# Allometric options for predicting tropical tree height and crown area from stem diameter

Moses Libalah Bakonck, Adeline Fayolle, Nicolas Barbier, Nicolas Picard, Stephane Momo Takoudjou, Yannick Enock Bocko, Gislain Ii Mofack, John Mukirania Katembo, Joel Loumeto, Olga Diane Yongo, et al.

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Moses Libalah Bakonck, Adeline Fayolle, Nicolas Barbier, Nicolas Picard, Stephane Momo Takoudjou, et al.. Allometric options for predicting tropical tree height and crown area from stem diameter. 2024. [hal-03996608](https://hal.inrae.fr/hal-03996608v1)

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# Allometric options for predicting tropical tree height and crown area from stem diameter

**Moses B. Libalah** (libalah_moses@yahoo.com)

University of Yaoundé I

**Adeline Fayolle**
University of Liège, Gembloux Agro-Bio Tech

**Nicolas Barbier**
UMR AMAP-IRD

**Nicolas Picard**
GIP Ecofor

**Stéphane Momo**
Plant Systematics and Ecology Laboratory (LaBosystE), Higher Teacher's Training College

**Yannick Bocko**
Marien Ngouabi University

**Gislain II Mofack**
University of Yaoundé I

**John Mukirania Katembo**
Institut Supérieur d'Etudes Agronomiques de Bengamisa

**Joël Loumeto**
Marien Ngouabi University

**Olga Diane Yongo**
University of Bangui

**Alfred Ngomanda**
Institut de Recherche en Ecologie Tropicale

**Pierre Couteron**
UMR AMAP-IRD

**Bonaventure Sonké**
Plant Systematics and Ecology Laboratory (LaBosystE), Higher Teacher's Training College

**Rossi Vivien**
CIRAD - UR Forêts et Sociétés

## Article

## Keywords:

**Posted Date:** November 8th, 2022

**DOI:** https://doi.org/10.21203/rs.3.rs-2209593/v1

**License:** This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
**Abstract**

Tree height and crown area are important predictors of aboveground biomass but difficult to measure on the ground. Numerous allometric models have been established to predict tree height from diameter (H–D) and crown area from diameter (CA–D). A major challenge is to select the most precise and accurate allometric model among existing ones, depending on the species composition and forest type where the model is to be applied.

To propose a principle to select tree H–D and tree CA–D allometric models, we build a method based on *k*-fold cross-validation using a large dataset spanning six forest types from central Africa. We then compared the errors and biases using 22 previously established H–D and CA–D allometric model forms via three inter-comparable scenarios: locally derived for the forest type *vs*. regional *vs*. pantropical; regional (encompassing the forest type) *vs*. pantropical; regional (not encompassing the forest type) *vs*. pantropical model.

H–D allometries were more variable across forest types in central Africa than CA–D allometries: (i) forest type explained 6% of the variance in H–D allometry and 2% of the variance in CA–D allometry, while species explained 9% and 2% of the variance in H–D allometry and CA–D allometry, respectively; (ii) for H–D allometry, the six forest types resulted in five best-fit models whereas, for CA–D allometry, four models provided the best fit for the six forest types. We recommend using allometric models specific to the forest type, preferentially to regional ones. Regional models should in turn be preferred to pantropical allometric models.

**Introduction**

African tropical forests play a key role in the global carbon cycle and climate change mitigation. Emerging evidence indicates that the carbon sink in live aboveground biomass (AGB) has been stable for over three decades since 1985 ¹ despite the environmental changes linked to increasing greenhouse gas concentrations ². Although recognized as a single biome, African tropical rainforests differ substantially within and across regions. This heterogeneity also implies variability of the response of forests to climate change. Pressure from human activities ³, deforestation ⁴ and degradation ⁵ also interplay with forest type. Therefore, efforts to implement effective conservation measures for climate change regulation and monitoring carbon credits over time must rely on accurate predictions of carbon stocks in the different forest types.

To reduce errors in the prediction of tropical tree AGB from tree diameter at breast height (D) and species wood density ($\rho$), it is strongly recommended to include an estimate of tree height ⁶,⁷ and tree crown dimension ⁸,⁹. Consequently, tree heights have been predicted using African regional models that accounted for environmental factors ¹⁰, or pantropical models that accounted either for biogeographical differences between continents ¹¹ or for climate ¹². These models encompassed different forest types. However, Africa was underrepresented in the dataset used to fit pantropical models ¹⁰,¹¹. Unveiling the importance of this sampling bias, Kearsley et al.¹³ showed that pantropical height–diameter allometric models led to significant overestimation of AGB in central Congo Basin forest and were outperformed by site-specific models ¹⁴. Studies focusing on few field sites in central Africa revealed contrasted performance of height–diameter models between sites ¹⁵, insinuating that tree height–diameter allometry may depend on the forest type ¹⁶ and species composition.

One historical challenge to predict tree height from stem diameter has been the choice of the allometric functional form. This challenge has been exacerbated by a plethora of proposed functional forms ¹⁷,¹⁸. However, there is now apparent convergence towards a few functional forms which are equally supported by ecological theories. For instance, the power law function ¹⁹,²⁰ is backed by the theory of simple allometry. The metabolic scaling theory further predicts a specific value for the coefficient of the power model: tree height scales with its stem diameter as $D^{2/3} 21^{-23}$. Also, the second order polynomial on the log-log scale ¹² is designed to mimic a saturation of tree height with diameter. Asymptotic models such as the Weibull ²⁴,²⁵ and the Michaelis-Menten ²⁶ models are easy to interpret because maximum height is one of the coefficients of the model ¹⁰,²⁴. The other coefficient of the Michaelis-Menten model is also easy-to-manipulate ²⁷. All these functions have been used to compare height–diameter allometries between forest types in central Africa ¹⁴,²⁸,²⁹. The power model often appeared to be the most pertinent among several mathematical functions in predicting tree height ³⁰,³¹ and biomass ²⁰,³².

Contrary to tree H–D allometry, the relationship between stem diameter and crown diameter has so far been overlooked in tropical rainforests (but see Loubota Panzou et al. ³³b). Yet, it is likely that large-stature species that realize faster height growth to reach crown exposure have relatively slender stems, and consequently narrow crowns to compensate for wind loads ³⁴,³⁵. It is also possible that short trees develop large crowns under well illuminated and open conditions ³⁶⁻³⁹. Another strategy can be to have a thicker stem made of lighter wood to ensure a tradeoff between the mechanical properties of the wood and the amount of matter needed to ensure a given resistance to buckling or stem damage ⁴⁰, while still ensuring other functions (water transport and storage, etc.). Thus, tree height–crown allometry may change between species depending on the position of trees in the illumination gradient ⁴¹⁻⁴³. Also, variation in tree height and crown may reflect the complex multi-layered structure of tropical forests. Therefore, incorporating crown dimension in tree height predictions may improve the precision of these predictions, and consequently AGB estimation ⁸,⁴².

Consider a user with some forest inventory data that include tree diameter and wants to predict tree height or crown area (typically to predict biomass in a second step). This user has to make a choice in an ensemble of available allometric models. The goal of this study is to propose a rigorous framework to guide the choice of the height–diameter (H–D) and crown area–diameter (CA–D) allometric model depending on whether the data used to fit this model partly come or not from a forest of the same type as the user’s forest. When the calibration data used to fit a model partly come from a forest of the same type as the subject forest, we shall say that the model encompasses the subject forest type. For each allometric model, D was the predictor while H (for H–D allometry) and CA (for CA–D allometry) were the dependent variables. We hypothesized that: (i) H–D and CA–D allometries differ between forest types and that these differences are due to species composition; (ii) allometric models specific to a forest type are more accurate than regional and pantropical allometric models; (iii) regional allometric models encompassing the subject forest type are more accurate than pantropical allometric models; (iv) regional
allometric models not encompassing the subject forest type are less accurate than pantropical allometric model. Regional models presumably incorporate the
architectural properties of trees better than pantropical models. However, compared to regional models that do not encompass the subject forest type,
pantropical allometries may have the advantage to capture a wider range of forest properties and architecture. To address these hypotheses, we compared
allometric models derived for each forest type with published regional and pantropical allometric models through three scenarios: allometries derived for the
forest types against regional and pantropical allometric models (scenario 1); regional allometric model encompassing the subject forest type against
pantropical allometric model (scenario 2); regional allometric model not encompassing the subject forest type against pantropical allometric model (scenario
3). Finally, we discussed the choice among specific-to-the-forest-type, regional or pantropical models depending on whether the models encompass the subject
forest type or not.

Results

**Effect of forest type and species composition on allometries.** Respectively for the H–D and CA–D allometries, the regional model with the lowest BIC was the log-normal model of the form: $log(\chi) = a_f + a_s + b \times log(D) + c \times log(D)^2$, and the linearized-power model of the form: $log(\chi) = a_f + a_s b \times log(D)$ where $\chi$ was tree height or crown area, $a_f$ was a fixed effect depending on forest type f, $a_s$ was a random effect depending on species s, and b and c were fixed coefficients. The conditional $R^2$ (fixed and random effects) was 80% for the H–D model and 72% for the CA–D model.

For the H–D model, the part of variance explained by tree diameter (that is $log(D) + log(D)^2$) was 66%, by forest type 6%, and by species composition (random-effect) 9%. When the forest type was not included in the H–D model, the proportion of variance explained by the species composition was 14%. Hence, the part of variance explained by the forest type was taken from the variance explained by the species composition. Post-hoc analysis showed three significant groups of forest types: TSE-DRC and SFM-CON; TSS-CAR and EFL-RGE; EVF-GAB and SEF-CAM (Fig. 2A).

For the CA–D model, the part of variance explained by tree diameter was 65%, by forest type 2%, and by species composition (random-effect) 2%. When the forest type was not included in the CA–D model, the proportion of variance explained by the species composition was still 5%. Hence, the variance explained by the forest type was independent of the variance explained by the species composition. Post-hoc analysis showed two significant groups of forest types: EVF-GAB, SFM-CON and TSE-DRC; TSE-DRC, TSS-CAR, SEF-CAM and EFL-RGE (Fig. 2B).

Hence, the hypothesis that H–D and CA–D allometries differ between forest types is verified. Moreover, for the H–D allometry, differences between forest types are due to species composition.

**Performance of H–D allometric models.** *Scenario 1.* (models derived for the forest type *vs.* regional models *vs.* pantropical models): For three out of the six forest types (*viz.* EVF-GAB, SEF-CAM and TSE-DRC), the locally fitted allometric model provided the best performance according to the RB and RMSE criteria. These three forest-type specific models corresponded to two different mathematical functions, namely the linear function (for EVF-GAB and SEF-CAM) and the power function (for TSE-DRC). The regional model of Feldpausch et al. (2012) for central Africa and the regional model of Banin et al. (2012) for tropical Africa provided the best performance in two other forest types (*viz.* SFM-CON and TSS-CAR, respectively). The pantropical climate-based model of Chave et al. (2014) provided the best performance in the remaining forest type EFL-RGE (Table 3; Fig. 3A-B; Supporting Information Table S3). Except for the central Congo regional model of Kearsley et al. (2013) that had outstanding error of 5 m to 7 m and bias of ~ 18% to ~ 19% in tree height predictions (results not shown in Fig. 3A-B), the errors generated by the other allometric models for each forest type were hardly greater than 2 m. These errors ranged from a minimum of 0.64–1.23 m to a maximum of 1.14–1.96 m across forest types (Supporting Information Table S3). Despite small errors, large ranges in bias were recorded by the models. These biases ranged from a minimum of 0.002–0.43% to a maximum of 2.28–4.43% across forest types (Supporting Information Table S3).

*Scenario 2.* (regional models encompassing the subject forest type vs. pantropical models): The regional model fitted using the Meyer function provided the best performance for one out of the five validation folds, while the model of Banin et al. (2012) for tropical Africa provided the best performance for the four other folds (Table 3; Fig. 3C-D). The central Congo regional model of Kearsley et al. (2013) had again outstanding error of 31 m to 34 m and bias of ~ 92% to ~ 93% for the five folds (result not shown in Fig. 3C-D). The error in predicted tree height by the other allometric models ranged from a minimum of 5.70–6.57 m to a maximum of 7.29–8.24 m across validation folds (Supporting Information Table S4). With the exception of Kearsley et al.'s model, the bias ranged from a minimum of 0.30–1.97% to a maximum of ~ (8.68–11.93)% across validation folds (Supporting Information Table S4).

*Scenario 3.* (regional models not encompassing the subject forest type vs. pantropical models): Best performances were obtained with three published regional models (Table 3). The regional model of Feldpausch et al. (2011) for central Africa provided the best performance when the forest type TSE-DRC was used as validation fold. The model of Banin et al. (2012) for tropical Africa provided the best performance when TSS-CAR or SFM-CON were used as validation folds. The model of Lewis et al. (2009) for tropical Africa provided the best performance for the other three validation folds (*viz.* forest types EFL-RGE, EVF-GAB and SEF-CAM). The central Congo regional model of Kearsley et al. (2013) had again outstanding error of 27 m to 37 m and bias of ~ 92% to ~ 93% for the six folds (and was not shown in Fig. 3E-F). The errors produced by the other models ranged from a minimum of 4.50–7.08 m to a maximum of 27.24–37.38 m across validation folds (i.e. forest types) (Fig. 3E-F; Supporting Information Table S5). The bias recorded among the forest types ranged from a minimum of 0.07–8.35% to a maximum of ~ (92.58–94.14)% across validation folds (Supporting Information Table S5).

**Performance of CA–D allometric models.** *Scenario 1.* Six locally fitted models using four different mathematical functions provided the best performance to predict crown area for the six forest types (Table 3). The linear model had the lowest error and bias for SFM-CON and SEF-CAM. The linearized power model had the lowest error and bias for TSE-DRC. The parabolic-log model had the lowest error and bias for TSS-CAR and EFL-RGE. The Michailoff model had the lowest error and bias for EVF-GAB (Fig. 4A-B; Supporting Information Table S6). The errors and biases in predicted crown area for all allometric models ranged from 11 to 572 m² and from 0.29 to 685%, respectively. The ranges of errors and biases for each forest type are reported in Supporting Information Table S6.
**Scenario 2.** Five fitted regional models using four different mathematical functions provided the best performance to predict crown area for the five validation folds (Table 3). The Naslund model had the lowest error and bias for two validation folds, while the linear model, the parabolic model and the parabolic-log model had the lowest error and bias for one fold each (Fig. 4C-D; Supporting Information Table S7). The errors and biases in predicted crown area ranged from 96 to 259 m² and from 0.30 to ~11.93%, respectively. The ranges of errors and biases for each validation fold are reported in Supporting Information Table S7.

**Scenario 3.** Five fitted regional models using four different mathematical functions and one published regional model provided the best performance to predict crown area for the six validation folds corresponding to the six forest types (Table 3). The log-normal model had the lowest error and bias when the forest types TSE-DRC or SEF-CAM were used as validation folds. The parabolic model, the parabolic-log model, the Korf model and the model by Blanchard et al. (2016) for central Africa had the lowest error and bias when the forest type TSS-CAR, EFL-RGE, SFM-CON and EVF-GAB was used as validation fold, respectively (Fig. 4E-F; Supporting Information Table S8). The errors and biases in predicted crown area ranged from 67 to 282 m² and from 0.29 to 685%, respectively. The ranges of errors and biases for each validation fold are presented in Supporting Information Table S8.

## Discussion

Analysing the accuracy of various allometric models relating tree diameter to either total tree height or crown area is a major step towards precise prediction of forest structural attributes such as biomass. To a greater extent, such analysis will facilitate the calibration of remote sensing products ⁵⁸ and inform on biogeographical processes driving forest communities ¹⁰,¹¹. Despite a plethora of published allometric models to predict tree height (H) and crown area (CA) from stem diameter at 1.3 m breast height (D), only a few are commonly used for the H-D relationship ¹⁰,¹¹,¹⁴,³¹,⁵⁹ (e.g. Feldpausch et al. ¹⁰,¹¹; Banin et al. ¹⁴; Ledo et al. ³¹; Kearsley et al. ⁵⁹) or for the CA-D relationship ³³,⁴¹,⁴²,³³,⁴¹,⁴²b. Sometimes, these models are calibrated on some species ²⁸, with or without using the forest type as a predictor. One could expect that a single allometric model could have the best precision (small RMSE) and accuracy (small relative bias) for different forest types but was not the case for this study. Thus, analysing the RMSE and relative bias of predictions from multiple allometric models can help elucidate the dependence of allometry on forest type. Furthermore, our strategy of analysing both RMSE for precision and relative bias for accuracy may be preferable for assessing the performance of allometric models, because most models may be precise with very small differences in RMSE but with large differences in accuracy, i.e. relative bias.

In this study, we showed that the best model describing the allometric relationship between tree diameter and height (H-D) differed among forest types as demonstrated in Madagascar ⁶⁰. Four different mathematical functions underlined the six models provided the lowest RMSE and relative bias for the six forest types in central Africa. The linear function outperformed the other functions in two forest types. Conversely, two asymptotic, one power and one log-normal functions had the lowest RMSE and relative bias for the four other forest types. Such variations of functional forms were also reported by Loubota Panzou et al. ⁴²a,b. Nevertheless, a close examination of the model performances showed that very small differences in RMSE but large differences in relative bias were recorded between the best performing allometric models and the other less performing models (see Supporting Information Tables 3–8). For instance, low relative bias is crucial in AGB predictions where a bias in height prediction of the largest trees may induce significant errors in AGB plot estimates ⁶¹. These results equally point to the plasticity of the H-D relationship to forest types, which could be controlled by abiotic and/or biotic factors. Indeed, a substantial share of the variance of the linear mixed-effect model was explained by the joint effect of species composition and forest type, thus providing support for biotic and abiotic effects (see hypothesis (i) in the Introduction). Similarly, H-D allometries have been reported to differ at various spatial scales: in tropical lowland forests across continents, allometries are modulated by precipitation seasonality and solar radiation ¹¹; in geographic regions within a continent, they are modulated by environment and forest structure ³¹; among lowland evergreen and transition forests, they are modulated by stem density ²⁸; and in tropical montane forest, they are modulated by altitude ⁶².

For H-D allometry, we showed that the mathematical functions describing the allometric relationship between tree diameter and crown area (CA-D) also change between forest types. Four models had lowest RMSE and relative bias across the six forest types, such variability was as also reported at pantropical scale ³³. Our results equally suggested that species composition and forest types may only partially explain the variability of CA-D allometry in conformity with ⁴¹,⁶³Antin et al. ⁴¹ and Shenkin et al. ⁶³. Ecological factors such as convergence in tree architecture, and stochastic processes such as crown packing, may have stronger influence on the relationship between diameter and crown dimension than abiotic factors. For instance, lida et al. ⁶⁴ suggested that convergence in architectural differences due to lateral crown extension for light interception may facilitate overlap in crown dimensions across species communities in Dipterocarp forests. However, some effects related to ontogeny or species regeneration guild may exist while being overshadowed by competitive convergence and stochastic processes (but see Shenkin et al. ⁶³). Therefore, more in depth studies are required to assess the latter hypothesis.

Another point to note from this study is that variation in allometry between the forest types in central Africa is much weaker for CA-D than for H-D. In concordance, ⁴²Blanchard et al. ⁴² highlighted that, across biogeographic areas, H-D allometry was characterized by inter-site heterogeneity and intra-site homogeneity, whereas the reverse held for CA-D allometry (i.e. inter-site homogeneity and intra-site heterogeneity). As a consequence, regional crown area-diameter models can be used to predict crown attributes (e.g. crown volume, width, depth, leaf area index, etc.) observed from remote sensing products ⁵⁸, whereas a general height-diameter allometric model will be less accurate for different forest types than site-specific models. Thus, site-specific height-diameter allometric models incorporating local environmental factors are needed to accurately predict forest structural attributes (e.g. volume, biomass).

**Limitations of the methods and correction.** Strictly speaking, ordinary least squares (OLS) are not suitable to fit models on untransformed heteroscedastic variables such as tree heights or crown dimensions. Models may then be biased. In addition, OLS with untransformed heteroscedastic data would favour large diameter trees since they have more weight in the RMSE than trees with small diameters. To minimize such biases, we carefully built folds in the cross-validation that preserved the regular distribution of trees across diameter classes that was designed by sampling in the full dataset. As alternative,
untransformed models could have been fitted using weighted least squares (WLS), by making the variance of residuals dependent on diameter. However, WLS would have penalized fitted models because the RMSE criterion used for model comparison would then have differed from the RMSE criterion used for fitting.

Cross-validation allowed us to fairly compare models from the literature to models fitted on the study data since the validation data were independent of the calibration data. Models from the literature had fixed coefficients for all folds, whereas fitted models had different estimated coefficients for each calibration fold. As a consequence, the error induced by the uncertainty on coefficients was taken into account for fitted models, while it was not for published models. To minimize this shortcoming, we averaged RMSE over the *k* validation folds. Moreover, in allometric models, the share of the prediction error due to the uncertainty on coefficients is very small compared to that induced by the choice of the model ⁶⁵⁻⁶⁷.

**Recommendation for selecting height and crown area allometries.** Locally derived allometric models were preferable over regional and pantropical climate-based allometric models. Indeed, even if locally derived, regional and pantropical climate-based models had equivalent RMSE, locally derived allometric models outperformed the other models in terms of relative bias.

Although our results support overall the use of local allometric models, situations will remain where no local height or crown area data are available at local scales despite efforts to collate such data globally ⁶⁸. In the absence of local models but presence of regional models, the recommended option will depend on whether the calibration data used to fit these regional models encompassed or not the subject forest type. If regional models are encompassing the subject forest type, we recommend their use. Pantropical climate-based allometric models are also the default option in the absence of regional models.

# Materials And Methods

**Study sites and forest types.** As a benchmark to assess the three scenarios, we used a large central African regional database collected during the PREREDD + project ⁴⁴ which equally acquired the relevant institutional, national, and international guidelines and legislation for the studies on plants. Destructive biomass data were collected in logging concessions in Cameroon, Central African Republic, Republic of Congo, Democratic Republic of the Congo (DR Congo), Equatorial Guinea and Gabon with the same standardized protocol, and using appropriate sampling (following the recommendations of Chave et al. ¹²). All the six sites are located at low to mid altitude (52–663 m) within the equatorial climate zone where important variation has been recorded for annual mean ranges of precipitation (1,400–2,500 mm) and temperature (20–30°C) ⁴⁵. Bedrock materials of these sites are mainly of metamorphic or sedimentary origins. Soils are ferralsols of different types (Table 1).

The six sites show contrasting floristic and functional compositions across climates, soil types and anthropogenic gradients ⁶⁶, in addition to their differences in deciduousness (evergreen and semi-deciduous), hydrology, geological substrates and dominant tree species (Table 1; Supporting Information Table S1). Hence, each site corresponded to a different forest type with a semi-deciduous forest in Cameroon (SEF-CAM), a transition between semi-deciduous and evergreen forest on sandstone plateau in Central African Republic (TSS-CAR), a seasonally flooded forest including monodominant *Gilbertiodendron dewevrei* (De Wild.) J.Leonard species in the Republic of Congo (SFM-CON), a transition between semi-deciduous and evergreen forest in the DR Congo (TSE-DRC), an evergreen forest of littoral type in Equatorial Guinea (EFL-RGE) and a mainland evergreen forest in Gabon (EVF-GAB) (Table 1; Supporting Information Table S1).

**Tree dataset.** A total of 845 trees (52 species, 49 genera and 17 families) were sampled covering a wide range of diameter (10–208 cm), height (8–67 m) and crown area (1.43–1,495 m²). Taxonomic identification of species, stem diameter, maximum height and crown area were measured prior to logging (Table 1; Supporting Information Table S1). Species taxonomic identification was initially made by trained botanists from respective logging concessions and confirmation in the field by our experienced botanists (ML, BS, JL, JMK, AN, ODY). Stem diameter (D, in cm) was measured at 1.3 m breast height or 30 cm away from any deformation using a diameter tape. Maximum tree height was measured using the *sine method* (sensu ⁴⁷). That is, a Haglöf Transponder T3® was placed on the tree at 1.3 m breast height and an observer carrying a Haglöf Vertex IV® was positioned at a relative horizontal distance from the tree that permitted viewing the topmost canopy of the tree. From this position, the maximum tree height (H in m) (average of two tallest measurements) were measured. Crown dimensions were measured as the horizontal distance from the trunk base to the projected edge of the canopy in the four cardinal directions (N, S, W and E). Whenever one of the cardinal directions could not be measured, the alternative directions of the crown (NE, SW, SE and NW, respectively) were considered. Using the values, the ellipsoidal crown area (CA in m²) was computed as $CA = \pi \times (NS_{mean} \times EW_{mean})$, where $NS_{mean}$ and $EW_{mean}$ are the average crown radii for the N–S and E–W directions, respectively.

**Mathematical functions for H–D and CA–D relationships.** We considered 22 existing mathematical functions from the literature and fitted these separately for the H–D and for the CA–D relationships (see Supporting Information Table S2). The 22 mathematical functions possessed either 2 parameters (10 functions) or 3 parameters (12 functions). They consisted of polynomials, asymptotic and power law functions. Most of these mathematical functions are incorporated in the *Imfor R*-package ⁴⁸. To ensure consistency with the performance criteria used (see section "Evaluating performance of the allometric models" below), all models were fitted using ordinary least-squares (OLS) regression and assuming Gaussian errors. Some functions were log-transformed prior to calibration (see Supporting Information Table S2) in order to easily use the Bayesian Information Criterion (BIC). In this case, no transformation was achieved but lognormal errors were used. When log-transformation was used for calibration, a bias correction factor was used to back-transform model predictions ⁴⁹,⁵⁰. For nonlinear functions, we first estimated their parameter starting values for the fitting algorithm following Huang et al.¹⁷ and Zeide ⁵¹.

**Published H–D and CA–D models.** In addition to the fitted models, seven published models were taken from the literature: five regional models for H–D allometry, one pantropical model for H–D allometry, and one regional model for CA–D allometry (Table 2).

**Statistical analysis.** Allometry differences between forest types and species effects. To assess differences in the H–D and CA–D allometric models between forest types due to species composition (hypothesis (i) of the Introduction), we fitted a linear mixed-effects model ⁵². Stem diameter and forest types were
used in the model as fixed effects while species as a random effect. All the 22 models were fitted using the entire tree data (Supporting Information Table S2). The best regional model was selected among these 22 models using the BIC⁵³. Post-hoc pairwise significant differences between the forest types were assessed by Tukey HSD via least square means.

**Comparing allometric models.** To compare the performance of allometric models for predicting tree H and CA from D (hypotheses (ii)–(iv) of the Introduction), we adopted a cross-validation scheme⁵⁴,⁵⁵. Some models in the comparison were fitted to data while others were taken from the literature with fixed coefficients. In this latter case, the cross-validation scheme boils down to a simple validation scheme. In any case, cross-validation is appropriate to evaluate the predictive power of models as it verifies the behaviour of the models on data not used for their calibration. We performed k-fold cross-validation that consisted of: first splitting the dataset into k folds; second, using k − 1 folds for the calibration of the models to be fitted and one fold for the validation of all models (whether fitted or taken from the literature). The second step was repeated k times to ensure that all the folds were used for validation (Fig. 1).

To compare the models in the three scenarios (i.e. scenario 1: models derived for the forest type vs. regional models vs. pantropical models, scenario 2: regional models encompassing the subject forest type vs. pantropical models, and scenario 3: regional models not encompassing the subject forest type vs. pantropical models), we used two folding schemes based on the dataset of 845 trees from all forest types. We ensured similarity in diameter structure for each of the schemes and within each fold by assigning trees into the following nine diameter classes [10–20[, [20–30[, [30–40[, [40–50[, [50–60[, [60–70[, [70–100[, [100–150[, > 150 cm. We then built the k-fold by randomly splitting each diameter class into k folds (Figs. 1 and Supporting Information Figure S1).

For H–D allometries, we compared six models from the literature with the subject forest type models based on 22 mathematical functions and the regional models based on the same 22 mathematical functions. Results were presented only for eight H–D allometric models; i.e. the best model for the subject forest type, the best regional model, and the six models from the literature (Table 2).

For CA–D allometries, we compared one model from the literature with subject forest type models based on 22 mathematical functions and regional models based on the same 22 mathematical functions. Results were presented only for three CA–D allometric models; i.e. the best model for the subject forest type, the best regional model, and the model from the literature (Table 2).

For both H–D and CA–D allometries, literature models were not re-calibrated on the training dataset during the k fold comparison.

**5-fold cross-validation for scenarios 1 and 2.** We randomly split each forest type dataset into 5 folds (Fig. 1). We repeated the following steps five times by: (i) combining 4 folds for calibration (80% of the dataset) and reserving 1 fold for validation (20% of the dataset); (ii) calibrating a local equation for each forest type, for scenario 1; (iii) calibrating a regional equation using all 4 × 6 calibration folds from the 6 forest types combined, for scenario 2. Steps (i)-(iii) were repeated 5 times so that each fold was used for validation (Fig. 1).

**6-fold cross-validation for scenario 3.** We split the whole tree dataset into 6 folds according to the six forest type (Supporting Information Figure S1). We repeated the following steps six times by: (i) combining 5 folds for calibration and reserving 1 fold for validation; (ii) calibrating a regional model using the 5 calibration folds. Steps (i)-(ii) were repeated 6 times so that each fold (i.e. each forest type) was used for the validation (Supporting Information Figure S1). Thus, the forest type of the validation fold is the one excluded from calibration.

**Evaluating the performance of the allometric models.** For each scenario, we evaluated the performance of the models from the literature, those of the subject forest type, and those of the regional models by averaging, over the k-fold iterations, two criteria computed on the validation fold:

$$ \text{Relative bias (\%): RB} = 100 \times \frac{1}{n} \sum_{i=1}^{n} \frac{\hat{X}_{i} - X_{i}}{X_{i}} $$

$$ \text{Root mean square error (m or m}^2\text{): RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (\hat{X}_{i} - X_{i})^2} $$

where $\hat{X}_i$ and $X_i$ are respectively, the predicted and observed height (or crown area) and n represents the total number of trees.

For each k fold iterations in scenario 1, RB and RMSE of forest type, regional and pantropical models were computed using the validation fold of each forest type separately. RB and RMSE were then averaged over the 5 iterations. For each k fold iterations in scenario 2, RB and RMSE of regional and pantropical models were computed on each the validation fold. For each k fold iterations in scenario 3, RB and RMSE of regional and pantropical models were computed on each the validation fold which corresponded to a forest type. Note that RMSE is always positive while the RB indicates whether the error was positive or negative. To determine the most suitable allometric model among the locally-derived forest type, regional and pantropical models for H–D and CA–D relationships, we compared their relative error (RMSE) and then relative bias (RB). We first selected the model with the lowest RMSE. Second, we selected other models whose difference in RMSE with the lowest RMSE was less than 1 unit (error of 1 m tall tree or 1 m² crown area seems meaningful for forest biometry). Lastly among this selection, we retained the one with the lowest RB as the best model.

All statistical analyses were performed using version 4.1.2 of the R statistical software⁵⁶.

# Declarations

## Data Availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.
## Acknowledgements

This study is a contribution from the regional project on REDD+ (PreREDD+) in the Congo basin that was funded by the Global Environment Fund (TF010038) and was administered by the World Bank to the COMIFAC. The second component of the project aimed at "Building allometric equations for the forests of the Congo basin" was led by the ONFi/TEREA/Nature+ consortium and data collection was carried out by national scientific institutions including INDEFOR-AP in Equatorial Guinea, IRET in Gabon, University of Yaoundé 1 in Cameroon supported by researchers from IRD, University of Bangui in CAR, University of Marien NGouabi in Congo and the University of Kisangani in DRC. Logistic support necessary for the field and laboratory measurements was provided by the six timber companies including COMALI in Equatorial Guinea, Rougier Gabon, GRUMCAM in Cameroon, SEFCA in CAR, CIB-OLAM in Congo, and CFT in DRC. The authors also thank the large number of technicians and students that were involved in the data collection and Sébastien BAUWENS for the data collection protocol, Adrien PEROCHES for data quality controls and Samuel QUEVAUVILLERS for data management.

## Author contributions

M.B.L, A.F, V.R. and N.B. designed the research; A.F, N.P, N.B., A.N., S.T.M., P.C., Y.B., G.M., J.M.K., J.L., B.S., O.D.Y., V.R. and participated in data collection; M.B.L, and V.R. analysed the data and wrote the first draft, A.F, N.P, N.B., A.N., S.T.M., P.C., and O.D.Y. provided useful feedback.

## Competing interests

The authors declare no competing interests.

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Tables

Table 1 Summary characteristics of the forest types in six different sites. Countries and forest types are abbreviated as follows: semi-deciduous forest in Cameroon (SEF-CAM), transition between semi-deciduous and evergreen forest on sandstone plateau in Central Africa Republic (TSS-CAR), seasonally flooded forest including monodominant *Gilbertiodendron dewevrei* (De Wild.) J.Leonard species in the Republic of Congo (SFM-CON), transition between semi-deciduous and evergreen forest in the DR Congo (TSE-DRC), evergreen forest of Littoral type in Equatorial Guinea (EFL-RGE), and mainland evergreen forest in Gabon (EVF-GAB). The geographical coordinates in latitude (Lat.) and longitude (Lon.), mean annual temperature range (MAT in °C), mean annual rainfall range (MAR in mm), sampling intensity (number of trees, number of species and diameter range in cm) and logging companies are equally provided.
<table><caption>Table 2 H-D and CA-D allometric models compared in this study.</caption><thead><tr><th>Country<br>(Country-<br>forest type<br>code)</th><th>Forest type</th><th>Logging<br>company</th><th>GPS<br>Coordinates<br>(Lat.; Lon.)</th><th>Geological<br>substrate</th><th>Seasons<br>(duration)</th><th>MAT<br>(°C)<br>min-<br>max.</th><th>MAR<br>(mm)</th><th>Soil<br>(colour)</th><th>Sampling<br>intensity</th></tr></thead><tbody><tr><td>Cameroon<br>(SEF-CAM)</td><td>Semi-deciduous</td><td>Alpicam-<br>Grumcam</td><td>3°42' - 4°3'<br>N; 14°14' -<br>14°34' E</td><td>Granites &<br>Schistes</td><td>Dry (Jun-Aug &<br>Nov-Mar); Rain<br>(Apr-May &<br>Sep-Dec)</td><td>20-<br>25</td><td>1500-<br>2000</td><td>Ferralsols<br>(Reddish-<br>brown)</td><td>Trees =<br>132;<br>Species =<br>15;<br>Diameter<br>range =<br>[11.5-180<br>cm]</td></tr><tr><td>Central<br>African<br>Republic (TSS-<br>CAR)</td><td>Transition between<br>Evergreen & Semi-<br>deciduous on<br>sandstone plateau</td><td>SEFCA</td><td>3.919;16.896</td><td>Sedimentary,<br>Metamorphic,<br>igneous</td><td>Dry (Jun-Aug &<br>Nov-Mar); Rain<br>(Apr-May &<br>Sep-Dec)</td><td>23-<br>27</td><td>1400-<br>1600</td><td>Ferralsols<br>(Reddish-<br>brown)</td><td>Trees =<br>143;<br>Species =<br>16;<br>Diameter<br>range =<br>[10.5-173<br>cm]</td></tr><tr><td>Republic of<br>Congo (SFM-<br>CON)</td><td>Seasonally flooded<br>including<br>monodominant species</td><td>CIB-<br>OLAM</td><td>2°13' -<br>2°14'N;<br>17°00' -<br>17°07'E</td><td>Quartzite</td><td>Dry (Jun-Aug &<br>Dec-Feb); Rain<br>(Mar-May &<br>Sep-Nov)</td><td>24-<br>28</td><td>1400-<br>1700</td><td>Xanthic<br>Ferralsols</td><td>Trees =<br>141;<br>Species =<br>16;<br>Diameter<br>range =<br>[10.3-208<br>cm]</td></tr><tr><td>Democratic<br>Republic of<br>the Congo<br>(TSE-DRC)</td><td>Transition between<br>Semi-deciduous &<br>Evergreen</td><td>CFT</td><td>0°1' - 0°8'<br>N; 25°20' -<br>25°31'E</td><td>Sedimentary</td><td>Dry (Jun-Sep &<br>Dec-Feb); Rain<br>(Mar-May &<br>Oct-Nov)</td><td>20-<br>26</td><td>1500-<br>2000</td><td>Ferralsols<br>(Yellowish-<br>red)</td><td>Trees =<br>142;<br>Species =<br>16;<br>Diameter<br>range =<br>[11.7-<br>160.5cm]</td></tr><tr><td>Gabon (EVF-<br>GAB)</td><td>Evergreen</td><td>Rougier<br>Haut-<br>Abanga</td><td>0°15' - 0°50'<br>N; 10°30' -<br>11°30'E</td><td>Metamorphic<br>or granites</td><td>Dry (Jun-Sep &<br>Dec-Jan); Rain<br>(Feb-May &<br>Oct-Nov)</td><td>24-<br>26</td><td>1800-<br>2000</td><td>Ferralsols</td><td>Trees =<br>178;<br>Species =<br>16;<br>Diameter<br>range =<br>[12.3-<br>169.3<br>cm]</td></tr><tr><td>Equatorial<br>Guinea (EFL-<br>RGE)</td><td>Littoral Evergreen</td><td>COMALI</td><td>1.316;9.537</td><td>Sedimentary</td><td>Dry (Jul-Sep &<br>Dec-Feb); Rain<br>(Mar-Jun &<br>Oct-Nov)</td><td>23-<br>30</td><td>2000-<br>2500</td><td>Ferralsols<br>(yellow-<br>Sandy)</td><td>Trees =<br>109;<br>Species =<br>14;<br>Diameter<br>range =<br>[11-172<br>cm]</td></tr></tbody></table>
<table><thead><tr><th>Allometric models</th><th>References</th></tr></thead><tbody><tr><td>H-D allometry</td><td></td></tr><tr><td>Best fitted model for the subject forest type</td><td>this study</td></tr><tr><td>Best fitted regional model for each fold</td><td>this study</td></tr><tr><td>Pantropical climate-based model</td><td>Chave et al., 2014</td></tr><tr><td>Central Congo regional equation for mixed forest type</td><td>Kearsley et al., 2013</td></tr><tr><td>Tropical Africa regional model</td><td>Banin et al., 2012</td></tr><tr><td>Tropical Africa regional model</td><td>Lewis et al., 2009</td></tr><tr><td>Central Africa regional model</td><td>Feldpausch et al., 2011</td></tr><tr><td>Central Africa regional model</td><td>Feldpausch et al., 2012</td></tr><tr><td>CA-D allometry</td><td></td></tr><tr><td>Best fitted model for the subject forest type</td><td>this study</td></tr><tr><td>Best fitted regional model for each fold</td><td>this study</td></tr><tr><td>Central Africa regional model</td><td>Blanchard et al., 2016</td></tr></tbody></table>

Table 3 Best performance height-diameter (H-D) and crown area-diameter (CA-D) allometric models for central African forest types. Forest types are described in Table 1. The name of fitted models is given by the mathematical function used (as given in Table S2) followed by “_FT” if the model was fitted at the forest type level or “_RG” if fitted at regional level. The values of coefficients *a*, *b*, *c* then are the estimates resulting from the model fit. The name of the models taken from the literature is after their author and date of publication. Coefficient values are then the published values.
<table><thead><tr><th rowspan="2">Scenario</th><th rowspan="2">Validation fold</th><th rowspan="2">Model name</th><th rowspan="2">Mathematical function</th><th colspan="2">Determination coefficients</th><th colspan="3">Model coefficients</th><th colspan="3">Starting values</th></tr><tr><th>RMSE (m)</th><th>RB (%)</th><th>a</th><th>b</th><th>c</th><th>A</th><th>B</th><th>C</th></tr></thead><tbody><tr><td colspan="12" style="text-align: left; font-weight: bold;">H-D Allometric models</td></tr><tr><td rowspan="6">Local forest type</td><td>SEF</td><td>Linear_FT</td><td>χ = a + b × D</td><td>1.526</td><td>-0.003</td><td>18.657</td><td>0.298</td><td></td><td></td><td></td><td></td></tr><tr><td>EVF</td><td>Linear_FT</td><td>χ = a + b × D</td><td>1.326</td><td>-0.439</td><td>21.070</td><td>0.242</td><td></td><td></td><td></td><td></td></tr><tr><td>TSE</td><td>Power_FT</td><td>χ = a × D<sup>b</sup></td><td>1.165</td><td>-0.065</td><td>9.418</td><td>0.271</td><td></td><td>6.161</td><td>0.360</td><td></td></tr><tr><td>SFM</td><td>Feldpausch et al. (2012)</td><td>χ = a × (1 - exp(-b × D<sup>c</sup>))</td><td>0.650</td><td>0.111</td><td>50.453</td><td>-0.047</td><td>0.812</td><td></td><td></td><td></td></tr><tr><td>TSS</td><td>Banin et al. (2012)</td><td>χ = a - b × exp(-c × D)</td><td>1.124</td><td>0.262</td><td>45.100</td><td>-42.800</td><td>0.025</td><td></td><td></td><td></td></tr><tr><td>EFL</td><td>Chave et al. (2014)</td><td>χ = exp(a - E + b × D - c × D<sup>2</sup>)</td><td>1.290</td><td>0.085</td><td>0.893</td><td>0.760</td><td>0.034</td><td></td><td></td><td></td></tr><tr><td rowspan="2">Regional encompassing the subject forest type</td><td>Region-Fold1 to 4</td><td>Banin et al. (2012)</td><td>χ = a - b × exp(-c × D)</td><td>6.140</td><td>-1.972</td><td>45.100</td><td>-42.800</td><td>0.025</td><td></td><td></td><td></td></tr><tr><td>Region-Fold5</td><td>Meyer_RG</td><td>χ = a × (1 - exp(-b × D))</td><td>6.150</td><td>0.305</td><td>46.125</td><td>0.028</td><td></td><td>85.475</td><td>0.007</td><td></td></tr><tr><td rowspan="6">Regional not encompassing the subject forest type</td><td>SFM</td><td>Banin et al. (2012)</td><td>χ = a - b × exp(-c × D)</td><td>4.760</td><td>-0.076</td><td>45.100</td><td>-42.800</td><td>0.025</td><td></td><td></td><td></td></tr><tr><td>TSS</td><td>Banin et al. (2012)</td><td>χ = a - b × exp(-c × D)</td><td>4.606</td><td>-1.477</td><td>45.100</td><td>-42.800</td><td>0.025</td><td></td><td></td><td></td></tr><tr><td>EFL</td><td>Lewis et al. (2009)</td><td>χ = a × (1 - exp(-b × D<sup>c</sup>))</td><td>5.064</td><td>-0.595</td><td>54.010</td><td>-0.053</td><td>0.759</td><td></td><td></td><td></td></tr><tr><td>SEF</td><td>Lewis et al. (2009)</td><td>χ = a × (1 - exp(-b × D<sup>c</sup>))</td><td>6.950</td><td>-1.053</td><td>54.010</td><td>-0.053</td><td>0.759</td><td></td><td></td><td></td></tr><tr><td>EVF</td><td>Lewis et al. (2009)</td><td>χ = a × (1 - exp(-b × D<sup>c</sup>))</td><td>6.045</td><td>0.331</td><td>54.010</td><td>-0.053</td><td>0.759</td><td></td><td></td><td></td></tr><tr><td>TSE</td><td>Feldpausch et al. (2011)</td><td>χ = a + b × log(D)</td><td>7.868</td><td>8.387</td><td>1.153</td><td>0.554</td><td></td><td></td><td></td><td></td></tr><tr><td colspan="12" style="text-align: left; font-weight: bold;">CA-D allometric models</td></tr><tr><td rowspan="6">Local forest type</td><td>SEF</td><td>Linear_FT</td><td>χ = a + b × D</td><td>18.636</td><td>3.045</td><td>-94.516</td><td>4.807</td><td></td><td></td><td></td><td></td></tr><tr><td>SFM</td><td>Linear_FT</td><td>χ = a + b × D</td><td>15.960</td><td>7.403</td><td>-78.431</td><td>3.778</td><td></td><td></td><td></td><td></td></tr><tr><td>EVF</td><td>Michailoff_FT</td><td>χ = a × exp(-b × D<sup>1</sup>)</td><td>13.631</td><td>5.982</td><td>609.076</td><td>92.745</td><td></td><td>247.054</td><td>49.395</td><td></td></tr><tr><td>TSS</td><td>Parabolic-log_FT</td><td>χ = a + b × log(D) + c × log(D)<sup>2</sup></td><td>11.851</td><td>0.299</td><td>1151.943</td><td>-757.198</td><td>125.665</td><td></td><td></td><td></td></tr><tr><td>TSE</td><td>Linearized-power_FT</td><td>log(χ) = a + b × log(D)</td><td>29.544</td><td>8.916</td><td>-1.681</td><td>1.609</td><td></td><td></td><td></td><td></td></tr><tr><td>EFL</td><td>Parabolic-log_FT</td><td>χ = a + b × log(D) + c × log(D)<sup>2</sup></td><td>12.429</td><td>3.844</td><td>653.583</td><td>-475.373</td><td>89.104</td><td></td><td></td><td></td></tr><tr><td rowspan="4">Regional encompassing the subject forest type</td><td>Region-Fold1</td><td>Linear_RG</td><td>χ = a + b × D</td><td>97.337</td><td>-1.662</td><td>-67.517</td><td>3.874</td><td></td><td></td><td></td><td></td></tr><tr><td>Region-Fold2</td><td>Parabolic-log_RG</td><td>χ = a + b × log(D) + c × log(D)<sup>2</sup></td><td>100.412</td><td>50.662</td><td>1128.264</td><td>-738.262</td><td>122.809</td><td></td><td></td><td></td></tr><tr><td>Region-Fold3</td><td>Naslund_RG</td><td>χ = D<sup>2</sup>/(a + b × D)<sup>2</sup></td><td>101.337</td><td>45.072</td><td>3.654</td><td>0.019</td><td></td><td>4.609</td><td>0.017</td><td></td></tr><tr><td>Region-Fold4</td><td>Naslund_RG</td><td>χ = D<sup>2</sup>/(a + b × D)<sup>2</sup></td><td>131.422</td><td>64.542</td><td>3.585</td><td>0.020</td><td></td><td>4.517</td><td>0.018</td><td></td></tr><tr><td></td><td>Region-Fold5</td><td>Parabolic_RG</td><td>χ = a + b × D + c × D<sup>2</sup></td><td>104.798</td><td>47.833</td><td>-46.120</td><td>3.162</td><td>0.004</td><td></td><td></td><td></td></tr></tbody></table>
<table><tr><td>Regional not encompassing the subject forest type</td><td>SEF</td><td>Log-normal_RG</td><td>log(χ) = a + b × log(D) + c × log(D)<sup>2</sup></td><td>122.152</td><td>60.397</td><td>-0.285</td><td>0.981</td><td>0.062</td></tr><tr><td></td><td>SFM</td><td>Korf_RG</td><td>χ = a × exp(-b × D<sup>c</sup>)</td><td>89.763</td><td>81.147</td><td>10833.950</td><td>18.270</td><td>0.359</td><td>1941.531</td><td>22.983</td><td>0.540</td></tr><tr><td></td><td>EVF</td><td>Blanchard et al. (2016)</td><td>χ = a + b × log(D)</td><td>107.375</td><td>15.656</td><td>1.240</td><td>0.718</td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>TSS</td><td>Parabolic_RG</td><td>χ = a + b × D + c × D<sup>2</sup></td><td>67.439</td><td>26.898</td><td>-41.010</td><td>3.056</td><td>0.005</td><td></td><td></td><td></td></tr><tr><td></td><td>TSE</td><td>Log-normal_RG</td><td>log(χ) = a + b × log(D) + c × log(D)<sup>2</sup></td><td>140.169</td><td>46.068</td><td>0.208</td><td>0.729</td><td>0.094</td><td></td><td></td><td></td></tr><tr><td></td><td>EFL</td><td>Parabolic-log_RG</td><td>χ = a + b × log(D) + c × log(D)<sup>2</sup></td><td>104.152</td><td>1.650</td><td>1219.950</td><td>-785.654</td><td>128.403</td><td></td><td></td><td></td></tr></table>

## Figures

<figure><img src="image_3.png" /><figcaption>Figure 1</figcaption></figure>

k-fold cross-validation schemes for the first and second scenarios. Green blocks represent training dataset and red blocks represent validation datasets. Green arrows represent fitting and red arrows represent performance evaluation. SEF-CAM: semi-deciduous forest type in Cameroon; TSS-CAR: transition between semi-deciduous and evergreen forest on sandstone plateau in Central Africa Republic; SFM-CON: seasonally flooded forest including monodominant *Gilbertiodendron dewevrei* (De Wild.) J.Leonard species in Republic of Congo; TSE-DRC: transition between semi-deciduous and evergreen forest in the Democratic Republic of Congo; EFL-RGE: evergreen forest of Littoral type in Equatorial Guinea; and EVF-GAB: mainland evergreen forest in Gabon.
<figure><img src="image_4.png" /><figcaption>Figure 2</figcaption></figure>

Pairwise comparison of forest type effect on H-D allometric models (A) and CA-D allometric models (B). Forest types are defined in Figure 1. Error bars with the same letters are not significantly different.
<figure><img src="image_5.png" /><figcaption>Figure 3</figcaption></figure>

Performances in terms of RMSE (left column) and bias (right column) of the height-diameter allometric models compared for three scenarios. Each bar corresponds to a model as identified by its colour. The different group of bars on the x-axis correspond to the different validation folds used to assess model performance. Some models were fitted: their name is given by the mathematical function used (as given in Table S2) followed by "_FT" if the model was fitted at the forest type level or "_RG" if fitted at regional level. Some models were taken from the literature: their name is after their author and date of publication. The model by Kearsley et al. (2013), although included in the model comparison, was not shown here due to its poor performance. Panels A and B: model comparison for scenario 1 (models derived for the forest type vs. regional models vs. pantropical models); the different forest types on the x-axis also correspond to those used for model calibration. Panels C and D: model comparison for scenario 2 (regional model encompassing the subject forest type vs. pantropical models). Panels E and F: model comparison for scenario 3 (regional model not encompassing the subject forest type vs. pantropical models); the different forest types on the x-axis also correspond to those excluded from model calibration. RMSE is relative mean squared error (A, C and D) and bias is relative bias (B, D and F). Abbreviations for forest types are defined in Figure 1.
<figure><img src="image_6.png" /><figcaption>Figure 4</figcaption></figure>

Performances in terms of RMSE (left column) and bias (right column) of the crown area-diameter allometric models compared for three scenarios. Each bar corresponds to a model as identified by its colour. The different blocks of bars on the x-axis correspond to the different validation folds used to assess model performance. Some models were fitted: their name is given by the mathematical function used (as given in Table S2) followed by "_FT" if the model was fitted at the forest type level or "_RG" if fitted at regional level. One model, named Blanchard et al. (2016), was taken from the literature. Panels A and B: model comparison for scenario 1 (models derived for the forest type vs. regional models vs. pantropical models); the different forest types on the x-axis also correspond to those used for model calibration. Panels C and D: model comparison for scenario 2 (regional model encompassing the subject forest type vs. pantropical models). Panels E and F: model comparison for scenario 3 (regional model not encompassing the subject forest type vs. pantropical models); the different forest types on the x-axis also correspond to those excluded from model calibration. RMSE is relative mean squared error (A, C and D) and bias is relative bias (B, D and F). Abbreviations for forest types are defined in Figure 1.

Supplementary Files

This is a list of supplementary files associated with this preprint. Click to download.

* LibalahetaSI12TreeHeightCrownAreaDiameterAllometriessrep.docx

* LibalahetaSI38TreeHeightCrownAreaDiameterAllometriessrep.xlsx