Improved tree height estimation of secondary forests in the Brazilian Amazon

Estimativa melhorada de altura de árvores em florestas secundárias da Amazônia brasileira

Henrique Luis Godinho CASSOL Yosio Edemir SHIMABUKURO João Manuel de Brito CARREIRAS Elisabete Caria MORAES About the authors

ABSTRACT

This paper presents a novel approach for estimating the height of individual trees in secondary forests at two study sites: Manaus (central Amazon) and Santarém (eastern Amazon) in the Brazilian Amazon region. The approach consists of adjusting tree height-diameter at breast height (H:DBH) models in each study site by ecological species groups: pioneers, early secondary, and late secondary. Overall, the DBH and corresponding height (H) of 1,178 individual trees were measured during two field campaigns: August 2014 in Manaus and September 2015 in Santarém. We tested the five most commonly used log-linear and nonlinear H:DBH models, as determined by the available literature. The hyperbolic model: H = a.DBH/(b+DBH) was found to present the best fit when evaluated using validation data. Significant differences in the fitted parameters were found between pioneer and secondary species from Manaus and Santarém by F-test, meaning that site-specific and also ecological-group H:DBH models should be used to more accurately predict H as a function of DBH. This novel approach provides specific equations to estimate height of secondary forest trees for particular sites and ecological species groups. The presented set of equations will allow better biomass and carbon stock estimates in secondary forests of the Brazilian Amazon.

KEYWORDS:
tree height-diameter (H:DBH) model; nested model; indicative variable; height growth; ecological species groups

RESUMO

Este trabalho apresenta uma nova abordagem para a estimativa de altura de árvores em florestas secundárias em duas áreas de estudo na Amazônia brasileira: Manaus (Amazônia central) e Santarém (Amazônia oriental). A abordagem consistiu em ajustar modelos hipsométricos separados por área de estudo e grupos ecológicos de espécies: pioneiras, secundárias iniciais e secundárias tardias. No total, 1178 árvores foram medidas em diâmetro e altura em duas etapas de campo: agosto de 2014 em Manaus e Setembro de 2015 em Santarém. Foram testados cinco modelos log-lineares e não lineares mais utilizados na literatura. O modelo hiperbólico: H = a.D/(b+D) foi o que apresentou o melhor ajuste quando avaliado com os dados de validação. Diferenças significativas nos parâmetros de ajuste foram observadas entre as espécies pioneiras e secundárias de Manaus e Santarém pelo teste F, significando que equações específicas por grupos ecológicos e área de estudo deveriam ser utilizadas para estimar a altura (H) a partir do diâmetro (D) com maior acurácia. Esta nova abordagem fornece equações específicas para localidade e grupo ecológico, para estimar a altura das árvores em florestas secundárias. O conjunto de equações desenvolvidas permitirá melhorar as estimativas de biomassa e a quantificação dos estoques de carbono nas florestas secundárias da Amazônia brasileira.

PALAVRAS-CHAVE:
modelos hipsométricos; modelos aninhados; variável indicadora; taxa de crescimento em altura; grupos ecológicos de espécies

INTRODUCTION

In the Amazon region, height-diameter at breast height (H:DBH) models are important because dense forest understory makes it difficult and time-consuming to view the top of the canopy to measure the tree heights. Several H:DBH models have been proposed for old-growth tropical forests for that purpose (Feldpausch et al. 2011Feldpausch, T.R.; Banin, L.; Phillips, O.L.; Baker, T.R.; Lewis, S.L.; Quesada, C.A. et al. 2011. Height-diameter allometry of tropical forest trees. Biogeosciences, 8: 1081-1106.; 2012Feldpausch, T.R.; Lloyd, J.; Lewis, S.L.; Brienen, R.J.W.; Gloor, W.; Mendoza, A.M. et al. 2012. Tree height integrated into pantropical biomass forest estimates. Biogeosciences, 9: 3381-3403.; Hunter et al. 2013Hunter, M.O.; Keller, M.; Victoria, D.; Morton, D.C. 2013. Tree height and tropical forest biomass estimation. Biogeosciences, 10: 8385-8399. ), however, they are scarce for secondary forests (Lucas et al. 2002Lucas, R.M.; Honzák, M.; Amaral, I.; Curran, P.J.; Foody, G.M.; 2002. Forest regeneration on abandoned clearances in central Amazonia. International Journal of Remote Sensing, 23: 965-988. ; Neeff and Santos 2005Neeff, T.; Santos, J.R. 2005. A growth model for secondary forest in Central Amazonia. Forest Ecology and Management, 216: 270-282. ). For instance, Lucas et al. (2002) used genus-specific nonlinear models to estimate tree height based on diameter for the most common species from a secondary forest in Manaus (central Amazon). Conversely, Neeff and Santos (2005) estimated tree height, and its increments, at stand-level age based on the Bertalanffy-Chapman-Richards model in a secondary forest in Santarém (eastern Amazon). Other models related to H:DBH include the logistic, Weibull, and Richards models (Fang and Bailey 1998Fang, Z.; Bailey, R.L. 1998. Height-diameter models for tropical forests on Hainan Island in southern China. Forest Ecology and Management, 110: 315-327.; Huang et al. 2000Huang, S.; Price, D.J.; Titus, S. 2000. Development of ecoregion-based height-diameter models for white spruce in boreal forests. Forest Ecology and Management, 129: 125-141.).

The choice of the best model, however, depends on the relation between tree height and DBH, which, in turn, can be associated with physical and biological factors at tree- and stand-level (Poorter and Bongers 2006Poorter, L.; Bongers, F. 2006. Leaf traits are good predictors of plant performance across 53 rain forest species. Ecology, 87: 1733-1743. ; Weiskittel et al. 2011Weiskittel, A.; Hann, D.; Kershaw, J.; Vanclay, J. 2011. Forest growth and yield modelling. John Wiley & Sons, Sussex, 430p. ). At tree level, H:DBH scaling may be represented by the stem-form factor, which can be indicative of the tree’s position within the forest stand (Weiskittel et al. 2011). The stem-form factor is defined as the ratio of the volume of a tree, or its part, to the volume of a cylinder with the same size (height) and cross section (DBH). Therefore, the tree may present a conical or cylindrical shape depending on its stem-form factor. For example, dominant trees often have a DBH greater than 30 cm, enjoy favorable light conditions, and have cylindrical shapes (Assmann 1970Assmann, E. 1970. The principles of forest yield studies. Pergamon Press, Oxford. 504p.). In these trees, the scaling exponent between H and DBH is equal or similar to two-thirds, and the allometry assumes an elastic similarity model (Norberg 1988Norberg, R.A. 1988. Theory of Growth Geometry of Plants and Self-Thinning of Plant Populations: Geometric Similarity, Elastic Similarity, and Different Growth Modes of Plant Parts. The American Naturalist, 131: 220-256.). Meanwhile, most sub-dominant and pioneer species follow a geometric similarity model (H:DBH scaling = 1.0), i.e., the trunk diameter will scale in direct proportion to the tree height (Sposito and Santos 2001Sposito, T.C.; Santos, F.A.M. 2001. Scaling of Stem and Crown in Eight Cecropia (Cecropiaceae) Species of Brazil. American Journal of Botany, 88: 939-949.). However, when H:DBH scaling ~2.0 there is a constant stress model, which is commonly caused by wind or other stresses (Sposito and Santos 2001).

At stand level, tree growth depends on forest structure, dominance type, tree density, species composition, and site environmental conditions (Weiskittel et al. 2011Weiskittel, A.; Hann, D.; Kershaw, J.; Vanclay, J. 2011. Forest growth and yield modelling. John Wiley & Sons, Sussex, 430p. ). Therefore, tree growth rate and H:DBH scaling are influenced by environmental conditions and functional traits at both tree and stand levels (Selaya et al. 2008Selaya, N.G.; Oomen, R.J.; Netten, J.J.C.; Werger, M.J.A.; Anten, N.P.R. 2008. Biomass allocation and leaf life span in relation to light interception by tropical forest plants during the first years of secondary succession. Journal of Ecology, 96: 1211-1221.; Chazdon 2014Chazdon, R.L. 2014. Second Growth: The promise of Tropical Forest Regeneration in an Age of Deforestation, Chicago Press, Chicago. 472p.). Sites with nutrient-rich soils and favorable climate conditions promote fast tree growth; pioneer species seek these resources in order to quickly colonize newly deforested areas (Chazdon 2014). The tree-height growth is highest at sites with better quality of environmental conditions, even though the maximum increase could be reached at the same age in poor sites (Weiskittel et al. 2011). Several studies have been carried out to develop site-based H:DBH models exploring these different environmental conditions in varying forest types (Pillsbury et al. 1995Pillsbury, N.H.; McDonald, P.M.; Simon, V. 1995. Reliability of Tanoak volume equations when applied to different areas. Western Journal of Applied Forestry, 10: 72-78.; Huang et al. 2000Huang, S.; Price, D.J.; Titus, S. 2000. Development of ecoregion-based height-diameter models for white spruce in boreal forests. Forest Ecology and Management, 129: 125-141.; Feldpausch et al. 2011Feldpausch, T.R.; Banin, L.; Phillips, O.L.; Baker, T.R.; Lewis, S.L.; Quesada, C.A. et al. 2011. Height-diameter allometry of tropical forest trees. Biogeosciences, 8: 1081-1106.). Huang et al. (2000) noted that the application of H:DBH models from one region to another may result in an average bias of 29%.

Different species make use of distinct strategies to reach sunlight, promoting fast or slow growth, depending on resource availability and plant physiology (Poorter et al. 2012Poorter, H.; Niklas, K.J.; Reich, P.B.; Oleksyn, J.; Poot, P.; Mommer, L. 2012. Biomass allocation to leaves, stems and roots: meta-analyses of interspecific variation and environmental control. New Phytologist, 193: 30-50. ). In Amazonian secondary forests dominated by Cecropia sp. and Vismia sp., the pioneer species showed fast growth and aboveground biomass (AGB) accumulation, reaching 110-115 Mg ha-1 during the first 10-15 years (Lucas et al. 2002Lucas, R.M.; Honzák, M.; Amaral, I.; Curran, P.J.; Foody, G.M.; 2002. Forest regeneration on abandoned clearances in central Amazonia. International Journal of Remote Sensing, 23: 965-988. ). As a strategy, these pioneer species intercept more light per unit leaf mass to support their fast growth than late successional species, contributing to the efficient conversion of mass to height (Selaya et al. 2008Selaya, N.G.; Oomen, R.J.; Netten, J.J.C.; Werger, M.J.A.; Anten, N.P.R. 2008. Biomass allocation and leaf life span in relation to light interception by tropical forest plants during the first years of secondary succession. Journal of Ecology, 96: 1211-1221.). To maintain rapid growth, pioneer species also present high leaf turnover in the upper-canopy, forming a monolayer leaf arrangement that covers bare soil. In contrast, these species need to form slender stems with low wood density to support such accelerated tree growth, which inevitably reduces their life span (Poorter and Bongers 2006; Selaya et al. 2008).

Late successional tree species are characterized by lower growth rates, resulting in the requirement for greater wood densities to support larger canopies and to reduce the risk of hollow stem formation (Poorter and Bongers 2006Poorter, L.; Bongers, F. 2006. Leaf traits are good predictors of plant performance across 53 rain forest species. Ecology, 87: 1733-1743. ). These species are generally taller and long-lived when compared to pioneer species, although the photosynthetic rate by leaf mass is smaller (Chazdon 2014Chazdon, R.L. 2014. Second Growth: The promise of Tropical Forest Regeneration in an Age of Deforestation, Chicago Press, Chicago. 472p.). Therefore, carbon assimilation by long-lived late successional species is lower and more persistent compared with short-lived pioneer species (Santiago et al. 2004Santiago, L.S.; Goldstein, G.; Meinzer, F.C.; Fisher, J.B.; Machado, K.; Woodruff, D. et al. 2004. Leaf photosynthetic traits scale with hydraulic conductivity and wood density in Panamanian forest canopy trees. Oecologia, 140: 543-550.). Such differences in vertical growth among species have significant implications for AGB accumulation in tropical forests (Feldpausch et al. 2011Feldpausch, T.R.; Banin, L.; Phillips, O.L.; Baker, T.R.; Lewis, S.L.; Quesada, C.A. et al. 2011. Height-diameter allometry of tropical forest trees. Biogeosciences, 8: 1081-1106.; Feldpausch et al. 2012). Tree height is highly variable in the Amazon forest, therefore it is important that this parameter is included in equations to estimate tree AGB more accurately (Lefsky et al. 2010Lefsky, M.A. 2010. A global forest canopy height map from the Moderate Resolution Imaging Spectroradiometer and the Geoscience Laser Altimeter System. Geophysical Research Letters, 37: L15401.; Chave et al. 2014Chave, J.; Réjou-Máchain, M.; Búrquez, A.; Chidumayo, E.; Colgan, M. S.; Delitti, W. B. C. et al. 2014. Improved allometric models to estimate the aboveground biomass of tropical trees. Global Change Biology, 20: 3177-3190.; Sawada et al. 2015Sawada, Y.; Suwa, R.; Jindo, K.; Endo, T.; Oki, K.; Sawada, H. et al. 2015. A new 500-m resolution map of canopy height for Amazon forest using spaceborne LiDAR and cloud-free MODIS imagery. International Journal of Applied Earth Observation and Geoinformation, 43: 92-101. ). Feldpausch et al. (2011) observed a tree height gradient from northeast to southwest Amazon, with the tallest trees in the Guiana Shield and the shortest in the southern Amazon. By including tree height in the AGB models, biomass estimates errors were consistently reduced from 66 to 48 Mg ha-1 from the eastern-central to the western Amazon, respectively (Feldpausch et al. 2012). Furthermore, the AGB of the Brazilian Amazon is often estimated by applying allometric equations generated from only primary or old-growth forest species, which may lead to overestimation (by 10-60%) when applied for AGB secondary forest trees (Nelson et al. 1999Nelson, B.W.; Mesquita, R.; Pereira, J.L.G.; De Souza, S.G.; Batista, G.T.; Couto, L.B. 1999. Allometric regressions for improved estimate of secondary forest biomass in the central Amazon. Forest Ecology and Management, 117: 149-167.).

In this study, we hypothesized that there are significant differences in H:DBH relationships among ecological species groups, i.e., pioneer, early, and late secondary species. We also expected to find significant differences between groups of ecological species across the study sites owing to different environmental and climate conditions. It has been reported that maximum tree heights at stand level vary among primary forests across the Amazon (Feldpausch et al. 2011Feldpausch, T.R.; Banin, L.; Phillips, O.L.; Baker, T.R.; Lewis, S.L.; Quesada, C.A. et al. 2011. Height-diameter allometry of tropical forest trees. Biogeosciences, 8: 1081-1106., 2012; Lefsky et al. 2010Lefsky, M.A. 2010. A global forest canopy height map from the Moderate Resolution Imaging Spectroradiometer and the Geoscience Laser Altimeter System. Geophysical Research Letters, 37: L15401.); however, it is unclear whether these differences also occur over secondary forests. For this investigation, we evaluated five commonly used H:DBH models adjusted to different ecological species groups occurring in two sites, with the aim of improving tree height estimation in secondary forests in the Brazilian Amazon.

MATERIAL AND METHODS

Study area and data

This study was carried out at two sites in the Brazilian Amazon: Manaus (Amazonas State) in the central Amazon region, and Santarém (Pará State) in the eastern Amazon region. At the Manaus site, the sampling plots were chosen on either side of the BR-174 highway, 70 km to the north of the city of Manaus. At the Santarém site, the sampling plots were chosen close to the Tapajós National Forest (FLONA Tapajós) on either side of the BR-163 highway, 100 km to the south of the city of Santarém (Figure 1).

Figure 1
Geographical distribution of the study sites. A. Map of South America detailing the geographical position of study sites of the REGROWTH-BR project (rectangles) in Amazonas and Pará states, Brazil. B. Distribution of plots in the Manaus site (triangles) on either side of the BR-174 highway, 70 km to the north of the city of Manaus. C. Distribution of plots in the Santarém site (triangles) on either side of the BR-163 highway, 100 km to the south of the city of Santarém.

According to Chave et al. (2005Chave, J.; Andalo, C.; Brown, S.; Cairns, M. A.; Chambers, J. Q.; Eamus, D. et al. 2005. Tree allometry and improved estimation of carbon stocks and balance in tropical forests. Oecologia, 145: 87-99.), both study sites are classified as ‘moist forest’, with less than 5 months averaging < 100 mm month-1 of rainfall during the dry season. The dry season length is shorter in Manaus (3.1 months) than in Santarém (4.5 months) (Malhi et al. 2004Malhi, Y.; Baker, T.R.; Phillips, O. L.; Almeida, S.; Alvarez, E.; Arroyo, L. et al. 2004. The above-ground coarse wood productivity of 104 Neotropical forest plots. Global Change Biology, 10: 563-591.). Manaus receives an average annual rainfall of 2,200 mm, which is slightly higher than that received at Santarém (2,000 mm) (Asner et al. 2003Asner G.P.; Bustamante, M.M.C.; Townsend, A.R. 2003. Scale dependence of biophysical structure in deforested areas bordering the Tapajo´s National Forest, Central Amazon. Remote Sensing of Environment, 87: 507-520.). The mean annual temperature at both sites is approximately 26 °C. Soils are predominantly nutrient-poor clay oxisols with some sandy ultisols (Silver et al. 2000Silver, W.L.; Ostertag, R.; Lugo, A.E. 2000. The potential for carbon sequestration through reforestation of abandoned tropical agricultural and pasture lands. Restoration Ecology, 8: 394-407.).

Secondary forests in Manaus and Santarém occur in a region dominated by terra firme old-growth dense forests, which have a similar average canopy height (26 and 28 m, respectively), but very different height distributions (Hunter et al. 2015Hunter, M.O.; Keller, M.; Morton, D.; Cook, B.; Lefsky, M.; Ducey, M. et al. 2015. Structural Dynamics of Tropical Moist Forest Gaps. PLoS One, 10: e0132144. ). Santarém primary forests present a bi-modal distribution of tree-canopy heights, one comprised of emergent trees (average 35-40 m heights) and the other comprised of sub-dominant trees (average 15-30 m), while Manaus primary forests show a near unimodal Gaussian distribution, with an average 26 m canopy height (Hunter et al. 2015). Additionally, open tropical forests occur in the east side of FLONA Tapajos, with these being widely dominated by palm trees such as babaçú (Attalea speciosa Mart.) and inajá (A. maripa (Aubl.) Mart.) on sandy soils (Prates-Clark et al. 2009Prates-Clark, C. da C.; Lucas, R.M.; dos Santos, J.R. 2009. Implications of land-use history for forest regeneration in the Brazilian Amazon. Canadian Journal of Remote Sensing, 35: 534-553.; personal observation).

In both study sites, only advanced secondary forests (age > 16 years) were measured in a 60 × 100 m nested plot. All sampling plots were randomly selected based on the age of the secondary forest and on land-use history (period of active land use and frequency of land clearance), assessed through the analysis of extensive Landsat sensor time-series data (Carreiras et al. 2014Carreiras, J.M.B.; Jones, J.; Lucas, R.M.; Gabriel, C. 2014. Land use and land cover change dynamics across the Brazilian Amazon: insights from extensive time-series analysis of remote sensing data. PLoS One, 9: e104144.). Field measurements were conducted during August 2014 in Manaus (23 plots) and September 2015 in Santarém (16 plots) (Figure 1) as part of the REGROWTH-BR project (Carreiras et al. 2014).

All trees with a DBH (at 1.3 m height) greater than or equal to 5 cm were measured within a 10 × 100 m plot. Trees with a DBH ≥ 10 cm were measured within a 20 × 100 m plot, and trees with a DBH ≥ 20 cm were measured within a 60 × 100 m plot. All trees were identified botanically to species level or marked as unknown (three cases; see Supplementary Material, Table S1 href="?AA-2017-0084"> ).

Trees were randomly selected and heights were measured at each nested plot (circa 25 measurements per plot) with a laser hypsometer (True Pulse 200TM, LaserInc Technology, Denver, CO, USA), whereas DBH was measured with a girth tape. All trees with broken or damaged crowns, and all palms, were excluded from the analysis.

The individuals were assigned to an ecological species group (ESG): pioneers (P), early secondary stage (ES), or late secondary stage (LS). This was based on the information collected from the literature and from the Global Wood Density Database (Zanne et al. 2009Zanne, A.E.; Lopez-Gonzalez, G.; Coomes, D.A.; Ilic, J.; Jansen, S.; Lewis, S.L. et al. 2009. Global wood density database. Dryad. ( (http://hdl.handle.net/10255/dryad.235 ). Accessed on 22/10/2016.
http://hdl.handle.net/10255/dryad.235...
, see Supplementary Material, Table S1). The formal Mann-Whitney U test was used to compare differences between wood densities among the three ESGs. The Bonferroni correction for pair-wise Mann-Whitney U test alpha was α/3 = ~0.0167. Therefore, we used median wood density thresholds to assign a species to a specific ESG when the previous classification was not found in the literature, e.g., pioneers ≤ 0.5 g cm-3, 0.5 g cm-3 < early secondary ≤ 0.59 g cm-3, and late secondary < 0.74 g cm-3.

Height and DBH data from 1,178 individual trees ranging from 5-70 cm in diameter, corresponding to 188 species and 52 families, were collected during the field campaign: 529 individuals in Manaus and 649 in Santarém. Before adjusting H:DBH models, the data were stratified by ecological species and study site, and then split into two subsets: the training subset (80%) for model fitting, and the remainder (testing subset) for model validation (Table 1). The H:DBH ratio was evaluated by study site using the Mann-Whitney U test to support a priori any difference in tree architecture (Feldpausch et al. 2011Feldpausch, T.R.; Banin, L.; Phillips, O.L.; Baker, T.R.; Lewis, S.L.; Quesada, C.A. et al. 2011. Height-diameter allometry of tropical forest trees. Biogeosciences, 8: 1081-1106.). The Mann-Whitney U test was performed using the R statistical program (R Development Core Team 2008R Development Core Team. 2008. R: A language and environment for statistical computing. ( (http://www.R-project.org ). Accessed on 17/05/2015.
http://www.R-project.org...
).

Table 1
Summary of the training and validation datasets (in parentheses) by study area and ecological species groups (ESG). N = number of trees, min = minimum, max = maximum, SD = standard deviation, DBH = diameter at breast height, P - pioneers, ES - early secondary, LS - late secondary.

Model selection and comparison of fitted models

Several linear and nonlinear allometric models have been proposed to describe the relationship between tree height and diameter (Fang and Bailey 1998Fang, Z.; Bailey, R.L. 1998. Height-diameter models for tropical forests on Hainan Island in southern China. Forest Ecology and Management, 110: 315-327.; Huang et al. 2000Huang, S.; Price, D.J.; Titus, S. 2000. Development of ecoregion-based height-diameter models for white spruce in boreal forests. Forest Ecology and Management, 129: 125-141.). In this study, we tested five widely used H:DBH models (Fang and Bailey 1998; Huang et al. 2000; Feldpausch et al. 2011Feldpausch, T.R.; Banin, L.; Phillips, O.L.; Baker, T.R.; Lewis, S.L.; Quesada, C.A. et al. 2011. Height-diameter allometry of tropical forest trees. Biogeosciences, 8: 1081-1106.) (Table 2). Only H:DBH models with up to three parameters were selected in order to avoid problems with over-parameterization in nonlinear regression estimation, as reported by Fang and Bailey (1998).

Table 2
Height-diameter models selected for analysis. H = total height (m); DBH = diameter at breast height (1.3 m above ground).

To select the most suitable model, we compared the ability of these five allometric models to predict tree height at each ESG by study site. The nonlinear least squares (nls) command from R was used to estimate the parameters in all nonlinear models (Bates and Watts 1990Bates, D.M.; Watts, D.G. 1990. Nonlinear Regression Analysis and Its Applications, 2nd ed. John Wiley & Sons, Inc., New York, 365p.), and the ordinary least squares (lm) command in the case of the log-linear model (m1).

The following statistics were used to select the best models in terms of goodness-of-fit using the training subset (Motulsky and Christopoulos 2003Motulsky, H.J.; Christopoulos, A. 2003. Fitting models to biological data using linear and nonlinear regression. GraphPad Software, Inc., San Diego, 352p.): (i) absolute and relative root mean square error (RMSE); and (ii) Akaike information criterion (AIC) weights (Wagenmakers and Farrel 2004Wagenmakers, E-J.; Farrell, S. 2004. AIC model selection using Akaike weights. Psychonomic Bulletin & Review, 11: 192-196. ). The relationship between standardized residuals and predicted height was evaluated visually through scatterplots in each model to account for heteroskedasticity. Additionally, a formal Breusch-Pagan test against heteroskedasticity (Neter et al. 1996Neter, J.; Kutner, M.; Wasserman, W.; Nachtsheim, C. 1996. Applied Linear Statistical Models, 4th ed. McGraw-Hill, Irwin. 1396p.) was performed using the lmtest package in R.

Model validation and presence of outliers

Prediction bias was calculated by subtracting the predicted height from the observed height (measured) using the testing subset. A null hypothesis, whereby the bias is equal to zero, was tested by t-test, with α = 0.05 significance level. Therefore, the root mean square error of prediction (RMSEP) was calculated by Eq. (1) (Hastie et al. 2009Hastie, T.; Tibshirani, R.; Friedman, J.H. 2009. The elements of statistical learning: data mining, inference, and prediction. 2nd ed. Springer, New York. 745p.): RMSEP = (bias² + variance)1/2. The first term in Eq. (1) is relative to the average prediction bias and the second term refers to the variance-bias, which in turn, is related to the spread of points around the mean prediction.

The presence of outliers was evaluated in both training and testing subsets using outlier in the “outliers” package of R program. The presence of outliers was verified by observing the spread of the residuals. If confirmed, the model selection and validation were iteratively repeated to improve model fitting. This process was performed twice with removal of 19 outliers from the analysis, including the training and testing subsets.

We arbitrary attributed a descending rank order to choose only one model based on highest AIC weight: value 5 for the best model (highest), and 1, for the worst (lowest). The best ranked fitted model (sum of rank values) was then used to analyze differences between ESG and study sites using an indicator regression approach.

Comparison of H:DBH models by ecological species group and study site

The indicator regression approach was used to evaluate full and reduced nested models with a simple ANOVA F-test (Bates and Watts 1990Bates, D.M.; Watts, D.G. 1990. Nonlinear Regression Analysis and Its Applications, 2nd ed. John Wiley & Sons, Inc., New York, 365p.; Neter et al. 1996Neter, J.; Kutner, M.; Wasserman, W.; Nachtsheim, C. 1996. Applied Linear Statistical Models, 4th ed. McGraw-Hill, Irwin. 1396p.). The indicator variable, or dummy variable, is an artificial variable created to represent an attribute with two or more distinct categories/levels, which, in our case, was represented by a study site or a specific ESG (Neter et al. 1996).

In the full model, the indicator variable could only take the values 0 and 1, corresponding to each study site or ESG, and the reduced model was fitted using the whole dataset without the indicator variable. However, to avoid over-parametrization of the full models, the ANOVA F-test was performed to compare each pair of ESGs per study site, because the difference in parameter estimation may be caused by only two or more indicator variables involved in the analysis, and this method reduces the number of parameters whilst retaining validation of the nested approach (Huang et al. 2000Huang, S.; Price, D.J.; Titus, S. 2000. Development of ecoregion-based height-diameter models for white spruce in boreal forests. Forest Ecology and Management, 129: 125-141.).

For instance, if the response function was modeled by the log-linear model between pioneers and early secondary forest species, the full-model of H:DBH would have three parameters (Neter et al. 1996Neter, J.; Kutner, M.; Wasserman, W.; Nachtsheim, C. 1996. Applied Linear Statistical Models, 4th ed. McGraw-Hill, Irwin. 1396p.) [Eq. (2): h = a+b log (DBH)+c G1 log (DBH)+ ε; where a and b are log-linear parameters, c represents the parameters related to indicator variable, and ε is the regression error; G1 refers to the indicator variable of a specific ESG (pioneer or early secondary)]. In this case, the reduced model has only two parameters (a and b). Considering that the response function (2) is for pioneers for which G1 = 0, then the model would take the form: h=a+b log(DBH). If the response function is for early secondary species for which G1 = 1, then Eq. (2) would take the form: h = a+b log(DBH)+c G2 log(DBH), and so on. Similarly, the analysis can be performed with all nonlinear models described in Table 1, and with all other ESG pairs or study sites.

The equality of the two models was tested by considering the null hypothesis, H 0 , whereby indicator parameters in the full model are equal to zero, against the alternative hypothesis, H 1 , whereby at least one parameter differs from zero using the F-test according to Motulsky and Christopoulos (2003Motulsky, H.J.; Christopoulos, A. 2003. Fitting models to biological data using linear and nonlinear regression. GraphPad Software, Inc., San Diego, 352p.). ANOVA F-test was performed in R (R Core Team 2008) with a 0.95 confidence level.

Finally, we estimated the relative growth height rate (HGR) by taking the derivative of the selected model by its diameter. The fitted curves for relationships between HGR and H:DBH were provided.

RESULTS

Ecological species groups

Median differences in wood density between ESG pairs differed from zero (Mann-Whitney U test: W = 64, p < 0.016), suggesting that wood density values could be used to separate species groups. Then, we used median wood density to assign species into an ESG when these were not available in the literature (in this case 22 of 323 species collected, Supplementary Material, Table S1).

Wood density outliers, marked with an open circle in Figure 2, indicate the low wood density of Hevea brasiliensis (Willd. ex A. Juss.) Müll.Arg. (0.40 g cm-3, late secondary species) in Manaus. In Santarém, outliers were represented by high wood density of Neea oppositifolia Ruiz & Pav. (0.89 g cm-3, pioneer species) and Sloanea nitida G. Don. (0.96 g cm-3, early secondary species), and low wood density of Jacaratia spinosa (Aubl.) A.DC. (0.14 g cm-3, early secondary species).

Figure 2
Distribution of wood density (g cm-3) by ecological species groups: (P) pioneer, (ES) early secondary, and (LS) late secondary species in secondary forests. A - Wood density values from Manaus species; B - Wood density values from Santarém species.

The simple ratio H:DBH of the secondary forest trees was significantly different between study sites, as determined by the Mann-Whitney U test: W = 133246, p < 0.001 (Manaus = 0.9037; Santarém = 1.0588). Tree diameters from secondary forests in Manaus (median 19.8 cm) were significantly different from those in Santarém (median 12.2 cm), and the same was observed for tree heights in Manaus (median 16.7 m) and Santarém (median 12.8 m), p < 0.001. This indicates that the H:DBH relationship followed a different distribution at each study site, considering that forests at both study sites are of similar average age (circa 23 years after clear cut).

Models’ goodness-of-fit

Two-parameter models showed the best goodness-of-fit given by the sum ranked order of the lowest AIC (Table 3): hyperbolic model (sum of 21 points) and log-log model (19 points). The monomolecular model (18 points) also had a low AIC among the three-parameter models. All regression parameters were significant at α = 0.05 for all models, with the exception of the Weibull model for early secondary species in Manaus, the Chapman-Richards model for early secondary species in Santarém, and for late secondary species in Manaus (Table 3).

Table 3
Fitting statistics of the tested H:DBH models by ecological species groups and study area. RMSE and RMSE are the absolute and relative root mean square error, respectively. RMSEP is the RMSE of prediction. R is the value of the rank order based on the lowest wiAIC (in bold). wiAIC - weights of Akaike information criterion; BP - Breusch-Pagan test. *Non-significant parameters for alpha = 0.05. NC - do not converge.

The visualization of standardized residuals against predicted height showed the absence of heteroskedasticity (Figure 3), which further supports the non-significant results of the Breusch-Pagan test (Table 3). The residuals were drawn only for the selected hyperbolic model.

Figure 3
Plots of standardized residuals against predicted height using nonlinear least squares fitting of the hyperbolic model for pioneer (A), early secondary (C), and late secondary (E) species in Manaus and Santarém (B, D, and F), respectively.

Based on the ranked model (Table 3), the hyperbolic model (m3) presented satisfactory results for all ESGs without being the best for a specific ESG. The prediction error of the hyperbolic model extended from RMSEP = 1.75 to 3.11 m (Table 3). Considering that bias is close to zero by the null hypothesis, we did not reject H 0 in any of the ESG cases, meaning that the average bias was equal to zero with d fF (n-1) degrees of freedom. Because the mean bias was not significantly different from zero in all models fitted by a one sample t-test (p > 0.05), variance of prediction was a large source of error. In general, the hyperbolic model performed well, although it overestimated tree height above 20 m, independent of age, as this seems to be the height at which this model begins to consistently underestimate values (Figure 4).

Figure 4
Scatterplot of observed vs. predicted tree heights using the validation subset for pioneer (A, B), early secondary (C, D) and late secondary (E, F) species from Manaus (A, C, and E) and Santarém (B, D, and F). Observed vs. predicted height is fitted using a continuous line; the dashed line refers to the perfect agreement (1:1).

Comparison of H-DBH models by study site and ESG

The null hypothesis was not rejected for the ESG 2-3 pair (early secondary and late secondary species) at both study sites (Table 4), suggesting that parameters c and d from the full models were different from zero in these cases (p > 0.05). Based on the results of the paired F-test, and the estimated parameters of the full model, we concluded that secondary species (early and late) had a similar H:DBH relationship in both study sites, hereafter grouped into one class, while pioneer species belonged to another class.

Table 4
Fitted parameters of the full (F) and reduced (R) hyperbolic model by ESG pairs. CI = 95% confidence interval, as shown in parentheses. SSE (F) and SSE (R) are the sum of square error for full and reduced models, respectively. a, b, c, and d are the parameters. ESG-Pair (ecological species group pairs): 1-2 (pioneers-early secondary species), 1-3 (pioneers-late secondary species), 2-3 (early-late secondary species).

We compared the differences in the H:DBH relationships of these new groups (pioneers and secondary species) by study site, in order to determine whether tree growth was also influenced by geographic location. A clear difference in the H:DBH relationship between pioneer and secondary species from Manaus and Santarém by statistical inference (Table 5) was strengthened by the low p-value obtained by the F-test. H:DBH models for the pioneer species took the form: h = 29.12 DBH/(13.65+DBH) for Manaus, and h = 40.94 DBH/(25.21+DBH) for Santarém (Table 5). Similarly, secondary species took the form: h = 42.84 DBH/(27.05+DBH) for Manaus, and h = 30.83 DBH/(15.81+DBH) for Santarém. Model adjustments for pioneer and secondary species for Manaus and Santarém are provided in Figure 5.

Table 5
Fitted parameters of full (F) and reduced (R) hyperbolic models by study area for pioneer and secondary species. CI = 95% confidence interval, as shown in parentheses. SSE (F) and SSE (R) are the sum of square error for full and reduced models, respectively. a, b, c, and d are the parameters.

Height growth by site and species groups

The hyperbolic model was relatively easy to fit, achieved good validation results, and was meaningful in terms of the biological interpretation of its parameters. In this function, a represents total height at maximum DBH (asymptote), and b is the DBH when tree height reaches half the asymptote. Thus, a first derivative of the hyperbolic model allows us to obtain the absolute rate of height growth by DBH unit [Eq. (3): dy/dx= ab/(b+x)²]. Therefore, when DBH approaches zero, a/b represents the maximum height increment by DBH unit (m cm-1). Disregarding other underlying dynamic processes of H:DBH relationships, we observed that pioneers in Manaus had the highest HGR. The HGR in pioneer species from Manaus was 2.13 m cm-¹, meaning that for every centimeter in diameter increment, height increased more than 2 m. Santarém pioneers had a HGR = 1.62 m cm-1) Figure 5. Conversely, secondary species in Santarém had a greater HGR than those in Manaus, HGR = 1.95 and 1.58 m cm-1, respectively.

Pioneer species had high initial HGR in Manaus compared with secondary species, and this decreased with increasing diameter. Compared with Manaus, pioneer species in Santarém showed a greater HGR for large trees (Figure 5). The increase in height growth fell below 0.20 m cm-1 at DBH > 40 cm. This decline can be expected to continue until the regenerating forest becomes structurally similar to the average canopy heights of the mature forest, which is reported to be 26 m in Manaus and 28 m in Santarém (Hunter et al. 2015Hunter, M.O.; Keller, M.; Morton, D.; Cook, B.; Lefsky, M.; Ducey, M. et al. 2015. Structural Dynamics of Tropical Moist Forest Gaps. PLoS One, 10: e0132144. ). Based on height modelling of secondary forests in Santarém, height initially increases by a maximum of 2 m per year, and then falls below 0.25 m per year at age 30 (Neeff and Santos 2005Neeff, T.; Santos, J.R. 2005. A growth model for secondary forest in Central Amazonia. Forest Ecology and Management, 216: 270-282. ). Pioneer species in Manaus exhibited fast growth in the first years; this was around 30% higher than that observed in Santarém (Figure 5). However, later in life, they had about 50% smaller HGR than pioneers in Santarém (DBH = ~40 cm).

Figure 5
Scatterplot of the hyperbolic model adjustment between diameter and tree height on the primary y-axis, and between DBH and tree height growth rate on the secondary y-axis.

DISCUSSION

The hyperbolic model presented the best validation results among the most common models. We found statistical differences between pioneer and secondary species for H:DBH relationships, but not between early and late secondary species. These differences were consistent across sites, probably due to environmental and climate conditions. The HGR presented distinct behavior among ESGs and between sites.

Model selection for goodness-of-fit comparison

According to Fang and Bailey (1998Fang, Z.; Bailey, R.L. 1998. Height-diameter models for tropical forests on Hainan Island in southern China. Forest Ecology and Management, 110: 315-327.), different H:DBH models with the same number of parameters usually result in similar goodness-of-fit when the nonlinear least square method is used on the same data set. Feldpausch et al. (2011Feldpausch, T.R.; Banin, L.; Phillips, O.L.; Baker, T.R.; Lewis, S.L.; Quesada, C.A. et al. 2011. Height-diameter allometry of tropical forest trees. Biogeosciences, 8: 1081-1106.) observed that log-log models (two parameters) were the most suitable for estimating tree height in dry and wet forests, with no trend observed in their residuals by diameter class. Asymptotic functions with three parameters, such as the Weibull model, provided good estimates of ecologically meaningful H max in moist forests (Feldpausch et al. 2011). Conversely, when one or two parameters are introduced in the model (e.g., three or four parameters instead of two), biological interpretation of parameters may be lost (Fang and Bailey 1998). Convergence could not be attained as easily as when using the Weibull and Chapman-Richards models (Table 3).

In this study, the hyperbolic model was found to produce the most satisfactory fit among the tested models, which was consistent with previous studies that also satisfactorily tested this model for adjusting H:DBH relationships (Fang and Bailey 1998Fang, Z.; Bailey, R.L. 1998. Height-diameter models for tropical forests on Hainan Island in southern China. Forest Ecology and Management, 110: 315-327.; Huang et al. 2000Huang, S.; Price, D.J.; Titus, S. 2000. Development of ecoregion-based height-diameter models for white spruce in boreal forests. Forest Ecology and Management, 129: 125-141.). Nevertheless, due to the adjusted asymptote being close to 40 m for secondary forest trees, the hyperbolic model tended to underestimate the height of large trees, therefore its application in old growth forest should be avoided.

Separating H:DBH models by study site and ESG

Statistical differences were found between study sites in H:DBH relationships. Considering that the secondary forest plots were at a similar age (~23 years), the most important local factors influencing H:DBH relationships are the stand density, basal area, and species composition (Gómez-García et al. 2016Gómez-García, E.; Fonseca, T.; Crecente-Campo, F.; Almeida, L.; Diéguez-Aranda, U.; Huang, S. et al. 2016. Height-diameter models for maritime pine in Portugal: a comparison of basic, generalized and mixed-effects models. iForest - Biogeosciences Forestry, 9: 72-78.). Basal area and stand density are the first parameters to reach similarity in mature forests (within 20-40 years), while similarity in species composition can take longer (Feldpausch et al. 2005Feldpausch, T.R.; Riha, S.J.; Fernandes, E.C.M.; Wandelli, E.V. 2005. Development of forest structure and leaf area in secondary forests regenerating on abandoned pastures in Central Amazônia. Earth Interactions. 9: 1-22.; Neeff and Santos 2005Neeff, T.; Santos, J.R. 2005. A growth model for secondary forest in Central Amazonia. Forest Ecology and Management, 216: 270-282. ).

Owing to resource competition, trees of the same DBH usually have greater height in denser stands. We estimated average stand basal area as 22.3 and 23.7 m² ha-1 in secondary forest plots in Santarém and Manaus, respectively, which may be indicative of greater average tree height in Manaus. Hunter et al. (2013Hunter, M.O.; Keller, M.; Victoria, D.; Morton, D.C. 2013. Tree height and tropical forest biomass estimation. Biogeosciences, 10: 8385-8399. ) reported a greater average basal area of primary forests in FLONA Tapajós (31 m² ha-1), with average canopy height taller than that in Reserva Ducke, near Manaus site (28.7 m² ha-1). Such differences are probably due to primary forests from Santarém having larger trees with DBH > 60 cm than Manaus primary forests (Vieira et al. 2005Vieira, S.; Trumbore, S.; Camargo, P.B.; Selhorst, D.; Chambers, J.Q.; Higuchi, N. et al. 2005. Slow growth rates of Amazonian trees: Consequences for carbon cycling. Proceedings of the National Academy of Sciences, 102: 18502-18507. ), increasing both the average basal area and the mean canopy height, which is not observed in secondary forests.

Some climatic variables, such as greater annual precipitation, shorter dry season length, and greater mean annual air temperature, could be drivers of greater relative tree growth in central Amazon secondary forests (Malhi et al. 2004Malhi, Y.; Baker, T.R.; Phillips, O. L.; Almeida, S.; Alvarez, E.; Arroyo, L. et al. 2004. The above-ground coarse wood productivity of 104 Neotropical forest plots. Global Change Biology, 10: 563-591.). From a hydraulic perspective, it would be expected that, for a given DBH, trees would be shorter with increasing water deficit. Hence, the application of H:DBH models from the moderately seasonal central Amazon may overestimate tree height in the dry forest, and underestimate it in the wet regions (Malhi et al. 2004).

Regarding ESG-specific H:DBH models, pioneer and secondary species may be regarded as different groups at our study sites. Although pioneer species grow faster than late successional species (Selaya et al. 2008Selaya, N.G.; Oomen, R.J.; Netten, J.J.C.; Werger, M.J.A.; Anten, N.P.R. 2008. Biomass allocation and leaf life span in relation to light interception by tropical forest plants during the first years of secondary succession. Journal of Ecology, 96: 1211-1221.), we found a different behavior in pioneer species in Santarém. In this study site, pioneer species showed similar behavior to early secondary species, which can be supported by interpretation of the magnitude of the confidence intervals of the regression parameters in Table 4.

Pioneer species were prevalent in Manaus with regard to their importance in species composition (% of total species number), and their relative coverage (by summing relative density and dominance in the stand level). In Manaus, pioneer species comprised 33% of species richness, and 52% of the total stand trees, while in Santarém, they represented 29% and 39%, respectively. The monodominance of pioneer species such as Cecropia spp. and Vismia spp., which form a monolayer canopy arrangement, may prevent the recruitment of taller and later secondary species in Manaus (Lucas et al. 2002Lucas, R.M.; Honzák, M.; Amaral, I.; Curran, P.J.; Foody, G.M.; 2002. Forest regeneration on abandoned clearances in central Amazonia. International Journal of Remote Sensing, 23: 965-988. ).

It is probable that pioneer species from Santarém are still competing for resources with other secondary trees, while in Manaus, short-lived species are being replaced by other long-lived secondary species. The most important pioneer species in Manaus, Vismia spp., Cecropia spp., and Bellucia spp., are short-lived (20-30 years), and are virtually absent from old growth forest (Lucas et al. 2002Lucas, R.M.; Honzák, M.; Amaral, I.; Curran, P.J.; Foody, G.M.; 2002. Forest regeneration on abandoned clearances in central Amazonia. International Journal of Remote Sensing, 23: 965-988. ). Secondary forests in Santarém are dominated almost exclusively by Guatteria poeppigianaMart., a pioneer species with a lifespan of 54 years (Holm et al. 2014Holm, J.A.; Chambers, J.Q.; Collins, W.D.; Higuchi, N. 2014. Forest response to increased disturbance in the central Amazon and comparison to western Amazonian forests. Biogeosciences, 11: 5773-5794.). The high growth rate of large trees (DBH > 60 cm) of late secondary species may be a major cause of faster carbon assimilation in the eastern Amazon than in the central Amazon (Vieira et al. 2005Vieira, S.; Trumbore, S.; Camargo, P.B.; Selhorst, D.; Chambers, J.Q.; Higuchi, N. et al. 2005. Slow growth rates of Amazonian trees: Consequences for carbon cycling. Proceedings of the National Academy of Sciences, 102: 18502-18507. ).

CONCLUSIONS

Among the models tested, the hyperbolic model presented the best performance for estimating tree height through diameter measured for secondary forests located near the cities of Manaus (central Amazon) and Santarém (eastern Amazon). In addition, we presented an alternative method of analyzing the height-diameter (H:DBH) relation of secondary forests species, separating them by ESGs. The results suggest that pioneer and secondary species belong to distinct groups in terms of H:DBH relationships, and that tree height growth differs between both study sites. Pioneer species from Manaus showed rapid tree height growth at low DBH compared with secondary species, while in Santarém the opposite trend was observed. We showed that separate H:DBH models are required to achieve more accurate predictions of tree height in secondary forests in Manaus and Santarém. These new H:DBH models are essential to provide improved estimation of tree height in secondary forests, as required for carbon stock estimation (Chave et al. 2014Chave, J.; Réjou-Máchain, M.; Búrquez, A.; Chidumayo, E.; Colgan, M. S.; Delitti, W. B. C. et al. 2014. Improved allometric models to estimate the aboveground biomass of tropical trees. Global Change Biology, 20: 3177-3190.; Poorter et al. 2016Poorter, L.; Bongers, F.; Aide, T.M.; Zambrano, A.M.A.; Balvanera, P. Becknell, J.M. et al. 2016. Biomass resilience of Neotropical secondary forests. Nature, 530: 211-214.).

ACKNOWLEDGMENTS

We thank José Luís Camargo and Niro Higuchi for permitting entry to the Biological Dynamics of Forest Fragments Project (BDFFP) and Biomass and Nutrient Experiment Projetct (BIONTE) sites near Manaus; and Elisângela Rabelo for permitting entry to LBA-Santarém. We also thank the campaign contributors Richard Lucas, Joana Melo, Joshua Jones, Egídio Arai, Virgílio Pereira, Letícia Kirsten, and taxonomic experts who identified plant material in this study: Movido, Francisco (Caroço), Graveto, and Chico. This work was supported by the Tropical Research Institute (IICT) [PTDC/AGR-CFL/114908, 2009] and the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) [400349, 2012-4], which encompassed expenses for the fieldwork in Manaus and Santarém, respectively.

  • Asner G.P.; Bustamante, M.M.C.; Townsend, A.R. 2003. Scale dependence of biophysical structure in deforested areas bordering the Tapajo´s National Forest, Central Amazon. Remote Sensing of Environment, 87: 507-520.
  • Assmann, E. 1970. The principles of forest yield studies Pergamon Press, Oxford. 504p.
  • Bates, D.M.; Watts, D.G. 1990. Nonlinear Regression Analysis and Its Applications, 2nd ed. John Wiley & Sons, Inc., New York, 365p.
  • Carreiras, J.M.B.; Jones, J.; Lucas, R.M.; Gabriel, C. 2014. Land use and land cover change dynamics across the Brazilian Amazon: insights from extensive time-series analysis of remote sensing data. PLoS One, 9: e104144.
  • Chave, J.; Andalo, C.; Brown, S.; Cairns, M. A.; Chambers, J. Q.; Eamus, D. et al 2005. Tree allometry and improved estimation of carbon stocks and balance in tropical forests. Oecologia, 145: 87-99.
  • Chave, J.; Réjou-Máchain, M.; Búrquez, A.; Chidumayo, E.; Colgan, M. S.; Delitti, W. B. C. et al 2014. Improved allometric models to estimate the aboveground biomass of tropical trees. Global Change Biology, 20: 3177-3190.
  • Chazdon, R.L. 2014. Second Growth: The promise of Tropical Forest Regeneration in an Age of Deforestation, Chicago Press, Chicago. 472p.
  • Fang, Z.; Bailey, R.L. 1998. Height-diameter models for tropical forests on Hainan Island in southern China. Forest Ecology and Management, 110: 315-327.
  • Feldpausch, T.R.; Riha, S.J.; Fernandes, E.C.M.; Wandelli, E.V. 2005. Development of forest structure and leaf area in secondary forests regenerating on abandoned pastures in Central Amazônia. Earth Interactions 9: 1-22.
  • Feldpausch, T.R.; Banin, L.; Phillips, O.L.; Baker, T.R.; Lewis, S.L.; Quesada, C.A. et al 2011. Height-diameter allometry of tropical forest trees. Biogeosciences, 8: 1081-1106.
  • Feldpausch, T.R.; Lloyd, J.; Lewis, S.L.; Brienen, R.J.W.; Gloor, W.; Mendoza, A.M. et al 2012. Tree height integrated into pantropical biomass forest estimates. Biogeosciences, 9: 3381-3403.
  • Gómez-García, E.; Fonseca, T.; Crecente-Campo, F.; Almeida, L.; Diéguez-Aranda, U.; Huang, S. et al 2016. Height-diameter models for maritime pine in Portugal: a comparison of basic, generalized and mixed-effects models. iForest - Biogeosciences Forestry, 9: 72-78.
  • Hastie, T.; Tibshirani, R.; Friedman, J.H. 2009. The elements of statistical learning: data mining, inference, and prediction 2nd ed. Springer, New York. 745p.
  • Holm, J.A.; Chambers, J.Q.; Collins, W.D.; Higuchi, N. 2014. Forest response to increased disturbance in the central Amazon and comparison to western Amazonian forests. Biogeosciences, 11: 5773-5794.
  • Huang, S.; Price, D.J.; Titus, S. 2000. Development of ecoregion-based height-diameter models for white spruce in boreal forests. Forest Ecology and Management, 129: 125-141.
  • Hunter, M.O.; Keller, M.; Victoria, D.; Morton, D.C. 2013. Tree height and tropical forest biomass estimation. Biogeosciences, 10: 8385-8399.
  • Hunter, M.O.; Keller, M.; Morton, D.; Cook, B.; Lefsky, M.; Ducey, M. et al 2015. Structural Dynamics of Tropical Moist Forest Gaps. PLoS One, 10: e0132144.
  • Lefsky, M.A. 2010. A global forest canopy height map from the Moderate Resolution Imaging Spectroradiometer and the Geoscience Laser Altimeter System. Geophysical Research Letters, 37: L15401.
  • Lucas, R.M.; Honzák, M.; Amaral, I.; Curran, P.J.; Foody, G.M.; 2002. Forest regeneration on abandoned clearances in central Amazonia. International Journal of Remote Sensing, 23: 965-988.
  • Malhi, Y.; Baker, T.R.; Phillips, O. L.; Almeida, S.; Alvarez, E.; Arroyo, L. et al 2004. The above-ground coarse wood productivity of 104 Neotropical forest plots. Global Change Biology, 10: 563-591.
  • Motulsky, H.J.; Christopoulos, A. 2003. Fitting models to biological data using linear and nonlinear regression GraphPad Software, Inc., San Diego, 352p.
  • Neeff, T.; Santos, J.R. 2005. A growth model for secondary forest in Central Amazonia. Forest Ecology and Management, 216: 270-282.
  • Nelson, B.W.; Mesquita, R.; Pereira, J.L.G.; De Souza, S.G.; Batista, G.T.; Couto, L.B. 1999. Allometric regressions for improved estimate of secondary forest biomass in the central Amazon. Forest Ecology and Management, 117: 149-167.
  • Neter, J.; Kutner, M.; Wasserman, W.; Nachtsheim, C. 1996. Applied Linear Statistical Models, 4th ed. McGraw-Hill, Irwin. 1396p.
  • Norberg, R.A. 1988. Theory of Growth Geometry of Plants and Self-Thinning of Plant Populations: Geometric Similarity, Elastic Similarity, and Different Growth Modes of Plant Parts. The American Naturalist, 131: 220-256.
  • Pillsbury, N.H.; McDonald, P.M.; Simon, V. 1995. Reliability of Tanoak volume equations when applied to different areas. Western Journal of Applied Forestry, 10: 72-78.
  • Poorter, L.; Bongers, F. 2006. Leaf traits are good predictors of plant performance across 53 rain forest species. Ecology, 87: 1733-1743.
  • Poorter, H.; Niklas, K.J.; Reich, P.B.; Oleksyn, J.; Poot, P.; Mommer, L. 2012. Biomass allocation to leaves, stems and roots: meta-analyses of interspecific variation and environmental control. New Phytologist, 193: 30-50.
  • Poorter, L.; Bongers, F.; Aide, T.M.; Zambrano, A.M.A.; Balvanera, P. Becknell, J.M. et al 2016. Biomass resilience of Neotropical secondary forests. Nature, 530: 211-214.
  • Prates-Clark, C. da C.; Lucas, R.M.; dos Santos, J.R. 2009. Implications of land-use history for forest regeneration in the Brazilian Amazon. Canadian Journal of Remote Sensing, 35: 534-553.
  • R Development Core Team. 2008. R: A language and environment for statistical computing. ( (http://www.R-project.org ). Accessed on 17/05/2015.
    » http://www.R-project.org
  • Santiago, L.S.; Goldstein, G.; Meinzer, F.C.; Fisher, J.B.; Machado, K.; Woodruff, D. et al 2004. Leaf photosynthetic traits scale with hydraulic conductivity and wood density in Panamanian forest canopy trees. Oecologia, 140: 543-550.
  • Sawada, Y.; Suwa, R.; Jindo, K.; Endo, T.; Oki, K.; Sawada, H. et al 2015. A new 500-m resolution map of canopy height for Amazon forest using spaceborne LiDAR and cloud-free MODIS imagery. International Journal of Applied Earth Observation and Geoinformation, 43: 92-101.
  • Selaya, N.G.; Oomen, R.J.; Netten, J.J.C.; Werger, M.J.A.; Anten, N.P.R. 2008. Biomass allocation and leaf life span in relation to light interception by tropical forest plants during the first years of secondary succession. Journal of Ecology, 96: 1211-1221.
  • Silver, W.L.; Ostertag, R.; Lugo, A.E. 2000. The potential for carbon sequestration through reforestation of abandoned tropical agricultural and pasture lands. Restoration Ecology, 8: 394-407.
  • Sposito, T.C.; Santos, F.A.M. 2001. Scaling of Stem and Crown in Eight Cecropia (Cecropiaceae) Species of Brazil. American Journal of Botany, 88: 939-949.
  • Wagenmakers, E-J.; Farrell, S. 2004. AIC model selection using Akaike weights. Psychonomic Bulletin & Review, 11: 192-196.
  • Weiskittel, A.; Hann, D.; Kershaw, J.; Vanclay, J. 2011. Forest growth and yield modelling John Wiley & Sons, Sussex, 430p.
  • Vieira, S.; Trumbore, S.; Camargo, P.B.; Selhorst, D.; Chambers, J.Q.; Higuchi, N. et al 2005. Slow growth rates of Amazonian trees: Consequences for carbon cycling. Proceedings of the National Academy of Sciences, 102: 18502-18507.
  • Zanne, A.E.; Lopez-Gonzalez, G.; Coomes, D.A.; Ilic, J.; Jansen, S.; Lewis, S.L. et al 2009. Global wood density database. Dryad. ( (http://hdl.handle.net/10255/dryad.235 ). Accessed on 22/10/2016.
    » http://hdl.handle.net/10255/dryad.235

  • CITE AS:

    Cassol, H. L. G.; Shimabukuro, Y. E.; Carreiras, J. M. B.; Moraes, E. C. 2018. Improved tree height estimation of secondary forests in the Brazilian Amazon. Acta Amazonica 48: 179-190.

SUPPLEMENTARY MATERIAL

(only available in the electronic version) CASSOL et al. Improved tree height estimation of secondary forests in the Brazilian Amazon

Table S1
List of species and their respective botanical families recorded in this study. Scientific names according to http://www.theplantlist.org/; WD - wood density in g cm-3; ESG - ecological species group: 1 - Pioneers, 2 - Early secondary, 3 - Late secondary/Climax, 4 - Exotic, 5 - Dead/Unknown; OCC - occurrence: 1 - Manaus, 2 - Santarem, 3 - Both; WD Ref - reference for wood density value; ESG Ref - reference for ecological species group.

Publication Dates

  • Publication in this collection
    Jul-Sep 2018

History

  • Received
    20 Mar 2017
  • Accepted
    23 Mar 2018
Instituto Nacional de Pesquisas da Amazônia Av. André Araujo, 2936 Aleixo, 69060-001 Manaus AM Brasil, Tel.: +55 92 3643-3030, Fax: +55 92 643-3223 - Manaus - AM - Brazil
E-mail: acta@inpa.gov.br