Palms were harvested in three tropical rain forest sites in the Caribbean lowlands of Costa Rica (Figure 1). The first two were La Selva Biological Station (10°26’N – 83°59’W, 30–150 masl, annual precipitation 4,162 mm) and Tirimbina Biological Reserve (10°24’N – 84°06W, 180–220 masl, annual precipitation 3,833 mm), both situated in Sarapiquí, Heredia. The third site was the lowland forest of the agroecological farm El Progreso (10°30’35” N – 83°44’39” W, 45 masl, annual precipitation of 4,000 to 5,000 mm), located in Pococí, Limón. The three sites present an average daily temperature of 25°C and have a weak climatic seasonality, with November, December and February being the rainiest months (McDade et al., 1994).

We selected four understory and three canopy palm species representing a wide range of growth forms and regeneration strategies. Understory species included Prestoea decurrens (n = 10), Chamaedorea tepejilote (n = 22), Geonoma interrupta (n = 10), and Asterogyne martiana (n = 15). Prestoea decurrens (Nicaragua to Ecuador, 0–900 masl), is a clonal species reaching 10 m in height in the tallest individuals (Grayum, 2003). Chamaedorea tepejilote (S Mexico to Colombia, 0–1,600 masl) is a dioecious species which can grow up to 5 m (Castillo-Mont et al., 1994; Grayum, 2003). Geonoma interrupta (S Mexico to Peru, 0–850 masl) has a solitary stem and may reach 6 m in height (or over 10 m in exceptional cases), being considered as one of the tallest species in the genus (Grayum, 2003). Finally, Asterogyne martiana (Belize to Ecuador, 0–1,000 masl) is shade-tolerant species with a decumbent stem often reaching 2 m in height, and with simple, bifid leaves. The canopy species Socratea exorrhiza (n = 10, S Nicaragua to Brazil, 0–750 masl) and Iriartea deltoidea (n = 10, SE Nicaragua to Brazil, 0–800 masl) can reach 25 and 30 m of stem height, respectively, and are characteristic canopy components of mature forests (Grayum, 2003). Both species have a cone of stilt roots, although roots in I. deltoidea are clustered at the base of the stem and grow up to 1.5 m above ground, and in S. exorrhiza roots are well-separated, covered by spines, and can grow up to 4 m above the ground (Henderson et al., 1995). Both species show plasticity in the diameter vs. height allometry associated with geographic location and terrain slope (Avalos et al., 2019). Euterpe precatoria (n = 10, Belize to Bolivia, 0–1,150 masl) var longevaginata (Henderson, 1995) is often classified as a subcanopy species (Zuidema and Boot, 2000). It is a single-stemmed palm that can reach 26 m in height, developing a stilt root cone that in extreme cases may reach over 2 m above the ground (Avalos and Schneider, 2011). It is a cryptic pioneer since it regenerates under disturbed conditions like canopy gaps but can also withstand shade and regenerates along with the forest as the gap closes (Avalos, 2019).

From September 2013 to May 2015, we harvested 87 palms, taking care to represent the full range of size classes representative of the population structure of each species (Appendix Table 1). We selected individual palms to obtain a sufficient spread of the data and reflect the size classes characteristic of the population of each species. We measured stem diameter at 1.3 m above the ground (DBH), at half the stem length in palms less than 1.3 m in height, or immediately above the stilt roots in palms with a stilt root cone higher than 1.3 m. We termed this measurement in all cases as diameter (abbreviated as diam), since strictly DBH was not measured in all cases. Harvested palms were separated into modules (stems, roots, and leaves) and we measured the total fresh biomass of each module using a Pesola^® Macro-Line Spring Scale (30 ± 0.25 kg). We carefully dug out the roots, collected all the root material to the extent that was possible, including fine roots (2–5 mm in diameter). In instances in which it was difficult to extract all the roots, due to their size or depth, a representative section was extracted, and from this, we estimated the total root biomass. We washed out the roots in the field and sun-dried them before weighing them in the laboratory. To determine the dry biomass (and carbon content) we collected 300 mg samples from each module. For leaves, this sample included one young, one intermediate, and one mature frond, determined according to their position from the tip of the apical meristem. In stems, the biomass sample was collected from the base, middle, and upper parts of the stem until reaching the base of the leaf crown. The total stem height of the palm (H_bc) was measured from stem base above the stilt roots (if present) to the base of the crown We also measured the height of the stilt root cone in stilt-rooted palms (S. exorrhiza, I. deltoidea, E. precatoria, and P. decurrens) from the ground to the base of the stem (H_sr). In palms without stilt roots, H_bc corresponded to the total length of the stem, from the connection with the first root to the base of the crown. In A. martiana H_bc also included the section of the subterranean stem from the first root to the insertion of the oldest frond. Finally, to estimate the tissue density of the stem (specific gravity, ρ), we used a Haglof 2-Thread Increment Borer, to collect a tissue sample from the stem, following the methods of Chave et al. (2005). Accordingly, we selected a point of entry for the increment borer near the base of the stem, in the middle, and near the base of the palm crown to place the borer at the center of the internode and carry out the perforation. Once the sclerotized tissue was extracted, the sample was placed in a test tube, sealed, and transferred back to the laboratory for the estimation of tissue density.

We dried the samples in an oven at 65°C for 48 h or until constant weight. Once dried, we ground the samples and determined their carbon content using an automatic analyzer TruSpec CN, LECO Corporation, at the Department of Systematic Botany at the University of Ulm, Germany, and an automatic elemental carbon and nitrogen analyzer, VarioMacrocube, at the University of Costa Rica. The magnitude of the carbon content in g was calculated by multiplying the total dry weight of each module by the percentage of carbon obtained in the laboratory and adding up all the dry biomass per individual palm. The average carbon fraction for the palms analyzed here was 43.9% ± 1.28 (Cambronero et al., 2018), but for our models we used the average carbon fraction obtained for each species. Stem tissue density (specific gravity, ρ) was calculated as the ratio of dry biomass (g) over volume (cm³). Volume was measured by water displacement. A summary table of all measured morphological characters is shown in (Appendix Table 1).

Palms were selected to represent a broad range of sizes characteristic of the species in the field. Thus, our sampling in these regards was not random and corresponded to an ordinary least squares regression (model I) since the magnitude of the predictor variable was selected by the experimenter. As a result, a model II regression with a random predictor variable was not practical.

We developed models including a combination of variables commonly measured under field conditions, such as diameter and stem height, aiming for simplicity. Therefore, only linear (or log-transformed) models were tested, and we did not consider non-linear models even though they could have provided better fits because we consider that linear (and logarithmic) models better represented the mechanistic relationship between the allometric variables.

We included stem tissue density to investigate the significance of this parameter in palms, even though measuring it requires access to instrumentation that may not be readily available in the field. To predict carbon content, we calculated linear and logarithmic backward stepwise regressions between the natural logarithm of the total amount of carbon content in kg per palm (LnC, response variable), and a set of explanatory variables including diameter in cm (diam), total stem height from the base of the stem to the base of the leaf crown (H_bc, m, excluding stilt roots if present), the height of the stilt root cone above the ground (H_sr) if present, the dry mass fraction or tissue moisture (dry mass over fresh mass, dmf), and stem tissue density (g cm^–3). This latter parameter was calculated so that we could compare our family-level models to those of Goodman et al. (2013), who include this variable. The predictor variables were included in the models with their Ln-transformed values as well as in their linear scales. We performed backward stepwise regression analysis for each species, and then chose the most parsimonious general regression models for all seven species based on the magnitudes of the R² value, the mean square of error (MSE), and the Akaike Information Criterion (AIC). The chosen models were listed in decreasing order of R², and the lowest MSE and AIC values. We chose models with at least one size-related variable (i.e., diameter and height). We discarded models that were not statistically significant or had R² values < 0.8 and included models with a single variable only if the model was statistically significant. Because the response variable required a logarithmic transformation, a correction factor was calculated following Sprugel (1983). The correction factor was used to remove the systematic bias introduced by the logarithmic transformation. The predicted value coming from the regression was multiplied by this correction factor, which is calculated as:

Where SEE = standard error of estimate of the regression (the absolute value of lny_i in boldface):

We combined all the data from the seven species to generate a series of family-level models to estimate total carbon per palm. The response variable was the natural logarithm of the total amount of carbon content in kg per palm (LnC), and the predictor variables were the set of morphological variables described above (except for Hsr, which was not present in all palms). We applied the same backward stepwise regression protocol to find the most parsimonious models based on the magnitudes of the R² value, MSE, the AIC, and in this case, the Mean Absolute Error (MAE), which is the average absolute difference between predicted and observed values. We compared the saturated model including all the predictor variables, with simpler, more parsimonious models coming from the stepwise regression, using a k-fold cross-validation protocol (James et al., 2013) where k = 8. We randomly divided the data into eight-folds of approximately equal size, one of which served as the test set and the rest as the training set. The resampling process was carried out in R using the library “caret,” which allowed us to estimate the value of MAE, in addition to the R², MSE and AIC values, and obtained the most parsimonious models by considering the number of predictor variables and the magnitude of the selection parameters (R², MSE, AIC). We used a similar cross-validation procedure to generate the AGC models.

To compare our Arecaceae AGC family model with those of Goodman et al. (2013) and Chave et al. (2014), we estimated the aboveground carbon content (AGC in kg) by adding the carbon content fractions of stems and leaves without considering the carbon content of roots (AGB). Goodman et al. (2013)’s model estimates AGB for nine species of neotropical palms, including E. precatoria, I. deltoidea and S. exorrhiza, examined here, using AGB^0.25 = 0.56*(dmfD²H_stem)^0.25, where dmf is the dry mass fraction defined above, D is DBH, and H_stem is the height of the palm from the ground to the highest leaf. To determine AGC, we applied the conversion factor of 50% of the dry biomass, which has traditionally been used to determine the carbon accumulated in trees (Chave et al., 2005; Houghton, 2007; Lorenz and Lal, 2010). This model is only valid for individuals with a stem height ≥ 1 m. The pantropical model of Chave et al. (2014) estimates AGB using 0.0673 (ρD²H)^0.976, where ρ corresponds to wood stem density (g cm^–3 or tissue density for palms), D is the DBH (cm), and H is the total height (m); this model is based on data from 4,004 trees ≥ 5 cm DBH. AGC was then calculated by applying the carbon fraction of 50% to AGB as in the case of Goodman et al. (2013)’s model. We did not include other models developed for palms such as the one by Frangi and Lugo (1985), or by Brown (1997) since these had lower performance and lower R² values when applied to our data (0.78 and 0.79, respectively).

We used the actual carbon fraction per palm species measured directly here (Cambronero et al., 2018) for the comparison with Goodman et al. (2013) and Chave et al. (2014) models. In both cases, the accuracy of all models was contrasted against the observed values of AGC using the R² value and the magnitude of their residuals. We used natural logarithmic models for the comparisons. For all regression analyses we used R software (R Core Team, 2022), and the library MASS with the function stepAIC().

In C. tepejilote, we did not find differences in morphological parameters among male and female plants, and thus, the analyses were done for the overall species. In this species, the best-fit model included the logarithmic form of total height and diameter. In P. decurrens, the best-fit model had the logarithmic forms of stem length and tissue density (R² value = 0.95). For A. martiana, the model with the highest R² had the logarithmic forms of the four predictor variables diameter, total height, dmf and tissue density. Finally, G. interrupta showed the highest fit for models including stem height (logarithmic and linear, with a R² of 0.98 and 0.91, respectively).

To predict total carbon content the saturated model (model 1, Table 2) included all predictor variables and served as a baseline against which the other models were compared. This model had the highest R², and the lowest MSE, AIC and MAE values, but its practical value was low. Models 2 and 3, which included logarithmic values of tissue density, diameter, stem length, and dmf, explained a similar proportion of the variation with fewer variables. From this point of view, model 4 is the most parsimonious since it reached an R² value comparable to that of the previous models with only two variables (diameter and stem height). MAE values for models 2, 3, and 4 were very similar showing that these models were not overfit. Model 5 reached the R² threshold value of 0.8 but its AIC and MAE values were the highest.

We followed a similar procedure to estimate AGC at the family level (Table 3). As in the previous case, the saturated model (model 1, Table 3) included all the predictor variables, serving as a baseline against which the other models could be compared. Model 2 explained a portion of the variation in Ln (AGC) similar to that of models 1 and 3, with lower MSE, AIC, and MAE values, but with an additional variable [Ln(dmf)] in comparison to model 3. Model 3 was the most parsimonious, since with two variables (Lndiam and LnH_bc) maintained a high R² (0.91) and low AIC and MAE. Model 4 met the threshold value of R² ≥ 0.80, but its efficiency in predicting Ln(AGC) was low.

We then compared model 3 to the pantropical model proposed by Chave et al. (2014) and the palm model of Goodman et al. (2013) using Ln (AGC). All three models predicted the observed Ln (AGC) with high R² values ranging from 0.89 to 0.913 (Figure 2). Our model had the highest R² value (0.913) followed by Goodman et al. (2013)’s with 0.875 and Chave et al. (2014) with 0.890. We consider all three models have similar ability to predict the AGC of the palm species analyzed here although ours is the most parsimonious because it uses two variables (diameter and stem height) vs. the three variables of Goodman et al. (2013), diameter, stem height and dmf, and the three variables of the Chave et al. (2014) model (diameter, height, and tissue density). Contrary to our prediction, the Chave et al. (2014)’s model satisfactorily predicted the stored AGC of palms despite of being a model generated for dicotyledonous trees.

Estimating root biomass and carbon content remains a significant challenge in palm allometric analyses. Because the data is still fragmentary and often limited to a few individual species (e.g., Goodman et al., 2013; Da Silva et al., 2015), much of the information focuses on aerial biomass. In general, the functional ecology of roots is still poorly understood, particularly in terms of the integration of above- and below-ground characters. When resources are scarce, for example, leaf life span does not correlate with fine root longevity (Weemstra et al., 2016). Under these conditions, long-lived leaves are preferred, but fine roots, which are responsible for increasing surface area and absorption capacity, have a high turnover rate. Future research should examine the degree of integration between above-ground and below-ground functional traits (Laliberté, 2017). In our case, as in other studies attempting to estimate root biomass (e.g., Da Silva et al., 2015), obtaining all roots, particularly fine roots, was difficult. Many palm species have shallow roots, which may explain their dominance in flooded environments and very wet forests, which are rich in palm species or are dominated by one or two species, because shallow roots perform better in wet environments (Eiserhardt et al., 2011). There have been few studies estimating root biomass for palms in the tropics (Frangi and Lugo, 1985), so comparative data is scarce (but see Da Silva et al., 2015).

This is the only recent study, following Goodman et al. (2013), to propose a family-level model to estimate not only AGC but also total carbon content per individual for Arecaceae. We also provided individual models for seven of the most common and abundant palm species in tropical rainforests, as well as estimates of their below-ground biomass (Appendix Table 1). Allometric models can be very complex because they include a multitude of variables often related non-linearly. The goal of this study was to simplify the selection of allometric models by considering variables of practical importance and easy to measure in forest inventories, as well as to investigate the role of morphological variables on carbon storage without proposing complex variable combinations. The models proposed here had a logarithmic form, which is consistent with the functional relationship between diameter, stem height, and other palm size traits.

To improve the accuracy of allometric models in general, and specifically for palms, more species, a greater diversity of growth forms, a wider range of sizes, and a larger sample size are required. Palm species that dominate wetlands are still lacking in this regard; despite dominating carbon-rich environments, there are few studies that include them, possibly due to the logistical difficulties of conducting research in flooded environments. Finally, progress in estimating carbon content using allometric approaches, which remains a viable and efficient option for estimating carbon stocks, necessitates greater consistency in data collection across plant groups.