CHARACTERIZING THE STRUCTURE AND BIOMASS OF MANGROVE SPECIES USING TERRESTRIAL LIDAR DATA, AND THE APPLICATION IN EXTENDING BIOMASS ALLOMETRIC EQUATIONS TO LARGE TREES1
Accurately determining biomass of large trees is crucial for reliable biomass analyses in most tropical forests, but most allometric models calibration are deficient in large trees data. This issue is a major concern for high-biomass mangrove forests, especially when their role in the ecosystem carbon storage is considered. As an alternative to the fastidious cutting and weighing measurement approach, we explored a non-destructive terrestrial laser scanning approach to estimate the aboveground biomass of large mangroves (diameters reaching up to 125 cm). Because of buttresses in large trees, we propose a pixel-based analysis of the composite 2D flattened images, obtained from the successive thin segments of stem point-cloud data to estimate wood volume. Branches were considered as successive best-fitted primitive of conical frustums. The product of wood volume and height-decreasing wood density yielded biomass estimates. This approach was tested on 36 A. germinans trees in French Guiana, considering available biomass models from the same region as references. Our biomass estimates reached ca. 90% accuracy and a correlation of 0.99 with reference biomass values. Based on the results, new tree biomass model, which had R2 of 0.99 and RSE of 87.6 kg of dry matter. This terrestrial LiDAR-based approach allows the estimates of large tree biomass to be tractable, and opens new opportunities to improve biomass estimates of tall mangroves. The method could also be tested and applied to other tree species. Keywords: Aboveground biomass; Coastal blue carbon; French Guiana; Mangrove; Terrestrial LiDAR; Tree allometry
Recent studies have demonstrated the importance of large trees as keystone ecological elements (Lindenmayer et al., 2012; Lutz et al., 2013) in forest ecosystems. Their significance extends beyond the characteristic contribution to regeneration as mother trees and the provision of food and shelter for many living organisms, because they also represent essential structures that shape ecosystem biomass productivity and recurrent forest dynamics (Slik et al., 2013). In terms of wood volume, biomass, and carbon stocks, they dominate the forest structure and this may explain variations in biomass distribution across forest landscapes (Bastin et al., 2015a). Thus, an accurate estimation of the biomass of large trees is crucial for obtaining reliable estimates of the total biomass in such forests.
One key challenge is that the biomass data of large tropical tree are generally scarce (e.g. only ca. 7% of the available pantropical tree biomass dataset, Chave et al. (2014))
This is also the case for the tall mangroves that grow in the equatorial region. Although the species diversity of mangroves is low compared with rainforests, the variability in the tree structure of Avicennia species, for example, is higher. Avicennia trees may exhibit a wide range of growth forms, from small to large/ tall trees, depending on the habitat condition. Considering this variation in tree structure, available models may actually fall short in their predictive power for out-of-sample application. This situation may also limit the extent to which the existing general pantropical biomass allometric models can be applied to mangrove trees, without significant bias in the resulting estimates.
Meanwhile, there is a growing interest in attaining highly precise estimates of biomass and carbon stock of tropical forests (Gibbs et al., 2007; Pistorius, 2012), including mangroves, as in the case of the blue carbon projects. This necessitates the refinement of the available methods, like the commonly used allometric models, for biomass measurement. All the same, the available biomass models for mangrove trees (Komiyama et al., 2008) only cover a range of small – medium sized trees (DBH ≤ 50 cm) and are deficient in respect of large trees. Collecting data, using the conventional cutting and weighing method, to validate mangrove biomass models for large trees is however difficult in the tidal environment.
The terrestrial laser scanning (TLS), also knowns as terrestrial LiDAR (light detection and ranging), offers a remote sensing technology that allows capturing the high resolution three-dimensional (3D) structure of trees with relatively low time and labour requirements. Earlier applications in the forest sciences and ecological studies include the description of forest structural parameters (Strahler et al., 2008), assessment of canopy metrics and gaps (Bayer et al., 2013; Hilker et al., 2010), individual tree volume and biomass estimation (e.g., Calders et al. (2015); Dassot et al. (2012)), to the application in estimating leaf area and foliage properties (Béland et al., 2014). Interestingly, various approaches have tested satisfactorily in the estimation of individual tree volume and biomass from TLS point cloud data: from tree features extraction (Kankare et al., 2013; Pueschel et al., 2013), shape reconstruction and primitive fittings (e.g., Raumonen et al. (2013)) to voxelization (Hauglin et al., 2013).
Some automatic techniques have been proposed for reconstructing and modelling of tree structure and topology (Åkerblom et al., 2015; Hackenberg et al., 2015; Raumonen et al., 2013), and they achieved notably good results with regular, cylindrical shaped tree trunks, and mostly in leaf-off conditions. Since such methods are based on segmental geometric primitive fits, irregularities in the shape of large tropical trees like mangroves remain challenging for direct application of such automatic tree reconstruction. For irregular trunk shapes, we presume that automatic techniques may require a combination with (semi-)manual interactive steps. In any case, the application of TLS in the study of mangrove species remains largely unexplored; the only pilot attempt was limited to mangrove trees with DBH < 43 cm (Feliciano et al., 2014). In the present study, our aims were (1) to describe and evaluate the performance of a simple TLS-based method for estimating the wood volume and biomass of large mangrove trees, and (2) to propose revised allometric models for the widespread mangrove tree species Avicennia germinans (L.) L. with a validation domain extended to very large trees.
The study was performed in French Guiana (hereafter referred to as FG) where mangroves stretch along a 320 km coastline (Figure 2-1), to cover an approximate area of 70,000 ha. This coast can be considered as pristine, because there are still no extensive industrial activities, and aquaculture and tree exploitation are not present. It is subjected primarily to sediment dispersal from the Amazon River (Baltzer et al., 2004). The spatiotemporal distribution of mangroves is controlled by a succession of rapid and acute erosion and accretion phases caused by the drifting of giant mud-banks to the northwest of the coastline (Anthony et al., 2010).
The mangrove forests encompass new colonization on the freshly consolidated mud-banks up to mature forests located several kilometers inland at the limit of tidal influence. In this area, mangroves are unaffected by coastal instability (Anthony et al., 2010) and this allows trees to reach their largest potential stature. Fromard et al. (1998) described the different mangrove forest types of FG; A. germinans (L.) L. is represented from pioneer to old-growth forest, spanning a wide range of growth stages. These growth stages are patchily distributed across the coastal landscape with clusters of young trees, sometimes in close vicinity to decaying stands (Proisy et al., 2007).
The sampling locations were selected in order to capture data from trees distributed over a wide DBH range. This DBH range was distributed in three distinct forest stands, as noted in Figure 2-1. First, a mixed old-growth Avicennia–Rhizophora forest stand near Petit Cayenne 10 km upstream of the Cayenne river, with a stand density of 504 trees per hectare, total basal area of 26.2 m2.ha-1 and A. germinans trees reaching a mean DBH of 56.2 cm. The second stand, located at about 3 km from the actual mangrove shoreline along Guatemala road, was made up of small-medium size and scattered large A. germinans trees. The tree density in this stand was 3733 trees per hectare with a total basal area of 25.5 m2.ha-1, and average DBH of 15 cm.
The third stand, we considered an even-aged A. germinans forest located 6 km backward of the mangrove seafront in the Sinnamary region. This stand contained mainly A. germinans in a density of 1132 trees per hectare with basal area totalling 21.8 m2.ha-1.
Essential features of Avicennia germinans (L.) L.
In this study, we employed A. germinans as a proxy species to test a new method for estimating the biomass of mangrove trees using TLS data. This is a keystone species and the most dominant mangrove species on the FG coast (Fromard et al., 1998; Fromard et al., 2004). A. germinans trees vary greatly in size and growth form. The species grows from low-scrubby (ca. 0.4–1.5 m tall) in the sub-optimal habitats (Vogt et al., 2014) to large trees approaching 42 m height and 125 cm diameter in favorable and stable growth conditions, as found in some parts of French Guiana. Trunks are roughly cylindrical to slightly angled or even canaliculated and may develop buttresses and short fascicles of aerial roots. The trees reiterate to produce coppice shoots when the main stem is damaged, resulting in frequently contorted stem development.
Existing biomass allometric models for A. germinans
Fromard et al. (1998) developed biomass allometric models for aboveground biomass (AGB) of mangrove trees in French Guiana. The models for A. germinans followed a power function, with two coefficients (Table 2-1). They were calibrated using data obtained from small to medium-sized trees with DBH of 4 – 42 cm and corresponding AGB between 4.8 and 1543.7 kg of dry matter, respectively. These models conformed to the biomass allometric model developed for the same species in Guadeloupe (Imbert and Rollet, 1989). Other mangrove biomass models applicable to A. germinans are the two generic equations develped by Chave et al. (2005) and Komiyama et al. (2005), which were also calibrated with trees DBH < 60 cm. An independent dataset obtained by direct cutting and weighing of sample trees (Fromard et al., 1998) at the same study locations as ours jointly with the predicted biomass estimates of currently sampled trees, using the allometric models of Fromard et al. (1998), were used for reference to evaluate the TLS-based biomass values and new models in this study.
Wood density (WD) measurements at different heights
In most studies of allometric relationships, the WD is estimated at breast height. To our knowledge, no WD measurements have been reported at different heights along the main axis for A. germinans so far. Thus, we initiated an experiment that involved coring A. germinans trees at different heights in various mangrove regions throughout French Guiana. We climbed 20 trees (10 < DBH < 110 cm) and used hand-powered drills to extract 52 samples. The wood core samples measured 4.3 mm in diameter with lengths of 2–13 cm over bark. The core heights along the stem axis ranged from 0.3 m for all trees up to 23 m for tall trees, corresponding to diameters varying from 4.8 cm, at the top of small trees, up to 110 cm at the base of large trees. All core samples were dried at a constant temperature of 105 C for several days until constant mass, and subsequently weighted in relation to wood volume to obtain WD as dry weight. High variability in the WD was observed at heights below 10 m, and also around the breast height. The distribution of wood density along the main stem vs. sampling height and diameter was fitted using a linear mixed effects model, with the individual tree as random factor. This analysis was based on WD density data from the outer wood core samples, since the outer wood density values are known to strongly correlate to the WD values from any point along the radial spectrum, without a significant bias (Bastin et al., 2015b).
TLS measurements and data processing
The TLS measurements used in this study were collected with a FARO Focus3D X330 device between August and September 2014. The instrument operates using a 1.55 m class 1 laser signal. The distance between the scanner and the object is determined by analyzing the shift in the wavelength of the return beam. The device can scan objects at a distance of up to 330 m; and with an accuracy of < 0.25 mm for dark objects at a distance of 25 m. The vertical and horizontal fields of view are 300 and 360 , respectively. Several scanning resolutions can be used for collecting point cloud data from the focal surface. However, we chose the second finest scanning configuration able to achieve complete scanning at about 20 min with a distance accuracy reaching ±3 mm over a horizontal range of 90° as the finest scan required more than 1 hour for an accuracy slightly improved to ±2 mm over the same distance. A flowchart that illustrates the procedure for data acquisition and subsequent processing is presented in Figure 2-2. Further methodical descriptions are provided in the subsequent sections.
Mangrove tree scanning
The number of trees selected for each scanning operation ranged from a single (large) tree to a group of six individual (small to medium-sized) trees. Before placing the instrument, several viewpoints were identified for TLS placement around selected individual(s), and subsequently distribution of the target spheres (reference objects to aid merging/ alignment of multiscans). This was a crucial step because it directly affected the quality of the 3D description of the focal mangrove tree(s). In this experiment, five white target spheres were positioned in the foreground and background surrounding the focal trees at different heights ranging from 0–2 m using stands made of metal rods and pipes, at a minimum distance of ca. 3 m from the tree base (Figure 2-3).
The TLS instrument was mounted on a sturdy tripod stand, with additional support from reinforced metal frames (ca. 60 cm long) embedded in the muddy sediment. One can adapt the length of these support metal frames as required, until adequate stability is reached before mounting the LiDAR system. The number of scan positions was selected as a function of the horizontal and vertical projections of the target trees. To minimize the chance of occlusions or missing parts in the 3D tree structure, it was essential to scan large individual trees with buttresses from at least 5 viewpoints at high scanning resolution. Table 2-2 provides the summary attributes of the sample trees.
Extraction of trunk and branches from point-cloud data
The TLS data processing comprised merging of multiple scans, filtering or removal of background vegetation, and generating point clouds for individual trees of interest. This process was conducted using the FARO SCENE 5.2 software. The process took from ca. 1 – 12 working hours to complete one large tree, depending on its structure. The main trunk and primary branches (in the case of large trees) were manually separated, and the 3D coordinates of the point cloud were exported for subsequent processing. The computation routine for wood volume and biomass was implemented in MATLAB. For control, we also fitted successive geometric primitives on point cloud data of trunks and branches (> 4 cm at the branch base) using the least squares method.
Computation of the trunk and branch volumes
Two volume computation procedures were performed for the trunks: (1) volume estimation of successive best-fitted geometric shapes (primitive fitting), and (2) an automatic pixel count on 2D flattened projection of segmented thin trunk sections. The trunk volume estimates from the composite primitive shapes fitted on the selected trunks served for the validation of the pixel-based analysis. The determination of the volume of tree branches was restricted to manual primitive shape fittings in this study due to computational complexity.
Stem volume estimation by primitive fitting
For each tree, sets of conical frustums were extracted that corresponded to the main trunk and each branch. The diameters at the base (Db) and the top (Dt), and the height (Hc) of each solid shape were recorded. Thereafter, the geometrical volume (Vc for trunk and Vcb for branches) of each primitive shape was estimated as a truncated cone, as given by equation 1.
All of the Vc values in a trunk were summed to obtain the trunk volume (VTrcone). The addition of the component Vcb of each branch yielded the branch volume.
Trunk volume estimation with the pixel-based method
We implemented a program routine that decomposed 3D trunk shapes into successive thin sections (Figure 2-4, a–c). The height of each section to the ground level was recorded. These sections were converted into two-dimensional (2D) binary images to obtain their flattened plan projections. Different segmentation heights (section thickness), ranging from 1 cm to 1 m, were tested to find a trade-off between complete shape outline and gaps in the 2D plan. When open shapes occurred in the point cloud (due to occlusion on trunk part during scanning), they were filled automatically by fitting a simple convex envelope around the missing region. The area covered by the boundary of the section was then divided into a grid of 1 cm2 pixels. The number of pixels in the flattened image of each section was summed to obtain its surface area, and the volume was obtained as the product of the surface area and its thickness, and the trunk volume was obtained as the total stacked constituent sections. These trunk volume estimates were compared with the volume obtained from primitive fittings (described above) to validate the pixel-based method.
Biomass estimation from TLS-derived wood volume
Conversion of stem volume to biomass
In this study, we systematically obtained two biomass estimates: the first used a mean WD derived from our wood density sampling; and the second employed a decreasing WD relative to height along the stem axis derived from the respective linear mixed-effects model. In the latter case, we interpolated the height WD model to obtain specific WD at each section height by reference to the bottom of the tree. The biomass estimates for each of the trunk (BTRTLS) and the branch (BBRTLS) components were obtained as the sum of the products of each section volume and the corresponding WD. The sum of the branch and trunk biomass of each tree provided its TLS-derived aboveground woody biomass (AGBWTLS). The leaf biomass was only considered in this study as a proportional relation following the model of Fromard et al. (1998) in Table 2-1, although it constituted an insignificant share of the AGB estimates.
Evaluation of TLS biomass estimates for trees DBH < 42 cm
We applied a cross-validation procedure to evaluate the accuracy of the TLS-derived trunk volume and biomass estimates of trees within the DBH range of the reference data (Fromard et al., 1998). We calculated the root mean squared error (RMSE) and the accuracy using equations 2 and 3, respectively:
n (FFi TLSi )2
RMSE i 1 , (2)
%RMSE 100 RMSE , (3)
where FFi denotes the reference values based on Fromard et al. (1998), TLSi is the corresponding TLS-derived estimate, and n is the number of trees.
Fitting of allometric models using TLS-derived biomass data
We employed TLS-derived data for calibrating easily applicable biomass allometric models. Based on tree diameter–biomass relationship of A. germinans, we fitted a new non-linear AGB model with DBH as the predictive variable using a maximum likelihood regression approach (AGB.M1, equation 4). The coefficients and are parameters that characterized the new biomass models we obtained. As suggested by Chave et al. (2005) and Komiyama et al. (2005), we considered other models (AGB.M2–AGB.M4) that incorporated WD (denoted as in the allometric equations) and/or tree height (H), as given by equations 5 – 7:
AGB.M1: AGBDBH, (4)
AGB.M2: AGBDBH, (5)
AGB.M3: AGB(DBH2H), (6)
AGB.M4: AGB(DBH2H), (7)
where is the model error, which considers factors that may explain the difference in biomass between two trees with the same DBH and H dimensions. The branch (BBR.M) and trunk (BTR.M) models were fitted according to the model formulated in AGB.M1. All of the variables in these models were considered as logarithmic transformed variables to eliminate heteroscedasticity. To obtain biomass values by back-transformation, we applied the correction factor (CF) described by Sprugel (1983), which relies on the residual standard error (RSE) of the models, as given in equation 8, thereby adjusting for the systematic bias associated with log-transformations of data.
Evaluation of the biomass models
A thorough validation of a new model normally requires the use of independent empirical datasets (Vanclay and Skovsgaard, 1997). However, due to the relatively small sample size and paucity of separate validation datasets, we decided to employ goodness-of-fit statistics, Akaike’s information criterion (AIC) for multi-model inference, and graphical analysis to assess the performances of the new models in comparison to the previous models produced by Fromard et al. (1998). All of the model fitting procedures and statistical evaluation were performed using MATLAB.
Height-dependent wood density
WD values ranged from 595 to 790 kg m–3 (Figure 2-5) for trees over a DBH range of 10.4 – 110 cm, with a mean value of 728.7 ± 8.91 kg m–3 around the breast height. The LME model fitted for WD as a function of sample height and tree DBH, with the individual tree as random factor, demonstrated a decreasing trend along the stem axis. From the tree base to the top, each increase the sampling height resulted in a 0.7% decrease in the basal mean WD value of 731.5 ± 17.2 kg m–3. The inclusion of a measure of individual tree DBH in the model resulted in ca. 0.08% increase in the predicted (P = 0.076). Thus, individual tree effect was not a significant factor in the total effects found in the distribution of wood density along the stem axis.
Accuracy of pixel-based trunk volume estimation from TLS data
Based on the performance test of the pixel-based method, the best results were achieved at a trunk section height of 10 cm during volume computation. These trunk volume estimates were compared with the geometric volume based on successive conical frustums for the analyzed trees (Figure 2-6, a & b). The RMSE between these two methods reached 6.7% of the mean value for 18 trees with no pronounced buttresses. The linear fit (R2 = 0.99) of the trunk volume estimates nearly overlaid the one-to-one line for the small, almost straight bole trees (Figure 2-6a). Higher volume estimates were obtained from trees with more pronounced buttresses, with the RMSE value increased to 16.7% of the mean value and the R2 decreased to 0.96 for larger trees (Figure 2-6b). Overall, the pixel-based method produced trunk volume with an accuracy of ca. 90%.
Figure 2-6: Comparison of the trunk volumes estimated using the automatic pixel-based analysis of TLS data and the successive trunk-fitted conical frustums for trees with DBH < 42 cm (a) and > 42 cm (b). Outline of girth form of typical trunks are shown in white with a grey background (arrows 1–4). The dashed line depicts a one-to-one relationship and the blue solid line corresponds to linear fit.
Accuracy of TLS-based tree volume-to-biomass conversion
The two specific WD values were combined with the pixel-based trunk volume estimates to produce biomass of trees in the diameter range of the reference data. The mean value of WD yielded a mean deviation of 16.5% (dry matter) compared with the reference biomass values for tree DBH < 42 cm. The dWD values lowered the mean deviation of the TLS-derived trunk biomass to 6.7% for the trees analysed in this study. Overall, the dWD-based biomass estimates strongly correlated with the reference values (R = 0.99), where the RMSE was 41.23 kg (14.21%) for the trunk biomass, 48.6 kg (13.6%) for the aboveground woody components, and 48.5 kg (13.5%) for the total AGB (Figure 2-7, a–c), with biomass values ranging from ca. 70 to 900 kg (dry matter).
Aboveground woody biomass of large A. germinans trees
The sum of the TLS-derived branch and trunk biomass yielded the aboveground woody biomass of large trees. These values ranged from 1242 kg for a tree with a DBH of 44.9 cm to 17,367 kg for a tree with a DBH of 124.5 cm. The branch biomass composition was almost uniform in small to medium-sized trees, i.e., 15–20% of the tree biomass. For large trees, the branch biomass varied from ca. 20% to almost 50% of the tree AGB in some cases (see Appendix).
Figure 2-7: Comparison of the TLS method relative to the estimates to the reference values for the trunk DBH<42 cm (a), trunk and branches (b), and total biomass estimates (c). The dots correspond to the biomass values of the sample trees (cf. Fromard et al. 1998), the dashed line is a 1:1 relationship, and the blue solid line indicates the linear fit
Revised allometric models of A. germinans trees
Using the new TLS-derived tree biomass and the available tree weight dataset, revised allometric models’ parameters were proposed (Table 2-3). For the tree branch biomass (BBR.M), we obtained a model with the same intercept coefficient ( = 0.03) as the reference model (BBRref). Meanwhile, the model parameter and R2 changed from 2.33 and 0.90 to 2.41 and 0.98, respectively. The curve describing BBR.M clearly shifted upward for trees larger than the diameter range of BBRref (Figure 2-8a), indicating that the BBRref underestimated the branch biomass of large trees. Our model for trunk biomass (BTR.M) was characterized by the model parameters = 0.11 and = 2.46, which yielded a clear power curve deflection below the reference model (Figure 2-8b). The R2 also increased from 0.95 in the reference model (BTRref) to 0.99 in the BTR.M. We obtained the best fit for a total AGB (AGB.M1) model, which has DBH as an explanatory variable (Table 2-3, Figure 2-8c). The model clearly had different parameters, where R2 = 0.99 and corrected AIC were significantly lower compared with the reference model (AGBref), but the corresponding residual standard error (RSE) only decreased by 1.2 kg (1.4%). With the exception of AGB.M2, which is similar to AGB.M1 in terms of model parameter and statistical attributes, AGB.M3 and AGB.M4 models with additional variable(s) (tree height and wood density) yielded higher residual standard errors compared with the AGBref.
Table of contents :
1 General introduction
1.1 Main motivation and challenges
1.1.1 Forests and plants adaptations to environmental change
1.1.2 Mangrove ecosystems and the relevance for investigations of tree morphological plasticity and forest dynamics in changing environments
1.1.3 Forest dynamics modelling and the incorporation of morphological plasticity
1.1.4 The prospects of coupling forest simulation models and remote sensing techniques
1.2 Research objectives
1.3 Study areas and datasets
1.3.1 Description of study sites
1.3.2 Data collection
1.4 Organization of the thesis
2 Characterizing the structure and biomass of mangrove species using terrestrial LiDAR data, and the application in extending biomass allometrice
2.2.1 Study area
2.2.2 Essential features of Avicennia germinans (L.) L.
2.2.3 TLS measurements and data processing
2.2.4 Computation of the trunk and branch volumes
2.2.5 Biomass estimation from TLS-derived wood volume
2.2.6 Fitting of allometric models using TLS-derived biomass data
2.3.1 Accuracy of pixel-based trunk volume estimation from TLS data
2.3.2 Accuracy of TLS-based tree volume-to-biomass conversion
2.3.3 Aboveground woody biomass of large A. germinans trees
2.3.4 Revised allometric models of A. germinans trees
2.4.1 Accuracy of the TLS-derived mangrove tree biomass
2.4.2 Modelling mangrove tree biomass with TLS-derived data
2.4.3 Challenges affecting the wider application of TLS in mangrove studies
3 Collective plastic tree attributes explain the dynamics of aboveground biomass in contrasting Amazon-influenced mangrove forests
3.2 Materials and methods
3.2.1 Study locations
3.2.2 The datasets
3.2.3 Data analyses and statistics
3.3.1 Regional differences in tree morphological allometries
3.3.2 Morphological plasticity and aboveground biomass allometry
3.3.3 Dynamics of stand aboveground biomass in divergent mangrove forests
4 Lollymangrove software: A standardized tool for data acquisition and 3D description of mangrove forest structure
4.2 Background and fundamentals
4.2.1 Sampling designs for characterizing mangrove forest structure
4.2.2 Tree and biomass allometric models
4.3 Description of the software package
4.3.1 Input module
4.3.2 Processing module
4.3.3 Visualization module
4.3.4 Output module
4.4 Example applications in South America
4.5 Coupling with ecological and remote-sensing models
4.6 Conclusion and perspectives
5 Simulating the influence of plastic tree morphology and biomass partitioning on the structural development of mangrove forests
5.2.1 Model description
5.2.2 Simulation settings
5.2.3 Benchmarks for model evaluation
5.2.4 Data analyses and statistics
5.3.1 Model evaluation
5.3.2 Example model application: relating tree biomass to crown structure
6 Concluding discussion
6.1 Main contributions
6.1.1 Morphological plasticity and allometric analyses at the tree scale
6.1.2 Relating morphological plasticity to the structural dynamics of forest stands
6.1.3 Predicting morphological plasticity and stand dynamics in changing environments
6.2 Methodological issues and perspectives
6.3 Towards an integrative modelling framework for mangrove dynamics
Résume Etendu (Extended summary in French)
Declaration of Independent Work