Study Area. —

I studied a population of G. morafkai in the northeastern Sonoran Desert near Sugarloaf Mountain in the Tonto National Forest, Maricopa County, Arizona, USA. The study area occurred within the paloverde-mixed cacti series of the Arizona Upland Subdivision of the Sonoran Desert (Turner and Brown 1982). Arroyos divided a rolling topography of steep, rocky slopes with boulders up to 4 m in diameter and elevations from 549 m to 853 m.

Data Collection. —

Thirty-five female tortoises (150–289 mm midline carapace length [CL]) were monitored weekly using radio telemetry in 1993 and from 1997 through 2005 as part of a reproductive ecology study (Averill-Murray 2002; Averill-Murray et al. 2018). A sample of 10 males (191–265 mm CL) also was monitored. Subsequently, Bridges et al. (2016) monitored 11 juveniles (< 180 mm CL) between April 2010 and December 2011. Bridges et al. (2016) and Averill-Murray et al. (2018) describe measurement, transmitter attachment, and tracking details. In addition, opportunistically encountered tortoises were also marked and measured, and additional tortoises were located and measured through 2016 during various site visits and informal surveys outside the periods of telemetry monitoring (n = 29 females, 34 males, 9 juveniles).

Hypotheses and Statistical Analyses. —

To better understand the growth characteristics of desert tortoises at Sugarloaf, I applied size data to the 4 commonly used growth functions described above. I also tested the hypothesis that growth parameters (e.g., asymptotic CL, L_∞, and intrinsic growth rate, k [i.e., the rate of approach toward L_∞]) did not vary by sex. I used the first CL measurement plus the last CL measurement in each subsequent year that each tortoise was measured to fit nonlinear mixed-effects models with the nlme package in R 4.3.2 (Pinheiro et al. 2023; R Core Team 2023). I fit the data to the interval form of the growth models (Table 1), and I used modified equations that divided k by L_∞ to minimize the correlation between these 2 parameters, which results when they are allowed to vary by individual (Armstrong and Brooks 2013). Twenty tortoises with CL < 174 mm had undetermined sexes at final measurement (Appendix 1). To balance improved model fit at the small end of the curves where fewer data were available with minimizing obfuscation of possible sex-specific growth effects, I excluded tortoises whose sex was not ultimately determined and whose CL at the end of any year exceeded 127 mm, which is the midpoint of the hatchling size and the minimum size at maturity for males (see below). This resulted in the inclusion of 11 growth intervals from nine tortoises as both male and female (CL range = 47–124 mm; Appendix 1). For each growth function, I first fit a random-effects model (L_∞ ∼ 1|tortoise ID) without sex as a predictor of the fixed effects; models with k as a random effect did not converge. Then I sequentially evaluated the effect of sex on each parameter with AICc (Burnham and Anderson 2002) until a final model of fixed effects was reached; I compared the final model with the analogous model lacking random effects to confirm the need for those effects (Pinheiro and Bates 2000). Given the lack of non-normal residuals, I computed bootstrapped confidence limits for growth parameters with package nlraa (Miguez 2023). I compared models with AICc to select the best overall model.

Table 1. Equations for age-specific and interval models of individual growth used in this study. Parameters: t = age (yrs), CL_t = carapace length (mm) at age t, k = characteristic growth-rate coefficient, L_∞ = asymptotic carapace length, m = shape constant, b = parameter related to carapace length at t₀, e = base of natural logarithm, CL₁ = carapace length at t₁, CL₂ = carapace length at t₂, Δt = time interval (t₂–t₁, yrs). L_∞ and m were allowed to vary by individual in nonlinear, mixed-effect models using the interval equations.

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I applied model parameters to the age-specific curve parameterizations (Table 1) to plot growth curves. Here I assigned hatchling size = 44 mm at age 0 based on the smallest marked individual in the database, which is similar to a 46-mm hatchling found emerging from a nest (unpublished data). I estimated age of maturity of females from growth models using a minimum size at maturity of 220 mm CL (Averill-Murray et al. 2018) and for males using a minimum size at maturity of 210 mm CL (Owens et al. 2019), both derived from this population. Solving models for age at CL = 220 or 210 mm (Table 1), I calculated the estimated range of age at maturity using the estimated parameters for the best-fitting model and their respective 95% bootstrapped confidence intervals. I also calculated the age at which tortoises attained 180 mm CL, when individuals are estimated to achieve adult-level survival rates (Zylstra et al. 2013).

I used short-term growth rates to evaluate factors that could affect seasonal or annual growth: CL₁ (initial measurement of the year), reproductive status, and 3 measures of seasonal precipitation to proxy vegetation production that could contribute to seasonal growth. Measures of precipitation included winter rainfall, early spring rainfall, and their sum, as reported by Averill-Murray et al. (2018). I followed Cox et al. (1991) to calculate relative daily instantaneous growth (ΔGR_d): $$△G{R}_d\hspace{0.17em}=\hspace{0.17em}\frac{\text{ln}C{L}_2\hspace{0.17em}-\hspace{0.17em}\text{ln}C{L}_1}{t_2\hspace{0.17em}-\hspace{0.17em}{t}_1},$$where CL₁ is size at first capture, CL₂ is size at last capture, and (t₂ – t₁) is the time between first and last capture in days. I used the subset of data for which I could estimate ΔGR_d from a minimum 90-day interval between CL measurements within a calendar year (91–274 days) and for which I knew reproductive status for that year (gravid female, nongravid female, adult male, immature). I excluded years with fewer than 13 cases (i.e., outside 1997–2002), and the final dataset included 121 cases. I used linear mixed-effects models with nlme to evaluate models with reproductive status plus CL₁ (in cm) and standardized seasonal precipitation, with and without interactions between the latter 2 predictors. All models included tortoise ID as a random effect. I used AICc to compare all models with 3 different variance structures on the factor CL₁ to correct for heteroscedasticity. The final model was ΔGR_d ∼ CL₁ + z.WinterRain + ReproductiveStatus, random = ∼1|ID, weights = varPower(∼CL₁). I further looked at variation in growth and reproduction in adult female tortoises by comparing the weighted means of females that reproduced or did not reproduce among those that exceeded or did not exceed the mean female L_∞ across years during which at least 2 females were of known reproductive status (1993, 1997–2002).

Finally, I extracted the 52 female tortoises with a CL > 219 mm and 34 males with a CL > 209 mm at any measurement, for which time between that observation and final measurement was at least 1 yr (1.0–22.7 yrs). Then I calculated each tortoise’s relative annual instantaneous growth (ΔGR_y). I used generalized least squares regression with nlme to determine how much ΔGR_y declined with CL₁. I used an identity variance structure on the factor sex to correct for heteroscedasticity and compared models with and without the sex predictor with AICc. For comparison, I calculated the ΔGR_y for 36 immature tortoises with capture intervals of 1.25–13.95 yrs.

Individual and Sex-Specific Variation. —

Given the variation seen in other biological traits, growth rates are expected to vary within and among individuals, populations, and species (Congdon et al. 2013). Therefore, it is not surprising that growth of G. morafkai varied substantially among individuals and differed by sex at Sugarloaf. Studies have consistently confirmed substantial variation in individual growth characteristics—whenever attempts have been made to model it (King et al. 2016; Armstrong et al. 2018; Harden et al. 2021). For example, individual variation in growth overshadowed differences in vegetation treatment in a population of eastern box turtles (Terrapene carolina carolina; Edmonds et al. 2020). Many studies also have documented decreasing growth rates with increasing body size across reptilian taxa, consistent with the general pattern of asymptotic lifetime growth (turtles: Plummer 1977; Kennett 1996; Dodd and Dreslik 2008; Nafus 2015; Siders et al. 2023; lizards: Smith et al. 2010; Jessup et al. 2022; snakes: Webb et al. 2003; Dreslik et al. 2017; crocodilians: Campos et al. 2014). Larger tortoises at Sugarloaf grew less per day than smaller tortoises, but growth of immature tortoises was highly variable, reflecting the broad range of immature sizes across a relatively small sample spread over 6 yrs (96–209 mm CL; n = 20).

Variation in immature growth may partly be attributable to sex-specific differences. For example, the greatest effect of not including tortoises of unknown sex with CL > 127 mm was in lowering male k/L_∞ by 0.01 and creating greater separation between the curves of the 2 sexes, which further slowed the approach to L_∞ and added 1.1 yrs to the estimated male age at maturity (not shown). Combining all individuals of unknown sex would have dampened these differences. Ultimately, Sugarloaf males reached a mean L_∞ 11 mm greater than females (262.5 mm vs. 251.6 mm). Differences in L_∞ are even greater for Mojave Desert tortoises (Gopherus agassizii), with male CLs exceeding females by > 30 cm (western Mojave male:female = 283.0:245.7 cm; eastern Mojave = 266.0:233.1 cm; Germano 1994).

Changes in growth coincide with shifts in energy allocation from growth to reproduction, i.e., decreasing as adult females begin developing ovarian follicles and during the onset of egg laying (Christiansen and Burken 1979; Galbraith et al. 1989; Marchand et al. 2018). This energetic shift appeared to be the case for gravid Sugarloaf females, which had lower growth rates than nongravid females, immature females, and males (Fig. 4). Males and females also had similar growth rates in a population of G. agassizii until the age of 23–25 yrs, when female growth slowed more than male growth (Medica et al. 2012). Male and female snapping turtles (Chelydra serpentina) and Galapagos tortoises (Chelonoidis spp.) also had similar growth rates before females began approaching their asymptotic carapace length upon reaching sexual maturity (Armstrong and Brooks 2013; Gibbs and Goldspiel 2021). However, many emydid turtles exhibit the opposite pattern, whereby females grow more slowly than males but reach larger sizes (e.g., Lindeman 1999; Lewis et al. 2018; Harden et al. 2021).

Both male and female turtles have the potential to experience increased reproductive success as size increases, males as consequence of greater mating success (Berry and Shine 1980; Brooks et al. 1992; Niblick et al. 1994; Sung et al. 2015; Blake et al. 2021) and females through enhanced fecundity (Congdon and Gibbons 1985; Turner et al. 1986; Mueller et al. 1998; Howell et al. 2019). However, despite the reproductive advantages of larger size, various external constraints likely limit optimum sizes, such as burrow use by desert tortoises (Nafus 2015) or distance to nesting areas in Galapagos tortoises (Gibbs and Goldspiel 2021). The former is especially true for G. morafkai, which often (or usually) excavates burrows below rocks and boulders that have less capacity for modification by ever-growing individuals than soil burrows (Averill-Murray et al. 2002a; Averill-Murray and Averill-Murray 2005; but see Riedle et al. 2008 and Sullivan et al. 2016).

Growth and Reproduction Relative to Size and Age at Maturity. —

High residual reproductive value of mature female turtles (Congdon et al. 1994; Cunnington and Brooks 1996) suggests that adult survival should be prioritized over reproduction, and growth should not be prioritized unless it enhances survival and future reproduction rather than compromising it (Williams 1966, in Armstrong et al. 2018). Accordingly, Sugarloaf females grew only ∼15% beyond their size at maturity, whereas males grew ∼25% more, based on the mean asymptotic size for each sex. However, some exceptional individuals (e.g., Female no. 3) continued growing beyond the mean size at maturity, mean asymptotic size, and the mean size at which relative annual growth ceased (Fig. 7). Larger females were more likely to reproduce each year, and they produced larger eggs compared to smaller females (Averill-Murray et al. 2018). This demonstrates the reproductive advantages of sustained growth beyond the size at maturity, despite potential constraints on upper size limits. Similarly, even with substantial variation in individual growth and reproductive output, female C. serpentina increased average clutch size and clutch mass between their minimum size at maturity and L_∞ by 37% and 107%, respectively (Armstrong et al. 2018). Female G. agassizii in a semicaptive population ceased growing at 258 mm CL on average, but 5% exceeded 301 mm, presumably with concomitant increases in reproductive output (Nafus 2015).

Age-at-size estimates from Germano et al. (2002) and Curtin et al. (2009) produced ages at maturity of 19–33 yrs for G. morafkai, leading to estimated generation lengths of 30–43 yrs (= Σxlxmx/Σlxmx, where x is age, lx is survivorship up to age x, and mx is fecundity at age x; Averill-Murray 2023). Applying the minimum age of female maturity of 15 yrs estimated here (and age at adult-level survival at 180-mm CL of 11 yrs) produces generation lengths of 23–28 yrs. Such generation lengths ultimately mean that, under the IUCN Red List assessment (Averill-Murray et al. 2023), the estimated 47.7% three-generation mean population decline occurred over as many as 60 fewer yrs than estimated with later ages at maturity (i.e., maximum difference in three-generation lengths of 69 [current] vs. 129 [previous] yrs). This estimate does not affect the assessment’s conclusions other than by highlighting the rate at which population change can happen based on potential variability in this demographic parameter. It also provides a degree of optimism about the relative rate at which populations might stabilize or recover if factors affecting declines are mitigated. However, the challenges and duration necessary for recovering long-lived species following declines should not be underestimated (Keevil et al. 2018); 23–28 yrs remains a long time for consistent, effective management, and of course even longer-term sustained management is necessary to ensure effective conservation.

In contrast to the relatively similar ages at maturity (within 2 yrs) estimated for male and female G. morafkai, sexual size dimorphism often leads to differences in age at maturity, i.e., sexual bimaturation (Bulté and Blouin-Demers 2009). The larger sex virtually always matures later (Stamps and Krishnan 1997) and almost always has a smaller k, approaching its asymptotic size more slowly (Germano 1994; Lindeman 1999; Bulté and Blouin-Demers 2009). Gopherus morafkai males did mature 1.8 yrs later than females on average, but at a smaller size than females, and they did approach their asymptotic size more slowly (Fig. 2). Sexually size-dimorphic species may reduce sexual bimaturation in 1 of 3 ways (Stamps and Krishnan 1997): 1) members of the larger sex have higher k (opposite for G. morafkai); 2) members of the larger sex have larger size at birth or hatching (no evidence for G. morafkai); or most commonly 3) members of the larger sex have a smaller relative size at maturity (L_mat:L_∞). The latter mechanism includes the relationship between male and female G. morafkai at Sugarloaf (male L_mat:L_∞ = 0.80; female L_mat:L_∞ = 0.87).

The small difference in age at maturity in G. morafkai also may be related to the relatively small difference in L_mat between the sexes; female L_mat is only 4.8% greater than male L_mat, and they matured 10.7% earlier than males. In contrast, among 7 species and 9 populations of sexually dimorphic emydid and chelid turtles, the larger sex was 25–118 mm larger (16%–157%) than the smaller sex at maturity and had corresponding ages at maturity 1.5–7.2 yrs later (14%–160%); the wood turtle (Glyptemys insculpta) was an exception in which males and females were estimated to have the same age at maturity (Kennett 1996; Bulté and Blouin-Demers 2009; Congdon et al. 2013). Gopherus morafkai was more similar to T. carolina carolina for which males matured at sizes 4.2% larger than females (∼124 mm vs. ∼119 mm CL) and 5.1% later (8.2 vs. 7.8 yrs; Edmonds et al. 2020).

Iteroparity with indeterminate growth (i.e., growth continues after reproduction begins) often is selected for in stochastic environments where fluctuating conditions result in uncertain fecundity and survival rates at younger ages rather than uncertain survival at older ages (Katsukawa et al. 2002). The need to diversify the risk of reproduction in stochastic environments leads to indeterminate growers reproducing before they reach an “optimal” body size, which maximizes the long-term population growth rate under constant environmental conditions averaged over several years (Katsukawa et al. 2002). The pattern of L_mat:L_∞ among G. agassizii and G. morafkai across the environmental gradient from the western Mojave Desert through the Sonoran Desert illustrates the degree to which environmental stochasticity contributes to indeterminate growth among these closely related species (Table 3). The western Mojave Desert is characterized by unpredictable, winter-dominated rainfall, and the female G. agassizii L_mat:L_∞ ≈ 0.72. This result compares to the L_mat:L_∞ = 0.87 for G. morafkai females at Sugarloaf in the more predictable, biphasic summer/winter rainfall in the Arizona Upland of the Sonoran Desert. Female G. agassizii in the intermediate eastern Mojave Desert have an intermediate L_mat:L_∞ ≈ 0.81. Estimates of male L_mat:L_∞ follow a similar pattern with western Mojave ≈ 0.60–0.67, eastern Mojave ≈ 0.68–0.75, and Sugarloaf = 0.80. Stamps and Krishnan (1997) found that both sexes in the lizard genus Anolis shared a strong positive correlation between L_mat and L_∞, and larger species tended to mature at smaller relative-to-maximum lengths than smaller species. They suggested that differences in L_∞ may result from selection on L_mat. Given the documented variation in L_∞ among local desert tortoise populations, additional study is necessary to determine if similar relationships exist within these taxa and how potential variation in L_mat affects population demography.

Table 3. Relative sizes of maturity (L_mat:L_∞) for desert tortoises in the Desert Southwest of the USA. L_mat = carapace length at maturity; L_∞ = asymptotic carapace length. L_mat is unavailable for male Gopherus agassizii, so an estimated range is bracketed around that for females.

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Not only does the relative size at maturity decrease as the environment becomes harsher and less predictable across the US Desert Southwest, but populations also vary in diversifying reproduction risks along the spectrum of environmental stochasticity and predictability. By delaying reproduction until near L_∞, G. morafkai females can produce eggs of a relatively uniform size that are larger than the long-term optimum via a conservative bet-hedging strategy (Ennen et al. 2017). In contrast, G. agassizii in the western Sonoran Desert (and probably throughout the Mojave Desert) begin reproduction at relatively smaller sizes and produce multiple clutches per year via a within-generation bet-hedging strategy. They combine this with a strategy that diversifies egg phenotypes (width) among clutches, with mean egg size decreasing in subsequent clutches within reproductive seasons (Ennen et al. 2017).

Geographic and Environmental Variation. —

Growth patterns across Gopherus species appeared not to be directly influenced by measures of precipitation and temperature within their range (Germano 1994). These conclusions may be compromised by pooling individuals across the range of each species, although mean annual growth was negatively correlated with mean annual precipitation across regions for G. agassizii (including populations now recognized as G. morafkai). Additional data would provide a more precise understanding of the role of winter rainfall, spring vegetation production, and growth, but winter rainfall did appear to contribute to interannual variation in individual growth of G. morafkai at Sugarloaf. Similarly, greater winter rainfall and spring plant production led to increased annual growth in a population of G. agassizii (Medica et al. 2012), and forage produced via rain supplementation stimulated increased growth in juvenile G. agassizii in natural enclosures in 2 parts of the range (Nagy et al. 2015; Nafus et al. 2017). Drought conditions also limited the growth of Galapagos tortoises (Gibbs and Goldspiel 2021) and painted turtles (Chrysemys picta) in Nebraska (Powell et al. 2023).

If growth is largely negligible in adults, as for most Sugarloaf tortoises, size differences must then be explained largely by variation in resource availability to different cohorts earlier in life (Madsen and Shine 2000), intrinsic differences between individuals or populations (Medica et al. 2012), or differences in other environmental conditions, such as length of activity/growing season (Seigel 1984; Marchand et al. 2018), differential mortality (Seigel 1984; Spencer et al. 2006), incubation temperature (Spotila et al. 1994; Spencer et al. 2006), or other site-specific characteristics (Siders et al. 2023). Individual differences in growth can have population-level implications for reproductive success and survival (Iverson et al. 1997; Rowe 1997; Congdon et al. 2013; Armstrong et al. 2018), which can ultimately affect long-term population recovery and viability (Dodd and Dreslik 2008; Ashton et al. 2015; Harden et al. 2021). For example, poor food quality early in life can limit growth throughout the life of the individual (Madsen and Shine 2000; Rueda-Zozaya et al. 2021), especially for herbivores. Food quality provided to young female Mexican black spiny-tailed iguanas (Ctenosaura pectinata) had a strong influence on growth such that they reached their minimum size at reproduction later when fed low-quality food (Rueda-Zozaya et al. 2021). In the US Desert Southwest, invasion of non-native grasses such as Bromus spp. and buffelgrass (Pennisetum ciliare) can reduce the quality and quantity of plant foods available, causing nutritional deficiencies that can affect growth, health and condition, and survival of G. agassizii and G. morafkai (Hazard et al. 2009; Gray and Steidl 2015; Drake et al. 2016).

Predictable and productive environments may allow turtles to maximize resource use and allocate more energy to growth so that fast growth leads to earlier maturity and larger body sizes (Lindeman 1996; Litzgus et al. 2004; Marchand et al. 2018). An exceptional cohort of captive male G. agassizii that was provided continuous, high-quality food underwent remarkable growth, achieving 233-mm CL at the end of 4 years (cf. ∼ 20 yrs for Sugarloaf G. morafkai); they also exhibited courtship behavior, and a 236-mm individual had mature spermatozoa during its fourth year (Jackson et al. 1978). The ability to accelerate growth has led to head-starting strategies to produce larger, more predator-resistant juveniles under more natural conditions to facilitate recovery efforts for G. agassizii (McGovern et al. 2020). However, juvenile Murray River turtles (Emydura macquarii) in low-recruitment, lower-density populations predicted to be free of density-dependent resource limitations grew more slowly than juveniles in a high-recruitment, denser population (Spencer et al. 2006). When survival is high or resources are abundant, larger neonatal body size may not always confer the expected fitness benefits because of costs associated with diverting resources to growth from developmental, behavioral, or physiological processes such as longevity or energy storage (Gadgil and Bossert 1970; Forsman and Lindell 1991; Jonsson et al. 1992.

Life history underlies population viability analysis and is a central determinant of the time frame over which assessments are made, as illustrated above. Predicted effects of management efforts may be incorrect if estimated transition and individual growth rates are biased or if they change substantially (Spencer and Janzen 2010). Geographic variation in growth rates, maximum size, age at maturity, and litter size in the Guthega skink (Liophilus guthega) suggested different conservation management approaches for different populations (Atkins et al. 2020). Likewise, variation in male diamondback terrapin (Malaclemys terrapin) growth across sites within a narrow portion of its range and variation in growth and reproduction across the range of the northwestern pond turtle (Actinemys marmorata) led to recommendations for expanded study and synthesis of growth rates throughout their respective distributions to provide data to better evaluate population trends and to help inform management (Harden et al. 2021; Germano et al. 2022). Among G. morafkai populations in Arizona, the asymptotic carapace lengths and intrinsic growth rates of Sugarloaf tortoises fall between those of the small tortoises at the Granite Hills and the larger tortoises at Little Shipp Wash and the Eagletail Mountains (Table 4; Murray and Klug 1996). The smaller sexes and populations tend to grow more rapidly early in life before reaching a smaller asymptotic size, except that sexes at the Granite Hills reach a similar size (Averill-Murray et al. 2002b). Demographic implications of such variability remain to be determined with information on population-specific size/age at maturity and reproductive output.

Table 4. Growth curve parameter estimates from 4 populations of Gopherus morafkai in Arizona. L_∞ = asymptotic carapace length (mm); k = intrinsic growth rate (k/L_∞ for Sugarloaf); m = shape constant for Richards curve; AAM = estimated age at maturity (yrs). Sugarloaf is from this study; the other 3 populations are from Murray and Klug (1996). AAM is estimated from each curve’s unique parameter estimates based on minimum sizes at maturity of 220 mm and 210 mm for females and males, respectively. Subscripts indicate known-sex plus unsexed individuals included in each analysis.

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Variation in resource availability or quality also may be reflected in the shape of individual growth curves. For example, the point of maximum growth (i.e., percentage of L_∞ at curve inflection, P) occurs progressively later during the growth period at P = 0%, ∼37%, and 50% for the von Bertalanffy, Gompertz, and logistic curves, respectively (Richards 1959; Bradley et al. 1984). High-quality food resulted in logistic growth (P = 0.5) of C. pectinata, which reached their maximum size faster than those fed low-quality food and whose growth fit the Gompertz growth model (P ≈ 0.37; Rueda-Zozaya et al. 2021). In another example, maximum growth of gopher tortoises (Gopherus polyphemus) in a Florida population occurred during late juvenile and subadult stages under the logistic model (P = 0.5; Mushinsky et al. 1994), but the most rapid growth in an Alabama population occurred for early juveniles under the von Bertalanffy model (P = 0), a difference attributed to inferior forage in Alabama that did not support a subadult growth spurt (Aresco and Guyer 1999). The logistic curve best fits the data for Sugarloaf G. morafkai, suggesting a similar late juvenile/subadult growth spurt during the study period. Habitat management can improve population growth rates by increasing individual growth and maturation rates (Folt et al. 2021), and a closer examination of growth curves relative to habitat conditions would be useful for other taxa. Likewise, a more detailed analysis of differences in individual growth and habitat conditions between G. morafkai populations may improve population management and conservation trajectories for this species.