Growth parameters and age estimates of the mouthless crab, Cardisoma crassum Smith, 1870 (Brachyura: Gecarcinidae) from the Montijo Gulf, Pacific coast of Panama

Abstract

The asymptotic carapace width (L _∞ ) and growth coefficient (k) parameters of the mouthless crab, Cardisoma crassum, were estimated, and the von Bertalanffy growth function was fitted to predict mean crab carapace width at different ages. From November 2014 to September 2015 and January 2021 to February 2024, a total of 967 crabs were sampled from five mangrove sites within the Montijo Gulf, Pacific coast of Panama. The modal decomposition method was applied to identify age groups, where the best model fit was obtained with eight age classes and the parameters: L _∞ = 91.51 mm, k = 0.24 year^-1, and L ₁ = 17.14 mm. Mean carapace width was 60.89 ± 7.70 mm with corresponding ages between 4.69-4.82 years. The estimated t _max was 12.81 years, corresponding to a carapace width of 86.96 mm, while the age at first maturity was estimated at 4.77 years, with a corresponding carapace width of 61.01 mm. The L _∞ exceeded the maximum observed carapace width (88.30 mm), suggesting that crabs can attain larger sizes than those observed. This is the first systematic estimate of growth parameters and age in C. crassum from the Montijo Gulf, providing valuable information for future management of this fishery resource.

Keywords:
Biometry; carapace width; fishery; land crab; maturity; modal decomposition

INTRODUCTION

Crustaceans play a significant role in the world's fisheries; however, they are under increasing pressure from growing human populations, particularly in developing tropical and sub-tropical nations (De Boer and Longamane, 1996; Krause et al., 2001; Macintosh et al., 2002; Boenish et al., 2022). Among these, land crab fisheries hold significant importance, e.g., serving as a crucial source of protein for coastal communities (Krause et al., 2001; Baine et al., 2007). All crabs of the family Gecarcinidae MacLeay, 1838 are highly adapted land crabs, represented by seven genera and 27 species (Ng and Ng, 2021; Ng and Shih, 2023). Within this group, the mouthless crab Cardisoma crassum Smith, 1870, a common inhabitant of higher mangrove forests in the Panamanian Pacific (Fig. 1), holds significant socio-economic importance in the eastern Pacific region; however, the status of its populations has received limited attention, and its fishery remains unregulated (Vázquez-López and Ramírez-Pérez, 2015; Vega et al., 2018; Lombardo and Rojas, 2022; De León et al., 2023; Lombardo and Cedeño, 2023).

Figure 1.
Location of Cardisoma crassum sampling sites within the Montijo Gulf, Veraguas, Panama. Montijo (MO), Ponuga (PA), Rio de Jesús (RJ), Calabazal (CB) and Hicaco (HI). Scale bar = 10 km.

Most gecarcinid crabs are extracted for subsistence in coastal communities (Hendrickx, 1995), where capture methods are manual and the fishing gear is artisanal (Vázquez-López and Ramírez-Pérez, 2015; Vega et al., 2018). Learning about the impact of extraction in C. crassum is important since stocks under non-industrialized extraction methods can still be driven to overexploitation (Lima et al., 2021; João et al., 2022). Despite their socio-economic significance, C. crassum population studies in Panama are lacking. This scenario raises concerns, as the estimation of growth parameters and the availability of population data are crucial for adequate resource management, as has been demonstrated in a closely related species, Cardisoma guanhumi Latreille, 1828 (Cardona et al., 2019; Govender, 2019; Schwamborn and Moraes-Costa, 2021; Santos et al., 2022).

The parameters from the von Bertalanffy growth function (von Bertalanffy, 1938) in C. crassum were studied in a population of El Salado, Jalisco, Mexico (Molina-Ortega and Vázquez-López, 2018); however, age data or its estimates have not been published yet. Except the above-mentioned study, no other research has aimed to support the fishery management of C. crassum through fitting the von Bertalanffy model to biometric data.

Successful population management requires an understanding of the rate at which crabs grow and mature (Corgos and Freire, 2006). This involves estimating the age of crabs, which in turn allows to identify the connections between individual size, maturity, and age (Pauly, 1983; Sparre and Venema, 1998; Pauly and Froese, 2014). Ageing crabs is complicated due to molting and the lack of growth marks in hardened structures. Alternatively, length-frequency analysis, growth models based on modal analysis of size structures, intermolt duration, and size increments during molting have gained wider acceptance for age determination (Vogt, 2012; 2019; Becker et al., 2018). These methods provide relative age estimates, which are important not only in an academic context but they also serve as the basis for determining growth rate (k), mortality rate (M), recruitment (R), and population dynamics. As a consequence, age determination is among the foremost influential biological factors for stock evaluation and management (Vogt, 2012; Pauly and Froese, 2014; Boenish et al., 2022).

Direct ageing methods cannot be applied to C. crassum because decapods in general lack structures that retain a record of growth episodes (Hartnoll, 2001; Vogt, 2012). However, insights into its growth rate and longevity can be derived from length-frequency analysis, as demonstrated in the closely related species C. guanhumi, which exhibits slow growth (k = 0.12 year^-1) and may live up to 20 years (Schwamborn and Moraes-Costa, 2021; Vogt, 2012; 2019). Similarly, analyzing the length-frequency distributions of C. crassum may provide estimates of its growth parameters and relative age. Such estimates depend on the recognition of modes in the size distribution, which can be paralleled with year classes or recruitment cohorts (Hartnoll, 2001), which provides information on cohort survivorship over time and species longevity (Vogt, 2012; 2019).

Understanding the growth parameters and age estimation of C. crassum is important, not only for safeguarding the species and managing its fisheries but also for upholding their essential role in the intricate balance of mangrove ecosystems. This involves activities such as turning over organic material (Robertson, 1986) and influencing soil through biological activity (Smith et al., 1991; Green, 2004 a ; Perger et al., 2013). Additionally, in Panama, C. crassum is also celebrated as an iconic figure in folkloric festivals (Lombardo, 2024). Thus, the present study aims to utilize modal analysis of length-frequency distributions and the von Bertalanffy growth function (vBGF) to establish fundamental growth parameters and estimating age groups of C. crassum from the Montijo Gulf, Panamanian Pacific.

MATERIAL AND METHODS

Study site and sampling procedure

The Montijo Gulf is a RAMSAR site of significant ecological and international importance, covering an area of 808 km² (RAMSAR, 2023). According to Köppen's classification, the Gulf of Montijo’s climate is humid-tropical (Beck et al., 2018). The gulf is characterized by precipitation exceeding 2,500 mm^-yr and temperatures varying between 24.8 and 35.9 °C (Vega et al., 2014; 2021).

Five sites within the Montijo Gulf were selected for sampling of the C. crassum population in Veraguas, Pacific coast of Panama (Fig. 1). At each sampling site, crab burrows were selected based on a combination of occupancy confirmation and indicators of recent activity at the entrance of burrows. These indicators included fresh mud, footprints, fecal pellets, and/or torn plant materials at the entrance (Lombardo and Rojas, 2022). Artisanal wooden traps (Fig. 2 A ) were deployed during the early morning hours (6:00 a.m.). These traps were baited with raw yuca (Manihot esculenta) to attract crabs, and were hourly checked for caught crabs until 4:00 p.m. After 4:00 p.m., the traps were left baited overnight and inspected the next morning. Once crabs were captured, a digital Vernier caliper (0.1 mm) was used to measure the carapace width (CW), their sex was determined by the abdomen shape (Hendrickx, 1995), and the reproductive status of females (ovigerous or not) was recorded. To avoid resampling, individuals received a mark with fast-drying white enamel paint; all crabs were returned to their original burrow.

Our dataset consisted of a total of 967 crabs. Biometric data for 337 crabs from Montijo (MO) were obtained from Vega et al. (2018), while an additional set of 32 crabs was measured by the author at the same location in October 2023. In Rio de Jesús (RJ), 42 crabs were sampled in November 2022 and 72 in January to February 2024. From Ponuga (PA), 161 crabs were sourced between January and June 2021, 141 from February to June 2022, and 72 in August 2023. Calabazal (CB) yielded 74 crabs between November and December 2023, while in Hicaco (HI) another 36 specimens were measured in February 2023. Descriptive statistics were computed, and Chi-square tests were conducted to analyze sex ratios, along with male-female CW t-tests.

Growth parameters and age estimation

The MCCT model “Modelo de crecimiento por componentes de tallas” (Canales and Arana, 2009) was applied to estimate the L _∞ and k parameters in a linear model. Through iterative calculation, this form of the von Bertalanffy growth function (vBGF) was fitted to C. crassum CW data to predict the mean CW of crabs at various ages. Model parameters L _∞ and k were estimated through modal decomposition of size structures, where each modal component was assumed to represent an age group (Pearson, 1894). Following Macdonald and Pitcher (1979), our size structure i was assumed to include “k” modal components (na age distributions). Under this assumption, the probability density function f _i (x) describes the distribution of the i-th individual component. Consequently, the overall probability density function g(x), suitable for samples drawn from the mixed population, can be expressed as:

$$g\left(x\right)={\pi }_1{f}_1\left(x\right){+}_{\cdots }+{\pi }_k{f}_k\left(x\right)$$ (eq. 1)

where π_i is the relative abundance of the i-th modal component as a proportion of the total population, and must therefore fulfill the following constrains:

$$1\ge {\pi }_1\ge \left(i={1,}_{\cdots },k\right)$$ (constr. 1)

$${\pi }_1{+}_{\cdots }+{\pi }_k=1$$ (constr. 2)

To identify individual modal components, we considered components with similar functional form but differing means and variances. In principle, the probability density function is:

$$f_i\left(x\right)=f\left(x|{\mu }_i,{\sigma }_i\right)$$ (eq. 2)

where μ_i and σ_i represent the mean and standard deviation, respectively, of the i-th modal component distribution. Age groups within the size structure were characterized using modes from normal distributions, with constrains for the standard deviation and the means:

$$f\left(x|\mu ,\sigma \right)=({2\pi {\sigma }^2)}^{-\frac{1}{2}}exp\left\{-\frac{1}{2}\left[\left(x-\mu \right)/\sigma \right]²\right\}$$ (eq. 3)

$${\sigma }_i>0\left(i={1,}_{\cdots },k\right)$$ (constr. 2)

$${\mu }_1<{\mu }_2{<}_{\cdots }<{\mu }_k$$ (constr. 3)

By imposing the constraint on the means, the multiplicity of parallel solutions to the number of modal components can be avoided, allowing for detection of modal groups with high degree of accuracy. This is the case, provided no two distinct sets of parameter values (π_k , μ_k , σ_k and x_n ) can produce the same mixed probability density function g(x). These constraints are naturally occurring in age-size analyses of fisheries, ensuring that restrictions are realistic and not overly speculative (Macdonald and Pitcher, 1979).

Modal decomposition was implemented as indicated in the Elefan I package (Pauly and David, 1981) and the Mix algorithm (Macdonald and Pitcher, 1979), which were programmed and solved in Matlab (v. 6.5) by Canales and Arana (2009) to create the MCCT routine, under the maximum likelihood principle (Sparre and Venema, 1998). In our analysis, the compiled MCCT routine was run in RStudio (v. 2023.06.0+421) using an executable file provided by C. Canales.

While running the MCCT, it is assumed that the size structure i is composed by na age distributions, as mentioned before, each conforming to a normal density distribution whose mean size characterizes each age group. Thus, in each age group a, the mean carapace width is defined by the following equation:

$${\stackrel{-}{L}}_a=L_{\infty }\left(1-{exp}^{-k}\right)+{exp}^{-k}{\stackrel{-}{L}}_{a-1}$$ (eq. 4)

where L_∞, k and L₁ (first age group modal size) are unknown parameters. Accordingly, the proportion of crabs at size l belonging to the a-th age group (p_l,a ) is equivalent to a normal distribution (eq. 5), where the relative abundance of the modal components corresponds to a proportion of the total population; thus, the mean and standard deviation σ of such normal distribution can be determined, and are hypothetically proportional to the mean modal CW ( 𝐿 𝑎 ) by way of the variation coefficient (VC):

$$p_{l,a}\approx N\left({\stackrel{-}{L}}_a,{\sigma }_a^2\right)$$ (eq. 5)

$${\sigma }_a=VC{\stackrel{-}{L}}_a$$ (eq. 6)

The size composition of each age group is represented as:

$${\widehat{f}}_{l,a,i}={\pi }_{a,i}\times p_{l,a}\times n_i$$ (eq. 7)

$$\sum _a^{na}{\pi }_{a,i}=1$$ (eq. 8)

π_a,i is the proportion of crabs making up each modal age group; n is the sample size observed in the i-th size composition. The i-th sample size composition was estimated by adding over each modal component as follows:

$${\widehat{F}}_{l,i}=\sum _a^{na}{\widehat{f}}_{l,a}$$ (eq. 9)

Growth parameters, the variation coefficient, and proportion of individuals in each age group were computed while reducing as much as possible a log-likelihood function (Canales and Arana, 2009). The multinomial distribution for the log-likelihood estimator used an effective sample size (nm = 250) that varied in proportion to the observed sample size of the i-th size composition.

$$logL=nm\sum _l\sum _t{\dot{f}}_{l,t}log\left({\widehat{f}}_{l,t}\right)+\sum _i{\left(\frac{log\left(\theta \right)-log\left({\theta }_{prior}\right)}{{vc}_{\theta }}\right)}^2$$ (eq. 10)

The penalty term to the right in Equation 10 works as a constraint on the probable values of the modeled asymptotic length through quadratic loss around the reference seed values in Table 1. After determining the parameter vector, a retro-calculation applying Equation 4, solved for L_a-1 was used to assess the lower bound for the modal size of a zero-year-old crab.

$$L_{a-1}=\frac{L_a-L_{\infty }\left(1-{exp}^{-k}\right)}{{exp}^{-k}}$$ (eq. 11)

This process facilitated the subsequent assignment of age within the ensuing modal components. The assignment was executed by calculating the von Bertalanffy t₀ parameter to create a curve, establishing age-at-carapace width.

$$t_0=t+\left(\frac{1}{k}\right)ln\left(\frac{L_{\infty }-{\stackrel{-}{L}}_a}{L_{\infty }}\right)$$ (eq. 12)

$$L_a=L_{\infty }\left(1-{exp}^{-k\left(a-t_0\right)}\right)$$ (eq. 13)

The age at which crabs approximate their maximum size was computed according to Taylor (1958), using the t₀ and growth rate constant k as follows:

$$t_{max}=t_0+\left(\frac{3}{k}\right)$$ (eq. 14)

Since females bear their egg mass externally (Fig. 2 B ), we could confidently assess their size at sexual maturity. In contrast, males do not display external signs of maturity, making it challenging to determine their sexual maturity based on size alone (Lombardo and Cedeño, 2023). According to Charnov and Berrigan (1990) and Charnov (1993), an approximation of the size at first sexual maturity in males would occur when individuals reach 2/3 of their asymptotic length. The model estimate for potential size at first maturation was tested against the carapace width of egg-carrying females collected in the field to approximate the size and age of females at first sexual maturity.

Figure 2.
Artisanal wooden trap (A) and Cardisoma crassum ovigerous female (B) captured in the Montijo Gulf, Veraguas, Panama. The wooden trap measures 25 cm (L) × 13 cm (W) × 15 cm (H), and the female carapace width is 65.46 mm.

To run the MCCT model, the relative length-frequency of crabs in the range of observed size classes was entered in rows representing the number of size compositions. In this case, 12 months of data were pooled into four size compositions of three months each to stabilize the sample size. The size intervals were set to three millimeters, ranging from 20-89 mm CW, which included the entire size distribution of the collected specimens. The columns represented 24 size intervals, while the number of possible annual size classes was progressively adjusted starting with six (see Schwamborn and Moraes-Costa, 2021), using C. guanhumi as reference. The best iteration of the MCCT routine was determined by the smallest Log‐likelihood (LL) and Akaike’s criterion (AIC) between the possible number of annual classes. To rule out artifacts stemming from the correlation between L_∞ and k (Gayanilo et al., 1996) and to evaluate the likelihood and potential emergence of multiple local maxima during the fitting of the vBGF, the contour of the likelihood function was plotted over different combinations of L_∞ and k (Schwamborn et al., 2019). The objective was to identify the L_∞ and k values at the center of the contour plot that maximized the likelihood function, thereby indicating the best fit of the model to the observed data. Although length-frequency distributions were obtained from monthly data, k was estimated on an annual scale to minimize short-term variability from monthly catch differences. This approach is reasonable because the data collectively comprise 12 months and aligns with common practice, facilitating comparison with studies where k is typically expressed annually (Macdonald and Pitcher, 1979; Schwamborn and Moraes-Costa, 2021).

The initial parameters (Tab. 1) for the vBGF include the intercept 𝐿 ∞ 1− 𝑒𝑥𝑝 −𝑘 and slope 𝑒𝑥𝑝 −𝑘 terms from Equation 4, which were adjusted to control the standard deviation variability (VC) in each age group. Although the intercept and slope depend on L_∞ and k, fixing either the intercept or slope to zero, allows for the controlled isolation of the effects of the other parameter on the VC. This approach enabled the testing of two hypotheses by fixing one parameter to zero while allowing the other to vary. The first hypothesis suggests that if the intercept is fixed at zero and the slope is allowed to vary (Eisenhauer, 2003; Legendre and Desdevises, 2009), the standard deviation would increase with longevity and be proportional to the average CW. This implies that the growth of individuals might not be dependent on age, but rather on their size (CW). The second hypothesis posits that if the slope is fixed at zero, the standard deviation would decrease constantly with age and be independent of average CW. This means that the growth rate may not be dependent of size, but rather of age. No assumption on size when age is zero was made under this scenario (Corgos and Freire, 2006; Ogle and Isermann, 2017).

Table 1.
Initial parameters for the von Bertalanffy growth function in Cardisoma crassum from length-frequency data obtained from specimens collected in the Montijo Gulf, Veraguas, Panama. VC and EP represent the variation coefficient and the parameter estimation phase, respectively. The asymptotic carapace width is L_∞ , and the modal carapace width of the first age group is L₁ , both in millimeters. The annual growth coefficient is k, while L_∞ (1 - exp^-k ) and exp^-k represent the intercept (INT) and slope (SLP) terms, respectively.

Size composition	N	Prior values	L ∞	k -y	L 1	INT	SLP
Jan.-Mar.	279	Input	90.00	0.30	14.00	3.1	0
Apr. -Jun.	341	VC	0.05	0.30	0.20	0.10	0.20
Jul. -Sept.	135	EP	4	2	3	1	-4
Oct. -Dec.	212	‐	‐	‐	‐	‐	‐

RESULTS

The average CW from a total of 967 individuals was 60.89 ± 7.70 mm, with the largest and smallest crabs measuring 88.30 and 22.74 mm CW, respectively. The sample contained 564 males (61.38 ± 8.52 mm CW) and 403 females (54.27 ± 9.88 mm CW), where the males were larger (t = 5.46, d.f. = 963, p < 0.001), and the overall sex ratio (1.4:1) was skewed towards males ((² = 26.81, p < 0.001, Tab. 2). A total of 17 ovigerous females were captured, with an average CW of 60.12 ± 6.75 mm. The largest and smallest ovigerous females measured 70.90 mm CW (MO) and 47.11 mm CW (PA), respectively. Four were captured in 2015 (August to September) in MO; three in 2021 (February to March), four in 2022 (June), and two in 2023 (August and September), all from PA; one in CB in November 2023, and three in RJ in 2024 (January to February); no ovigerous females were obtained in HI.

Table 2.
Descriptive statistics of Cardisoma crassum carapace width by sex and sampling sites [Montijo (MO), Rio de Jesús (RJ), Ponuga (PA), Calabazal (CB) and Hicaco (HI)] from the Montijo Gulf, Veraguas, Panama. Carapace width (CW) is given in millimeters.

Sex, Site	N	CW		Sex ratio, χ2, p	♂ vs.♀ CW t-test, d.f., p
		Mean ± SD	Max. - Min.
♂	564	61.38 ± 8.52	88.30-22.74	1.4:1, 26.81, p < 0.001	5.46, 963, p < 0.001
♀	403	54.27 ± 9.88	77.78-33.70
MO ♂	227	62.93 ± 7.43	88.30-48.30	1.6:1, 19.58, p < 0.001	28.35, 367, p < 0.001
MO ♀	142	43.97 ± 6.13	65.42-33.70
RJ ♂	58	59.76 ± 7.52	76.63-43.76	1:1, 0.04, p = 0.85	0.68, 112, p = 0.50
RJ ♀	56	57.33 ± 6.75	70.71-43.78
PA ♂	204	59.36 ± 9.01	78.30-22.74	1.2:1, 3.10, p = 0.08	‐0.86, 372, p = 0.39
PA ♀	170	60.06 ± 6.28	77.78-37.98
CB ♂	49	60.57 ± 9.01	79.75-40.14	2:1, 7.78, p < 0.01	‐0.60, 72, p = 0.55
CB ♀	25	61.76 ± 5.87	76.68-53.69
HI ♂	25	69.15 ± 8.12	83.42-55.26	2.3:1, 5.44, p = 0.02	0.63, 34, p = 0.54
HI ♀	11	64.15 ± 5.91	76.09-54.56

Polymodality was confirmed throughout the four size compositions, with four to six modes (Fig. 3). Convergence between the observed and predicted data supports a common distribution origin; they closely approximate linearity, which is further confirmed by normality of the residuals (Fig. 4 A -B). When the intercept was fixed at zero, none of the model runs produced lower LL and AIC values in comparison with runs where the slope term was fixed to zero. The inclusion of eight age groups, with the slope at zero, resulted in the best model fit, as indicated by the LL and AIC (Tab. 3, Fig. 4 C ). These findings support the second hypothesis, where growth rate is not dependent of size, but rather of age.

Figure 3.
Cardisoma crassum size compositions based on proportions of individuals at different carapace widths collected in the Montijo Gulf, Veraguas, Panama. The gray bars are observed proportions, the red curve is the predicted proportion of sizes, and the blue curves denote the modes assumed to represent age groups.

Table 3.
Estimated von Bertalanffy growth function parameters at different annual (age) classes in Cardisoma crassum from the Montijo Gulf, Veraguas, Panama. Parentheses contain the standard error of the parameter estimate. The data for number of annual classes (AC), non-convergence (NC), asymptotic carapace width (L_∞ ), the modal carapace width of first age group (L₁ ), both in millimeters, are indicated. Abbreviations: annual growth coefficient (k); intercept (INT) and slope (SLP); the number of parameters (PN); Log-likelihood (LL); Akaike’s criterion (AIC). The asterisk indicates best fit iteration.

AC	L ∞	k -y	L 1	INT	SLP	PN	d.f.	LL	AIC
6	90.65 (4.30)	0.23 (0.02)	12.74 (2.38)	6.29	0	28	6.53×10-06	2314.15	4684.30
7	88.60 (4.29)	0.19 (0.02)	13.25 (2.52)	6.48	0	32	7.57×1006	2314.51	4693.02
8	91.51 (3.29)	0.24 (0.02)	17.14 (2.35)	3.83	0	36	3.12×10-06	2301.20	4674.40*
9	90.64 (3.10)	0.24 (0.02)	17.33 (2.36)	3.72	0	40	4.48×10-06	2298.81	4677.62
6	93.30 (4.56)	0.85 (0.09)	16.05 (3.38)	0	0.12	28	9.05×10-06	2329.06	4714.12
7NC	75.24	0.29	10.85	0	0.11	32	2162.65	2502.06	5068.12
8	87.21 (4.14)	0.32 (0.03)	15.12 (2.88)	0	0.12	36	7.03×10-06	2315.19	4702.38
9	87.24 (4.25)	0.32 (0.03)	15.14 (2.89)	0	0.12	40	1.46×10-05	2315.08	4710.16

In total, there were 36 model parameters, with 32 of these parameters representing the relative composition of each age group, spanning four trimesters across eight distinct age groups (Fig. 4 D ), while the remaining four parameters pertain to L_∞ , k, L₁ , and the CV. The asymptotic length (L_∞ = 91.51 mm CW; 95% CI: 85.29-98.19 mm) of C. crassum exceeded the maximum observed CW from the field (88.30 mm CW) and surpassed the average size of specimens above the third quartile in this study (70.08 ± 4.57 mm CW). The growth coefficient was 0.24 year^-1 (CI: 0.19-0.29), while L₁ was 17.14 mm CW (CI: 13.09-22.44 mm). Moreover, the retro-calculation result for L₀ was -2.70 mm CW (Fig. 5 A ). The von Bertalanffy growth equation for C. crassum is:

$${\stackrel{-}{L}}_a=91.51\left(1-{exp}^{-0.24\left(a-0.1229\right)}\right)$$ (eq. 15)

The change in length per year of crabs as per subtraction between L_a+1 and L_a (Tab. 4), indicated a decreasing curve when plotted against relative age (Fig. 4 B ), with the following equation:

$$∆L_{a{y}^{-1}}=25.13{\times exp}^{\left(-0.24\times a\right)}$$ (eq. 16)

Table 4.
Average carapace width and age estimates of Cardisoma crassum in the Montijo Gulf, Veraguas, Panama. The L_a /L_∞ ratio indicates how the size at a given age compares to the crab's expected maximum size. The asymptotic length (L_∞ ), carapace width-at-age (L_a ), and carapace width (CW) are given in millimeters. The estimated age of ovigerous females is EA, and their site of origin includes Montijo (MO), Río de Jesús (RJ), Ponuga (PA), and Calabazal (CB). The age at which growth slows significantly is t_max , and LOC represents the largest observed crab.

von Bertalanffy model		Age (years)	L a	L a /L ∞	Ovigerous females
					Site	CW	EA
Retro-calculated		0	-2.70	-2.95%	PA	47.11	3.18
Estimated		1	17.14	18.73%	PA	51.52	3.62
		2	32.80	35.84%	MO	51.60	3.63
		3	45.16	49.35%	PA	55.25	4.04
		4	54.92	60.02%	MO	55.60	4.08
		5	62.63	68.43%	RJ	56.61	4.20
		6	68.71	75.08%	PA	58.63	4.45
		7	73.51	80.33%	PA	58.74	4.47
		8	77.30	84.47%	RJ	59.50	4.57
Projection		9	80.29	87.74%	PA	62.81	5.03
		10	82.66	90.32%	RJ	62.93	5.04
		11	84.52	92.36%	MO	63.30	5.10
		12	85.99	93.97%	PA	63.36	5.11
	tmax	12.81	86.96	95.02%	PA	66.60	5.63
	LOC	13	87.16	95.24%	PA	66.69	5.64
		14.29	88.30	96.49%	CB	70.87	6.42
		-	-	-	MO	70.90	6.43

Figure 4.
Q-Q plot diagram after the von Bertalanffy growth function fit in Cardisoma crassum from the Montijo Gulf, Veraguas, Panama. (A) Regression on predicted vs. observed proportions in size structures. (B) Residuals histogram of the growth model fit. (C) Likelihood surface plot of the L_∞ (asymptotic carapace width) and k (growth coefficient) relationship. (D) Size-age probability plot; the dashed lines represent the estimated carapace width modes with corresponding values in blue (rounded) on the upper y-axis.

The 95% confidence interval (60.40-61.38 mm CW) for the pooled mean (60.89 ± 7.70 mm CW) suggests that most of the captured crabs correspond to ages between 4.69-4.82 years. The estimated t_max was 12.81 years; however, according to Equation 15, the smallest and largest crabs (22.74-88.30 mm CW) might have been 1.33 and 14.29 years of age, respectively. The theoretical age at which the first maturation occurs was estimated at 4.77 years, with a corresponding size of 61.01 mm CW, falling within the size range observed in ovigerous females (Tab. 4).

Figure 5.
von Bertalanffy model curves for carapace width in Cardisoma crassum from the Montijo Gulf, Veraguas, Panama. (A) Relative size-at-age curve, including L₀ retro-calculation (circle), L₁ to L₈ model estimates (squares), and projected L₉ to L₁₄ (triangles). Dashed lines represent modal size classes. (B) Relationship between age and carapace width growth rate.

DISCUSION

This study marks the first report of growth parameters for C. crassum in the Montijo Gulf. The best fit iteration of the MCCT model resulted from eight possible age classes and the slope restrained at zero, while its likelihood was verified in the L_∞ and k relationship plot. Furthermore, the model converged in all but one iteration (AC = 7, INT = 0), suggesting the entry values for the model parameters were within a reasonable range for the model fit, and related inferences were well supported. The observed asymptotic size in this study was larger than the average size of C. crassum specimens above the third quartile. As noted by Canales and Arana (2009) for the golden crab, Chaceon chilensis, and Schwamborn and Moraes-Costa (2021) for C. guanhumi, this suggests that data collected in the Montijo Gulf contain meaningful information regarding the growth of C. crassum, where individuals in the gulf may be capable of attaining larger sizes than the observed. Anecdotal accounts from locals suggest that larger crabs were captured in the distant past, an observation aligned with Bright's (1966) report of the largest C. crassum specimens (♂ 132 mm, ♀ 75 mm CW) from Costa Rica. This scenario is in strong contrast with current C. crassum biometry, where an L_∞ greater than the largest caught individuals implies that certain cohorts may be missing possibly due to a combination of temporal variations in population processes or fishing mortality (Schwamborn and Moraes-Costa 2021; Szuwalski, 2022). The only other published estimates of von Bertalanffy growth parameters in C. crassum are from Molina-Ortega and Vázquez-López (2018) from Mexico with an L_∞ of 95.1 mm CW, which is within the calculated L_∞ confidence interval (85.29-98.19 mm CW) for the Montijo Gulf. However, their calculation of the k parameter yielded a value of 0.88, a rather high and unusual growth rate for gecarcinid crabs (Vogt, 2012, 2019), which contrasts with the k value of 0.24 year^-1 found in the present study. Compared to Molina-Ortega and Vázquez-López (2018), our k value suggests a slower growth rate, consistent with a species of moderate longevity (t_max = 12.81 years). Molina-Ortega and Vázquez-López (2018) did not specify the time scale of their estimated growth coefficient; however, the disparity between k values could be possibly attributed to the sampling method of Molina-Ortega and Vázquez-López (2018), which was limited to the rainy season and involved manual catches. In contrast, the growth parameters estimated in the present study derive from a 12-month sample acquired through trapping in dry and rainy seasons. Our findings for C. crassum align with the longevity of other gecarcinid species. For instance, Gecarcinus lateralis Guérin, 1832 and Gecarcinus quadratus Saussure 1853 have estimated lifespans of 10 years (Rademacher and Mengedoht, 2011); Cardisoma armatum Herklots, 1851 is reported to live up to 12 years (Rademacher and Mengedoht, 2011); Gecarcinus ruricola Linnaeus, 1758 has a lifespan of 15 years (Hartnoll et al., 2006); C. guanhumi (Wolcott, 1988) and Gecarcoidea natalis Pocock, 1889 (Wolcott, 1988; Linton and Greenaway, 1997; Green, 2004b) have both estimated lifespans of up to 20 years (see Vogt, 2012; 2019). Interestingly, the average longevity among brachyurans from tropical and sub-tropical species is highest in semiterrestrial and terrestrial environments (Vogt, 2012). Behavioral adaptations to terrestrial habitats, such as burrow construction, are likely to exert a significant influence on crab longevity. This influence stems from the strong association between burrow utilization, enhanced survival and reproductive success (Christy, 2007; Laidre, 2018). Consistently, behavioral adaptations in C. crassum such as the construction, maintenance and defense of burrows with a high degree of fidelity (Lombardo and Rojas, 2022) suggest that burrows are of significant value for their tenants (Hughes and Heuring, 2018; Laidre, 2018).

The longevity of C. crassum and other gecarcinids may be mechanistically linked to their slow growth rate (Green, 2004 b ; Cardona et al., 2019; Schwamborn and Moraes-Costa, 2021), which could be influenced by reduced molting increments due to limited water access, low calorie and nitrogen diets, and pathogens (Burggren and McMahon, 1988; Linton and Greenaway, 1997; Shields, 2012; Vogt, 2012). The considerable variation in size among ovigerous females indicates that C. crassum likely continues to grow through molting even after reaching puberty. However, when the model slope was fixed at zero and the intercept was allowed to vary, the standard deviation between modal components decreased with age, independent of average CW. This suggests that crabs may continue to grow at a progressively slow rate, while a larger proportion of energy may be invested in reproduction as crabs age (Hartnoll, 1988; 2001; McLay 2015). One evolutionary outcome of increased longevity is a rise in cumulative lifetime fecundity, although the mechanisms differ slightly between sexes. For females, it leads to maximized egg production, while for males, it translates into improved mating success (Beverton, 1987; Jivoff, 2003). Considering the later, C. crassum stocks may be at risk, provided their fishery is unregulated, and extraction pressure is known to focus mainly on the largest individuals (Lima et al., 2021). In C. crassum (this study), and gecarcinids in general, males generally reach larger sizes than females (Hartnoll, 1988; 2001; Hartnoll et al., 2006), which makes them vulnerable to extraction. Furthermore, crab species commonly exhibit sex ratios skewed towards males (Wenner, 1972). These aspects are particularly sensitive for C. crassum fishery and conservation, because asymmetries in extraction can alter the mating system by shifting the size structure and sex ratio (Hines et al., 2003; Jivoff, 2003). While the sex ratio of C. crassum in the Montijo Gulf continues to be skewed towards males, such shifts are known to influence aspects of male mating success, especially when size assortative mating cannot occur and mature males become rare. This situation can affect female reproductive potential, leading to limitations in sperm availability (Hines et al., 2003; Sato and Goshima, 2006; Pardo et al., 2015; 2017).

The estimated size at first sexual maturity (2/3 L_∞ ) for C. crassum in the Montijo Gulf was 61.01 mm CW, falling within the observed size range of ovigerous females, indicating that the model performed well in predicting the size at first sexual maturity. Additionally, Zambrano and Olivares (2020) from Ecuador also estimated the size at first maturity for C. crassum (♂ 66.69-85.63 mm, ♀ 66. 02 mm CW) and recommended a minimum extraction size of 80 mm CW. This recommendation follows spawning-stock-biomass-per-recruit (SPR) reference points, particularly values of F_20% to F_30% (Rosenberg and Restrepo, 1996; Gabriel and Mace, 1999). In agreement with these reference points, a minimum extraction size for C. crassum in the Montijo Gulf, at least for females, would be 73.21 mm to 79.31 mm CW (6.93-8.64 years of age). This recommendation is particularly valuable as a starting point for future management plans; however, more information is required, particularly direct measurements of size-at-maturity in C. crassum for both males and females, in order to establish more precise minimum extraction sizes and ensure the sustainability of the species in the Montijo Gulf.

ACKNOWLEDGEMENTS

Our gratitude goes to Maryory Rojas, Leidys Cedeño, and Julio Cruz for their assistance during field work. We also thank Cristian Canales for the MCCT model file, and Ángel Vega for sharing biometrical data. Our appreciation goes to the anonymous reviewers for their constructive comments, which significantly contributed to the improvement of earlier versions of the manuscript.

REFERENCES

• Baine, M; Howard, M; Taylor, E; James, J; Velasco, A; Grandas, Y and Hartnoll, R. 2007. The development of management options for the black land crab (Gecarcinus ruricola) catchery in the San Andres Archipelago, Colombia. Ocean & Coastal Management, 50: 564-589. https://doi.org/10.1016/j.ocecoaman.2007.02.007
  » https://doi.org/10.1016/j.ocecoaman.2007.02.007
• Beck, HE; Zimmermann, NE; McVicar, TR; Vergopolan, N; Berg, A and Wood, EF. 2018. Present and future Köppen-Geiger climate classification maps at 1-km resolution. Scientific Data, 5: 180214. https://doi.org/10.1038/sdata.2018.214
  » https://doi.org/10.1038/sdata.2018.214
• Becker, C; Dick, JTA; Cunningham, EM; Schmitt, C and Sigwart, JD. 2018. The crustacean cuticle does not record chronological age: New evidence from the gastric mill ossicles. Arthropod Structure & Development, 47: 498-512. https://doi.org/10.1016/J.ASD.2018.07.002
  » https://doi.org/10.1016/J.ASD.2018.07.002
• Beverton RJH 1987. Longevity in fish: Some ecological and evolutionary considerations. p. 161-185. In: Woodhead AD and Thompson KH (Eds.), Evolution of Longevity in Animals, USA, Springer.
• Boenish, R; Kritzer, JP; Kleisner, K; Steneck, RS; Werner, KM; Zhu, W; Schram, F; Rader, D; Cheung, W; Ingles, J; Tian, Y and Mimikakis, J. 2022. The global rise of crustacean fisheries. Frontiers in Ecology and the Environment, 20: 102-110. https://doi.org/10.1002/FEE.2431
  » https://doi.org/10.1002/FEE.2431
• De Boer WF and Longamane FA 1996. The exploitation of intertidal food resources in Inhaca Bay, Mozambique, by shorebirds and humans. Biological Conservation, 78: 295-303. https://doi.org/10.1016/S0006-3207(96)00050-X
  » https://doi.org/10.1016/S0006-3207(96)00050-X
• Bright DB 1966. The land crabs of Costa Rica. Revista de Biología Tropical, 14: 183-203. https://doi.org/10.15517/REV.BIOL.TROP.1966.28533
  » https://doi.org/10.15517/REV.BIOL.TROP.1966.28533
• Burggren W and McMahon B 1988. Biology of the Land Crabs. 1st ed. New York, Cambridge University Press. https://doi.org/10.1017/CBO9780511753428
  » https://doi.org/10.1017/CBO9780511753428
• Canales C and Arana P 2009. Crecimiento, mortalidad y evaluación de la población de cangrejo dorado (Chaceon chilensis) explotado en el archipiélago de Juan Fernández, Chile. Latin American Journal of Aquatic Research, 37: 313-326. https://doi.org/10.1017/CBO9780511753428 10.3856/vol37-issue3-fulltext-4
  » https://doi.org/10.1017/CBO9780511753428 10.3856/vol37-issue3-fulltext-4
• Cardona, L; Campos, N and Hernández, E 2019. Parámetros de crecimiento de Cardisoma guanhumi en el Departamento del Magdalena, Colombia. Boletín de Investigaciones Marinas y Costeras, 48: 27-41.
• Charnov EL 1993. Life History Invariants: Some Explorations of Symmetry in Evolutionary Ecology. 1st ed. London, Oxford University Press.
• Charnov EL and Berrigan D 1990. Dimensionless numbers and life history evolution: Age of maturity versus the adult lifespan. Evolutionary Ecology, 4: 273-275. https://doi.org/10.1017/CBO9780511753428 10.1007/BF02214335/METRICS
  » https://doi.org/10.1017/CBO9780511753428 10.1007/BF02214335/METRICS
• Christy JH 2007. Predation and the reproductive behavior of fiddler crabs (Genus Uca). p. 211-231. In: Duffy EJ and Thiel M (Eds.), Evolutionary Ecology of Social and Sexual Systems: Crustaceans as Model Organisms. New York, Oxford University Press.
• Corgos A and Freire J 2006. Morphometric and gonad maturity in the spider crab Maja brachydactyla: a comparison of methods for estimating size at maturity in species with determinate growth. ICES Journal of Marine Science, 63: 851-859. https://doi.org/10.1017/CBO9780511753428 10.1016/j.icesjms.2006.03.003
  » https://doi.org/10.1017/CBO9780511753428 10.1016/j.icesjms.2006.03.003
• De León, A; Abrego, A; Vega, Á and Añino, Y 2023. Size and weight of Cardisoma crassum and Ucides occidentalis collected by artisanal fishing in Chame, Panamanian Pacific. Gayana, 87: 197-204. https://doi.org/10.4067/S0717-65382023000200197
  » https://doi.org/10.4067/S0717-65382023000200197
• Eisenhauer JG 2003. Regression through the origin. Teaching Statistics, 25: 76-80. https://doi.org/10.1017/CBO9780511753428 10.1111/1467-9639.00136
  » https://doi.org/10.1017/CBO9780511753428 10.1111/1467-9639.00136
• Gabriel WL and Mace PM 1999. A review of biological reference points in the context of the precautionary approach. p. 34-35. In: Proceedings of the fifth National NMFS Stock Assessment Workshop: Providing Scientific Advice to Implement the Precautionary Approach under the Magnuson-Stevens Fishery Conservation and Management Act. NOAA Tech Memo NMFS-F/SPO-40.
• Gayanilo, FC Jr; Sparre, P and Pauly, D 1996. FAO-ICLARM stock assessment tools (FiSAT). User’s guide. 1st ed. Report 8. Rome, FAO Computerized Information Series (Fisheries).
• Govender Y 2019. Long-term monitoring of crab Cardisoma guanhumi (Decapoda: Gecarcinidae) captures in Jobos Bay estuary, Puerto Rico. Revista de Biologia Tropical, 67: 879-887. https://doi.org/10.15517/rbt.v67i4.35124
  » https://doi.org/10.15517/rbt.v67i4.35124
• Green PT 2004a. Burrow dynamics of the red land crab Gecarcoidea natalis (Brachyura, Gecarcinidae) in rain forest on Christmas Island (Indian Ocean). Journal of Crustacean Biology, 24: 340-349. https://doi.org/10.1651/C-2447
  » https://doi.org/10.1651/C-2447
• Green PT 2004b. Field observations of moulting and moult increment in the Red Land Crab, Gecarcoidea natalis (Brachyura, Gecarcinidae), on Christmas Island (Indian Ocean) . Crustaceana, 77: 125-128. https://doi.org/10.1163/156854004323037937
  » https://doi.org/10.1163/156854004323037937
• Hartnoll RG 1988. Growth and molting. p. 186-210. In: Burggren W and McMahon B (Eds.), Biology of the Land Crabs. Cambridge, Cambridge University Press.
• Hartnoll RG 2001. Growth in Crustacea - Twenty years on. Hydrobiologia, 449: 111-122. https://doi.org/10.1023/A:1017597104367/METRICS
  » https://doi.org/10.1023/A:1017597104367/METRICS
• Hartnoll, RG; Baine, MSP; Grandas, Y; James, J and Atkin, H 2006. Population biology of the black land crab, Gecarcinus Ruricola, in the San Andres Archipelago, Western Caribbean. Journal of Crustacean Biology, 26: 316-325. https://doi.org/10.1651/C-2640.1
  » https://doi.org/10.1651/C-2640.1
• Hendrickx ME 1995. Cangrejos. p. 581-636. In: Fisher, W; Krupp, F; Schneider, W; Sommer, C; Carpenter, K and Niem, V (Eds.), Guía FAO para la identificación de especies para los fines de la pesca: Pacifico Centro-Oriental. Rome, FAO, 646p.
• Hines, AH; Jivoff, PR; Bushmann, PJ; Van Montfrans, J; Reed, SA; Wolcott, DL and Wolcott, TG 2003. Evidence for sperm limitation in the blue crab, Callinectes sapidus. Bulletin of Marine Science, 72(2): 287-310. https://www.ingentaconnect.com/contentone/umrsmas/bullmar/2003/00000072/00000002/art00004#
  » https://www.ingentaconnect.com/contentone/umrsmas/bullmar/2003/00000072/00000002/art00004#
• Hughes M and Heuring WL 2018. Uncharted territories: Defense of space in Crustacea. p. 258-279. In: Thiel M and Wellborn G (Eds.), Life Histories. New York, Oxford University Press .
• Jivoff P 2003. A review of male mating success in the blue crab, Callinectes sapidus, in reference to the potential for fisheries-induced sperm limitation. Bulletin of Marine Science, 72(2): 273-286. https://www.ingentaconnect.com/contentone/umrsmas/bullmar/2003/00000072/00000002/art00003#
  » https://www.ingentaconnect.com/contentone/umrsmas/bullmar/2003/00000072/00000002/art00003#
• João, MCA; Duarte, RC; da Silva, LSB; Freire, AS and Pinheiro, MAA 2022. Sexual maturity of an endemic insular land crab: Priority information toward the conservation of Johngarthia lagostoma. The Biological Bulletin, 243: 14-27. https://doi.org/10.1086/720581
  » https://doi.org/10.1086/720581
• Krause, G; Schories, D; Glaser, M and Diele, K 2001. Spatial patterns of mangrove ecosystems: The bragantinian mangroves of northern Brazil (Bragança, Pará). Ecotropica, 7: 93-107.
• Laidre ME 2018. Evolutionary ecology of burrow construction and social life. p. 280-302. In: Thiel M and Wellbon G (Eds.), Life Histories. New York, Oxford University Press .
• Legendre P and Desdevises Y 2009. Independent contrasts and regression through the origin. Journal of Theoretical Biology, 259: 727-743. https://doi.org/10.1016/J.JTBI.2009.04.022
  » https://doi.org/10.1016/J.JTBI.2009.04.022
• Lima, MC; Pereira, CAM; Araújo, MSLC; Rodrigues, GG and Nicacio, G 2021. Seasonal variation in biometric parameters in a population of the endangered blue land crab (Cardisoma guanhumi): Indicators for assessment and management. Regional Studies in Marine Science, 45: 101804. https://doi.org/10.1016/J.RSMA.2021.101804
  » https://doi.org/10.1016/J.RSMA.2021.101804
• Linton SM and Greenaway P 1997. Urate deposits in the gecarcinid land crab Gecarcoidea natalis are synthesised de novo from excess dietary nitrogen. Journal of Experimental Biology, 200: 2347-2354. https://doi.org/10.1242/JEB.200.17.2347
  » https://doi.org/10.1242/JEB.200.17.2347
• Lombardo RC 2024. The biometry of Cardisoma crassum (Brachyura: Gecarcinidae) from two folkloric festivals in Veraguas, Panama. Revista Científica Vida Natural, 1: 29-45. https://doi.org/10.59722/RCVN.V1I2.705
  » https://doi.org/10.59722/RCVN.V1I2.705
• Lombardo RC and Cedeño LM 2023. Segregation by size in the mouthless crab Cardisoma crassum (Brachyura: Gecarcinidae) from Ponuga, Veraguas, Panama. Revista Ciencias Marinas y Costeras, 15: 27-44. https://doi.org/10.15359/revmar.15-1.2
  » https://doi.org/10.15359/revmar.15-1.2
• Lombardo RC and Rojas M 2022. Burrow fidelity in the blue crab, Cardisoma crassum Smith, 1870 (Brachyura: Gecarcinidae) from the Ponuga River, Veraguas, Panama. Nauplius, 30: e2022033. https://doi.org/10.1590/2358-2936e2022033
  » https://doi.org/10.1590/2358-2936e2022033
• Macdonald PDM and Pitcher TJ 1979. Age-groups from size-frequency data: A versatile and efficient method of analyzing distribution mixtures. Fisheries Research Board of Canada, 36: 987-1001. https://doi.org/10.1139/F79-137
  » https://doi.org/10.1139/F79-137
• Macintosh, DJ; Ashton, EC and Havanon, S 2002. Mangrove rehabilitation and intertidal biodiversity: A study in the Ranong mangrove ecosystem, Thailand. Estuarine, Coastal and Shelf Science, 55: 331-345. https://doi.org/10.1006/ecss.2001.0896
  » https://doi.org/10.1006/ecss.2001.0896
• McLay C 2015. Moulting and growth in Brachyura. p. 245-316. In: Castro P, Davie P, Schram GDF and von Vaupel C (Eds.), Treatise on Zoology - Anatomy, Taxonomy, Biology. The Crustacea. . Leiden, Brill.
• Molina-Ortega MG and Vázquez-López H 2018. Relative growth of Cardisoma crassum Smith, 1870 (Decapoda: Gecarcinidae) in the estuary El Salado, Puerto Vallarta, Jalisco Mexico. BIOCYT Biología Ciencia y Tecnología, 11: 808-823.
• Ng PKL and Ng PYC. 2021. Land crabs (Crustacea: Brachyura: Gecarcinidae) of Singapore. Nature in Singapore, 14: e2021001. https://doi.org/10.26107/NIS-2021-0001
  » https://doi.org/10.26107/NIS-2021-0001
• Ng PKL and Shih H Te 2023. Tuerkayana latens, a new species of land crab from French Polynesia, with a discussion on the phylogeny of the genus (Crustacea: Decapoda: Brachyura: Gecarcinidae). Zoological Studies, 62: e10. https://doi.org/10.6620/ZS.2023.62-10
  » https://doi.org/10.6620/ZS.2023.62-10
• Ogle DH and Isermann DA 2017. Estimating age at a specified length from the von Bertalanffy growth function. North American Journal of Fisheries Management, 37: 1176-1180. https://doi.org/10.1080/02755947.2017.1342725
  » https://doi.org/10.1080/02755947.2017.1342725
• Pardo, LM; Rosas, Y; Fuentes, JP; Riveros, MP and Chaparro, OR 2015. Fishery induces sperm depletion and reduction in male reproductive potential for crab species under male-biased harvest strategy. PLoS One, 10: e0115525. https://doi.org/10.1371/journal.pone.0115525
  » https://doi.org/10.1371/journal.pone.0115525
• Pardo, LM; Riveros, MP; Fuentes, JP; Pinochet, R; Cárdenas, C and Sainte‐Marie, B 2017. High fishing intensity reduces females’ sperm reserve and brood fecundity in a eubrachyuran crab subject to sex- and size-biased harvest. ICES Journal of Marine Science, 74: 2459-2469. https://doi.org/10.1093/icesjms/fsx077
  » https://doi.org/10.1093/icesjms/fsx077
• Pauly D 1983. Some simple methods for the assessment of tropical fish stocks. FAO Fisheries Technical Paper, 234: 1-52.
• Pauly D and David N 1981. ELEFAN I, a basic program for the objective extraction of growth parameters from length-frequency data. Meeresforschung - Berichte der Deutschen Wissenschaftlichen Kommission für Meeresforschung, 28: 205-211.
• Pauly D and Froese R 2014. Fisheries management. p. 1-6. In: eLS. Chichester, John Wiley & Sons, Ltd. https://doi.org/10.1002/9780470015902.a0003252.pub3
  » https://doi.org/10.1002/9780470015902.a0003252.pub3
• Pearson K 1894. Contributions to the mathematical theory of evolution. Proceedings of the Royal Society of London, 54: 329-333. https://doi.org/10.1098/RSPL.1893.0079
  » https://doi.org/10.1098/RSPL.1893.0079
• Perger, R; Cortés, J and Pacheco, C 2013. Closing a distributional gap of over 3000 km and encountering an invisible barrier: New presence/absence data for Johngarthia planata Stimpson, 1860 (Decapoda, Brachyura, Gecarcinidae) for Central America and biogeographic notes on East Pacific Gecarcinidae. Crustaceana, 86: 268-277. https://doi.org/10.1163/15685403-00003172
  » https://doi.org/10.1163/15685403-00003172
• Rademacher M and Mengedoht O. 2011. Krabben-Fibel. 1st ed. 1. Ettlingen, Germany, Dähne Verlag, 95p.
• RAMSAR 2023. The List of Wetlands of International Importance. Ramsar List. Available at Available at https://www.ramsar.org/document/list-wetlands-international-importance-ramsar-list Accessed 15 August 2023.
  » https://www.ramsar.org/document/list-wetlands-international-importance-ramsar-list
• Rosenberg A and Restrepo V 1996. Precautionary management reference points and management strategies. p. 129-140. In: Food and Agricultural Organization (FAO) 1995a. Precautionary approach to fisheries. Part II: Scientific papers. Prepared for the Technical Consultation on the Precautionary Approach to Capture Fisheries (Including Species Introductions). Lysekil, Sweden, FAO Technical Paper No. 350, Part 2.
• Robertson AI 1986. Leaf-burying crabs: Their influence on energy flow and export from mixed mangrove forests (Rhizophora spp.) in northeastern Australia. Journal of Experimental Marine Biology and Ecology, 102: 237-248. https://doi.org/10.1016/0022-0981(86)90179-6
  » https://doi.org/10.1016/0022-0981(86)90179-6
• Santos, LCM; Boos, H; Sano, EE; de Freitas, DM and Pinheiro, MAA 2022. Management and conservation of the land crab Cardisoma guanhumi (Crustacea: Gecarcinidae) based on environmental and fishery factors: a case study in Brazil. Wetlands Ecology and Management, 30: 389-403. https://doi.org/10.1007/S11273-022-09868-2/METRICS
  » https://doi.org/10.1007/S11273-022-09868-2/METRICS
• Sato T and Goshima S 2006. Impacts of male-only fishing and sperm limitation in manipulated populations of an unfished crab, Hapalogaster dentata. Marine Ecology Progress Series, 313: 193-204. https://doi.org/10.3354/MEPS313193
  » https://doi.org/10.3354/MEPS313193
• Schwamborn R and Moraes-Costa DF 2021. Growth and mortality of the endangered land crab Cardisoma guanhumi assessed through tagging with PITs and novel bootstrapped methods. Pan-American Journal of Aquatic Sciences, 16: 57-78. http://panamjas.org/pdf_artigos/PANAMJAS_16(1)_57-78.pdf
  » http://panamjas.org/pdf_artigos/PANAMJAS_16(1)_57-78.pdf
• Schwamborn, R; Mildenberger, TK and Taylor, MH 2019. Assessing sources of uncertainty in length-based estimates of body growth in populations of fishes and macroinvertebrates with bootstrapped ELEFAN. Ecological Modelling, 393: 37-51. https://doi.org/10.1016/J.ECOLMODEL.2018.12.001
  » https://doi.org/10.1016/J.ECOLMODEL.2018.12.001
• Shields JD 2012. The impact of pathogens on exploited populations of decapod crustaceans. Journal of Invertebrate Pathology, 110: 211-224. https://doi.org/10.1016/J.JIP.2012.03.011
  » https://doi.org/10.1016/J.JIP.2012.03.011
• Smith, TJ; Boto, KG; Frusher, SD and Giddins, RL 1991. Keystone species and mangrove forest dynamics: the influence of burrowing by crabs on soil nutrient status and forest productivity. Estuarine, Coastal and Shelf Science, 33: 419-432. https://doi.org/10.1016/0272-7714(91)90081-L
  » https://doi.org/10.1016/0272-7714(91)90081-L
• Sparre P and Venema SC 1993. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, 306: 1-407.
• Szuwalski C 2022. Estimating time-variation in confounded processes in population dynamics modeling: A case study for snow crab in the eastern Bering Sea. Fisheries Research, 251: 106298. https://doi.org/10.1016/J.FISHRES.2022.106298
  » https://doi.org/10.1016/J.FISHRES.2022.106298
• Taylor CC 1958. Cod growth and temperature. ICES Journal of Marine Science, 23: 366-370. https://doi.org/10.1093/ICESJMS/23.3.366
  » https://doi.org/10.1093/ICESJMS/23.3.366
• Vázquez-López H and Ramírez-Pérez T 2015. Aspects of growth in the terrestrial crab Cardisoma crassum Smith, 1870 (Crustacea: Brachyura: Gecarcinidae) from El Salado estuary, Puerto Vallarta, Jalisco, México. Mitteilungen Klosterneuburg, 65: 82-99.
• Vega, ÁJ; Mena, C and Robles, Y 2018. Pesca artesanal Cardisoma crassum (Cangrejo) y Ucides occidentalis (Mangote) en el sector nororiental del Golfo de Montijo, Pacifico de Panamá. Tecnociencia, 20: 5-22. https://revistas.up.ac.pa/index.php/tecnociencia/article/view/264/230
  » https://revistas.up.ac.pa/index.php/tecnociencia/article/view/264/230
• Vega, ÁJ; Robles, YA and Torres, L 2014. Análisis biológico y pesquero de la extracción del poliqueto Americonuphis reesei en el Golfo de Montijo, Pacífico panameño. Tecnociencia, 16: 77-93. https://doi.org/10.48204/NH
  » https://doi.org/10.48204/NH
• Vega, ÁJ; Robles, YA; Alvarado, O and Cedeño-Mitre, C 2021. Estructura de tallas, distribución y abundancia de Anadara tuberculosa (Bivalvia: Arcidae) en dos sistemas de manglar del Pacífico de Panamá. Revista de Biología Tropical, 69: 422-433. https://doi.org/10.15517/RBT.V69I2.43934
  » https://doi.org/10.15517/RBT.V69I2.43934
• Vogt G 2012. Ageing and longevity in the Decapoda (Crustacea): A review. Zoologischer Anzeiger - A Journal of Comparative Zoology, 251: 1-25. https://doi.org/10.1016/J.JCZ.2011.05.003
  » https://doi.org/10.1016/J.JCZ.2011.05.003
• Vogt G 2019. A compilation of longevity data in decapod crustaceans. Nauplius , 27: e2019011. https://doi.org/10.1590/2358-2936e2019011
  » https://doi.org/10.1590/2358-2936e2019011
• von Bertalanffy L 1938. A quantitative theory of organic growth (Inquiries on growth laws. II). Human Biology, 10(2): 181-213. https://www.jstor.org/stable/41447359
  » https://www.jstor.org/stable/41447359
• Wenner AM 1972. Sex ratio as a function of size in marine Crustacea. The American Naturalist, 106: 321-350. https://doi.org/10.1086/282774
  » https://doi.org/10.1086/282774
• Wolcott TG 1988. Ecology. p. 55-95. In: Burggren W and McMahon B (Eds.), Biology of the Land Crabs. Cambridge, Cambridge University Press .
• Zambrano R and Olivares S 2020. Alometría y madurez sexual morfométrica de Cardisoma crassum (Decapoda: Gecarcinidae) en la costa continental norte de Ecuador. Geomare Zoologica, 2: 25-33. https://geomarerevista.wixsite.com/geomare/volumen-2
  » https://geomarerevista.wixsite.com/geomare/volumen-2

• Zoobank:
  http://zoobank.org/urn:lsid:zoobank.org:pub:9311914B-DFFB-4BE0-B730-967B17D0D352

ADDITIONAL INFORMATION AND DECLARATIONS

• Funding and grant disclosures
  There were no external funding sources for this study.
• Data availability
  All study data is included in the article and available on request from the author.

Edited by

• Associate Editor:
  Ingo Wehrtmann

• Editor-in-chief:
  Christopher Tudge

Data availability

All study data is included in the article and available on request from the author.

Publication Dates

• Publication in this collection
  15 Aug 2025
• Date of issue
  2025

History

• Received
  03 Dec 2023
• Accepted
  23 Sept 2024