Species-Specific Allometric Models for Aboveground Biomass Estimation in Two Cinchona Species in the Peruvian Andes

2.1 Location

The study was carried out in the community of La Cascarilla, province of Jaen, Cajamarca region, located in the jungle (Figure 1) between the coordinates 5.671994° S, 72.898198° W at an altitude of 1968 m a.s.l., with an annual rainfall of 1730 mm, minimum temperature of 13 ℃, and maximum of 20.5 ℃.

Figure 1. Location map of the study area

Individuals with a diameter at breast height (DBH) greater than 5 cm were selected using a stratified random sampling approach to cover the entire observed diameter range and ensure representativeness of size classes in the remnant Cinchona forests. A total of 51 individuals of C. micrantha (DBH range: 5–12.1 cm, mean 6.7 cm) and 60 individuals of C. pubescens (DBH range: 5–20.37 cm, mean 8.8 cm) were sampled. These specimens were identified in Cinchona forest remnants within the community's jurisdiction. For each individual, the following variables were recorded: DBH in cm, commercial height in m, and basic wood density (g/cm³) was determined from stem samples.

2.2 Density determination

Wood density was determined by a non-destructive method using a Pressler auger (diameter = 0.43 cm). The extraction of the samples (dowels) was performed at a height of 1.30 m from the ground [26]. Once the wood sample was extracted, it was weighed and stored in a plastic container to preserve its integrity during transport to the Forestry and Environmental Engineering Laboratory of the National University of Jaén.

The samples were placed in an oven at 105 ℃ for 48 hours until they reached constant weight, thus eliminating moisture. Finally, the dry weight was recorded, and the basic density (g/m³) was calculated using the following formula:

$\delta=P / V$   (1)

where, δ = basic density of the wood (g/cm³), P = dry weight of the wood (g) and V = volume of the wood in green state (cm³).

2.3 Biomass content of the stem

Biomass was estimated indirectly by the product of stem volume and basic wood density, obtained by non-destructive methods (Pressler) [12, 21, 27]. A form factor of 0.79 was used, recommended for hardwoods [28].

2.4 Allometric regression models used for the estimation of biomass

The allometric models evaluated (Table 1) were selected from functional forms widely reported in the scientific literature [28, 29], complemented with morphometric combinations adapted to the structural characteristics of C. micrantha and C. pubescens. These forms include linear, exponential, logarithmic, polynomial, and potential regressions, and were applied following the methodological criteria suggested by studies [21, 25]. The predictor variables used were DBH (in cm), individual height (H, in m), and the combination of both.

Table 1. Allometric models proposed to estimate the biomass content in the stems of C. micrantha and C. pubescens

*DBH: Diameter at breast height, H: Commercial height.

Although the extensive use of bilateral logarithmic transformations (i.e., log-log) in allometric models to stabilize variance and linearize nonlinear relationships has been documented in the literature [28, 29], in this study, we chose to keep the variables in their original scale (linear and untransformed) for two main reasons. First, because the natural scale equations allow a direct and transparent interpretation of the results by technical users and forest managers, facilitating their practical application in the field. Second, because the approach focused on evaluating the actual predictive fit to the data without introducing distortions associated with back-transformation of logarithms, which can induce biases if not properly corrected, e.g., using smearing correction factors such as the one proposed by the study [30].

2.5 Data analysis

Once the field and laboratory data were collected, violin plots were used to graphically represent the distribution of density and biomass of the analyzed species. Subsequently, the proposed mathematical models were applied with the selected variables to estimate the biomass in the stems. The evaluation of model performance was based on the calculation of the root mean square error (RMSE) and the Akaike information criterion (AIC). The selection of the optimal allometric model was based on the combination of a higher coefficient of determination (R²) and lower RMSE and AIC values. Additionally, the average absolute bias (ABL) was calculated to identify possible deviations between the estimated and observed values, considering that a lower ABL value indicates a lower tendency to bias, reflecting a better model fit.

Although the Pressler increment borer provides a reliable estimate for many species, its small core diameter (0.43 cm) may limit representativeness in heterogeneous hardwoods like Cinchona, where radial variations in density occur due to differences between sapwood and heartwood, or the presence of tension/stress wood. To mitigate potential bias, future studies could consider extracting multiple cores from different radial orientations (e.g., north-south-east-west) and averaging values, or combining with resistance drilling for validation [31-33]. In this study, a single core per tree was used due to conservation constraints on these threatened species.

A form factor of 0.79 was applied, as this is a commonly recommended general value for hardwoods in tropical and subtropical forests when species-specific measurements are unavailable [34, 35]. This value approximates the ratio of actual stem volume to the cylinder volume (DBH² × H × π/4), and has been widely used in biomass studies of broadleaf species. However, it is not derived from direct measurements on Cinchona spp. or closely related Andean hardwoods, which may introduce uncertainty (typically ±10–20% in volume estimates). Species-specific form factors, if developed in future work through destructive sampling on non-threatened analogs or advanced non-destructive techniques (e.g., terrestrial LiDAR), would improve precision.

One notable limitation of this study is the relatively small sample size (n = 51 for C. micrantha and n = 60 for C. pubescens) and the narrow DBH ranges sampled (5–12.1 cm for C. micrantha, mean = 6.7 cm; 5–20.37 cm for C. pubescens, mean = 8.8 cm), which primarily represent juvenile or small-diameter trees in remnant Andean forests. This constraint arises from the critically endangered status of these Cinchona species, driven by historical overexploitation and habitat fragmentation, necessitating non-destructive sampling to minimize further population impacts [9, 10]. Consequently, the allometric models developed here may exhibit reduced predictive accuracy when extrapolated to larger individuals (e.g., DBH > 30 cm), where allometric scaling relationships often shift due to changes in tree architecture, wood density gradients, or biomechanical constraints [28, 36]. Such extrapolation could lead to systematic biases in biomass estimates, potentially over- or underestimating carbon stocks in mature stands and compromising applications in REDD+ programs or large-scale ecological restoration [27, 37]. To address this, future research should prioritize expanding datasets to include broader DBH classes through collaborative inventories in protected areas, while adhering to non-destructive protocols such as terrestrial laser scanning (TLS) for volume validation or integrating remote sensing data (e.g., LiDAR) for independent model testing [38, 39]. Additionally, bootstrapping or cross-validation techniques could be employed to quantify uncertainty in current models, ensuring robust applicability across ontogenetic stages [37].

Accurate estimation of aboveground biomass is a fundamental tool for assessing the carbon stocks of forest ecosystems, especially in threatened species or species with ecological and medicinal relevance, such as Cinchona micrantha and C. pubescens. This study demonstrates that allometric equations adjusted specifically for each species allow modeling stem biomass with high accuracy, as evidenced by high R² values (up to 0.95 for C. micrantha and 0.97 for C. pubescens) and low prediction errors (RMSE and AIC). These results are consistent with previous work highlighting the importance of locally calibrated models to improve the accuracy of biomass estimates in tropical forests [25, 28]. Unlike classical approaches that seek only the best-fit equation, this study emphasizes the empirical validation of specific models for little-studied species of the genus Cinchona, whose biocultural and ecological relevance has been underestimated. The novelty lies in the conservationist approach based on non-destructive methods and in the applicability of the models in REDD+ programs and carbon monitoring in vulnerable high Andean ecosystems.

The superior performance of models based on the composite variable DBH² × H stems from strong theoretical and geometric foundations in plant allometry. DBH² × H approximates the volume of a cylindrical stem (basal area × height), which directly scales with biomass assuming relatively constant wood density and taper across individuals. This variable integrates the two primary dimensions of tree structure, horizontal expansion (DBH² captures cross-sectional area) and vertical extension (H), better than single predictors like DBH or H alone, which fail to account for the three-dimensional allocation of biomass in stems, branches, and foliage [21, 40]. In tropical trees, where biomass is not uniformly distributed but follows scaling principles influenced by mechanical stability, hydraulic constraints, and resource allocation, composite variables like DBH² × H reduce residual variance by capturing volumetric proportionality more effectively than simpler forms (e.g., DBH alone often yields R² < 0.90 in heterogeneous stands). This is particularly relevant in montane Andean contexts, where environmental stresses (e.g., wind, slope) may alter taper and height-diameter relationships, making volume proxies especially robust [41].

The high R² values obtained here (0.95–0.97) indicate excellent model fit and are superior to or comparable to those reported in many pantropical and regional studies. Pantropical generic models, e.g., research [21], typically achieve R² around 0.80–0.93 when validated across diverse sites, with higher uncertainty in montane or secondary forests due to site-specific allometry. In younger secondary tropical forests, improved models incorporating DBH, H, and wood density reach adjusted R² ≥ 0.96 [42], similar to our results. In Andean montane forests, local equations often yield R² = 0.90–0.96, but generic pantropical models applied without calibration show larger biases (e.g., overestimation by 20–50% in high-elevation sites). Our species-specific, non-destructive models outperform many generalized approaches, likely due to the focus on threatened remnant populations with limited structural variability and the use of polynomial forms on composite variables, which better capture non-linear scaling in these Andean hardwoods. This underscores the value of locally fitted equations for precise carbon accounting in vulnerable ecosystems, where generic models may introduce substantial errors.

The morpho-structural patterns observed between the two species reflect functional differences that should be considered when selecting predictor variables. C. pubescens showed greater variability and biomass accumulation capacity than C. micrantha, with an average stem biomass of 47.25 kg vs. 14.78 kg, which coincides with its larger average size and diameter. This structural divergence highlights the need to develop species-specific allometric models, as the application of generic equations can generate significant biases [12, 24].

Likewise, the composite variable D² × H showed superior performance in the fitted models, supporting its use as a robust predictor in polynomial and exponential equations. As indicated by studies [20, 21], the use of variables that simultaneously integrate potential volume and vertical tree structure substantially improves the explanatory power of the model. DBH remains one of the most robust predictors for estimating aboveground biomass in trees [43]. Previous studies [28, 44-46] support this and highlight the fundamental role of DBH in the quantification of dry biomass, consolidating its use as a key variable in allometric models. Recent studies show that ecological conditions influence the selection of variables to estimate tree biomass. For example, Henry et al. [47] revealed that including tree height significantly improves the accuracy of models in humid areas, where vertical growth is determinant in biomass accumulation. Research [48, 49] has shown that environmental factors (such as water availability and temperature) can modify the relationship between diameter, height, and biomass. In particular, Daba et al. [50] highlighted that bioclimatic variables directly influence the predictive ability of metrics such as height (h) and wood density (ρ), which could explain the discrepancies between different studies. These findings indicate that there is no universal hierarchy of predictive variables, but rather that their usefulness depends on the ecological and climatic context of each region. In this study, models with the variable DBH² × H achieved the best fit indices for both species, suggesting their applicability to other tropical taxa with morphological characteristics.

On the other hand, the use of the non-destructive method to estimate the basic density of wood by the Pressler auger and controlled drying constitutes an efficient and replicable methodological strategy. Although destructive methods have historically been considered more accurate [19], their application is limited in conservation studies. The alternative employed in this research preserves the integrity of individuals and allows extending the assessment to populations at risk, such as those of Cinchona in the Peruvian Andes [4, 11].

In the context of global climate change, quantifying biomass and carbon stored in forest ecosystems represents a key component for assessing the balance of emissions, especially in areas subject to forest management or anthropogenic disturbances with adverse effects. Incorporating carbon content as an explanatory variable in allometric models is fundamental, as it provides critical information to more accurately estimate carbon stocks and emissions derived from forest intervention or management activities [12].

Finally, this study contributes significantly to the body of knowledge on allometric modeling in native species of biocultural and medicinal importance. In a context of climate change and anthropogenic pressure on Andean-Amazonian ecosystems, having empirically validated tools to estimate carbon and biomass is essential to strengthen conservation policies and sustainable management of forest resources. As indicated by the study [13], the accuracy of these models not only supports technical and scientific decisions but also has direct implications for compliance with international environmental commitments.