Age and growth of the silky shark Carcharhinus falciformis (Muller & Henle, 1839) in the Ecuadorian Pacific

Sampling

Field surveys were conducted at the ‘Playita Mía’ landing site in Manta, Ecuador, from September 2021 to September 2022 (Fig. 1). Fisheries in this area operate using fibreglass vessels equipped with longlines and gillnets. The primary target species are teleost fishes from the Scombridae, Istiophoridae, and Coryphaenidae families, while elasmobranchs frequently occur as incidental catch year-round.

Fig. 1.

Location of the sampling site ‘Artisanal port Playita Mía’. Ecuador, Manabí, Manta.

Upon landing, biometric data were collected from 542 sharks (see Supplementary Table S1). Of these, some had already been processed for commercial use, preventing vertebral sampling, so vertebrae were obtained from only 290 individuals. Sex was determined based on the presence (males) or absence (females) of claspers. Measurements, including total length (TL), fork length (FL), pre-caudal length (PCL), and interdorsal length (IDL) were recorded using a centimetre-graded measuring tape. As some sharks were landed eviscerated or without caudal fins or heads, morphometric relationships were established to enable comparisons across studies. Simple linear regressions were used to assess the relationships between TL and other length measurements (PCL, FL, and IDL), with coefficient of determination values and F-tests applied to evaluate statistical significance, as has been done in other shark studies (e.g. De Wysiecki and Braccini 2017; Mejía and Briones-Mendoza 2024).

Sample processing and cutting

The vertebrae were extracted from the cervical region of each shark and subsequently frozen. The processing of the vertebral centra following the methods described by Cailliet and Goldman (2004). For preservation, samples were stored frozen for several months before cleaning. To clean, vertebrae were immersed in hot water and treated with a 5% sodium hypochlorite (NaClO) solution for several minutes to soften excess tissue and facilitate removal.

For subsequent readings, the vertebral centra were longitudinally sectioned to 0.3 mm using a low-speed IsoMet saw with a double diamond disc, then stained with silver nitrate (AgNO₃) to enhance growth band pair visibility. The sections were mounted on slides and observed under transmitted light for improved visualisation.

Age estimation

Independently, two readers conducted readings of the sectioned vertebral centra from photographs, without prior knowledge of the shark’s total length or sex. Using transmitted light and a stereomicroscope with an integrated camera, they analysed band pairs (one opaque and one translucent) along the corpus calcareum. Following the widely accepted methodology for age estimation in elasmobranchs (Cailliet and Goldman 2004), each band pair was assumed to represent 1 year of individual growth. This assumption is based on previous studies that have verified, through indirect methods, the annual band pair deposition in C. falciformis (Joung et al. 2008; Hall et al. 2012). It was assumed that the birth mark was the first translucent band accompanied by a change in the angle of the corpus calcareum. Therefore, this first translucent band, along with the adjacent opaque band, was interpreted as representing age 0. A band pair was considered complete if it extended from the corpus calcareum on the left side of the section, traversed through the intermedialia, and continued back through the corpus calcareum on the right side. Agreement between both readers estimated the age; in cases of disagreement, consensus was reached through discussion. If no consensus was reached, the sample was discarded (D’Alberto et al. 2017).

To assess precision and bias, the percentage of agreement between readers (PA) (Goldman 2005), average percentage error (APE) (Beamish and Fournier 1981), and the coefficient of variation (CV) (Chang 1982) were utilised (Table 1). Systematic bias in the counts between readers was statistically evaluated using Bowker’s symmetry test. The bias plot from Campana et al. (1995), along with the analyses of precision and bias, were calculated using the FSA package (Ogle 2018). All analyses in this study were conducted within the R programming language ver. 2024.12.0.467 (R Core Team 2020).

Age verification

The formation of band pairs was verified using two widely recognised methods in shark age and growth studies: (1) the marginal increment ratio (MIR); and (2) centrum edge analysis (CEA). Band pair measurements; i.e. the radius of the vertebra and each of its band pairs was measured from the centre of the vertebrae to the centre of each band pair. Measurements were performed using ImageJ 1.54 g software (Schneider et al. 2012) under transmitted light with a stereomicroscope Pallipartners (1080p, 12 MP) equipped with an integrated camera. Adobe Photoshop ver. 21.0.2 was then used to adjust brightness and contrast, optimising band pair clarity. Since the vertebral samples were collected over a 12-month period, MIR was employed to indirectly verify ageing protocols (Natanson et al. 1995):

where V_r is the vertebral radius, R_n the last complete band, and R_n−1 is the band next to last complete band (Fig. 2).

Fig. 2.

Photograph of a sectioned vertebral centrum with a thickness of 0.3 mm, corresponding to a male Carcharhinus falciformis captured in the Ecuadorian South Pacific measuring 181.4 cm TL, with an estimated age of 11 years. The photo was taken prior to staining. F, focus; BB, birth band; r, annual bands; Rn-1, penultimate band; Rn, last band; R, ribbon radius.

Additionally, CEA was used to complement MIR in verifying the formation of growth band pairs (Cailliet and Goldman 2004). This analysis enables the classification of vertebral centra edges as either opaque or translucent, based on the month of the year. Furthermore, the statistical method developed by Okamura and Semba (2009) was applied to validate the periodicity of the band pair formation using three models: (1) acyclic (N); (2) annual (A); (3) and biennial (B). The model that best fit the data was selected based on the lowest value of the Akaike Information Criterion (AIC) (Burnham and Anderson 2002).

Growth models

Two analytical approaches were employed to determine which method yields the most biologically plausible estimates: (1) the frequentist; and (2) Bayesian approaches. To avoid assuming an a priori model that may be inappropriate, three growth models were applied in both approaches: (1) the von Bertalanffy Growth Function (VBGF; von Bertalanffy 1938); (2) the Logistic model (Log; Ricker 1979); and (3) the Gompertz model (Gom; Gompertz 1825) (Table 2). Model selection for the frequentist approach was based on minimising the AIC, whereas for the Bayesian approach, the Leave-One-Out Information Criterion (LOOIC) was employed, with higher weights indicating a better model fit. All models utilised L₀ (length-at-birth) instead of t₀ (age when length is zero), as the latter does not have a consistent definition across different growth models, whereas L₀ universally refers to the length at birth (Smart et al. 2016; Smart 2019). Moreover, the biological significance of L₀ is more meaningful in this context than t₀.

Frequentist models generally perform well when a broad size range is available (Smart and Grammer 2021). However, when the size range is narrow or biased, this can lead to under-estimation or over-estimation of age and growth parameters (Harry et al. 2022). Therefore, in this study, we tested this by applying both frequentist and Bayesian approaches. For the frequentist approach, models were fitted using nonlinear least squares via the AquaticLifeHistory package, employing the function ‘Estimate_Growth’ (Smart et al. 2016; Smart 2019).

The Bayesian approach is particularly suitable for situations where large specimens are scarce, likely due to fishing gear selectivity, as it effectively handles missing data and incorporates prior biological knowledge. Both small and large sharks are critical to accurately characterising the extremes of the growth curve; omitting these sizes may lead to inaccuracies in growth parameter estimation, potentially causing over- or under-estimation (Smart and Grammer 2021). The Bayesian framework effectively handles missing data and incorporates informative priors from biological knowledge (prior distributions), improving parameter estimates and reducing uncertainty in growth models. This is particularly beneficial when length-at-age data (likelihood distributions) are limited, especially for extreme sizes of captured individuals (Smart and Grammer 2021). Using the ‘Estimate_MCMC_Growth’ function in the BayesGrowth package (Smart 2020), the Bayesian analysis incorporated prior information for four key parameters: (1) L₀ (length-at-birth); (2) L_∞ (asymptotic length); (3) k/g (growth coefficients); and (4) σ (residual s.e.). This was achieved via the Markov Chain Monte Carlo (MCMC) method, where length-at-birth and asymptotic length were modelled using normal distributions with defined means (μ) and s.e. (σ):

Accordingly, the average minimum and maximum lengths reported in the scientific literature for the Pacific were used as prior values for L₀ and L_∞, respectively (Oshitani et al. 2003: L_min = 81 cm LT, L_max = 292 cm TL; Joung et al. 2008: L_min = 75.5 cm TL, L_max = 256 cm TL; Martínez-Ortíz et al. 2011: L_min = 62 cm TL, L_max = 309 cm TL; Sánchez-de Ita et al. 2011: L_min = 76.5 cm TL, L_max = 260 cm TL; Grant et al. 2018: L_min = 71 cm TL, L_max = 271.3 cm TL; Briones-Mendoza et al. 2022: L_min = 66 cm TL, L_max = 272 cm TL). Therefore, the prior values for L₀ and L_∞ were defined as:

For the growth coefficient and residual s.e., uniform distributions were specified:

These priors were non-informative, incorporating only minimum thresholds to ensure realistic parameter ranges (Smart and Grammer 2021). This approach is justified within a multi-model framework, where growth coefficients are not directly comparable, and the majority of C. falciformis studies have employed the VBGF. Therefore, using a non-informative prior ensures that all three candidate models can be specified with identical prior distributions (Emmons et al. 2021). In contrast, L₀ and L_∞ are comparable across models, warranting the use of informative priors derived from the literature (Smart and Grammer 2021). Thus, k/g were defined as:

The MCMC simulation was conducted with four chains, each running 10,000 iterations with a burn-in of 5000 simulations. Convergence was assessed via the Gelman–Rubin diagnostic, and diagnostic plots for Bayesian growth parameter estimates were generated using the Bayesplot package (Gabry and Mahr 2024; see Supplementary materials).

To test for significant sex-based differences in growth model estimates, the likelihood ratio test (Kimura 1980) was applied in the frequentist framework, whereas the Bayesian approach used posterior distribution overlap assessment between males and females via the overlapping package (Pastore 2018).

Sample collection

Vertebral samples were collected from 290 individuals of C. falciformis, of which 161 were females (55.52%) and 129 were males (44.48%). Females exhibited lengths ranging from 79.2 cm to 238 cm TL (mean ± s.d.: 178.6 ± 38.17), while males ranged from 80.2 cm to 234.6 cm TL (169.1 ± 36.06). Estimated ages ranged from 0 to 19 years (9.55 ± 4.26) for females and 0 to 18 years (8.65 ± 3.93) for male sharks (Fig. 3). The most common age group in females was 12 years, accounting for 11.8%, while in males, it was the 11-year group, comprising 15.5%. The data met the assumption of homoscedasticity (Bartlett’s test χ² = 0.45538, d.f. = 1, P = 0.4998; χ² = 0.93745, d.f. = 1, P = 0.3329 for length and age, respectively); however, they did not meet the assumption of normality (Lilliefors test D = 0.088621, P = 9.709 × 10⁻⁶; D = 0.096942, P = 6.308 × 10⁻⁷ for length and age, respectively). Therefore, the Mann–Whitney U test was used, this indicated significant differences in size distribution (W = 12172, P = 0.0118) but not in ages (W = 11726, P = 0.0582) for both sexes.

Fig. 3.

(a) Size distribution and (b) ages of silky sharks (Carcharhinus falciformis) in the Ecuadorian South Pacific. The lines indicate the average for each sex.

Morphometric relationships

Of the 542 specimens measured, all linear regression models showed a strong correlation and a significant fit (R² > 0.97, P < 0.05) between the different length metrics (TL, FL, PCL, and IDL) for combined sexes, males, and females (Table 3). This allowed the estimation of TL for individuals that arrived mutilated at port (without a head, caudal fin, or both) (Fig. S1), which was subsequently used in age and growth models.

Precision and bias

The analysis of precision and bias yielded the following results: CV = 3.33, APE = 2.35, PA = 64.8. There were no significant variations in the bias plot regarding the readings of both readers (Fig. 4), except for age groups >16 years. Despite this, the results of the Bowker symmetry test showed that there was no systematic bias between the readings of the first and second reader (χ² = 33.66, d.f. = 29, P = 0.29).

Fig. 4.

Bias plot between Reader 1 and Reader 2 of sectioned vertebral centra of Carcharhinus falciformis. The reference line indicates equivalence (1:1), and error bars represent 95% confidence intervals.

Age verification

Regarding the marginal increment analysis, the Kruskal–Wallis (K–W) test detected significant differences among the different months (χ² = 23.2, d.f. = 11, P = 0.02). July had the lowest MIR values, while January had the highest MIR values (Fig. 5). The MIR results possibly suggest that one growth band pair forms per year, between June and July. Opaque edges predominated in January, while translucent edges were more common between July and August (Fig. 6).

Fig. 5.

Marginal increment ratio (MIR) plot for combined sexes of Carcharhinus falciformis, based on sampling months and the number of samples measured in each month. All age groups with age estimations ≥1 year were included (n = 286). K–W refers to the Kruskal–Wallis statistical test.

Fig. 6.

Progression of opaque and translucent edges during the sampled months, along with the average sea surface temperature (SST) (n = 286). The numbers reflect the quantity of opaque and translucent bands observed during the different months.

The statistical method of Okamura and Semba (2009), which verifies edge deposition, provided contrasting results to the MIR analysis. It demonstrated that the band pairs of C. falciformis in this study exhibited an acyclic pattern, as indicated by the Akaike Information Criterion (AIC) values (Model N: 398.2564). In comparison, the annual deposition scenario (Model A: 399.088) and biennial deposition (Model B: 401.8413) received less support. However, the AIC difference between Models N and A was less than 2, suggesting that both models were competitive. Nevertheless, following the principle of parsimony, Model N was preferred as the more parsimonious explanation.

Age and growth parameters

In the frequentist analysis, the model that best fit the data was the Logistic model for combined sexes, yielding the following parameters: asymptotic length (L_∞) = 230.52 cm TL; growth coefficient (g) = 0.22 year⁻¹; and length-at-birth (L₀) = 79.97 cm TL. For females, the parameters were L_∞ = 229.17 cm TL, g = 0.23 year⁻¹, and L₀ = 77.24 cm TL. For males, the parameters were L_∞ was 229.19 cm TL, g = 0.20 year⁻¹, and L₀ = 82.07 cm TL (Table 4; Fig. 7). There were no significant differences in the estimated growth parameters between sexes for the von Bertalanffy model (Likelihood ratio test: χ² = 5.417, P = 0.144), the Logistic model (χ² = 5.519, P = 0.137), and the Gompertz model (χ² = 5.517, P = 0.138).

Fig. 7.

Growth curves for (a) combined sexes, (b) females, and (c) males using frequentist methods, and (d) combined sexes, (e) females, and (f) males using Bayesian methods for Carcharhinus falciformis. Points represent observed age-by-size values (n = 290), and the range of curves reflects 95% confidence and credibility intervals for frequentist and Bayesian analyses, respectively. The best-fitting models were the von Bertalanffy model for the Bayesian framework and the Logistic model for the frequentist approach.

For the Bayesian approach, the Gelman–Rubin test statistics indicated convergence in the growth parameters of the VBGF model for combined sexes (L_∞ = 1.001404, k = 1.001250, L₀ = 1.000054, σ = 1.000083; Figs S2 and S3), females (L_∞ = 1.0001456, k = 1.0002739, L₀ = 1.0002721, σ = 0.9999791, Figs S4, S5), and males (L_∞ = 1.0001694, k = 1.0001526, L₀ = 1.0001463, σ = 0.9998547; Figs S6 and S7). The model that provided the best estimations was the VBGF for combined sexes (L_∞ = 271.54 cm TL, k = 0.09 year⁻¹, L₀ = 72.21 cm TL), females (L_∞ = 271.83 cm TL, k = 0.09 year⁻¹, L₀ = 71.61 cm TL), and males (L_∞ = 273.60 cm TL, k = 0.08 year⁻¹, L₀ = 72.99 cm TL) (Table 5; Fig. 7), according to LOOIC. The age and growth data extracted from the VBGF model showed an overlap between sexes of 78.52%, 57.51%, and 89.87% for the parameters L₀, k, and L_∞, respectively (Fig. S20). Therefore, the growth estimates obtained from the models were interpreted for combined sexes.

Morphometric relationships

Shark landings in Ecuador are very common throughout the year, with most of these sharks being eviscerated when they arrive at artisanal ports. This activity complicates the collection of morphometric measurements due to the absence of their extremities, resulting in a lack of information regarding their lengths, which are crucial for fisheries management (De Wysiecki and Braccini 2017; Mejía and Briones-Mendoza 2024). Considering these issues, our study established new coefficients to estimate TL from partial length measurements of C. falciformis. The choice of equation for future studies will largely depend on the condition in which the shark arrives at port. For instance, if a shark is missing only its caudal fin, the TL-PCL relationship may be the most appropriate. Conversely, if the specimen arrives without its head and fins, the TL-IDL relationship might be more suitable. Therefore, these equations facilitate the reconstruction of TL for mutilated specimens, thereby improving the accuracy of studies that rely on such biological data.

Precision and bias

The counts conducted by both readers on the vertebrae of C. falciformis resulted in a coefficient of variation of 3.32 and an average percent error of 2.35. These values fall within the acceptable error range proposed by Campana (2001) (7.6 and 5.5, respectively), indicating a reliable level of precision in our age estimations. The obtained indices were lower than those reported by Grant et al. (2018) (CV = 10.8, APE = 7.6) and Santander-Neto et al. (2021) (APE = 5.61), who also used vertebral centra sectioned with a thickness of 0.3–0.4 mm. These differences may be associated with the difficulty of estimating ages in larger sharks. The samples presented in this study consisted primarily of small and young individuals compared to the study by Grant et al. (2018) who provided much higher age estimates and demonstrated systematic bias (Bowker, P < 0.05). This likely reflects the impact of larger individuals in this species, as they exhibit more band pairs deposited in their vertebral centra, which can lead to increased uncertainty in age determination (Goldman et al. 2012; Harry 2018).

Age verification

Various methodological procedures exist for verifying and validating age in elasmobranchs, including captive growth studies, oxytetracycline (OTC) mark–recapture analysis, and carbon bomb techniques (Cailliet and Goldman 2004). In this study, we opted for MIR method, which has been employed to determine the periodicity of band pairs in sharks’ vertebrae (Goldman 2005), owing to its minimal sampling needs and cost-effectiveness (Campana 2001).

The lowest MIR median was observed during July, subsequently increasing until January. This pattern aligns with findings by Hall et al. (2012) and Santander-Neto et al. (2021) for C. falciformis, who reported that band pair deposition occurred in June and July, respectively. In contrast, Joung et al. (2008) and Sánchez-de Ita et al. (2011) reported low values of this index during the early months of the year. Such variations in trends are often associated with seasonal cycles, where opaque bands are deposited during warmer periods, while translucent bands are deposited in winter (Cailliet et al. 2006).

The deposition of band pairs appeared to correlate with temperature variables, with translucent bands likely forming in July, coinciding with the dry season in the Ecuadorian Pacific, during which sea surface temperatures are relatively low (Chinacalle-Martínez et al. 2021). However, the method proposed by Okamura and Semba (2009) demonstrated that CEA in this study did not exhibit any annual or biennial patterns, likely due to the low number of samples collected during certain months or the difficulty in measuring and determining edge types in semi-adult and adult individuals. Due to the inconclusiveness of our results, we considered assumptions from other studies indicating that band pair deposition in C. falciformis likely occurs annually.

It has been reported that species within the Lamnidae and Sphyrnidae families may exhibit biennial deposition of growth band pairs during certain life cycle stages (e.g. Isurus oxyrinchus, David Wells et al. 2013; Sphyrna lewini, Anislado-Tolentino and Robinson-Mendoza 2001). In the case of C. falciformis shark, band pair deposition has been described solely using MIR method, with researchers assuming annual periodicity in its band pairs of C. falciformis (Branstetter 1987; Bonfil et al. 1993; Oshitani et al. 2003; Joung et al. 2008; Sánchez-de Ita et al. 2011).

However, as an indirect method for age verification in elasmobranchs, it is challenging to determine whether the deposition of band pairs remains annual throughout the entire life cycle. An unvalidated age interpretation can pose significant risks to the population dynamics of a species (Ardizzone et al. 2006). Given that age in C. falciformis has not been validated using more robust and direct methods (e.g. oxytetracycline injection, bomb radiocarbon), it is recommended that future studies validate both early and advanced ages of this species to ascertain whether bands pairs maintain a consistent annual deposition pattern across different life stages.

Age and growth parameters

The inferences drawn from the growth multimodels in this study differed between the two approaches considered (frequentist and Bayesian). In the frequentist approach, the model that received the most support based on AIC was the Logistic model across all three scenarios (combined sexes, females, and males) (Table 4). However, it resulted in under-estimated growth estimates for certain parameters, such as the L_∞ of this species, which was notably shorter than reported maximum lengths in the Pacific (>150 cm TL; Oshitani et al. 2003; Martínez-Ortíz et al. 2011; Sánchez-de Ita et al. 2011; Grant et al. 2018; Briones-Mendoza et al. 2022) and deviated from findings reported in other age-growth studies from different regions (Table 6). For example, Grant et al. (2018) found a greater L_∞ (268 cm TL, frequentist Logistic model) in the western-central Pacific compared to this study (230.52 cm TL, frequentist Logistic model). The estimated values were likely influenced by sampling bias towards larger individuals (>238 cm TL), compared to other reports that included larger sizes in their samples (Table 6). Indeed, it has been previously shown that growth models are very sensitive to the absence of young and adult individuals, as these data points are crucial for defining the growth curve’s extremes (Haddon 2011; Smart and Grammer 2021).

In this context, the von Bertalanffy Bayesian model, which utilises prior information on length-at-birth and maximum observed length of the species for size-at-age analysis (Smart and Grammer 2021), provided more accurate estimates of growth parameters. Therefore, these estimates should be used in future population models. In the present study, the high overlap of growth parameters between sexes indicated no significant differences in growth between males and females, consistent with previous studies on age and growth in C. falciformis (Table 6). Grant et al. (2018) and Santander-Neto et al. (2021) suggest that this pattern may reflect similar growth rates between sexes for this species.

The length-at-birth obtained using the von Bertalanffy Bayesian model (L₀ = 71 cm TL) falls within the range reported for this species at birth across various geographical areas: north-east Taiwan (63.5– 75.5 cm TL; Joung et al. 2008), Campeche Bank (76 cm TL; Bonfil et al. 1993), north-western Gulf of Mexico (72 cm TL; Branstetter 1987), south-western Atlantic (76 cm TL; Santander-Neto et al. 2021), central-west Pacific (65–71 cm TL; Grant et al. 2018), and eastern Indonesia (57.1–99.2 cm TL; Hall et al. 2012). This is consistent with the length-at-birth suggested by Oshitani et al. (2003) for the Pacific Ocean regions (65–81 cm TL), indicating that our results reflect realistic estimates aligned with the biology of C. falciformis.

The asymptotic length of the von Bertalanffy Bayesian model (L_∞ = 271.14 cm TL) was similar to that estimated by Grant et al. (2018) (L_∞ = 268.3 cm TL) and higher than that reported by Sánchez-de Ita et al. (2011) (L_∞ = 240 cm TL) in the Pacific Ocean. However, it differed from reports in the Atlantic Ocean, where C. falciformis appear to reach a greater L_∞ and grow more rapidly (Table 6). These variations are presumed to be due to latitudinal differences, as has been observed in some elasmobranch species (e.g. Sphyrna tiburo and Dipturus chilensis), where variations in life history parameters were evident at different latitudes (Lombardi-Carlson et al. 2003; Licandeo and Cerna 2007). Cope (2006) indicated that certain shark populations may exhibit greater growth at higher latitudes, as well as larger size, longer lifespan, and slightly delayed sexual maturity compared to their counterparts at mid and adjacent latitudes. However, other factors such as local fishing pressure, fishing gear and methods, methodological differences, diet, and environmental and genetic influences may also contribute to variations in life history traits (Baje et al. 2019; Vinyard et al. 2019; Estupiñán-Montaño et al. 2021). Therefore, further investigation is necessary to understand the actual mechanisms driving C. falciformis to display divergent life history traits across different latitudinal scales.

In Ecuadorian waters, the estimated maximum length (L_∞ = 335 cm TL, Gilces-Anchundia 2013) and the observed maximum lengths (TL = 310 cm, Estupiñán-Montaño et al. 2018; TL = 309 cm, Martínez-Ortíz et al. 2007) of C. falciformis were substantially higher than the estimates obtained in this study. However, the biological sampling records from these studies date back over 10 years, and it is possible that large, mature specimens may have experienced historical mortality due to overfishing, owing to the selectivity of fishing gear (Thorson and Simpfendorfer 2009). This could largely explain this phenomenon and why our study evidenced a high frequency of younger ages compared to other age and growth studies reported for this species (Table 6). While gear selectivity cannot be ruled out as a contributing factor, biased sampling may also have influenced the results. However, this study did not allow for detailed documentation of the fishing gear and methods used. Therefore, future research should prioritise collecting this information.

The estimated growth coefficient (k = 0.09 year⁻¹) using the von Bertalanffy Bayesian model was lower than that observed in the Atlantic Ocean (Branstetter 1987; Bonfil et al. 1993; Santander-Neto et al. 2021) but similar to that reported by Hall et al. (2012) in the Indian Ocean (Table 6). Although the k and g parameters cannot be compared across models as they do not represent an empirical growth rate (Smart et al. 2015), the growth curve for the Central Western Pacific (Grant et al. 2018) using the Logistic function appears similar to that obtained in Ecuadorian waters in this study, in contrast to the curves observed in other previous studies of the Pacific Ocean, which differed significantly (Fig. 8). Genetic studies of C. falciformis suggest population genetic differentiation in the Pacific Ocean (Galván-Tirado et al. 2013; Clarke et al. 2015), which could explain these divergences. Another detail that may also explain these variations among studies is the estimation of growth parameters using frequentist methods when the sample is not sufficiently representative and does not cover the entire size range for the species (Table 6). This is one of the significant issues that leads to under-estimations or over-estimations of the asymptotic length, as observed in this study, where the under-estimation of L_∞ is likely due to the absence of larger individuals. Differences affecting L_∞ also influence k, as there is a negative correlation between the parameters L_∞ and k/g (Pardo et al. 2013).

Fig. 8.

Comparison of the overall growth curves of Carcharhinus falciformis from various studies: Branstetter (1987) in the Gulf of Mexico; Bonfil et al. (1993) in the Campeche Bank, Oshitani et al. (2003) in the central Pacific; Joung et al. (2008) in north-east Taiwan; Sánchez-de Ita et al. (2011) in the east Pacific; Hall et al. (2012) in eastern Indonesia; Gilces-Anchundia (2013) in Pacific Ecuadorian waters, Grant et al. (2018) in the central-west Pacific; and Santander-Neto et al. (2021) in the south-western Atlantic.

These discrepancies could also be due to the different methodologies used in the various studies. For example, Grant et al. (2020), in an intraspecific demographic analysis of C. falciformis, suggest that many of the differences in C. falciformis growth parameters could be due to sampling design and methodological differences. Other factors such as diet and environmental conditions have also been argued (Estupiñán-Montaño et al. 2018). Another reason may be that most age and growth studies on this species, except for Grant et al. (2018) and Santander-Neto et al. (2021), have emphasised the exclusive use of the von Bertalanffy growth model without considering multimodel evidence. It has been shown that not considering multimodel inference can lead to potentially inaccurate estimates, even when VBGM is recognised to provide the best fit (Katsanevakis 2006). However, the notion that a model perfectly aligns with the life history characteristics of a species is not entirely true; Smart et al. (2016) refuted this theory and demonstrated that the selection of a specific growth model is not related to the taxon or reproductive method exhibited. Therefore, it is likely that the variations in growth parameters for this species across different regions are due to both real and methodological differences, as has previously emerged in other shark species (Harry et al. 2011, 2013). Therefore, the discrepancies in these results remind us of the complexity and uncertainty that surrounds studies of age and growth. Thus, it is necessary that future population and demographic studies that use the parameters presented here include the uncertainty that exists around the age and growth parameters.