.mordax.Recruitment ratio of U. mordax in the Itamambuca mangrove throughout a year period.Bars with at least one same letter in common did not differ statistically (p > 0.05) Source: Research data.

Figure 4 -
Figure 4 -U.mordax.Sex ratio by months for population from Itamambuca.Asterisks above the columns indicate signifi cant differences between the proportions of males and females (p < 0.05) Source: Research data.

Figure 5 -
Figure 5 -U.mordax.Sex ratio by size classes of carapace width (mm) for population from Itamambuca.Asterisks above the columns indicate significant differences between the proportions of males and females (p < 0.05) Source: Research data.