Novel growth models of three valuable timber species from the Brazilian Atlantic Forest

Novel growth models of three valuable timber species from the Brazilian Atlantic Forest | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Novel growth models of three valuable timber species from the Brazilian Atlantic Forest João Paulo Bispo Santos, Angélica Faria de Resende, Allana Katiussya Silva Pereira, and 7 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5422550/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Native timber production offers a promising pathway to make large-scale tropical forest restoration financially viable. However, there are still many gaps in knowledge on this subject. This study develops species-specific growth models for three valuable and threatened native timber species from the Brazilian Atlantic Forest – Cariniana legalis , Dalbergia nigra , and Zeyheria tuberculosa – and evaluate their timber production potential. We collected data from 14 tree plantations distributed in the states of São Paulo, Espírito Santo, and Bahia, with a total of 5,564 sampled trees. The plantations span a broad climatic gradient, with ages ranging from 1 to 50 years. We developed and compared six models for predicting tree diameter and total height. We modeled and compared the growth patterns among the species and determined their commercial rotation ages, based on time needed to reach a diameter of 35 cm. Z. tuberculosa exhibited the lowest diameter increment (0.90 cm/year) and did not reach the threshold DBH, making it more suitable for non-premium uses, such as utensils and pallets. In contrast, D. nigra demonstrated the highest growth rate (1.33 cm/year) and a first harvest age of 22 years, demonstrating that it is a promising species to produce timber for furniture, and construction. C. legalis showed a slightly lower growth rate (1.16 cm/year) and required 31 years to reach first harvest, with wood ideal for construction and furniture. These findings highlight the potential of these species for timber production in restoration projects and the importance of timely silvicultural practices to enhance growth rates and wood quality. Bioeconomy Ecosystem Services Sustainable forestry Tropical timber production Reforestation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Forest restoration is increasingly recognized as a critical strategy for provisioning ecosystem services such as climate change mitigation, biodiversity conservation, food and water security (Pires et al. 2021 ; Di Sacco et al. 2021 ). As a result, restoration efforts have proliferated worldwide, including ambitious restoration commitments from 60 countries to restore greater than 200 million hectares of forest landscapes by 2030 (Brancalion et al. 2022 ). However, scaling up restoration efforts faces numerous challenges, starting with socioeconomic barriers (Löf et al. 2019 ; Fagan et al. 2020 ), as restoration success relies on the motivations and engagement of stakeholders, which is often highly associated with the financial returns on land use (Brancalion and Holl 2024 ; Ashton et al. 2024 ). By addressing these factors, restoration efforts can become more effective, achieve larger scales, and generate multiple benefits for a range of stakeholders (Miller et al. 2017 ; Martin et al. 2021 ). Sustainable timber production in restoration plantations presents a promising solution to address ecological, social, and economic challenges (Di Sacco et al. 2021 ). The production of high-quality native timber within these plantations offers a multi-faceted strategy that not only supports forest recovery and biodiversity conservation but can also function as a carbon sink. Cultivated native timber may alleviate pressure on natural forests by reducing illegal logging, and generate socioeconomic benefits, such as job creation and income generation (FAO 2022 ; Brancalion et al. 2022 ; Krainovic et al. 2023 ). This dual-purpose strategy can drive large-scale restoration initiatives while meeting the future global demand for timber products, which is estimated to grow exponentially over the next few decades due to population growth and increased demand, and from the depletion of native timber stocks in natural forests (Gurgel et al. 2019 ; Di Sacco et al. 2021 ; FAO 2022 ). To effectively implement such strategies, it is essential to fulfill knowledge gaps on native timber production, going beyond the exploitation of natural forests (Santos et al. 2023 ). These gaps include elucidating species-specific growth rates and understanding lengths of rotation times (Sharma et al. 2019 ; Santos et al. 2023 ). In this context, tree height and trunk diameter are crucial inputs for developing tree growth models that can be used to predict species lengths of rotation and for provide merchantable timber harvest volumes (Sharma et al. 2019 ). However, while tree growth models are fundamental for forest management and decision-making, they are still scarce for native species. Only recently growth models were developed for Brazilian native timber species in restoration plantations and silvicultural trials (Rolim and Piotto 2019 , 2024 ; Krainovic et al. 2023 ) Nonetheless, currently, most models for native species are either too generalized (non-species-specific models) or tailored for exotic species, resulting in biased and inaccurate growth estimates ( e.g. , basal area, trunk diameter, and wood volume) when applied to a single native timber species (Chave et al. 2014 ; Jucker et al. 2016 ). Most existing models for native species have therefore been based upon multi-species data derived across a wide range of bioclimatic conditions (Chave et al. 2014 ; Jucker et al. 2016 ). While these generalized models are useful for generating predictions, they fail to capture species-specific' auto-ecology and regional variations (Seidl et al. 2010 ). Conversely, local models are more reliable for making predictions within the geographic range considered in model fitting, but they are not capable of making accurate predictions outside of this range (Charlène et al. 2019 ; Rolim and Piotto 2024 ). Recent literature supports that species-specific models covering a wide range of biogeographic and climatic conditions often outperform generic models with the same characteristics (Duncanson et al. 2015 ; Charlène et al. 2019 ), thus better supporting the development of silvicultural approaches to produce native timber in forest restoration. Here, we analyzed a large dataset of 5,564 trees, including trunk diameter measurements and total tree height for three valuable Brazilian native timber species: Cariniana legalis (Mart.) Kuntze (Lecythidaceae), Dalbergia nigra (Vell.) Allemão ex Benth. (Fabaceae), and Zeyheria tuberculosa (Vell.) Bureau ex Verl (Bignoniaceae). The dataset spans a broad range of the natural distribution of the studied species. We used this dataset to develop growth models exploring the scaling relationship between D : age and Ht : D , allowing for an accurate and unbiased estimation of a tree's diameter at the breast level (DBH) and total tree height. We used the following questions to guide our study: (i) Can tree's diameter and total height be estimated accurately based on its scaling relationship between D : age and Ht : D ? (ii) What is the best model for predicting a tree diameter and total height? (iii) What is the ideal rotation age for each native timber species based on the time needed to reach a minimum DBH of 35 cm, commonly used as a threshold for harvesting trees for saw wood production? Material and Methods Species selection and site locations For this study, we selected three native tree species from the Brazilian Atlantic Forest: Cariniana legalis (Mart.) Kuntze (Lecythidaceae), Dalbergia nigra (Vell.) Allemão ex Benth. (Fabaceae), and Zeyheria tuberculosa (Vell.) Bureau ex Verl. (Bignoniaceae). These species are known for their straight trunks and high timber quality that can be used for construction, furniture, and flooring (Rolim and Piotto 2019 ). C. legalis and Z. tuberculosa have indistinct heartwood and sapwood, with medium basic wood densities of 0.53 and 0.60 g/cm³, respectively. Both species exhibit high stability, with C. legalis considered to have excellent workability and Z. tuberculosa good workability (Rolim and Piotto 2019 ).In contrast, D. nigra has distinct heartwood and sapwood, a basic wood density of 0.63 g/cm³, and a low tendency to twist and warp (Rolim and Piotto 2019 ). As a result of their high-quality timber, these species have been historically overexploited through illegal logging from natural forests and are now threatened (CNCFlora 2022 ). These species are broadly distributed across several geographic regions within the Brazilian Atlantic Forest (Flora do Brasil - in construction. 2023; GBIF 2024 ). Additionally, the studied species are recognized for their high growth rate, at least considering other native timber species, and have a consolidated market value (Rolim and Piotto 2024 ). We sampled trees in 14 experimental ( i.e ., plantations established to test silvicultural performance of native tree species) and commercial plantations distributed in the states of São Paulo (n = 6), Espírito Santos (n = 2), and Bahia (n = 6), covering different environmental conditions and tree sizes (Fig. 1). Importantly, most of the sampled tree plantations did not use conventional silvicultural treatments often applied to commercial timber plantations, such as fertilization, irrigation, pruning, and thinning. Some of the sampled tree plantations were also designed to test a variety of different ways of plantation establishment. This includes the effect of planting spacing, alternating monospecific planting lines, and native timber species intercropped with exotic species. See supplementary material 1 for more details about study site characteristics. Our dataset covers a broad range of the natural range of the species studied, from latitudes − 13.3319 in the north to -22.7174° in the south, and longitudes from − 48.1681° in the west to -39.1433° in the east (Fig. 1). Additionally, the database encompasses a wide bioclimatic range that represents different site conditions (Fig. 1). The mean annual precipitation varies between 574 mm and 1740 mm, while the mean annual temperature ranges from 25.5°C to 21.5°C (Fig. 1). Figure 1 Overview of the study sites and database. Panel (a) shows the geographic coverage of the database (n = 14). Panel (b) highlights differences in the mean annual precipitation and temperature among study sites. Each point represents the forest inventory conducted in different years. Climate data were obtained from the NASA Prediction of Worldwide Energy Resources (POWER) database (NASA Power 2024 ), which consists of gridded annual mean values covering the date when the forest inventory was performed at each study site. In panel (c) violin plots show the diameter at the breast height (DBH) size distribution of trees in the database. The number of records available for each study site type is displayed on the right. See supplementary material 1 for detailed description of the site codes and more detailed description of the sites studied Tree growth database Although our database includes multi-year inventory data for 7 of the 14 sites studied, it is structured as a chronosequence with non-replicated measurements for individual trees. We measured at least 30 trees of each species at 14 sites throughout the study region (Fig. 1). As shown by Sullivan et al. ( 2018 ), growth models built with as few as 20 locally measured trees often predict tree size with low error. At each site, we measured uneven- or even-aged forest plantations with the native species studied (see supplementary material 1 for detailed information about the characterization of our study sites). For each tree, we measured the stem diameter at the breast height ( D , in cm) and total tree height ( Ht , in m) for all individuals with metric tape and digital hypsometry vertex, respectively. Our database yielded a total of 5,564 trees, of which 2,032 were of C. legalis , 2,078 of D. nigra , and 1,554 of Z. tuberculosa . The database encompasses a large range of tree sizes for each native species ( C. legalis – Age : 1–41 years; D : 0.4–62.4 cm; Ht : 1.3–42.8 m; D. nigra – Age : 1–50 years; D : 0.6–60.8 cm; Ht : 1.3–29.6 m; and Z. tuberculosa – Age : 1–50 years; D : 0.8–37 cm; Ht : 1.3–29.6 m). It reflects a variety of tree sizes, and developmental stages. Model development To identify the most accurate equation to estimate tree diameter and total height, we used a set of regressions to compare D (expressed as a function of age ), and total tree height ( Ht ) using equations that describe the Ht : D ratio. We fitted and compared the prediction accuracy of six models for each dependent variable ( D , and Ht ) (Table 1 ). These models are known as generic equations once they assume that the scaling relationship between D : Age and Ht : D are invariant across biogeographic regions. Table 1 Growth models selected for modeling the scaling relationship between D:Age and Ht:D . The parameters to be estimated are A (asymptote, random effect), c (fixed effect), and k (fixed effect) Model Authors Growth model 1 Richards (Richards 1959 ) Ln(y) = A * (1-exp (- k * Ln( x ))) c + ε 2 Weibull (Yang et al. 1978 ) Ln(y) = A * (1-exp (- k * Ln( x ) c ) + ε 3 Logistic (Tsoularis and Wallace 2002 ) Ln(y) = A * (1 + c * exp (- k * Ln( x ))) −1 + ε 4 Gompertz (Gompertz 1825 ) Ln(y) = A * exp (- c * exp (- k * Ln( x ))) + ε 5 Korf (Zeide 1993 ) Ln(y) = A * exp (- k * Ln( x )) − c + ε 6 Terazaki (Rolim and Piotto 2019 ) Ln(y) = A * exp (- k * Ln( x ) −1 ) + ε Frequently, growth models are built by fitting a linear or non-linear regression directly to log-transformed raw data. However, it does not fix the measurement error problem in the independent variable because when the dependent variable is log-transformed, this procedure tends to fall into regression dilution bias, typically leading to an underestimation of the regression slope (Warton et al. 2006 ). For inventory data, dealing with systematic bias is worse due to an unbalanced tree size distribution. Since small trees tend to dominate the regression signal, they outnumber the large ones (Duncanson et al. 2015 ). To address this, Duncanson et al. ( 2015 ) proposed fitting models to binned data instead of raw data values. This approach reduces tree-level variation in diameter and height to a mean value, thus minimizing bias. We performed a preliminary analysis to compare whether the binned data approach was more appropriate to yield less unbiased estimates of D and Ht . Our preliminary analysis led us to focus on the binned data approach. In supplementary material 2, we provided a more detailed discussion about the binned data approach compared to raw data. Following Jucker et al. ( 2016 ), mean D and Ht were calculated for each logarithmic bin of 50 stem diameters of constant width. As in Jucker et al. ( 2016 ), we also used logarithmic binning to better capture the asymmetric distribution of the dependent variable in the right and left extremes of the tree size distribution. Nonlinear log-log models were fit to binned data using generalized nonlinear least-squares regression (Table 1 ). It is common for data variance from trees with different sizes and measured across several site conditions to be inconsistent. This inconsistency is due to the increasing response variable, which affects the distribution of errors leading to biased estimates if not accounted for (Zuur et al. 2009 ; Rolim and Piotto 2019 ). To address this, we modeled the variance using the varPower argument of the gnls (Generalized Nonlinear Least Squares) function of the nlme R package (Pinheiro et al. 2011 ). Model validation To evaluate the model performance and accuracy of the different D and Ht models, we followed the same steps as Jucker et al. ( 2016 ) to ensure the robustness. That is, we: (i) divided the database into a training set (60% of the data) and a validation set with the remaining database (40% of the data used exclusively to evaluate model performance); (ii) fitted D and Ht models to the training dataset using the binning approach described above; (iii) used fitted equations to predict D and Ht for all trees in the validation dataset; and (iv) quantified the prediction error of each model by comparing predicted and observed values in the validation dataset and by comparing performance metrics as described below. Steps (i – iv) were repeated 100 times to avoid problems with the randomization procedure in step (i). To compare the model performance, we choose two statistical performance metrics as in Chave et al. ( 2014 ) and Jucker et al. ( 2016 ): the root mean square error (RMSE, in cm or m) and the relative systematic error (bias, in %). The bias at the tree level was evaluated by comparing the empirical values of D and Ht at tree j Y obs ( j ) to the estimated value Y pred ( j ). According to Jucker et al. ( 2016 ), the model bias was defined as follows: $$\:\text{B}\text{i}\text{a}\text{s}\:\left(j\right)=\:\frac{1}{\text{N}}{\sum\:}_{\text{i}=1}^{N}\left(\frac{{Y}_{obs}\left(j\right)-{Y}_{pred}\left(j\right)}{{Y}_{obs}\left(j\right)}\right)$$ $$\:\text{R}\text{M}\text{S}\text{E}\:\left(j\right)=\sqrt{\frac{1}{N}{\sum\:}_{i=1}^{N}{\left({Y}_{obs}\left(j\right)-{Y}_{pred}\left(j\right)\right)}^{2}}\:$$ Model performance statistics for each species are provided in supplementary material 3. In addition, we also used complementary goodness-of-fit statistics from the models in our analysis, including parameter significance and distribution of residuals. Models with non-significant parameters (p > 0.05) or when the convergence of parameters was not reached were disregarded at the model comparison stage because, in general, non-significant model parameters tend to generate poorly realistic predictions (Burkhart and Tomé 2012 ). As in Rolim and Piotto ( 2024 ), we also consider the biological realism of the asymptote for model evaluation because, in some cases, when a model is applied to different tree-size classes, the realism of the asymptotic estimate is unrealistic. Model uncertainty and error propagation Using the data binning approach has the advantage of underestimating the uncertainty of the model and thus underestimating the true variability of biometric scaling relationships at the tree level (Jucker et al., 2016 ). This underrating occurs mainly because in the data binning approach, the residual standard deviation ( σ ) is not calculated for individual trees but for values averaged from multiple trees, making it difficult to quantify uncertainty (Jucker et al. 2016 ). Nonetheless, Jucker et al. ( 2016 ) developed a simple approach to quantify uncertainty and error propagation when the data binning approach is used, as follows: $$\:{\sigma\:}_{v}=\sqrt{\frac{\sum\:{\left(\text{l}\text{n}\left({Y}_{obs}\right)\:-\text{l}\text{n}\left({Y}_{pred}\right)\:\right)}^{2}}{n-2}}$$ Where \(\:n\) is the number of observations, \(\:{Y}_{obs}\) is the observed value, and \(\:{Y}_{pred}\) is the predicted value. This simple, but straight forward method allows the generation of more realistic estimates of predictive uncertainty for models fitted using the data binning approach when an independent dataset is used for model validation. Jucker et al. ( 2016 ) provided a R code for implementing and replicating the model uncertainty and error propagation analysis. Given that, to generate reliable predictions for any tree using our selected models, we used model 1 in Table 1 as an example, where the predicted diameter (D pred ) is estimated as follows: $$\:{D}_{pred}=\text{e}\text{x}\text{p}({A\:\times\:\left(1-\text{exp}\left(-k\times\:\text{ln}\left(age\right)\right)\right)}^{c}+{\epsilon\:})$$ Assuming ε is normally distributed, the mean of exp(ε) can be approximated by exp(σ 2 /2), where σ 2 is the mean square error of the regression (Jucker et al. 2016 ). From this, an unbiased estimate of D can, therefore, be calculated using the following equation: $$\:{D}_{pred}=\text{e}\text{x}\text{p}\left({A\:\times\:\left(1-\text{exp}\left(-k\times\:\text{ln}\left(age\right)\right)\right)}^{c}+\:{\epsilon\:}\right)\times\:\:\text{e}\text{x}\text{p}({\sigma\:}^{2}/2)$$ Growth performance of the three native species Finally, to compare growth rates among species, we generated diameter growth predictions using the diameter growth equations obtained for each species and thus estimated the mean annual increment in DBH at 30 years (MAI 30 ) (Rolim and Piotto 2024 ). In addition, we also used our species-specific growth models to estimate total height, allowing us to compare the total height when each species reached 35 cm DBH (Ht 35 ). We used a minimum DBH of 35 cm as our harvest criterion because this is a standard criterion traditionally used to determine the ideal time to harvest timber in Brazilian sawmills. Results Diameter and total tree height growth models for C. legalis Among the candidate models evaluated for estimating D and Ht for C. legalis , models 3 and 6 (Table 1 ) were identified as the best-fit models (Eq. 1 – 2 ). These models demonstrated relatively low RMSE values, with 5.6 for the diameter model and 4.7 for the total height model. Additionally, they exhibited minimal average systematic bias, with − 0.8 for diameter and 3.8 for total height. Eq. 1 is more suitable for generating unbiased predictions, offering a lower RMSE compared to its alternatives. While Eq. 2 had a slightly higher mean RMSE compared to the other equations it is likely to yield much less biased predictions, making it more reliable. $$\:{\text{L}\text{n}(\:D}_{est})=3.730\:\times\:(1+36.02\:\times\:\text{e}\text{x}\text{p}(-1.906\times\:{\text{L}\text{n}\left(age\right)\left)\right)}^{-1})\times\:\:\text{e}\text{x}\text{p}({0.148}^{2}/2)$$ 1 $$\:{\text{L}\text{n}(Ht}_{est})=68.9078\times\:\text{e}\text{x}\text{p}(-4.759387077\times\:{\text{Ln}\left(D\right)}^{-0.343760186})\times\:\text{e}\text{x}\text{p}({0.169}^{2}/2)$$ 2 These equations (Eq. 1 – 2 ) were able to generate less biased estimates of D and Ht for C. legalis across a broad biogeographical range, outperforming the other models tested. Most importantly, the models for C. legalis showed no evidence of over- or underprediction for both D and Ht values since the error predictions were very close to zero across a wide range of tree sizes (Fig. 2 a-c). Eq. 1 showed only a negative bias for large D values (> 40 cm) (Fig. 2 a-b). Similarly, Eq. 2 also had a consistently lower error across the tree height size classes, with no tendency to under- or overestimate Ht values, confirming the model's robustness for predicting total tree height (Fig. 2 c-d). Through the independent validation dataset, the standard deviation ( σ v ) for Eqs. 1 and 2 were 0.48 and 0.45, respectively, considered as lower standard deviation values. Diameter and total tree height growth models for Diameter and total tree height growth models for D. nigra The best-fit models for predicting trunk diameter and total height of D. nigra are represented by Eqs. 3 and 4 . For Eq. 3 , the RMSE and average systematic bias were 6.05 and − 8.63, respectively, while Eq. 4 had an RMSE of 4.6 and an average systematic bias of 3.8. Both models presented lower standard deviations ( σ v for diameter = 0.61, and σ v for total height = 0.47). Eq. 3 tended to overestimate stem diameter by 30–50% for trees with an observed diameter of less than 6 cm and to underestimate trees with diameters between 10–20 cm by approximately 25% (Fig. 3a-b). Due to the spread of values for D and the greater within-site variation in growth rates for D. nigra , it was not possible to develop a model that fully reduces this bias. For the Ht model, Eq. 4 showed no tendency to overestimate or underestimate the total height across tree sizes classes (Fig. 3c-d). $$\:{\text{L}\text{n}(D}_{est})=3.825\times\:\text{e}\text{x}\text{p}(-21.15\:\times\:\:\text{e}\text{x}\text{p}(-1.769\times\:\text{L}\text{n}\left(age)\right)\times\:\:\text{e}\text{x}\text{p}({0.373}^{2}/2)$$ 3 $$\:{\text{L}\text{n}(Ht}_{est})=9.003\times\:\text{e}\text{x}\text{p}\left(-3.761\times\:{\text{Ln}\left(D\right)}^{-1}\right)\times\:\:\text{e}\text{x}\text{p}({0.245}^{2}/2)$$ 4 Figure 3 Goodness of fit for the diameter and total height growth model for D. nigra ( i.e ., Eqs. 3 and 4 in the main text, respectively). Panel (a-c) reports the mean relative error for different tree size classes. The thick black line represents a spline regression of the data points used to illustrate the predictive accuracy of the models. Relative errors were calculated for a random subset of trees corresponding to 40% of the data ( n = 831 trees), which were used exclusively to validate the models. This randomization procedure was repeated 100 times to avoid the randomization procedure in step (i) having an undue effect on the model evaluation process, and at each iteration regression splines (orange lines) were used to illustrate how the magnitude of the relative errors varies as a function of tree size. Panel (b-d) compares predicted vs . observed diameter and total height, with the dashed orange line corresponding to a 1:1 relationship Diameter and total tree height growth models for Z. tuberculosa For Z. tuberculosa , the best-fit models for estimating D and Ht were described in Eqs. 5 and 6 , respectively. The mean RMSE for these equations was 3.2 cm for D and 2.8 m for Ht , with corresponding average systematic biases of -1.45 and 0.25. These models exhibited no strong tendency to over- or underestimate tree diameter and total height, as evidenced by the slight deviation of the error curve (black spline) from zero (Fig. 4 ). Moreover, both equations showed low standard deviations (σ v for diameter = 0.4 and σ v for height = 0.6). Eq. 5 had a slight tendency to overestimate D values for small trees ( 4 cm) (Fig. 4 a). Eq. 6 shows a rapid positive bias (< 25%) in predicting Ht for smaller trees ( 5 m), leading to zero error for mid-range trees (Fig. 4 c). $$\:{\text{L}\text{n}(D}_{est})=3.281\times\:(1+37.24\:\times\:\text{e}\text{x}\text{p}(-2.266\times\:{\text{L}\text{n}\left(age\right)\left)\right)}^{-1}\times\:\:\text{e}\text{x}\text{p}({0.213}^{2}/2)$$ 5 $$\:{\text{L}\text{n}(Ht}_{est})=7.895\times\:\text{e}\text{x}\text{p}(-3.407\times\:{\text{Ln}\left(D\right)}^{-1})\times\:\text{e}\text{x}\text{p}({0.261}^{2}/2)$$ 6 Species growth performance and optimal harvest age In terms of growth potential, D. nigra had the highest growth rate among the species studied, with an MAI 30 of 1.33 cm/year and a Ht 35 of 14.8 m, followed by C. legalis with an MAI 30 of 1.16 cm/year and a Ht 35 of 20.7 (Table 2 ). In contrast, Z. tuberculosa had the lowest MAI 30 , with a growth rate of 0.90 cm/year (Table 2 ). Based on the time required for each species to reach 35 cm DBH – a common harvesting diameter for saw wood production –, D. nigra had the faster time to first harvesting (22 years), and C. legalis required a time of 31 years to first harvest (Fig. 5; Table 2 ). Notably, Z. tuberculosa did not reach the minimum DBH of 35 cm during the 40-year period in which we make growth predictions (Fig. 5). Figure 5 shows that the diameter growth curve of this species stabilizes much earlier, at approximately 16 years when its growth rate begins to decrease (supplementary material 4). Based on these results, we recommend an optimal harvest age of 16 years, as the growth curve of this species does not tend to increase significantly after this age. The growth predictions generated by our models and calculations that we have used to compare the performance of each species are shown in supplementary material 4. Table 2 Species growth rate patterns estimated at 40 years. DBH – mean estimated diameter at the breast height; Ht – mean estimated total height; Ht 35 – estimated total height when a tree reaches 35 cm DBH; MAI – mean annual increment in diameter at 30 years; OHA – Optimal harvest age Species Dbh (cm) Ht (m) Ht 35 (m) MAI 30 (cm/year) OHA (years) Cariniana legalis 24.3 14.3 21.6 1.16 31 Dalbergia nigra 27.9 13.5 14.8 1.33 22 Zeyheria tuberculosa 20.9 13.5 - 0.90 16 Fig 5 Diameter growth curves as a function of the tree age for three native Atlantic Forest species. The curves represent different species: C. legalis – green line; D. nigra – orange line; Z. tuberculosa – blue line. The dashed vertical grey line indicates the minimum harvest diameter of 35 cm DBH Discussion In this study, we developed species-specific growth models with strong predictive power for estimating the bole diameter and total height of three Brazilian native timber species, widely recognized for their valuable timber (Rolim and Piotto 2019 ; Krainovic et al. 2023 ). In this context, our study provides critical information for establishing and managing commercial tree plantations of these species. This can provide strong technical support for scaling up forest restoration initiatives in the Brazilian Atlantic Forest. The diameter and tree height growth models were developed based on the scaling relationship between D : age and Ht:D for a large dataset consisting of 5,564 trees of three native species. These variables can be obtained from forest inventory data, which can facilitate the adoption of our models. As far as we are concerned, this study is the first one to fit species-specific growth models for Atlantic Forest species comprising a wide range of bioclimatic conditions. Due to historical overexploitation, these species are ecologically threatened and commercially extinct. This makes it necessary to establish plantations to produce their unique timber for market (CNCFlora 2022 ; FAO 2022 ). Thus, transitioning from illegal exploitation to sustainable plantation-based production offers a viable solution to mitigate these impacts, such as the overharvesting of these endangered species, the degradation of natural forests, and the associated loss of biodiversity (Silva et al. 2019 ; Betts et al. 2021 ). This approach reduces the pressure on natural forests, but also promotes a more sustainable and reliable source of timber, as well re-new the timber market by revamping commercially extinct species. By shifting to legally managed plantations, these species can be conserved while still contributing to economic development, in a conserving through use approach (Pryde et al. 2015 ). Stem diameter and total tree height growth models We found that it is feasible to accurately predict unbiased stem diameter and total tree height growth through the D : age and Ht : D relationships. Through this scaling relationship, we were able to derive a species-specific equation for estimating diameter and total tree height growth for the species studied across various bioclimatic conditions (Eq. 1 – 6 ). The models have proved to be significantly robust across a large range of tree sizes, bioclimatic space, and site conditions, as seen in the model validation step (Fig. 2 – 4 ). While general models developed from multi-species data are helpful, they may introduce systematic bias when applied to a single species. This occurs because these models incorporate different scaling relationships from several tree species with distinct phylogenetic legacies ( e.g ., angiosperms and gymnosperms) and contrasting growth forms ( e.g ., trees, shrubs, and palms) (Chave et al. 2014 ; Jucker et al. 2016 ). Our species-specific models can generate more accurate predictions across biogeographic regions once they account for a single species' auto-ecology and physiological traits, which are more consistent across biogeographic regions (Duncanson et al. 2015 ; Charlène et al. 2019 ; Quang et al. 2020 ). The developed models allow for more robust species growth predictions, revealing the potential unique and better estimates for timber production for each species (Fig. 5). Currently, the timber production potential of these native species is either under- or overestimated by inaccurate and non-validated models, most of which have been developed for native or exotic species at local conditions (Rolim and Piotto 2024 ), or that lack multi- year data sets (Krainovic et al. 2023 ). In fact, it has been argued that local equations are paramount to accurately reflect the variability in tree growth and tree size distribution, thereby reducing potential biases in growth predictions (Chave et al. 2014 ). However, as in Chave et al. ( 2014 ) and Jucker et al. ( 2016 ), it has been shown that global equations ( i.e. , those fitted using a global dataset from multi-species) are consistent across sites, and local equations do not perform much better than global equations in terms of model uncertainty and error propagation. A few authors have confronted local models with the global models to test their performance (Chave et al. 2014 ; Jucker et al. 2016 ). Here, we did not follow this procedure for two simple reasons: i) although we modeled tree growth across a broad biogeographic range, this range is covered by a unique forest type dominated by the Brazilian Atlantic Forest representing the entire natural range of the species studied (IBGE, 2012); ii) using species-specific data results in less dispersion and error propagation (Uller et al. 2021 ); and iii) scaling relationships of structural, physiological, and ecological traits ( i.e. , species auto-ecology) with stem diameter and tree height are not expected to vary among individuals of the same species, conserving their growth responses (Anderson-Teixeira et al. 2015 ). This suggests that species-specific factors significantly influence scaling relationships. Thus, by focusing on the auto-ecology and growth rates of a single species, we expected that the scaling relationship between the dependent and independent variables did not strongly differ within the studied sites. Species growth rate patterns and commercial rotations Based on minimum commercial diameter, we have defined rotation cycles for the three native timber species we studied (Table 2 ). The species proved to be promising for timber production (Fig. 5). In comparison to fast-growing exotic timber species in Brazil, such as eucalyptus, which have harvest cycles of about 20 years for saw wood production (Rolim and Piotto 2024 ), the three native species demonstrated potential for short-to-medium rotation cycles. This positions them as competitive and viable alternatives for commercial timber production (Rolim and Piotto 2024 ). However, while these native species can offer quicker income returns, it is essential to consider their ecological roles and ensure that their exploitation is balanced with conservation efforts. Our results showed distinct growth rate patterns among the species, revealing their harvest age and growth potential differences. These differences can potentially be combined in planting mixture, where the faster-growing species or species that maximize size class early are harvested over the course of a rotation of the slowest growing. Alternatively, plantations may be designed to promote continuous cover over time, potentially ensuring both ecological balance and long-term economic benefits (Laiho et al. 2011 ; Banaś et al. 2018 ). It is also important to consider revenue at different times, as trunks with smaller diameters ( e.g., Z. tuberculosa ) may be sold for specific purposes, such as utensils and structural materials (Rolim and Piotto 2019 ). In contrast, larger trunks ( e.g., C. legalis , and D. nigra ) tend to have higher value when sold for premium uses, such as furniture (Rolim and Piotto 2019 ). With shorter harvesting cycles of approximately 16 years, Z. tuberculosa offers the potential to accelerate revenue generation. Rolim and Piotto ( 2019 ) found similar growth rate patterns for Z. tuberculosa with a diameter increment at 35 years of 0.8 cm/year, which is close to our results at 35 years (0.79 cm/year) (supplementary material 4). Similarly, the diameter growth models developed by Rolim and Piotto ( 2019 , 2024 ) and De Mendonça et al. ( 2017 ) also demonstrated that Z. tuberculosa did not reach the minimum logging diameter of 35 cm DBH over the measurement period. Z. tuberculosa usually develops straight stems when planted in full sun conditions, but still requires some pruning (Rolim and Piotto 2019 ). Although it is considered a fast-growing, light-demanding species that easily colonizes open areas like extensive pastures, Z. tuberculosa also demonstrates high longevity and can persist for many years in forestry systems (Rolim and Piotto 2019 ). Consequently, the growth performance of this species in mixed plantations may be reduced or limited by shading from other species, particularly as the canopy develops and expands in the years following planting (José et al. 2024 ). In fact, tropical timber species tend to grow faster in full sun than in the understory of restoration plantations (José et al. 2024 ). This makes Z. tuberculosa more suitable for pure plantations, thinned when needed, or intercropping systems with low planting densities, which can reduce tree competition for light. All of this suggests that our results can be considered conservative, as the growth data were primarily collected from mixed tree plantations where this species were dominated from the 10th year forward. On the other hand, C. legalis and D. nigra require a medium-term investment of about 22 and 31 years, respectively, before harvest (Table 2 ). In this study, C. legalis reaches 35 cm DBH at 31 years, about 10–12 years less than estimated by Krainovic et al. ( 2023 ) and Rolim and Piotto ( 2024 ). In Rolim and Piotto ( 2019 , 2024 ), the diameter growth rates of C. legalis were 0.94 and 1.10 cm/year, which is lower than the growth rate of 1.16 cm/year in our study. Surprisingly, D. nigra reached the minimum logging diameter of 35 cm DBH in just 22 years in our study, which is about 10 years earlier than estimates by others (Rolim and Piotto 2019 , 2024 ). The estimated MAI in diameter observed in this study (1.33 cm/year) is also higher than the values reported by Rolim and Piotto ( 2019 , 2024 ), which were 0.87 and 1.07 cm/year, respectively. Despite the considerable timber production potential of C. legalis and D. nigra , several important factors must be considered. For example, D. nigra often develops irregular stem shapes that limit its potential timber yield when planted in full sunlight, a common condition in young plantations and for legume trees. Although many tropical timber species tend to grow faster in full sun (José et al., 2024 ), increased light availability promotes the growth of multiple and tortuous stems, which is undesirable in the forestry market (Krainovic et al., 2023 ). Therefore, this species may require specific planting models, in which seedlings are planted in higher density to increase competition or under some level of shading, and demand further pruning. Conversely, C. legalis develops naturally straight stems when planted in full sun with other species, although some level of pruning have been recommended in pure plantations. However, its growth and stem quality are enhanced in mixed plantations, as this late-successional species tends to overtop the crowns of other species In general, the differences in growth rate observed in our study compared to others can be attributed to several factors. For instance, the lower growth rates reported by Rolim and Piotto ( 2019 , 2024 ) for C. legalis and D. nigra may be because of the low soil fertility and sandy soils of their study sites, which are known to limit nutrient availability and water retention (Lévesque et al. 2016 ). Furthermore, the non-commercial, restoration plantations studied by Krainovic et al. ( 2023 ), with limited species-specific data covering different ages, might explain the longer timeframes required for C. legalis to reach harvestable sizes. This underscores the importance of the availability of data in modeling species growth, and the need of conducting multi-site assessments to fully capture the growth potential of each species. Our database consists of growth data collected from experimental and commercial plantations that did not receive common silvicultural treatments, such as thinning, pruning, and fertilization, often applied in forestry to enhance growth rates and wood quality. Consequently, the species in these plantations did not benefit from these management practices that could have maximized their development. This represents a limitation since, once under optimal management conditions, these species would have better growth performance. Therefore, while the results reported in this study are promising, they should be considered conservative, as the true potential of these species could be significantly greater with appropriate and intensive management (Grotta et al. 2004 ; Rolim and Piotto 2024 ). Conclusions This study is a valuable contribution to understanding the growth patterns of three valuable native timber species from the Brazilian Atlantic Forest, particularly in terms of their potential for timber production and sustainable forest management. By developing species-specific growth equations, we could accurately predict diameter and total tree height across a wide range of bioclimatic conditions. Additionally, we defined commercial rotation cycles for three native species, providing valuable insights for optimizing timber yield. Furthermore, the different times to first harvest for each species highlights the potential to diversify income streams, which can increase the internal rate of return for stakeholders such as governments, private investors, and local communities. By staggering harvests, practitioners can generate a more stable income stream while reducing financial risks. Our findings underscore the importance of tailored silvicultural practices to improve growth rates and wood quality, highlighting the potential for these species to play a central role in large-scale forest restoration and conservation efforts. Declarations Acknowledgments This study was supported by São Paulo Research Foundation (FAPESP) (grant numbers 2018/18416-2, 2020/08081-3, 2022/14695-0, 2019/24049-5, and 2022/14605-0), Re.green (grant number 0011-2022-ESA), and by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), with finance code 001. The authors also thank the National Council for Scientific and Technological Development (CNPq) (grant number 306152/2019-3). The authors would also like to express our sincere gratitude to the plantation owners and partners who generously opened their doors and allowed us to conduct our field measurements on their lands. 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Forest Science 39:594–616. https://doi.org/10.1093/FORESTSCIENCE/39.3.594 Zuur AF, Ieno EN, Walker N, et al (2009) Mixed effects models and extensions in ecology with R. Springer New York, New York, NY Additional Declarations Competing interest reported. The authors P.H.S.B. and R.R.R. are partners of the Re.green company. Supplementary Files Supplementarymaterial1.docx Supplementarymaterial2.docx Supplementarymaterial3.docx Supplementarymaterial4.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5422550","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":377109814,"identity":"548f331e-fe5d-4b89-a08c-d5d238f53b5d","order_by":0,"name":"João Paulo Bispo Santos","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzklEQVRIiWNgGAWjYBACA2YwxcbAD6ISCkjRItkA0mJAjBY44wAKFw8wZ2d/9uDDH7484/OrEz88MGCQ5xc7gF+LZTOPueHMNrZisxtvN0sAHWY4c3YCAYcd5mGT5m1gS9x24+wGkJYEg9sEtbA/k+b5w5a4ecbZzT+I1MJgJs3Dxpa4gb93G3G2wP0icYN3m0WCgQRhv5jzHweF2LE8/v6zm2/+qLCR55cmoIUBFI0MDMcSGCTAKiUIKodpqUlg4D9AlOpRMApGwSgYgQAAnRxCS/y/oDMAAAAASUVORK5CYII=","orcid":"","institution":"State University of Campinas (UNICAMP), University City Zeferino Vaz","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"João","middleName":"Paulo Bispo","lastName":"Santos","suffix":""},{"id":377109815,"identity":"889dfa3b-bac3-4cd0-b22c-ace4f34cfc6f","order_by":1,"name":"Angélica Faria de Resende","email":"","orcid":"","institution":"University of São Paulo","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Angélica","middleName":"Faria","lastName":"de Resende","suffix":""},{"id":377109816,"identity":"75914beb-67bd-49c1-8058-05aaa2564d92","order_by":2,"name":"Allana Katiussya Silva Pereira","email":"","orcid":"","institution":"University of São Paulo","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Allana","middleName":"Katiussya Silva","lastName":"Pereira","suffix":""},{"id":377109817,"identity":"1d6fbcb1-63c6-4da2-9735-790fda809e40","order_by":3,"name":"Miguel Luiz Menezes Freitas","email":"","orcid":"","institution":"Institute of Environmental Research – IPA","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Miguel","middleName":"Luiz Menezes","lastName":"Freitas","suffix":""},{"id":377109818,"identity":"d462df33-ebbf-4ac0-ae4a-115d895cd0e3","order_by":4,"name":"Mark S. 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Panel (a) shows the geographic coverage of the database (n= 14). Panel (b) highlights differences in the mean annual precipitation and temperature among study sites. Each point represents the forest inventory conducted in different years. Climate data were obtained from the NASA Prediction of Worldwide Energy Resources (POWER) database (NASA Power 2024), which consists of gridded annual mean values covering the date when the forest inventory was performed at each study site. In panel (c) violin plots show the diameter at the breast height (DBH) size distribution of trees in the database. The number of records available for each study site type is displayed on the right. See supplementary material 1 for detailed description of the site codes and more detailed description of the sites studied\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-5422550/v1/1c17c6fd59be2f5838f03f76.png"},{"id":70192828,"identity":"b1b22cac-e8fd-486d-a5c1-bf7edeb5cbf8","added_by":"auto","created_at":"2024-11-29 10:48:47","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":304230,"visible":true,"origin":"","legend":"\u003cp\u003eGoodness of fit for the diameter and total height growth model for \u003cem\u003eC. legalis\u003c/em\u003e (\u003cem\u003ei.e\u003c/em\u003e., Eq. 1 and 2 in the main text, respectively). Panel (a-c) reports the mean relative error for different tree size classes. The thick black line represents a spline regression of the data points used to illustrate the predictive accuracy of the models. Relative errors were calculated for a random subset of trees corresponding to 40% of the data (\u003cem\u003en \u003c/em\u003e=\u003cem\u003e \u003c/em\u003e812 trees), which were used exclusively to validate the models. This randomization procedure was repeated 100 times to avoid the randomization procedure in step (i) having an undue effect on the model evaluation process, and at each iteration regression splines (orange lines) were used to illustrate how the magnitude of the relative errors varies as a function of tree size. Panel (b-d) compares predicted \u003cem\u003evs\u003c/em\u003e. observed diameter and total height, with the dashed orange line corresponding to a 1:1 relationship\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5422550/v1/9920ba9f76f8150ab12de0a3.png"},{"id":70193773,"identity":"25716a2f-ff2c-4dcf-a069-70a7204e843a","added_by":"auto","created_at":"2024-11-29 11:04:47","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":303251,"visible":true,"origin":"","legend":"\u003cp\u003eGoodness of fit for the diameter and total height growth model for \u003cem\u003eD. nigra\u003c/em\u003e (\u003cem\u003ei.e\u003c/em\u003e., Eq. 3 and 4 in the main text, respectively). \u0026nbsp;Panel (a-c) reports the mean relative error for different tree size classes. The thick black line represents a spline regression of the data points used to illustrate the predictive accuracy of the models. Relative errors were calculated for a random subset of trees corresponding to 40% of the data (\u003cem\u003en \u003c/em\u003e=\u003cem\u003e \u003c/em\u003e831 trees), which were used exclusively to validate the models. This randomization procedure was repeated 100 times to avoid the randomization procedure in step (i) having an undue effect on the model evaluation process, and at each iteration regression splines (orange lines) were used to illustrate how the magnitude of the relative errors varies as a function of tree size. Panel (b-d) compares predicted \u003cem\u003evs\u003c/em\u003e. observed diameter and total height, with the dashed orange line corresponding to a 1:1 relationship\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-5422550/v1/35896fe914977206a7a2ff80.png"},{"id":70193447,"identity":"bedf5955-86f7-477b-84fe-36d29bdab38d","added_by":"auto","created_at":"2024-11-29 10:56:48","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":280259,"visible":true,"origin":"","legend":"\u003cp\u003eGoodness of fit for the diameter and total height growth model for \u003cem\u003eZ. tuberculosa\u003c/em\u003e (\u003cem\u003ei.e\u003c/em\u003e., Eq. 5 and 6 in the main text, respectively). Panel (a-c) reports the mean relative error for different tree size classes. The thick black line represents a spline regression of the data points used to illustrate the predictive accuracy of the models. Relative errors were calculated for a random subset of trees corresponding to 40% of the data (\u003cem\u003en \u003c/em\u003e=\u003cem\u003e \u003c/em\u003e621 trees), which were used exclusively to validate the models. This randomization procedure was repeated 100 times to avoid the randomization procedure in step (i) having an undue effect on the model evaluation process, and at each iteration regression splines (orange lines) were used to illustrate how the magnitude of the relative errors varies as a function of tree size. Panel (b-d) compares predicted \u003cem\u003evs\u003c/em\u003e. observed diameter, with the dashed orange line corresponding to a 1:1 relationship\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-5422550/v1/b604cacd091c1b4e1cac6c8c.png"},{"id":70193444,"identity":"ac477fa5-718c-4c5f-921d-2b48e974dbee","added_by":"auto","created_at":"2024-11-29 10:56:47","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":100332,"visible":true,"origin":"","legend":"\u003cp\u003eDiameter growth curves as a function of the tree age for three native Atlantic Forest species. The curves represent different species: \u003cem\u003eC. legalis\u003c/em\u003e – green line\u003cem\u003e; D. nigra\u003c/em\u003e– orange line; \u003cem\u003eZ. tuberculosa\u003c/em\u003e – blue line. The dashed vertical grey line indicates the minimum harvest diameter of 35 cm DBH\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-5422550/v1/86c0ec328a4a57a2122650e9.png"},{"id":70869449,"identity":"2929560c-0be8-424c-bbd0-b9fccfaaf69b","added_by":"auto","created_at":"2024-12-08 14:46:53","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1959921,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5422550/v1/f919de77-6ae2-4973-b86d-6ccd8c618011.pdf"},{"id":70192829,"identity":"79d81d58-4c73-420c-953d-c8de8f5a164d","added_by":"auto","created_at":"2024-11-29 10:48:47","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":47512,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementarymaterial1.docx","url":"https://assets-eu.researchsquare.com/files/rs-5422550/v1/26dda033296a934867738b3d.docx"},{"id":70192834,"identity":"45f28bc0-9618-4a73-a182-0fe2fd048fdd","added_by":"auto","created_at":"2024-11-29 10:48:48","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":5240558,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementarymaterial2.docx","url":"https://assets-eu.researchsquare.com/files/rs-5422550/v1/622b19a4d25be5307a073600.docx"},{"id":70192836,"identity":"91e6a6c6-cad3-41a7-bdf8-71267fdb7ed6","added_by":"auto","created_at":"2024-11-29 10:48:48","extension":"docx","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":36178,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementarymaterial3.docx","url":"https://assets-eu.researchsquare.com/files/rs-5422550/v1/d1e6a1158768cbb9ca46fcb2.docx"},{"id":70192832,"identity":"e54a802e-a3e8-4337-90cb-9353199381a7","added_by":"auto","created_at":"2024-11-29 10:48:47","extension":"docx","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":30979,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementarymaterial4.docx","url":"https://assets-eu.researchsquare.com/files/rs-5422550/v1/80ad5ecc91aa8088f7913129.docx"}],"financialInterests":"Competing interest reported. The authors P.H.S.B. and R.R.R. are partners of the Re.green company.","formattedTitle":"Novel growth models of three valuable timber species from the Brazilian Atlantic Forest","fulltext":[{"header":"Introduction","content":"\u003cp\u003eForest restoration is increasingly recognized as a critical strategy for provisioning ecosystem services such as climate change mitigation, biodiversity conservation, food and water security (Pires et al. \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Di Sacco et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). As a result, restoration efforts have proliferated worldwide, including ambitious restoration commitments from 60 countries to restore greater than 200\u0026nbsp;million hectares of forest landscapes by 2030 (Brancalion et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). However, scaling up restoration efforts faces numerous challenges, starting with socioeconomic barriers (L\u0026ouml;f et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Fagan et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), as restoration success relies on the motivations and engagement of stakeholders, which is often highly associated with the financial returns on land use (Brancalion and Holl \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Ashton et al. \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). By addressing these factors, restoration efforts can become more effective, achieve larger scales, and generate multiple benefits for a range of stakeholders (Miller et al. \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Martin et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eSustainable timber production in restoration plantations presents a promising solution to address ecological, social, and economic challenges (Di Sacco et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The production of high-quality native timber within these plantations offers a multi-faceted strategy that not only supports forest recovery and biodiversity conservation but can also function as a carbon sink. Cultivated native timber may alleviate pressure on natural forests by reducing illegal logging, and generate socioeconomic benefits, such as job creation and income generation (FAO \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Brancalion et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Krainovic et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). This dual-purpose strategy can drive large-scale restoration initiatives while meeting the future global demand for timber products, which is estimated to grow exponentially over the next few decades due to population growth and increased demand, and from the depletion of native timber stocks in natural forests (Gurgel et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Di Sacco et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; FAO \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eTo effectively implement such strategies, it is essential to fulfill knowledge gaps on native timber production, going beyond the exploitation of natural forests (Santos et al. \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). These gaps include elucidating species-specific growth rates and understanding lengths of rotation times (Sharma et al. \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Santos et al. \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In this context, tree height and trunk diameter are crucial inputs for developing tree growth models that can be used to predict species lengths of rotation and for provide merchantable timber harvest volumes (Sharma et al. \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). However, while tree growth models are fundamental for forest management and decision-making, they are still scarce for native species. Only recently growth models were developed for Brazilian native timber species in restoration plantations and silvicultural trials (Rolim and Piotto \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Krainovic et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2023\u003c/span\u003e)\u003c/p\u003e \u003cp\u003eNonetheless, currently, most models for native species are either too generalized (non-species-specific models) or tailored for exotic species, resulting in biased and inaccurate growth estimates (\u003cem\u003ee.g.\u003c/em\u003e, basal area, trunk diameter, and wood volume) when applied to a single native timber species (Chave et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Jucker et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Most existing models for native species have therefore been based upon multi-species data derived across a wide range of bioclimatic conditions (Chave et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Jucker et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). While these generalized models are useful for generating predictions, they fail to capture species-specific' auto-ecology and regional variations (Seidl et al. \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Conversely, local models are more reliable for making predictions within the geographic range considered in model fitting, but they are not capable of making accurate predictions outside of this range (Charl\u0026egrave;ne et al. \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Rolim and Piotto \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Recent literature supports that species-specific models covering a wide range of biogeographic and climatic conditions often outperform generic models with the same characteristics (Duncanson et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Charl\u0026egrave;ne et al. \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), thus better supporting the development of silvicultural approaches to produce native timber in forest restoration.\u003c/p\u003e \u003cp\u003eHere, we analyzed a large dataset of 5,564 trees, including trunk diameter measurements and total tree height for three valuable Brazilian native timber species: \u003cem\u003eCariniana legalis\u003c/em\u003e (Mart.) Kuntze (Lecythidaceae), \u003cem\u003eDalbergia nigra\u003c/em\u003e (Vell.) Allem\u0026atilde;o ex Benth. (Fabaceae), and \u003cem\u003eZeyheria tuberculosa\u003c/em\u003e (Vell.) Bureau ex Verl (Bignoniaceae). The dataset spans a broad range of the natural distribution of the studied species. We used this dataset to develop growth models exploring the scaling relationship between \u003cem\u003eD\u003c/em\u003e:\u003cem\u003eage\u003c/em\u003e and \u003cem\u003eHt\u003c/em\u003e:\u003cem\u003eD\u003c/em\u003e, allowing for an accurate and unbiased estimation of a tree's diameter at the breast level (DBH) and total tree height. We used the following questions to guide our study: (i) Can tree's diameter and total height be estimated accurately based on its scaling relationship between \u003cem\u003eD\u003c/em\u003e:\u003cem\u003eage\u003c/em\u003e and \u003cem\u003eHt\u003c/em\u003e:\u003cem\u003eD\u003c/em\u003e? (ii) What is the best model for predicting a tree diameter and total height? (iii) What is the ideal rotation age for each native timber species based on the time needed to reach a minimum DBH of 35 cm, commonly used as a threshold for harvesting trees for saw wood production?\u003c/p\u003e"},{"header":"Material and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eSpecies selection and site locations\u003c/h2\u003e \u003cp\u003eFor this study, we selected three native tree species from the Brazilian Atlantic Forest: \u003cem\u003eCariniana legalis\u003c/em\u003e (Mart.) Kuntze (Lecythidaceae), \u003cem\u003eDalbergia nigra\u003c/em\u003e (Vell.) Allem\u0026atilde;o ex Benth. (Fabaceae), and \u003cem\u003eZeyheria tuberculosa\u003c/em\u003e (Vell.) Bureau ex Verl. (Bignoniaceae). These species are known for their straight trunks and high timber quality that can be used for construction, furniture, and flooring (Rolim and Piotto \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). \u003cem\u003eC. legalis\u003c/em\u003e and \u003cem\u003eZ. tuberculosa\u003c/em\u003e have indistinct heartwood and sapwood, with medium basic wood densities of 0.53 and 0.60 g/cm\u0026sup3;, respectively. Both species exhibit high stability, with \u003cem\u003eC. legalis\u003c/em\u003e considered to have excellent workability and \u003cem\u003eZ. tuberculosa\u003c/em\u003e good workability (Rolim and Piotto \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).In contrast, \u003cem\u003eD. nigra\u003c/em\u003e has distinct heartwood and sapwood, a basic wood density of 0.63 g/cm\u0026sup3;, and a low tendency to twist and warp (Rolim and Piotto \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). As a result of their high-quality timber, these species have been historically overexploited through illegal logging from natural forests and are now threatened (CNCFlora \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). These species are broadly distributed across several geographic regions within the Brazilian Atlantic Forest (Flora do Brasil - in construction. 2023; GBIF \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Additionally, the studied species are recognized for their high growth rate, at least considering other native timber species, and have a consolidated market value (Rolim and Piotto \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWe sampled trees in 14 experimental (\u003cem\u003ei.e\u003c/em\u003e., plantations established to test silvicultural performance of native tree species) and commercial plantations distributed in the states of S\u0026atilde;o Paulo (n\u0026thinsp;=\u0026thinsp;6), Esp\u0026iacute;rito Santos (n\u0026thinsp;=\u0026thinsp;2), and Bahia (n\u0026thinsp;=\u0026thinsp;6), covering different environmental conditions and tree sizes (Fig.\u0026nbsp;1). Importantly, most of the sampled tree plantations did not use conventional silvicultural treatments often applied to commercial timber plantations, such as fertilization, irrigation, pruning, and thinning. Some of the sampled tree plantations were also designed to test a variety of different ways of plantation establishment. This includes the effect of planting spacing, alternating monospecific planting lines, and native timber species intercropped with exotic species. See supplementary material 1 for more details about study site characteristics. Our dataset covers a broad range of the natural range of the species studied, from latitudes \u0026minus;\u0026thinsp;13.3319 in the north to -22.7174\u0026deg; in the south, and longitudes from \u0026minus;\u0026thinsp;48.1681\u0026deg; in the west to -39.1433\u0026deg; in the east (Fig.\u0026nbsp;1). Additionally, the database encompasses a wide bioclimatic range that represents different site conditions (Fig.\u0026nbsp;1). The mean annual precipitation varies between 574 mm and 1740 mm, while the mean annual temperature ranges from 25.5\u0026deg;C to 21.5\u0026deg;C (Fig.\u0026nbsp;1).\u003c/p\u003e \u003cp\u003e \u003cb\u003eFigure\u0026nbsp;1\u003c/b\u003e Overview of the study sites and database. Panel (a) shows the geographic coverage of the database (n\u0026thinsp;=\u0026thinsp;14). Panel (b) highlights differences in the mean annual precipitation and temperature among study sites. Each point represents the forest inventory conducted in different years. Climate data were obtained from the NASA Prediction of Worldwide Energy Resources (POWER) database (NASA Power \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), which consists of gridded annual mean values covering the date when the forest inventory was performed at each study site. In panel (c) violin plots show the diameter at the breast height (DBH) size distribution of trees in the database. The number of records available for each study site type is displayed on the right. See supplementary material 1 for detailed description of the site codes and more detailed description of the sites studied\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eTree growth database\u003c/h3\u003e\n\u003cp\u003eAlthough our database includes multi-year inventory data for 7 of the 14 sites studied, it is structured as a chronosequence with non-replicated measurements for individual trees. We measured at least 30 trees of each species at 14 sites throughout the study region (Fig.\u0026nbsp;1). As shown by Sullivan et al. (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), growth models built with as few as 20 locally measured trees often predict tree size with low error. At each site, we measured uneven- or even-aged forest plantations with the native species studied (see supplementary material 1 for detailed information about the characterization of our study sites). For each tree, we measured the stem diameter at the breast height (\u003cem\u003eD\u003c/em\u003e, in cm) and total tree height (\u003cem\u003eHt\u003c/em\u003e, in m) for all individuals with metric tape and digital hypsometry vertex, respectively.\u003c/p\u003e \u003cp\u003eOur database yielded a total of 5,564 trees, of which 2,032 were of \u003cem\u003eC. legalis\u003c/em\u003e, 2,078 of \u003cem\u003eD. nigra\u003c/em\u003e, and 1,554 of Z. \u003cem\u003etuberculosa\u003c/em\u003e. The database encompasses a large range of tree sizes for each native species (\u003cem\u003eC. legalis\u003c/em\u003e \u0026ndash; \u003cem\u003eAge\u003c/em\u003e: 1\u0026ndash;41 years; \u003cem\u003eD\u003c/em\u003e: 0.4\u0026ndash;62.4 cm; \u003cem\u003eHt\u003c/em\u003e: 1.3\u0026ndash;42.8 m; \u003cem\u003eD. nigra\u003c/em\u003e \u0026ndash; \u003cem\u003eAge\u003c/em\u003e: 1\u0026ndash;50 years; \u003cem\u003eD\u003c/em\u003e: 0.6\u0026ndash;60.8 cm; \u003cem\u003eHt\u003c/em\u003e: 1.3\u0026ndash;29.6 m; and \u003cem\u003eZ. tuberculosa\u003c/em\u003e \u0026ndash; \u003cem\u003eAge\u003c/em\u003e: 1\u0026ndash;50 years; \u003cem\u003eD\u003c/em\u003e: 0.8\u0026ndash;37 cm; \u003cem\u003eHt\u003c/em\u003e: 1.3\u0026ndash;29.6 m). It reflects a variety of tree sizes, and developmental stages.\u003c/p\u003e\n\u003ch3\u003eModel development\u003c/h3\u003e\n\u003cp\u003eTo identify the most accurate equation to estimate tree diameter and total height, we used a set of regressions to compare \u003cem\u003eD\u003c/em\u003e (expressed as a function of \u003cem\u003eage\u003c/em\u003e), \u003cem\u003eand\u003c/em\u003e total tree height (\u003cem\u003eHt\u003c/em\u003e) using equations that describe the \u003cem\u003eHt\u003c/em\u003e:\u003cem\u003eD\u003c/em\u003e ratio. We fitted and compared the prediction accuracy of six models for each dependent variable (\u003cem\u003eD\u003c/em\u003e, and \u003cem\u003eHt\u003c/em\u003e) (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). These models are known as generic equations once they assume that the scaling relationship between \u003cem\u003eD\u003c/em\u003e:\u003cem\u003eAge and Ht\u003c/em\u003e:\u003cem\u003eD\u003c/em\u003e are invariant across biogeographic regions.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eGrowth models selected for modeling the scaling relationship between \u003cem\u003eD:Age\u003c/em\u003e and \u003cem\u003eHt:D\u003c/em\u003e. The parameters to be estimated are A (asymptote, random effect), \u003cem\u003ec\u003c/em\u003e (fixed effect), \u003cem\u003eand k\u003c/em\u003e (fixed effect)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAuthors\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGrowth model\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRichards (Richards \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e1959\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLn(y)\u0026thinsp;=\u0026thinsp;\u003cem\u003eA\u003c/em\u003e * (1-exp (-\u003cem\u003ek\u003c/em\u003e * Ln(\u003cem\u003ex\u003c/em\u003e)))\u003csup\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sup\u003e + ε\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWeibull (Yang et al. \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e1978\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLn(y)\u0026thinsp;=\u0026thinsp;\u003cem\u003eA\u003c/em\u003e * (1-exp (-\u003cem\u003ek\u003c/em\u003e * Ln(\u003cem\u003ex\u003c/em\u003e)\u003csup\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sup\u003e) + ε\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLogistic (Tsoularis and Wallace \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2002\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLn(y)\u0026thinsp;=\u0026thinsp;\u003cem\u003eA\u003c/em\u003e * (1\u0026thinsp;+\u0026thinsp;\u003cem\u003ec\u003c/em\u003e * exp (-\u003cem\u003ek\u003c/em\u003e * Ln(\u003cem\u003ex\u003c/em\u003e)))\u003csup\u003e\u0026minus;1\u003c/sup\u003e + ε\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGompertz (Gompertz \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1825\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLn(y)\u0026thinsp;=\u0026thinsp;\u003cem\u003eA\u003c/em\u003e * exp (-\u003cem\u003ec\u003c/em\u003e * exp (-\u003cem\u003ek\u003c/em\u003e * Ln(\u003cem\u003ex\u003c/em\u003e))) + ε\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eKorf (Zeide \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e1993\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLn(y)\u0026thinsp;=\u0026thinsp;\u003cem\u003eA\u003c/em\u003e * exp (-\u003cem\u003ek\u003c/em\u003e * Ln(\u003cem\u003ex\u003c/em\u003e))\u003csup\u003e\u0026minus;\u003cem\u003ec\u003c/em\u003e\u003c/sup\u003e + ε\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTerazaki (Rolim and Piotto \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLn(y)\u0026thinsp;=\u0026thinsp;\u003cem\u003eA\u003c/em\u003e * exp (-\u003cem\u003ek\u003c/em\u003e * Ln(\u003cem\u003ex\u003c/em\u003e)\u003csup\u003e\u0026minus;1\u003c/sup\u003e) + ε\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFrequently, growth models are built by fitting a linear or non-linear regression directly to log-transformed raw data. However, it does not fix the measurement error problem in the independent variable because when the dependent variable is log-transformed, this procedure tends to fall into regression dilution bias, typically leading to an underestimation of the regression slope (Warton et al. \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). For inventory data, dealing with systematic bias is worse due to an unbalanced tree size distribution. Since small trees tend to dominate the regression signal, they outnumber the large ones (Duncanson et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). To address this, Duncanson et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) proposed fitting models to binned data instead of raw data values. This approach reduces tree-level variation in diameter and height to a mean value, thus minimizing bias. We performed a preliminary analysis to compare whether the binned data approach was more appropriate to yield less unbiased estimates of \u003cem\u003eD\u003c/em\u003e and \u003cem\u003eHt\u003c/em\u003e. Our preliminary analysis led us to focus on the binned data approach. In supplementary material 2, we provided a more detailed discussion about the binned data approach compared to raw data.\u003c/p\u003e \u003cp\u003eFollowing Jucker et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), mean \u003cem\u003eD\u003c/em\u003e and \u003cem\u003eHt\u003c/em\u003e were calculated for each logarithmic bin of 50 stem diameters of constant width. As in Jucker et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), we also used logarithmic binning to better capture the asymmetric distribution of the dependent variable in the right and left extremes of the tree size distribution. Nonlinear log-log models were fit to binned data using generalized nonlinear least-squares regression (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). It is common for data variance from trees with different sizes and measured across several site conditions to be inconsistent. This inconsistency is due to the increasing response variable, which affects the distribution of errors leading to biased estimates if not accounted for (Zuur et al. \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Rolim and Piotto \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). To address this, we modeled the variance using the \u003cem\u003evarPower\u003c/em\u003e argument of the \u003cem\u003egnls\u003c/em\u003e (Generalized Nonlinear Least Squares) function of the nlme R package (Pinheiro et al. \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2011\u003c/span\u003e).\u003c/p\u003e\n\u003ch3\u003eModel validation\u003c/h3\u003e\n\u003cp\u003eTo evaluate the model performance and accuracy of the different \u003cem\u003eD\u003c/em\u003e and \u003cem\u003eHt\u003c/em\u003e models, we followed the same steps as Jucker et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) to ensure the robustness. That is, we: (i) divided the database into a training set (60% of the data) and a validation set with the remaining database (40% of the data used exclusively to evaluate model performance); (ii) fitted \u003cem\u003eD\u003c/em\u003e and \u003cem\u003eHt\u003c/em\u003e models to the training dataset using the binning approach described above; (iii) used fitted equations to predict \u003cem\u003eD\u003c/em\u003e and \u003cem\u003eHt\u003c/em\u003e for all trees in the validation dataset; and (iv) quantified the prediction error of each model by comparing predicted and observed values in the validation dataset and by comparing performance metrics as described below. Steps (i \u0026ndash; iv) were repeated 100 times to avoid problems with the randomization procedure in step (i).\u003c/p\u003e \u003cp\u003eTo compare the model performance, we choose two statistical performance metrics as in Chave et al. (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) and Jucker et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e): the root mean square error (RMSE, in cm or m) and the relative systematic error (bias, in %). The bias at the tree level was evaluated by comparing the empirical values of \u003cem\u003eD\u003c/em\u003e and \u003cem\u003eHt\u003c/em\u003e at tree \u003cem\u003ej Y\u003c/em\u003e\u003csub\u003e\u003cem\u003eobs\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003ej\u003c/em\u003e) to the estimated value \u003cem\u003eY\u003c/em\u003e\u003csub\u003e\u003cem\u003epred\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003ej\u003c/em\u003e). According to Jucker et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), the model bias was defined as follows:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\text{B}\\text{i}\\text{a}\\text{s}\\:\\left(j\\right)=\\:\\frac{1}{\\text{N}}{\\sum\\:}_{\\text{i}=1}^{N}\\left(\\frac{{Y}_{obs}\\left(j\\right)-{Y}_{pred}\\left(j\\right)}{{Y}_{obs}\\left(j\\right)}\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:\\text{R}\\text{M}\\text{S}\\text{E}\\:\\left(j\\right)=\\sqrt{\\frac{1}{N}{\\sum\\:}_{i=1}^{N}{\\left({Y}_{obs}\\left(j\\right)-{Y}_{pred}\\left(j\\right)\\right)}^{2}}\\:$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eModel performance statistics for each species are provided in supplementary material 3. In addition, we also used complementary goodness-of-fit statistics from the models in our analysis, including parameter significance and distribution of residuals. Models with non-significant parameters (p\u0026thinsp;\u0026gt;\u0026thinsp;0.05) or when the convergence of parameters was not reached were disregarded at the model comparison stage because, in general, non-significant model parameters tend to generate poorly realistic predictions (Burkhart and Tom\u0026eacute; \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). As in Rolim and Piotto (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), we also consider the biological realism of the asymptote for model evaluation because, in some cases, when a model is applied to different tree-size classes, the realism of the asymptotic estimate is unrealistic.\u003c/p\u003e\n\u003ch3\u003eModel uncertainty and error propagation\u003c/h3\u003e\n\u003cp\u003eUsing the data binning approach has the advantage of underestimating the uncertainty of the model and thus underestimating the true variability of biometric scaling relationships at the tree level (Jucker et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). This underrating occurs mainly because in the data binning approach, the residual standard deviation (\u003cem\u003eσ\u003c/em\u003e) is not calculated for individual trees but for values averaged from multiple trees, making it difficult to quantify uncertainty (Jucker et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Nonetheless, Jucker et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) developed a simple approach to quantify uncertainty and error propagation when the data binning approach is used, as follows:\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:{\\sigma\\:}_{v}=\\sqrt{\\frac{\\sum\\:{\\left(\\text{l}\\text{n}\\left({Y}_{obs}\\right)\\:-\\text{l}\\text{n}\\left({Y}_{pred}\\right)\\:\\right)}^{2}}{n-2}}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n\\)\u003c/span\u003e\u003c/span\u003e is the number of observations, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Y}_{obs}\\)\u003c/span\u003e\u003c/span\u003e is the observed value, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Y}_{pred}\\)\u003c/span\u003e\u003c/span\u003e is the predicted value.\u003c/p\u003e \u003cp\u003eThis simple, but straight forward method allows the generation of more realistic estimates of predictive uncertainty for models fitted using the data binning approach when an independent dataset is used for model validation. Jucker et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) provided a R code for implementing and replicating the model uncertainty and error propagation analysis.\u003c/p\u003e \u003cp\u003eGiven that, to generate reliable predictions for any tree using our selected models, we used model 1 in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e as an example, where the predicted diameter (D\u003csub\u003epred\u003c/sub\u003e) is estimated as follows:\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$$\\:{D}_{pred}=\\text{e}\\text{x}\\text{p}({A\\:\\times\\:\\left(1-\\text{exp}\\left(-k\\times\\:\\text{ln}\\left(age\\right)\\right)\\right)}^{c}+{\\epsilon\\:})$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAssuming ε is normally distributed, the mean of exp(ε) can be approximated by exp(σ\u003csup\u003e2\u003c/sup\u003e/2), where σ\u003csup\u003e2\u003c/sup\u003e is the mean square error of the regression (Jucker et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). From this, an unbiased estimate of \u003cem\u003eD\u003c/em\u003e can, therefore, be calculated using the following equation:\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$$\\:{D}_{pred}=\\text{e}\\text{x}\\text{p}\\left({A\\:\\times\\:\\left(1-\\text{exp}\\left(-k\\times\\:\\text{ln}\\left(age\\right)\\right)\\right)}^{c}+\\:{\\epsilon\\:}\\right)\\times\\:\\:\\text{e}\\text{x}\\text{p}({\\sigma\\:}^{2}/2)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eGrowth performance of the three native species\u003c/h2\u003e \u003cp\u003eFinally, to compare growth rates among species, we generated diameter growth predictions using the diameter growth equations obtained for each species and thus estimated the mean annual increment in DBH at 30 years (MAI\u003csub\u003e30\u003c/sub\u003e) (Rolim and Piotto \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). In addition, we also used our species-specific growth models to estimate total height, allowing us to compare the total height when each species reached 35 cm DBH (Ht\u003csub\u003e35\u003c/sub\u003e). We used a minimum DBH of 35 cm as our harvest criterion because this is a standard criterion traditionally used to determine the ideal time to harvest timber in Brazilian sawmills.\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cp\u003e \u003cb\u003eDiameter and total tree height growth models for\u003c/b\u003e \u003cb\u003eC. legalis\u003c/b\u003e\u003c/p\u003e \u003cp\u003eAmong the candidate models evaluated for estimating \u003cem\u003eD\u003c/em\u003e and \u003cem\u003eHt\u003c/em\u003e for \u003cem\u003eC. legalis\u003c/em\u003e, models 3 and 6 (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) were identified as the best-fit models (Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). These models demonstrated relatively low RMSE values, with 5.6 for the diameter model and 4.7 for the total height model. Additionally, they exhibited minimal average systematic bias, with \u0026minus;\u0026thinsp;0.8 for diameter and 3.8 for total height. Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e is more suitable for generating unbiased predictions, offering a lower RMSE compared to its alternatives. While Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e had a slightly higher mean RMSE compared to the other equations it is likely to yield much less biased predictions, making it more reliable.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{\\text{L}\\text{n}(\\:D}_{est})=3.730\\:\\times\\:(1+36.02\\:\\times\\:\\text{e}\\text{x}\\text{p}(-1.906\\times\\:{\\text{L}\\text{n}\\left(age\\right)\\left)\\right)}^{-1})\\times\\:\\:\\text{e}\\text{x}\\text{p}({0.148}^{2}/2)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{\\text{L}\\text{n}(Ht}_{est})=68.9078\\times\\:\\text{e}\\text{x}\\text{p}(-4.759387077\\times\\:{\\text{Ln}\\left(D\\right)}^{-0.343760186})\\times\\:\\text{e}\\text{x}\\text{p}({0.169}^{2}/2)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThese equations (Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) were able to generate less biased estimates of \u003cem\u003eD\u003c/em\u003e and \u003cem\u003eHt\u003c/em\u003e for \u003cem\u003eC. legalis\u003c/em\u003e across a broad biogeographical range, outperforming the other models tested. Most importantly, the models for \u003cem\u003eC. legalis\u003c/em\u003e showed no evidence of over- or underprediction for both \u003cem\u003eD\u003c/em\u003e and \u003cem\u003eHt\u003c/em\u003e values since the error predictions were very close to zero across a wide range of tree sizes (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003ea-c). Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e showed only a negative bias for large \u003cem\u003eD\u003c/em\u003e values (\u0026gt;\u0026thinsp;40 cm) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003ea-b). Similarly, Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e also had a consistently lower error across the tree height size classes, with no tendency to under- or overestimate \u003cem\u003eHt\u003c/em\u003e values, confirming the model's robustness for predicting total tree height (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003ec-d). Through the independent validation dataset, the standard deviation (\u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003ev\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)\u003c/em\u003e for Eqs.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e were 0.48 and 0.45, respectively, considered as lower standard deviation values.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eDiameter and total tree height growth models for \u003c/h3\u003e\n\u003cdiv class=\"Heading\"\u003eDiameter and total tree height growth models for \u003cem\u003eD. nigra\u003c/em\u003e\u003c/div\u003e \u003cp\u003eThe best-fit models for predicting trunk diameter and total height of \u003cem\u003eD. nigra\u003c/em\u003e are represented by Eqs.\u0026nbsp;\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. For Eq.\u0026nbsp;\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the RMSE and average systematic bias were 6.05 and \u0026minus;\u0026thinsp;8.63, respectively, while Eq.\u0026nbsp;\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e had an RMSE of 4.6 and an average systematic bias of 3.8. Both models presented lower standard deviations (\u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003ev\u003c/em\u003e\u003c/sub\u003e for diameter\u0026thinsp;=\u0026thinsp;0.61, and \u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003ev\u003c/em\u003e\u003c/sub\u003e for total height\u0026thinsp;=\u0026thinsp;0.47). Eq.\u0026nbsp;\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e tended to overestimate stem diameter by 30\u0026ndash;50% for trees with an observed diameter of less than 6 cm and to underestimate trees with diameters between 10\u0026ndash;20 cm by approximately 25% (Fig.\u0026nbsp;3a-b). Due to the spread of values for \u003cem\u003eD\u003c/em\u003e and the greater within-site variation in growth rates for \u003cem\u003eD. nigra\u003c/em\u003e, it was not possible to develop a model that fully reduces this bias. For the \u003cem\u003eHt\u003c/em\u003e model, Eq.\u0026nbsp;\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e showed no tendency to overestimate or underestimate the total height across tree sizes classes (Fig.\u0026nbsp;3c-d).\u003c/p\u003e \u003cp\u003e \u003cdiv id=\"Equ3\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{\\text{L}\\text{n}(D}_{est})=3.825\\times\\:\\text{e}\\text{x}\\text{p}(-21.15\\:\\times\\:\\:\\text{e}\\text{x}\\text{p}(-1.769\\times\\:\\text{L}\\text{n}\\left(age)\\right)\\times\\:\\:\\text{e}\\text{x}\\text{p}({0.373}^{2}/2)$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e \u003cdiv id=\"Equ4\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{\\text{L}\\text{n}(Ht}_{est})=9.003\\times\\:\\text{e}\\text{x}\\text{p}\\left(-3.761\\times\\:{\\text{Ln}\\left(D\\right)}^{-1}\\right)\\times\\:\\:\\text{e}\\text{x}\\text{p}({0.245}^{2}/2)$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eFigure\u0026nbsp;3\u003c/b\u003e Goodness of fit for the diameter and total height growth model for \u003cem\u003eD. nigra\u003c/em\u003e (\u003cem\u003ei.e\u003c/em\u003e., Eqs.\u0026nbsp;\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e in the main text, respectively). Panel (a-c) reports the mean relative error for different tree size classes. The thick black line represents a spline regression of the data points used to illustrate the predictive accuracy of the models. Relative errors were calculated for a random subset of trees corresponding to 40% of the data (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;831 trees), which were used exclusively to validate the models. This randomization procedure was repeated 100 times to avoid the randomization procedure in step (i) having an undue effect on the model evaluation process, and at each iteration regression splines (orange lines) were used to illustrate how the magnitude of the relative errors varies as a function of tree size. Panel (b-d) compares predicted \u003cem\u003evs\u003c/em\u003e. observed diameter and total height, with the dashed orange line corresponding to a 1:1 relationship\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eDiameter and total tree height growth models for \u003cem\u003eZ. tuberculosa\u003c/em\u003e\u003c/h2\u003e \u003cp\u003eFor \u003cem\u003eZ. tuberculosa\u003c/em\u003e, the best-fit models for estimating \u003cem\u003eD\u003c/em\u003e and \u003cem\u003eHt\u003c/em\u003e were described in Eqs.\u0026nbsp;\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, respectively. The mean RMSE for these equations was 3.2 cm for \u003cem\u003eD\u003c/em\u003e and 2.8 m for \u003cem\u003eHt\u003c/em\u003e, with corresponding average systematic biases of -1.45 and 0.25. These models exhibited no strong tendency to over- or underestimate tree diameter and total height, as evidenced by the slight deviation of the error curve (black spline) from zero (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Moreover, both equations showed low standard deviations (σ\u003csub\u003ev\u003c/sub\u003e for diameter\u0026thinsp;=\u0026thinsp;0.4 and σ\u003csub\u003ev\u003c/sub\u003e for height\u0026thinsp;=\u0026thinsp;0.6). Eq.\u0026nbsp;\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e had a slight tendency to overestimate \u003cem\u003eD\u003c/em\u003e values for small trees (\u0026lt;\u0026thinsp;3 cm), but this tendency disappear as tree diameter increases (\u0026gt;\u0026thinsp;4 cm) (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e4\u003c/span\u003ea). Eq.\u0026nbsp;\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows a rapid positive bias (\u0026lt;\u0026thinsp;25%) in predicting \u003cem\u003eHt\u003c/em\u003e for smaller trees (\u0026lt;\u0026thinsp;4 m), where the predicted values tend to be slightly underestimated. This underestimation disappears as the tree height increases (\u0026gt;\u0026thinsp;5 m), leading to zero error for mid-range trees (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e4\u003c/span\u003ec).\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{\\text{L}\\text{n}(D}_{est})=3.281\\times\\:(1+37.24\\:\\times\\:\\text{e}\\text{x}\\text{p}(-2.266\\times\\:{\\text{L}\\text{n}\\left(age\\right)\\left)\\right)}^{-1}\\times\\:\\:\\text{e}\\text{x}\\text{p}({0.213}^{2}/2)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{\\text{L}\\text{n}(Ht}_{est})=7.895\\times\\:\\text{e}\\text{x}\\text{p}(-3.407\\times\\:{\\text{Ln}\\left(D\\right)}^{-1})\\times\\:\\text{e}\\text{x}\\text{p}({0.261}^{2}/2)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eSpecies growth performance and optimal harvest age\u003c/h2\u003e \u003cp\u003eIn terms of growth potential, \u003cem\u003eD. nigra\u003c/em\u003e had the highest growth rate among the species studied, with an MAI\u003csub\u003e30\u003c/sub\u003e of 1.33 cm/year and a Ht\u003csub\u003e35\u003c/sub\u003e of 14.8 m, followed by \u003cem\u003eC. legalis\u003c/em\u003e with an MAI\u003csub\u003e30\u003c/sub\u003e of 1.16 cm/year and a Ht\u003csub\u003e35\u003c/sub\u003e of 20.7 (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). In contrast, \u003cem\u003eZ. tuberculosa\u003c/em\u003e had the lowest MAI\u003csub\u003e30\u003c/sub\u003e, with a growth rate of 0.90 cm/year (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Based on the time required for each species to reach 35 cm DBH \u0026ndash; a common harvesting diameter for saw wood production \u0026ndash;, \u003cem\u003eD. nigra\u003c/em\u003e had the faster time to first harvesting (22 years), and \u003cem\u003eC. legalis\u003c/em\u003e required a time of 31 years to first harvest (Fig.\u0026nbsp;5; Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Notably, \u003cem\u003eZ. tuberculosa\u003c/em\u003e did not reach the minimum DBH of 35 cm during the 40-year period in which we make growth predictions (Fig.\u0026nbsp;5). Figure\u0026nbsp;5 shows that the diameter growth curve of this species stabilizes much earlier, at approximately 16 years when its growth rate begins to decrease (supplementary material 4). Based on these results, we recommend an optimal harvest age of 16 years, as the growth curve of this species does not tend to increase significantly after this age. The growth predictions generated by our models and calculations that we have used to compare the performance of each species are shown in supplementary material 4.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSpecies growth rate patterns estimated at 40 years. DBH \u0026ndash; mean estimated diameter at the breast height; Ht \u0026ndash; mean estimated total height; Ht\u003csub\u003e35\u003c/sub\u003e \u0026ndash; estimated total height when a tree reaches 35 cm DBH; MAI \u0026ndash; mean annual increment in diameter at 30 years; OHA \u0026ndash; Optimal harvest age\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpecies\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDbh\u003c/p\u003e \u003cp\u003e(cm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHt\u003c/p\u003e \u003cp\u003e(m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHt\u003csub\u003e35\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMAI\u003csub\u003e30\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(cm/year)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eOHA\u003c/p\u003e \u003cp\u003e(years)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCariniana legalis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e14.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e21.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDalbergia nigra\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e27.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e13.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e14.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZeyheria tuberculosa\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e13.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eFig 5\u003c/b\u003e Diameter growth curves as a function of the tree age for three native Atlantic Forest species. The curves represent different species: \u003cem\u003eC. legalis\u003c/em\u003e \u0026ndash; green line; \u003cem\u003eD. nigra\u003c/em\u003e \u0026ndash; orange line; \u003cem\u003eZ. tuberculosa\u003c/em\u003e \u0026ndash; blue line. The dashed vertical grey line indicates the minimum harvest diameter of 35 cm DBH\u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eIn this study, we developed species-specific growth models with strong predictive power for estimating the bole diameter and total height of three Brazilian native timber species, widely recognized for their valuable timber (Rolim and Piotto \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Krainovic et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In this context, our study provides critical information for establishing and managing commercial tree plantations of these species. This can provide strong technical support for scaling up forest restoration initiatives in the Brazilian Atlantic Forest. The diameter and tree height growth models were developed based on the scaling relationship between \u003cem\u003eD\u003c/em\u003e:\u003cem\u003eage\u003c/em\u003e and \u003cem\u003eHt:D\u003c/em\u003e for a large dataset consisting of 5,564 trees of three native species. These variables can be obtained from forest inventory data, which can facilitate the adoption of our models. As far as we are concerned, this study is the first one to fit species-specific growth models for Atlantic Forest species comprising a wide range of bioclimatic conditions.\u003c/p\u003e \u003cp\u003eDue to historical overexploitation, these species are ecologically threatened and commercially extinct. This makes it necessary to establish plantations to produce their unique timber for market (CNCFlora \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; FAO \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Thus, transitioning from illegal exploitation to sustainable plantation-based production offers a viable solution to mitigate these impacts, such as the overharvesting of these endangered species, the degradation of natural forests, and the associated loss of biodiversity (Silva et al. \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Betts et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). This approach reduces the pressure on natural forests, but also promotes a more sustainable and reliable source of timber, as well re-new the timber market by revamping commercially extinct species. By shifting to legally managed plantations, these species can be conserved while still contributing to economic development, in a conserving through use approach (Pryde et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/p\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eStem diameter and total tree height growth models\u003c/h2\u003e \u003cp\u003eWe found that it is feasible to accurately predict unbiased stem diameter and total tree height growth through the \u003cem\u003eD\u003c/em\u003e:\u003cem\u003eage\u003c/em\u003e and \u003cem\u003eHt\u003c/em\u003e:\u003cem\u003eD\u003c/em\u003e relationships. Through this scaling relationship, we were able to derive a species-specific equation for estimating diameter and total tree height growth for the species studied across various bioclimatic conditions (Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). The models have proved to be significantly robust across a large range of tree sizes, bioclimatic space, and site conditions, as seen in the model validation step (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e4\u003c/span\u003e). While general models developed from multi-species data are helpful, they may introduce systematic bias when applied to a single species. This occurs because these models incorporate different scaling relationships from several tree species with distinct phylogenetic legacies (\u003cem\u003ee.g\u003c/em\u003e., angiosperms and gymnosperms) and contrasting growth forms (\u003cem\u003ee.g\u003c/em\u003e., trees, shrubs, and palms) (Chave et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Jucker et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Our species-specific models can generate more accurate predictions across biogeographic regions once they account for a single species' auto-ecology and physiological traits, which are more consistent across biogeographic regions (Duncanson et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Charl\u0026egrave;ne et al. \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Quang et al. \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe developed models allow for more robust species growth predictions, revealing the potential unique and better estimates for timber production for each species (Fig.\u0026nbsp;5). Currently, the timber production potential of these native species is either under- or overestimated by inaccurate and non-validated models, most of which have been developed for native or exotic species at local conditions (Rolim and Piotto \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), or that lack multi- year data sets (Krainovic et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In fact, it has been argued that local equations are paramount to accurately reflect the variability in tree growth and tree size distribution, thereby reducing potential biases in growth predictions (Chave et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). However, as in Chave et al. (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) and Jucker et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), it has been shown that global equations (\u003cem\u003ei.e.\u003c/em\u003e, those fitted using a global dataset from multi-species) are consistent across sites, and local equations do not perform much better than global equations in terms of model uncertainty and error propagation.\u003c/p\u003e \u003cp\u003eA few authors have confronted local models with the global models to test their performance (Chave et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Jucker et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Here, we did not follow this procedure for two simple reasons: i) although we modeled tree growth across a broad biogeographic range, this range is covered by a unique forest type dominated by the Brazilian Atlantic Forest representing the entire natural range of the species studied (IBGE, 2012); ii) using species-specific data results in less dispersion and error propagation (Uller et al. \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2021\u003c/span\u003e); and iii) scaling relationships of structural, physiological, and ecological traits (\u003cem\u003ei.e.\u003c/em\u003e, species auto-ecology) with stem diameter and tree height are not expected to vary among individuals of the same species, conserving their growth responses (Anderson-Teixeira et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). This suggests that species-specific factors significantly influence scaling relationships. Thus, by focusing on the auto-ecology and growth rates of a single species, we expected that the scaling relationship between the dependent and independent variables did not strongly differ within the studied sites.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eSpecies growth rate patterns and commercial rotations\u003c/h2\u003e \u003cp\u003eBased on minimum commercial diameter, we have defined rotation cycles for the three native timber species we studied (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The species proved to be promising for timber production (Fig.\u0026nbsp;5). In comparison to fast-growing exotic timber species in Brazil, such as eucalyptus, which have harvest cycles of about 20 years for saw wood production (Rolim and Piotto \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), the three native species demonstrated potential for short-to-medium rotation cycles. This positions them as competitive and viable alternatives for commercial timber production (Rolim and Piotto \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). However, while these native species can offer quicker income returns, it is essential to consider their ecological roles and ensure that their exploitation is balanced with conservation efforts.\u003c/p\u003e \u003cp\u003eOur results showed distinct growth rate patterns among the species, revealing their harvest age and growth potential differences. These differences can potentially be combined in planting mixture, where the faster-growing species or species that maximize size class early are harvested over the course of a rotation of the slowest growing. Alternatively, plantations may be designed to promote continuous cover over time, potentially ensuring both ecological balance and long-term economic benefits (Laiho et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Banaś et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). It is also important to consider revenue at different times, as trunks with smaller diameters (\u003cem\u003ee.g., Z. tuberculosa\u003c/em\u003e) may be sold for specific purposes, such as utensils and structural materials (Rolim and Piotto \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). In contrast, larger trunks (\u003cem\u003ee.g., C. legalis\u003c/em\u003e, and \u003cem\u003eD. nigra\u003c/em\u003e) tend to have higher value when sold for premium uses, such as furniture (Rolim and Piotto \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eWith shorter harvesting cycles of approximately 16 years, \u003cem\u003eZ. tuberculosa\u003c/em\u003e offers the potential to accelerate revenue generation. Rolim and Piotto (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) found similar growth rate patterns for \u003cem\u003eZ. tuberculosa\u003c/em\u003e with a diameter increment at 35 years of 0.8 cm/year, which is close to our results at 35 years (0.79 cm/year) (supplementary material 4). Similarly, the diameter growth models developed by Rolim and Piotto (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) and De Mendon\u0026ccedil;a et al. (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) also demonstrated that \u003cem\u003eZ. tuberculosa\u003c/em\u003e did not reach the minimum logging diameter of 35 cm DBH over the measurement period. \u003cem\u003eZ. tuberculosa\u003c/em\u003e usually develops straight stems when planted in full sun conditions, but still requires some pruning (Rolim and Piotto \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Although it is considered a fast-growing, light-demanding species that easily colonizes open areas like extensive pastures, \u003cem\u003eZ. tuberculosa\u003c/em\u003e also demonstrates high longevity and can persist for many years in forestry systems (Rolim and Piotto \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Consequently, the growth performance of this species in mixed plantations may be reduced or limited by shading from other species, particularly as the canopy develops and expands in the years following planting (Jos\u0026eacute; et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). In fact, tropical timber species tend to grow faster in full sun than in the understory of restoration plantations (Jos\u0026eacute; et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). This makes \u003cem\u003eZ. tuberculosa\u003c/em\u003e more suitable for pure plantations, thinned when needed, or intercropping systems with low planting densities, which can reduce tree competition for light. All of this suggests that our results can be considered conservative, as the growth data were primarily collected from mixed tree plantations where this species were dominated from the 10th year forward.\u003c/p\u003e \u003cp\u003eOn the other hand, \u003cem\u003eC. legalis\u003c/em\u003e and \u003cem\u003eD. nigra\u003c/em\u003e require a medium-term investment of about 22 and 31 years, respectively, before harvest (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). In this study, \u003cem\u003eC. legalis\u003c/em\u003e reaches 35 cm DBH at 31 years, about 10\u0026ndash;12 years less than estimated by Krainovic et al. (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) and Rolim and Piotto (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). In Rolim and Piotto (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), the diameter growth rates of \u003cem\u003eC. legalis\u003c/em\u003e were 0.94 and 1.10 cm/year, which is lower than the growth rate of 1.16 cm/year in our study. Surprisingly, \u003cem\u003eD. nigra\u003c/em\u003e reached the minimum logging diameter of 35 cm DBH in just 22 years in our study, which is about 10 years earlier than estimates by others (Rolim and Piotto \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The estimated MAI in diameter observed in this study (1.33 cm/year) is also higher than the values reported by Rolim and Piotto (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), which were 0.87 and 1.07 cm/year, respectively. Despite the considerable timber production potential of \u003cem\u003eC. legalis\u003c/em\u003e and \u003cem\u003eD. nigra\u003c/em\u003e, several important factors must be considered. For example, \u003cem\u003eD. nigra\u003c/em\u003e often develops irregular stem shapes that limit its potential timber yield when planted in full sunlight, a common condition in young plantations and for legume trees. Although many tropical timber species tend to grow faster in full sun (Jos\u0026eacute; et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), increased light availability promotes the growth of multiple and tortuous stems, which is undesirable in the forestry market (Krainovic et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Therefore, this species may require specific planting models, in which seedlings are planted in higher density to increase competition or under some level of shading, and demand further pruning. Conversely, \u003cem\u003eC. legalis\u003c/em\u003e develops naturally straight stems when planted in full sun with other species, although some level of pruning have been recommended in pure plantations. However, its growth and stem quality are enhanced in mixed plantations, as this late-successional species tends to overtop the crowns of other species\u003c/p\u003e \u003cp\u003eIn general, the differences in growth rate observed in our study compared to others can be attributed to several factors. For instance, the lower growth rates reported by Rolim and Piotto (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) for \u003cem\u003eC. legalis\u003c/em\u003e and \u003cem\u003eD. nigra\u003c/em\u003e may be because of the low soil fertility and sandy soils of their study sites, which are known to limit nutrient availability and water retention (L\u0026eacute;vesque et al. \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Furthermore, the non-commercial, restoration plantations studied by Krainovic et al. (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), with limited species-specific data covering different ages, might explain the longer timeframes required for \u003cem\u003eC. legalis\u003c/em\u003e to reach harvestable sizes. This underscores the importance of the availability of data in modeling species growth, and the need of conducting multi-site assessments to fully capture the growth potential of each species.\u003c/p\u003e \u003cp\u003eOur database consists of growth data collected from experimental and commercial plantations that did not receive common silvicultural treatments, such as thinning, pruning, and fertilization, often applied in forestry to enhance growth rates and wood quality. Consequently, the species in these plantations did not benefit from these management practices that could have maximized their development. This represents a limitation since, once under optimal management conditions, these species would have better growth performance. Therefore, while the results reported in this study are promising, they should be considered conservative, as the true potential of these species could be significantly greater with appropriate and intensive management (Grotta et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Rolim and Piotto \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThis study is a valuable contribution to understanding the growth patterns of three valuable native timber species from the Brazilian Atlantic Forest, particularly in terms of their potential for timber production and sustainable forest management. By developing species-specific growth equations, we could accurately predict diameter and total tree height across a wide range of bioclimatic conditions. Additionally, we defined commercial rotation cycles for three native species, providing valuable insights for optimizing timber yield. Furthermore, the different times to first harvest for each species highlights the potential to diversify income streams, which can increase the internal rate of return for stakeholders such as governments, private investors, and local communities. By staggering harvests, practitioners can generate a more stable income stream while reducing financial risks. Our findings underscore the importance of tailored silvicultural practices to improve growth rates and wood quality, highlighting the potential for these species to play a central role in large-scale forest restoration and conservation efforts.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was supported by S\u0026atilde;o Paulo Research Foundation (FAPESP) (grant numbers 2018/18416-2, 2020/08081-3, 2022/14695-0, 2019/24049-5, and 2022/14605-0), Re.green (grant number 0011-2022-ESA), and by the Coordena\u0026ccedil;\u0026atilde;o de Aperfei\u0026ccedil;oamento de Pessoal de N\u0026iacute;vel Superior (CAPES), with finance code 001. The authors also thank the National Council for Scientific and Technological Development (CNPq) (grant number 306152/2019-3). The authors would also like to express our sincere gratitude to the plantation owners and partners who generously opened their doors and allowed us to conduct our field measurements on their lands. Their cooperation and support were invaluable to the success of this research\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests:\u0026nbsp;\u003c/strong\u003eThe\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eauthors P.H.S.B. and R.R.R. are partners of the Re.green company.\u003c/p\u003e\n"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAnderson-Teixeira KJ, Mcgarvey JC, Muller-Landau HC, et al (2015) Size-related scaling of tree form and function in a mixed-age forest. Funct Ecol 29:1587\u0026ndash;1602. https://doi.org/10.1111/1365-2435.12470\u003c/li\u003e\n\u003cli\u003eAshton MS, Martin MP, Vincent JR (2024) People today who plant trees successfully do it for livelihoods and income not for biodiversity or climate mitigation. 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J Exp Bot 10:290\u0026ndash;301. https://doi.org/10.1093/JXB/10.2.290\u003c/li\u003e\n\u003cli\u003eRolim S, Piotto D (2019) Silviculture and Wood Properties of Native Species of the Atlantic Forest of Brazil. Editora Rona, Belo Horizonte, Brazil\u003c/li\u003e\n\u003cli\u003eRolim SG, Piotto D (2024) Diameter growth models and performance of 100 tropical tree species in silvicultural trials in Brazil. For Ecol Manage 569:122202. https://doi.org/10.1016/J.FORECO.2024.122202\u003c/li\u003e\n\u003cli\u003eSantos JPB, Romanelli JP, Gardon FR, et al (2023) Multifunctional Forest Restoration in Brazil: A Critical Analysis of the Trends and Knowledge Gaps in the Scientific Literature. Sustainability 2023, Vol 15, Page 15782 15:15782. https://doi.org/10.3390/SU152215782\u003c/li\u003e\n\u003cli\u003eSeidl R, Rammer W, Bellos P, et al (2010) Testing generalized allometries in allocation modeling within an individual-based simulation framework. 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Springer New York, New York, NY\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Bioeconomy, Ecosystem Services, Sustainable forestry, Tropical timber production, Reforestation","lastPublishedDoi":"10.21203/rs.3.rs-5422550/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5422550/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eNative timber production offers a promising pathway to make large-scale tropical forest restoration financially viable. However, there are still many gaps in knowledge on this subject. This study develops species-specific growth models for three valuable and threatened native timber species from the Brazilian Atlantic Forest \u0026ndash; \u003cem\u003eCariniana legalis\u003c/em\u003e, \u003cem\u003eDalbergia nigra\u003c/em\u003e, and \u003cem\u003eZeyheria tuberculosa\u003c/em\u003e \u0026ndash; and evaluate their timber production potential. We collected data from 14 tree plantations distributed in the states of S\u0026atilde;o Paulo, Esp\u0026iacute;rito Santo, and Bahia, with a total of 5,564 sampled trees. The plantations span a broad climatic gradient, with ages ranging from 1 to 50 years. We developed and compared six models for predicting tree diameter and total height. We modeled and compared the growth patterns among the species and determined their commercial rotation ages, based on time needed to reach a diameter of 35 cm. \u003cem\u003eZ. tuberculosa\u003c/em\u003e exhibited the lowest diameter increment (0.90 cm/year) and did not reach the threshold DBH, making it more suitable for non-premium uses, such as utensils and pallets. In contrast, \u003cem\u003eD. nigra\u003c/em\u003e demonstrated the highest growth rate (1.33 cm/year) and a first harvest age of 22 years, demonstrating that it is a promising species to produce timber for furniture, and construction. \u003cem\u003eC. legalis\u003c/em\u003e showed a slightly lower growth rate (1.16 cm/year) and required 31 years to reach first harvest, with wood ideal for construction and furniture. These findings highlight the potential of these species for timber production in restoration projects and the importance of timely silvicultural practices to enhance growth rates and wood quality.\u003c/p\u003e","manuscriptTitle":"Novel growth models of three valuable timber species from the Brazilian Atlantic Forest","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-11-29 10:48:43","doi":"10.21203/rs.3.rs-5422550/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"3f96b09e-d4f2-4ab1-8913-ffdd8c14680a","owner":[],"postedDate":"November 29th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-12-08T14:38:44+00:00","versionOfRecord":[],"versionCreatedAt":"2024-11-29 10:48:43","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5422550","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5422550","identity":"rs-5422550","version":["v1"]},"buildId":"ehx78VzkSd0WSzXnipQa-","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}