Pantropical variability in tree crown allometry

Aim: Tree crowns determine light interception, carbon and water exchange. Thus, understanding the factors causing tree crown allometry to vary at the tree and stand level matters greatly for the development of future vegetation modelling and for the calibration of remote sensing products. Nevertheless, we know little about large-scale variation and determinants in tropical tree crown allometry. In this study, we explored the continental variation in scaling exponents of site-specific crown allometry and assessed their relationships with environmental and stand-level variables in the tropics.


| INTRODUC TI ON
Tree crowns form the interface between the terrestrial biosphere and the atmosphere and determine light interception and gas exchange of carbon and water through photosynthesis and evapotranspiration (Santiago et al., 2004;Strigul et al., 2008). As a result, tree crowns not only influence the growth, mortality and fecundity of individual trees (Pacala et al., 1996), but they also shape the local light environment, microclimate and biogeochemical fluxes of ecosystems (Montgomery & Chazdon, 2001). Characterizing tree crowns is of increasing importance for remote sensing methods, a crucial suite of tools to improve the monitoring of terrestrial ecosystems . Nowhere is this more urgent than in tropical forests and savannas, which store 40-50% of the global vegetation carbon (Pan et al., 2011). For instance, taking into account crown dimensions in tropical forests can substantially improve estimation of tree biomass at the tree scale (Goodman et al., 2014;Ploton et al., 2016) and explain plot-scale spatial variation in biomass and carbon stocks Meyer et al., 2018). However, ground measurements of tree crowns are challenging and time consuming; therefore, they are available for only few sites and trees within inventory plots.
Tree crown allometry, which describes scaling relationships between the crown dimensions (crown area, crown depth and crown volume) and more easily measurable variables, such as stem diameter, is widely used in plant ecology to quantify ecosystem functions. For a wide range of plants, the power-law model has been used to describe plant allometry between two tree dimensions (Niklas, 1994), and there has been much debate about the meaning of the power-law scaling exponents for tropical trees (Sileshi, 2014).
For example, the scaling exponent from tree height-stem diameter and crown dimensions-stem diameter allometric relationships reveals mechanical constraints that prevent trees from buckling under their own weight (Greenhill, 1881;McMahon, 1971) and/or hydraulic constraints (Ryan et al., 2006). In the tropics, scaling exponents from crown allometric relationships have been shown to vary between forests and savannas, with savanna tree crowns tending to be larger for a given stem diameter than those of forest trees at the Location: Global tropics.
Time period: Early 21st century.

Major taxa studied: Woody plants.
Methods: Using a dataset of 87,737 trees distributed among 245 forest and savanna sites across the tropics, we fitted site-specific allometric relationships between crown dimensions (crown depth, diameter and volume) and stem diameter using power-law models. Stand-level and environmental drivers of crown allometric relationships were assessed at pantropical and continental scales.

Results:
The scaling exponents of allometric relationships between stem diameter and crown dimensions were higher in savannas than in forests. We identified that continental crown models were better than pantropical crown models and that continental differences in crown allometric relationships were driven by both stand-level (wood density) and environmental (precipitation, cation exchange capacity and soil texture) variables for both tropical biomes. For a given diameter, forest trees from Asia and savanna trees from Australia had smaller crown dimensions than trees in Africa and America, with crown volumes for some Asian forest trees being smaller than those of trees in African forests.

Main conclusions:
Our results provide new insight into geographical variability, with large continental differences in tropical tree crown allometry that were driven by stand-level and environmental variables. They have implications for the assessment of ecosystem function and for the monitoring of woody biomass by remote sensing techniques in the global tropics.

K E Y W O R D S
crown allometry, environment, forest, precipitation, savanna, soil, stand-level variable, tropical biomes species scale (Archibald & Bond, 2003) and the site scale (Shenkin et al., 2020). However, the scaling exponents of crown allometric relationships do not change when comparing three neighbouring forest typologies (mixed forests, edge forests and regrowth forests) that have different light availability .
Previous studies showed variation in crown allometry among tropical sites or regions (Blanchard et al., 2016;Moncrieff et al., 2014;Shenkin et al., 2020). At a large scale, environmental variables are important in explaining differences in crown allometry among sites or regions in tropical biomes.
For a given stem diameter, longer dry seasons appear to induce narrower crowns in the forest biome (Barbier et al., 2010) and in the savanna biome (Moncrieff et al., 2014). Likewise, mean annual temperatures were negatively related to crown diameters of trees at 20 cm stem diameter in savannas (Moncrieff et al., 2014) but no consistent pattern in species crown diameters was reported in Mediterranean forests for a range of mean annual temperatures varying from c. 6 to 17°C (Lines et al., 2012) at a given stem diameter.
Soil physical and/or chemical properties might also affect variation in crown dimensions. For example, high rainfall regimens combined with poor drainage have been found to favour small crown dimensions in certain regions of the Amazon Basin (Barbier et al., 2010).
Likewise, trees in sites with high sand content tended to have small crown diameters at 20 cm stem diameter in African and Australian savannas (Moncrieff et al., 2014).
Interspecific relationships with wood density in crown allometric relationships can also reflect environmental filtering, because species with high wood density are more likely to be found in highly shaded environments (Wright et al., 2010) and on soils with lower fertility (Muller-Landau, 2004;Quesada et al., 2012). At a given tree height, species with high wood density show wider and deeper crowns than species with low wood density . However, increased competition between individual trees has a negative influence on crown width Lines et al., 2012) and a positive influence on crown depth . All else being equal, narrower crowns in savannas have been associated with higher tree densities (Moncrieff et al., 2014).
In the tropics, there have been only three studies in the whole tropics to assess tree crown allometric relationships and their drivers at a large scale (Blanchard et al., 2016;Moncrieff et al., 2014;Shenkin et al., 2020), and none has yet evaluated such relationships at the pantropical scale. Nevertheless, understanding the exact nature of crown allometry and the factors causing tree crown allometry to vary at the tree or stand level matters greatly for the development of future vegetation modelling and for the calibration of remote sensing products.
The aim of this study was to identify the determinants of crown allometry in tropical biomes by fitting site-specific crown allometric relationships between crown dimensions and stem diameter using power-law models and assessing their statistical associations with stand-level and environmental variables and their fit to theoretical predictions. We addressed two research questions. First, do scaling exponents derived from crown allometric relationships differ among tropical forests and savannas? We expect that scaling exponents from crown allometric relationships are smaller for trees in forest than in savanna at continental scale. Second, how do stand-level and environmental variables influence crown allometric relationships at pantropical and continental scales? We expect that there are continental differences in crown allometry after accounting for stand-level and environmental variables, as reported by Feldpausch et al. (2011) and Banin et al. (2012) for tree height allometries. We tested these hypotheses by assembling the largest pantropical dataset compiled to date of ground-acquired, geographically dispersed information on tree crown dimensions (crown depth, diameter and volume) from 205 forest and 40 savanna sites, totalling 87,737 trees in Africa, America, Asia and Australia ( Figure 1).

| Data collection
We assembled information on tree crown dimensions available from published and unpublished sources for the two major tropical biomes: forest and savanna (for data sources, see the Appendix Table A1). We considered the limit between open-canopy (savanna) and closed-canopy (forest) systems as 50% of tree cover (Torello-Raventos et al., 2013;Veenendaal et al., 2015). For this pantropical analysis, we included sites that were unlogged areas and where ≥30 trees over a large range of stem diameter had crown dimensions measured for each site. A total of 245 sites, including 205 forest sites and 40 savanna sites, were compiled across the tropics (within 23° north and south of the Equator) from Africa, America, Asia and Australia ( Figure 1). Within each site, most trees were identified to species, but unidentified trees were also kept in the database.
For each tree, we considered three crown dimensions, namely crown depth (C dep , in metres), crown diameter (C dia , in metres) and crown volume (C vol , in cubic metres), which were associated with stem diameter (D, in centimetres) measured at breast height (1.3 m) for regular stems or above the top of the buttresses for irregular stems. The C dep was defined as the depth of the crown, calculated as the difference between total tree height (H, in metres) and the bole height, defined as the height from the ground to the first living branch or to the lowest foliage (H f , in metres). Heights were measured for most trees using a trigonometric approach with either a manual clinometer or an electronic hypsometer. The C dia was the crown width or diameter for regular crowns, most often obtained from ground measurements of several crown radii (corresponding to the cardinal and inter-cardinal directions) that were averaged and multiplied by two. In a few sites, values of C dia were derived from manually delimited crowns on high-resolution aerial photographs. The C vol was calculated from crown depth and crown diameter, assuming an ellipsoid shape. For most crown data, the crown measurement protocols were standardized (Loubota Panzou & Feldpausch, 2020) with quality-controlled tropical crown data uploaded to ForestPlots.net , which includes major tropical plot networks, such as RAINFOR in Amazonia (Malhi et al., 2002;Quesada et al., 2012), AfriTRON in Africa , T-FORCES in South-East Asia (Qie et al., 2017) and TROBIT at the global interface of savanna and forest . The criteria for including individual crown measurements were as follows: (a) tree stems were not broken; and (b) height measurements for determining crown depth were measured using clinometers, laser rangefinders, laser hypsometers or directly by climbing. After screening for quality control, our dataset consisted of 87,737 trees, including 59,162 trees for C dep , 72,998 trees for C dia and 44,422 trees for C vol (Figure 1) over a large range of D, 0.22-293 cm in forests and 1-200 cm in savannas.

| Stand-level and environmental variables
For each site, the stand-level variables included stand structural variables, such as maximum height (H max , in metres) and wood density (⍴, in grams per cubic centimetre), also known as wood specific gravity (Supporting Information Table S1). These two stand-level variables depend on the subset of trees/species selected for allometry measurements and reflect the successional stage of the studied sites, where young regenerating stands in the wet tropics will have low H max and ⍴ relative to old-growth stands. The H max was calculated for each site as the 95th percentile total height of the sampled trees.
The ⍴ was estimated using species names that allow assignment of ⍴ corresponding to the species or genus average from the global wood density database Zanne et al., 2009). Site-level ⍴ means were weighted by the number of stems of each taxon.  The climate water deficit (C) and environmental stress factor (E) were obtained from the global gridded layer at 2.5 arc s resolution (http://chave.ups-tlse.fr/pantr opical_allom etry.htm). Two soil chemical properties [pH in water (pH) and cation exchange capacity (CEC)] and three soil physical properties [sand content (50-2,000 µm), silt content (2-50 µm) and clay content (0-2 µm) mass fraction] were extracted from the SOILGRIDS project (https://soilg rids.org/, licensed by ISRIC, World Soil Information), downloaded at 250 m resolution. We generated predictions at seven standard depths for all numerical soil properties: 0, 5, 15, 30, 60, 100 and 200 cm. Averages over (standard) depth intervals, 0-30 cm, were derived by taking a weighted average of the predictions within the depth interval using the method developed by Hengl et al. (2017).
To avoid collinearity and reduce the number of environmental variables to test in our models, we retained only weakly correlated variables (|r| < .6) for modelling purposes. For the analyses, we re-  (Table S1).

| Data analysis
As a preliminary analysis, we ignored site-level differences and aggregated data for all sites within each continent according to three stem diameter (D) classes: the lower stratum with small trees (D ≤ 20 cm), the middle stratum with large trees, most of which reach the canopy (20 cm < D ≤ 40 cm), and the upper stratum corresponding to the largest trees, which are either in the canopy or emergent, with D > 40 cm. This distribution of three stem diameter classes has been used to take into account the variability in crown dimensions that can exist between different strata of the ecosystem, as shown by several studies on forest structure in the tropics (Bastin et al., 2018;Slik et al., 2013). Given the non-normality and skewed distributions of the data, we used the nonparametric Kruskal-Wallis rank sum test to evaluate differences in crown dimensions by continent according to stem diameter classes. For the nonparametric Kruskal-Wallis test (Hollander & Wolfe, 1973), the null hypothesis was "no difference between medians for each variable". When the null hypothesis was rejected, we conducted post hoc Kruskal-Wallis multiple comparisons between medians (Siegel & Castellan, 1988).
Crown allometric relationships were fitted between crown dimensions and stem diameter using power model (Y ∼ βD + e i ) which is linearized via the log 10 -transformation: where α and β are the scaling exponent (slope) and intercept, respectively, e is the error term, D is stem diameter, and y represents crown depth, crown diameter or crown volume of tree i.
To investigate variation in the scaling exponent among crown dimensions-stem diameter allometric relationships, we first estimated the model coefficients (intercept and slope) from crown allometric relationships for each site and the means across sites for each continent. Next, we used Student's unpaired t tests to compare the means of scaling exponents for crown allometric relationships at the continental level between the forest and savanna.
To examine how crown-stem diameter allometric relationships at the tree level were influenced by stand-level (H max and ⍴) and environmental variables (A, S, Q, U, CEC, pH, clay and silt), log-log regressions were used. In these regressions, log 10 -transformed crown dimensions (depth, diameter and volume) were the response variable and log 10 -transformed stem diameter was an independent variable.
These regressions were performed as mixed-effects linear models, where site (nested in geographical location) was incorporated as a random effect factor. The incorporation of appropriate random effects ensured that the model parameters were accurate and appropriate to generalize the conclusions (Bolker et al., 2009) (Burnham & Anderson, 2002). A pseudo-R-squared (R 2 ) for log-log mixed regressions was used to assess the quality of model fit. We report both the marginal R 2 (R 2 m ), which includes the variance of fixed factors, and the conditional R 2 (R 2 c ), which includes the variance of both the fixed and random factors and is, as a result, always higher (Nakagawa & Schielzeth, 2013).
All statistical analyses were computed using the open-source R environment (R Core Team, 2018), using the following packages: "lme4" for linear mixed regression (Bates et al., 2015); "MuMIn" for calculating pseudo-R-squared (R 2 ) values for linear mixed regression (Barton, 2019); PGIRMESS package for post hoc test (Giraudoux, 2013); and "ggplot2" for graphical outputs (Wickham, 2016). The conditions of normality and homoscedasticity of residuals were checked graphically and with Shapiro-Wilk and Breusch-Pagan tests, respectively. When these conditions were invalidated, a nonparametric test (Kruskal-Wallis rank sum test) was used to test the differences in crown dimensions. We chose nonparametric tests because most of the variables had skewed (1) log y i = β + α × log D i + e i distributions that would have required data transformations to meet the assumptions of parametric tests.

| Overview of the pantropical crown dimensions
Intercontinental differences in crown dimensions were visible through all three stem diameter classes (Figure 2). Following the stem diameter classes, the rank order of crown size for each continent was from largest to smallest for forest trees. The patterns were less clear for savanna trees. The differences of tree crowns between Africa and America were substantial but differed by biome.
African trees had larger median crown dimensions for forests, and American trees had the larger median crown dimensions for savannas. Interestingly, the differences between Africa and Australia in all crown dimensions could be observed solely in the smallest stem diameter class for forest trees, and for crown diameter in the highest stem diameter class for the savanna trees.

| Scaling exponent of crown allometry
Our pantropical analysis provided strong support for the hypothesis that the scaling of crown dimensions-stem diameter allometric relationships differed between trees in savanna compared with trees in forest at the continental scale (Figure 3). For all trees together in each biome, the mean scaling exponent of crown allometric relationships tended to be significantly higher in savanna than in forest (Table 1).

| Continental-stand-environment model
Crown dimensions-stem diameter allometric relationships including a continent effect had a slightly better fit to the data, based on F I G U R E 2 Distribution of crown depth, crown diameter and crown volume according to three stem diameter (D) classes: the lower stratum with small trees (D ≤ 20 cm), the middle stratum with large trees, most of which reach the canopy (20 cm < D ≤ 40 cm), and the upper stratum corresponding to the largest trees, which were either in the canopy or emergent, with D> 40 cm. Lines with median (filled circle) indicate upper and lower .05 quantiles for crown depth and crown diameter or .5 quantiles for crown volume. Different letters and numbers within each panel indicate significant differences (p < .05 with Kruskal-Wallis test) among continents for the forest and savanna biome, respectively AIC and BIC values, than the general pantropical models for four alternative log-log mixed regressions in both biomes (Table 2). At the continental scale, the goodness-of-fit (R 2 m and R 2 c ) of both biomes was high for four alternative log-log mixed regressions, with an average of R 2 m = .52 (range = .45-.59) and R 2 c = .61 (range = .56-.65) for crown depth-stem diameter allometric relationships, R 2 m = .55 (range = .38-.72) and R 2 c = .80 (range = .62-.99) for crown diameterstem diameter allometric relationships, and R 2 m = .55 (range = .31-.77) and R 2 c = .77 (range = .73-.80) for crown volume-stem diameter allometric relationships (Table 2). Among the four alternative log-log mixed regressions, we identified that continental models including both stand-level and environmental variables were the best models (Table 2), indicating that continental crown allometric relationships were influenced by both stand-level and environmental variables rather than by only one set of variables in both biomes.
The precipitation influenced the slope and the intercept of crown allometric relationships in both biomes (Supporting Information   Table S2). A higher scaling exponent from crown allometric relationships was related negatively to precipitation. The wind speed and solar radiation were also significant in crown allometric relationships in the forest biome. For the same stem diameter, trees with deeper and wider crowns were associated with higher wind speed and lower solar radiation in the forest biome. In addition, the soil chemical properties (CEC) and soil texture (silt and clay) showed contrasting influence on the slopes and intercepts of crown allometric relationships in both biomes (Supporting Information Table S2). For a given stem diameter, high CEC was associated with deeper and narrower crowns than low CEC. Crown depth was associated positively with clay and negatively with silt content, whereas the crown diameter and crown volume were associated negatively with clay and silt contents for the same stem diameter. Finally, the wood density was the main stand-level variable that influenced the crown depth-stem diameter allometry positively and the crown volume-stem diameter allometry negatively (Supporting Information Table S2).
When the same best crown dimensions-stem diameter allometric model, which includes environmental variables and stand-level variables, was applied to all continents (Table 3)

| D ISCUSS I ON
In this study, we found that stand-level (wood density) and environmental (precipitation, CEC and soil texture) variables explained the variation of crown dimensions-stem diameter allometric relationships within both tropical biomes. Crown allometric relationships differed between trees in savanna compared with trees in forest.
Scaling exponents for savanna trees tended to be much higher compared with that of forest trees. The comparison of models among continents highlighted that forest trees from Asia and savanna trees from Australia have smaller crown dimensions than trees in Africa and America. Our results provide new important insights into the geographical variability of tropical tree crown allometry, which will improve the assessment of woody biomass by remote sensing techniques in the tropics.

| Contrasting crown allometry between forest and savanna trees
The hypothesis of contrasting crown dimensions-stem diameter allometric relationships between the two major tropical biomes has been confirmed by this study, in agreement with the results of F I G U R E 3 Crown allometric relationships between stem diameter and: (a) crown depth; (b) crown diameter; and (c) crown volume, for each continent in the forest and savanna. Mean values of the model coefficients with 95% confidence intervals of the scaling exponent [Colour figure can be viewed at wileyonlinelibrary. com] TA B L E 1 Mean and 95% confidence interval [lower-upper] of scaling exponent with Student's unpaired t test (p-value) for the significant differences between forest and savanna for crown depth-stem diameter (C dep -D allometry), crown diameter-stem diameter (C dia -D allometry) and crown volume-stem diameter (C vol -D allometry) allometries  Individuals with smaller stem diameter have a higher vulnerability to vascular cambium and xylem damage from fire (Lawes et al., 2011;. Likewise, browsing pressure by large mammals that roam in savanna areas should be important, and might alter crowns of small trees. For instance, wider canopies in savanna might protect inner canopy leaves from herbivory by non-arboreal mammals (Archibald & Bond, 2003). In this study, we found smaller scaling exponent values for crown allometric relationships for forest trees. The scaling relationships between crown dimensions and stem TA B L E 2 Summary of statistical tests using mixed-effects models to determine the effects of structural and environmental (climate and soil) variables for crown depth-stem diameter (C dep -D allometry), crown diameter-stem diameter (C dia -D allometry) and crown volume-stem diameter (C vol -D allometry) allometries in the forest and savanna biomes

Note: Significant relationships are shown in bold. Common indices [Akaike information criterion (AIC) and Bayesian information criterion (BIC) values]
with marginal R 2 (R 2 m ) and conditional R 2 (R 2 c ) for four alternative log-log mixed regressions: a null model without fixed effects (simple); a model with stand-level variables (stand); a model with environmental variables (environment); and a model including stand-level and environmental variables (all), at pantropical and continental scales. diameter govern how forest trees utilize canopy space and compete for light (Farrior et al., 2016;Muller-Landau et al., 2006). Once trees are freed from competition for light in the understorey, the dramatic increase in light availability elicits a change in the pattern of resource allocation towards more investment in lateral crown expansion in the canopy and less investment in height growth (Alves & Santos, 2002;Barthélémy & Caraglio, 2007).

TA B L E 3
The fitted model has be written in terms of its fixed effects only, including (H max = maximum height; ⍴ = wood density,) and environmental (A = precipitation; CEC = cation exchange capacity; pH, silt and clay content; Q = solar radiation; S = precipitation seasonality; U = wind speed) variables for crown depth-stem diameter (C dep -D allometry), crown diameter-stem diameter (C dia -D allometry) and crown volume-stem diameter (C vol -D allometry) allometries in the forest and savanna biomes C dep -D allometry C dia -D allometry C vol -D allometry

Forest biome
Pantropical Continental log(  Table S1), with negative effects on crown allometric relationships (Supporting Information Table S2). These high average wind speeds are likely to perturb the display of individual leaves, branches and tree crowns, resulting in increased light availability. In addition, low solar radiation was associated with deeper and narrower crowns in the forest and wider crowns in the savanna (Supporting Information   Table S2). This could be explained by there being less lateral light availability owing to neighbouring canopies in forest compared with the more widely spaced canopies in savanna (Forrester et al., 2018).
Soil variables were also environmental determinants of crown allometry and explained continental differences in crown allometric relationships in tropical forests. In general, crown width and volume, but not crown depth, were negatively related to silt and clay content for forest trees. Forest sites on clay-rich soils had shallower and narrower crowns than trees growing on sandy soils. This indicates that water availability is a key factor, with drier, well-drained, coarse-textured soils supporting higher crown dimensions, as shown in the Amazon (Barbier et al., 2010).
Lastly, wood density had a significant influence in the forest crown allometric models. Forest trees with low wood density were able to increase crown depth substantially with stem diameter in tall canopy forest trees. Tall, mature forests usually consist of species with high wood density, with branches that persist for a longer time in deeper crowns because the leaves can be stacked in more layers (Slik, 2005).

| Continental differences in tropical crown allometry
Crown dimensions-stem diameter allometric relationships differed substantially across continents for the two tropical biomes, but these differences were better explained by the differing stand-level and environmental variables found on each continent than by biogeography. This indicates that crown dimensions could be predicted with some certainty for tropical areas, even those with access limitations, based solely on environmental data that are available from global databases, rather than stand-level variables.  et al., 2006). In contrast, there is a unique phytogeographical affinity between African and American forests that is likely to be attributable to the dominance of a particular lineage, the Fabaceae, the most basal members of the legume family, and with similar dominances of the same or closely related genera (LaFrankie, 2005). This might explain the similarity in crown allometric relationships between Africa and America. These intercontinental differences in composition and traits of the different forest strata remain to be explored further.

| Conclusions
Based on a large dataset of tree crown dimensions available from published and unpublished sources of tropical plot data, this study advances the understanding of large-scale variation and determinants in tropical tree crown allometry. By analysing variation in crown dimensions-stem diameter allometric relationships across the global tropics and by accounting for their drivers, we found a general pattern for significantly smaller scaling exponents in crown allometric relationships in forests than in savannas. Our results highlight a significant role of environmental factors, including precipitation, wind speed and soil texture, in explaining intercontinental differences in the crown allometric relationships of tropical trees. These findings provide important insights, both for the development of future vegetation modelling (e.g., to understand competition for light and its impacts on tree and forest structure) and for the calibration of remote sensing products (e.g., estimating crown attributes and the biomass of trees observed from air or from space). This worldwide analysis of tropical tree crowns should therefore contribute to improving both the modelling and the assessment of tropical canopy and ecosystem function.

ACK N OWLED G M ENTS
This work is the product of a postdoctoral project (G.J.L.P.) funded by Wallonia-Brussels-International (WBI). We thank Dr Andrew Kerkhoff and two anonymous reviewers for their insightful comments on an earlier version of this manuscript. The major portion of the tree crown data was collected with the support of NERC, in-