The global spectrum of tree crown architecture

Domain: earth_science
Published: 2025-05-26
Editorial outcome: minor_revision

Abstract
Trees can differ enormously in their crown architectural traits, such as the scaling relationships between tree height, crown width and stem diameter. Yet despite the importance of crown architecture in shaping the structure and function of terrestrial ecosystems, we lack a complete picture of what drives this incredible diversity in crown shapes. Using data from 374,888 globally distributed trees, we explore how climate, disturbance, competition, functional traits, and evolutionary history constrain the height and crown width scaling relationships of 1914 tree species. We find that variation in height–diameter scaling relationships is primarily controlled by water availability and light competition. Conversely, crown width is predominantly shaped by exposure to wind and fire, while also covarying with functional traits related to mechanical stability and photosynthesis. Additionally, we identify several plant lineages with highly distinctive stem and crown forms, such as the exceedingly slender dipterocarps of Southeast Asia, or the extremely wide crowns of legume trees in African savannas. Our study charts the global spectrum of tree crown architecture and pinpoints the processes that shape the 3D structure of woody ecosystems.

Introduction
Trees come in all shapes and sizes – from incredibly tall and slender, to short with wide, flat crowns1–7. This incredible diversity in tree crown architecture plays an important role in driving variation in growth, water use and competition among tree species1,4,8–10. Moreover, tree crown architecture underpins key emergent properties of woody ecosystems, including their 3D canopy structure, aboveground biomass, primary productivity and hydrology8,11–16. Consequently, uncovering the environmental, ecological and evolutionary drivers that shape the crown architecture of the world’s trees is central to better understanding the processes that constrain the structure and function of woody ecosystems. It is also essential for developing more realistic representations of these ecosystems in vegetation models17–20 and bridging the gap between field and remote sensing observations21–24 – both of which are needed to track how terrestrial ecosystems are responding to rapid global change.

Differences in crown architecture among trees are the result of species employing a variety of strategies to meet a series of competing physiological, structural, competitive, defensive and reproductive demands (Table 1). Trees expand their crowns vertically and laterally to intercept light, compete with neighbours and disperse seeds, while also needing to maintain water transport to their leaves and mechanical stability4,6,7,10,25–32. The balance different trees species strike between these various priorities depends on their environment, ecological strategy and evolutionary history, and will be reflected in the scaling relationships between different axes of trees size, such as their height, crown width and stem diameter8,9,22,33–41. For instance, in arid climates woody biomass allocation tends to shift away from height growth and towards crown expansion to limit the risk of hydraulic failure and maximise energy capture, resulting in trees that are shorter for a given diameter and have wider crown profiles2,8,33,34,38,42–44. Conversely, when water and nutrients are non-limiting to photosynthesis, strong competition for light leads to greater investment in height growth and relative allocation of carbon to woody tissues44, pushing trees closer to their structural and hydraulic safety margins7,8,16,26,27,32,33. Similarly, tree species have also adapted the size and shape of their crowns to minimise the risk of damage from wind, fire, snow and browsing40,45–50. Yet despite clear evidence that crown allometric scaling relationships can vary considerably among tree species, we lack a unified picture of how and why they do so. Nor do we understand how different axes of crown size and shape covary with one another, how they relate to other key plant functional traits, or how they vary among plant lineages.

Here, we assemble a global dataset capturing information on the stem diameter (D), height (H), crown diameter (CD) and crown aspect ratio (CAR, defined as CD/H) for over half a million trees (Fig. 1). Using these data, we develop an approach for modelling variation in H–D, CD–D and CAR–D scaling relationships among species that allows us to compare their crown sizes and shapes while explicitly controlling for differences in their stem sizes. We apply this method to 1914 well-sampled tree species that span all major woody biomes and clades and use it to: (1) characterise the full spectrum of crown architectural types observed across the world’s tree species and biomes; (2) explore whether crown architectural traits are phylogenetically constrained and identify which clades have crown sizes and shapes that are particularly extreme; and (3) test a series of predictions about how H–D, CD–D and CAR–D scaling relationships vary in relation to climate, competition, disturbance and other functional traits related to plant metabolism, hydraulics, structural stability and dispersal (Table 1). We show that tree species span a broad range of crown architectural types, encompassing everything from slender to stout stems and narrow to broad crowns. Variation in H–D scaling relationships is primarily controlled by water availability and light competition, with tropical forests in Southeast Asia home to disproportionately high concentrations of species with tall, slender growth forms. Conversely, crown width is predominantly shaped by exposure to wind and fire, with legume trees in African savannas achieving some of the widest crowns for their stem diameters.

Results
Global variation in crown architectural types
We used data from 374,888 individual trees to generate size-standardised estimates of H, CD and CAR for 1914 well-sampled species using two complimentary statistical approaches (see Methods for details). The first involved using linear mixed effects models to estimate the height, crown diameter and crown aspect ratio of each species for a tree with a stem diameter of 30 cm (hereafter H_D=30, CD_D=30 and CAR_D=30). The second approach is conceptually and quantitatively similar to the first, but avoids the need to choose an arbitrary stem size at which to compare species (Supplementary Fig. 1). It uses the residuals of a linear regression model to determine if a species has H, CD and CAR values that are – on average – larger (positive residuals) or smaller (negative residuals) than expected for their range of stem sizes (hereafter H_RESID, CD_RESID and CAR_RESID; see Fig. 1e–g for a graphical representation of the method).

Acrossthe 1914 tree species considered in our analysis, we found enormous variation in size-standardized estimates of tree height, crown diameter and crown aspect ratio (Fig. 2). Specifically, H_D=30 varied 12.1-fold across species, ranging from <4 m in species like Juniperus osteosperma and Maerua crassifolia to >30 m in several species of the genera Shorea, Parashorea, Hopea and Vatica (all Dipterocarpaceae) and as much as 43.2 m in Eucalyptus regnans. By contrast, CD_D=30 was less than half as variable among species, ranging 5.4-fold from <4 m in several species of the genus Picea to >14 m in ones like Brachystegia wangermeeana and Pterocarpus tinctorius in the Fabaceae. As for crown profile shape, CAR_D=30 ranged 10.5-fold across species. At one end of the spectrum, species like Abies sibirica and Vatica dulitensis were more than five times as tall as their crowns are wide (CAR_D=30 <0.2), whilst several species of the genera Acacia, Vachellia and Senegalia (all Fabaceae) had crowns that are noticeably wider than they are tall (CAR_D=30 >1.2).

For the 1309 species for which we were able to estimate both H_RESID and CD_RESID, we found that these two axes of crown architecture were positively correlated with one another (Pearson correlation coefficient, ρ=0.26, P<0.001). However, despite a general trend of taller trees also having wider crowns, the relationship between H_RESID and CD_RESID was relatively weak. Species occupied all possible combinations of the tree height vs crown diameter spectrum (Fig. 2a), including short and narrow (9.3% of species), short and wide (5.4%), tall and wide (7.9%), and tall and narrow (1.0%).

Where species fell within this spectrum depended, at least in part, on their biome association (Fig. 2b). For example, a high proportion of species found in drylands, temperate woodlands, tropical savannas and tropical dry forests had either short and/or wide crowns (59.6–100% of species, depending on the biome), but almost none were tall (0–8.8%). By contrast, boreal, temperate and tropical rainforests had a considerably higher proportion of species with tall and/or narrow crowns (28.0–60.5%). Overall, differences among biomes were more pronounced for height and crown aspect ratio than for crown width, with biome association explaining 33%, 39% and 5% of the variation in H_RESID, CAR_RESID, and CD_RESID among species, respectively (see Supplementary Table 4 for pairwise comparisons among biomes based on ANOVAs). However, our results also revealed considerable variation in tree architectural types within biomes (Fig. 2b), highlighting how tree species with very different crown architectures can be found in similar environments.

Fingerprint of evolution history on crown architecture
From a macroevolutionary perspective, angiosperms and gymnosperms had very similar mean values of H_D=30 (17.8 m and 17.3 m, respectively). However, angiosperms spanned a considerably larger range of heights (3.9–42.3 m), particularly at the tall end of the spectrum, where they included 99 of the 100 species with the highest H_D=30 values. By contrast, both crown diameter and aspect ratio were noticeably larger in angiosperms compared to gymnosperms (CD_D=30 = 6.4 m vs 5.3 m; CAR_D=30 = 0.43 vs 0.36). When we placed estimates of H_RESID, CD_RESID, and CAR_RESID onto a time-calibrated phylogeny of seed plants, we found that all three exhibited a significant degree of phylogenetic signal (Fig. 3), with Pagel’s λ values of 0.70, 0.54, and 0.63, respectively (P<0.001 in all cases).

In particular, we found several plant genera and families that standout based on their tree height, crown size, and shape (Fig. 3 and Supplementary Tables 5–6). For tree height, 25 out of 63 families and 31 out of 86 genera that we tested had mean H_RESID values that were significantly different from zero. For angiosperms, species in the Dipterocarpaceae (H_D=30 = 24.1 m), Myristicaceae (H_D=30 = 24.4 m), Burseraceae (H_D=30 = 21.3 m), Annonaceae (H_D=30 = 21.3 m) and Betulaceae (H_D=30 = 19.6 m) were particularly tall for their stem diameters (Fig. 3a). From a biogeographic standpoint, we found that Southeast Asia was home to an especially high concentration of species with tall and slender growth forms, with nine of the 10 species with the highest H_RESID values native to this region, including species in the genera Shorea, Parashorea and Vatica (Dipterocarpaceae) and Knema (Myristicaceae). At the opposite end of the spectrum, species in the Ericaceae (H_D=30 = 11.4 m), Combretaceae (H_D=30 = 13.3 m), Fagaceae (H_D=30 = 15.1 m) and Fabaceae (H_D=30 = 16.2 m) were significantly shorter than average for a given stem diameter.

The picture within gymnosperms was equally varied. Cupressaceae were generally shorter than expected (H_D=30 = 14.8 m), despite including species like Sequoia sempervirens which can grow incredibly tall in absolute terms. Conversely, within the Pinaceae we found a clear divide between species in the genus Pinus which are shorter than average (H_D=30 = 16.2 m) and those belonging to Larix and Picea that are taller (H_D=30 = 22.2 m and 20.6 m, respectively).

In terms of crown size and shape, we found that 21/56 families and 26/60 genera (CD_RESID) and 12/56 families and 16/60 genera (CAR_RESID) had values that departed significantly from zero (Supplementary Tables 5–6). One clade that stood out in particular is the Fabaceae (Fig. 3b, c). Of the top 10 species with the highest CD_RESID and CAR_RESID values, four and six were Fabaceae, respectively. Fabaceae had crowns that are both much wider than average (CD_D=30 = 7.6 m) and more horizontal in their aspect ratio (CAR_D=30 = 0.58). This trend was predominantly driven by species that occupy savannas in Africa and the Americas, including ones in the genera Senegalia, Acacia, Brachystegia, Vachellia and Pterocarpus (mean CD_D=30 and CAR_D=30 across 40 tropical savanna specialists = 8.6 m and 0.88, respectively). By contrast, Fabaceae from tropical rainforests (CD_D=30 = 7.2 m; CD_D=30 = 0.39) and temperate forests (CD_D=30 = 6.5 m; CD_D=30 = 0.37) had crown sizes and profiles that were very similar to other species in these biomes.

Within gymnosperms, species in the Podocarpaceae (CD_D=30 = 5.2 m), Cupressaceae (CD_D=30 = 5.3 m) and Pinaceae (CD_D=30 = 5.3 m) all exhibited narrower than average crowns (Fig. 3b). In the Pinaceae this effect was far stronger than any variation observed in tree height, resulting in crown aspect ratios that are also much smaller than average (CAR_D=30 = 0.34; Fig. 3c). A similar trend emerged for the Rubiaceae and Lauraceae, where species were generally both tall and with narrow crowns, resulting in low crown aspect ratios (CAR_D=30 = 0.35 and 0.37, respectively). The exact opposite was true for species in the Combretaceae, Ulmaceae and Fagaceae, which, due to their relatively short stature and wide crowns had particularly large crown aspect ratios (CAR_D=30 = 0.73, 0.55, and 0.48, respectively).

Drivers crown architectural variation in the world’s trees
Phylogenetic generalised least squares models relating variation in tree crown architecture among species to climate, tree cover, disturbance, and functional traits explained 55%, 28% and 34% of the variation in H_RESID, CD_RESID and CAR_RESID, respectively (Fig. 4). Differences in height among species were predominantly controlled by water availability (aridity, and to a lesser extent rainfall seasonality) and tree cover (Fig. 4a), with H_RESID decreasing rapidly with rising aridity and increasing steadily as tree cover increased (Fig. 5a, b). On average, species growing where potential evapotranspiration was equal to or less than mean annual precipitation (aridity index ≤ 1) were almost twice as tall for a given stem diameter (H_D=30 = 20.1 m) as those where the aridity index was ≥ 2 (H_D=30 = 11.1 m). Similarly, H_D=30 increased from 11.5 m to 21.4 m when comparing species growing where tree cover was ≤ 20% and ≥ 80% (Fig. 5a). However, we also found that when water was non-limiting (aridity index ≤ 1), trees could vary hugely in their investment in height growth, with H_D=30 ranging anywhere between 6.4 m and 43.2 m (Fig. 5b). In contrast to aridity and tree cover, we only observed a modest positive association between H_RESID and mean annual temperature (MAT). Temperature did however indirectly influence H_RESID through its interaction with aridity (Supplementary Fig. 6). Specifically, we found that H_RESID declines with increasing aridity was much less pronounced for trees growing in cold climates (MAT < 10 °C) compared to warm ones (MAT > 20 °C).

Water availability and tree cover also emerged as significant predictors of CD_RESID, with species generally having narrower crowns in more arid and seasonal climates, and where tree cover was higher (Fig. 4b). But these effects were much less pronounced than for tree height (Fig. 5d, e). Consequently, we found that variation in CAR_RESID along aridity and tree cover gradients was mostly driven by changes in H_RESID, with crown profiles becoming markedly more vertical as aridity decreased and tree cover increased (Figs. 4c, 5g, h). For example, the average CAR_D=30 of species growing where tree cover was ≤ 20% (0.77) was more than twice that of those where tree cover was ≥ 80% (0.36).

Conversely, crown diameter was much more strongly influenced by disturbances such as wind and fire (Fig. 4b). In particular, CD_RESID decreased markedly as maximum wind gust speeds increased (Fig. 5f). Species also tended to be shorter for a given stem diameter where wind speeds were higher (Fig. 5c), but this effect was more subtle than for crown diameter, meaning that overall crown profiles became significantly narrower as wind speeds increased (Fig. 5i). By contrast, areas with higher frequencies of wildfires harboured species with wider crowns and higher crown aspect ratios (Fig. 4b, c), but with similar H_RESID values.

While variation in H_RESID, CD_RESID, and CAR_RESID among tree species was predominantly associated with climate, tree cover and risk of disturbance, we also found that these crown architectural traits covaried with other plant functional traits (Fig. 4). After accounting for environmental effects, we found that both H_RESID and CD_RESID were significantly greater in species with higher leaf nitrogen content, with H_RESID also positively correlated to specific leaf area. Additionally, while we observed no clear relationships between H_RESID and wood density, we did find that species with wider crowns and more horizontal crown profiles had denser wood. By contrast, none of the three crown architectural traits exhibited any relationship with seed mass.

Methods
Individual tree height and crown size data
We compiled 528,311 georeferenced records of individual trees for which stem diameter (D, cm), height (H, m) and/or crown diameter (CD, m) were measured (Fig. 1a). For trees where both H and CD were measured (n=340,221; 64.4%), we also calculated their crown aspect ratio (CAR) as CD/H, where CAR<1 denotes a vertical crown profile and CAR>1 a flat or horizontal profile1,86. These data were obtained from 62,435 globally distributed sites which encompass all major terrestrial biomes and span a gradient in mean annual temperature of −15.1–30.1 °C and 143–7157 mm yr-1 in rainfall. Sampled trees span multiple orders of magnitude in size and crown shape (Fig. 1b–d) and represent 5161 tree species from 1451 genera and 187 plant families. Most of the data (94.4% of records) were sourced from the Tallo database2. Additionally, we also obtained data from Alberta’s Permanent Sample Plots network in Canada (n=12,171 trees) and the ICP Forests network in Europe (n=17,540 trees). Allometric data were quality controlled following the protocols of the Tallo database2. Briefly, we first used Mahalanobis distance to identify and remove possible data entry errors by screening for trees with unrealistically large or small H and CD values for a given stem diameter. Species names were then standardized against those of The Plant List (TPL) using the taxonstand package87 in R (version 4.2.2)88. Lastly, we excluded records from species that did not meet our working definition of trees: perennial woody seed plants with a single dominant stem that are self-supporting and undergo secondary growth (i.e., excluding ferns, palms, short multi-stemmed shrubs, and lianas).

Species level, size-standardized estimates of tree height, crown diameter, and crown aspect ratio
Tree species can differ considerably in their maximum size and developmental strategies, so to directly compare their crown architecture, we used two complimentary approaches to generate size-standardized estimates of H, CD, and CAR at the species level. For these and all subsequent analyses, we focused on species with at least 10 trees sampled within the same biome and spanning a minimum D range of 20 cm between the smallest and largest measured tree (see Environmental data for details on how trees were assigned to biomes). In total, 1914 species represented by 374,888 individual trees met these criteria for at least one of the three axes of crown size and shape and 1309 species represented by 251,733 trees had sufficient data for all three (1910 species for H, 1313 for CD and 1309 for CAR; see Supplementary Table 1 for details). These 1914 species cover 755 genera and 131 plant families.

The first approach to comparing species’ crown architectures involved generating estimates of H, CD, and CAR for a tree of fixed size (D=30 cm) for each species33,52. To do this, we modelled variation in H, CD and CAR among individual trees as a power-law function of D by fitting linear mixed-effects regressions to log-log transformed data8,33,34:

log(Y) = α_f=g=s + β_f=g=s log(D) (1)

where Y denotes either H, CD or CAR, α is the intercept (or normalization constant) and β is the slope (or scaling exponent). Models were fit using the lme4 package89 and both the intercept and slope of the regressions were allowed to vary among tree species, genera, and families with a nested random effects structure (denoted by the f/g/s subscripts in the equation above). R2 values accounting for both fixed and random effects components of the models were 0.82, 0.74, and 0.45 for H, CD, and CAR, respectively90. The fitted models were then used to predict H, CD, and CAR for each species, assuming a fixed stem size of 30 cm (hereafter H_D=30, CD_D=30 and CAR_D=30). Models were fit using least squares regression (as opposed to approaches such as major axis regression) as we were not interested in comparing scaling coefficients among species, but in using the fitted models to generate predictions91. For the H–D model, we compared the power-law with a saturating Michaelis-Menten function, as previous work has suggested that the latter might fit the data better37. We found that both approaches yielded very similar estimates of H_D=30 (ρ=0.93), but that overall the power-law provided a better fit to the data (Supplementary Fig. 2).

The second approach we developed to capture variation in crown architecture among species is conceptually similar to the first, but avoids the need to choose an arbitrary stem size at which to compare species8. As for the previous method, we began by using the tree-level data to model variation in H, CD and CAR as a power-law function of D. However, in this case we explicitly ignored differences among species and simply estimated the overall scaling relationships between H–D, CD–D and CAR–D across the whole dataset by fitting ordinary linear regressions to log-log transformed data. Using the residuals of the models (i.e., the difference between observed and predicted values of H, CD and CAR on a log-log scale), we then determined post hoc whether a given species has H, CD and CAR values that are – on average – larger (positive residuals) or smaller (negative residuals) than expected after accounting for differences in stem size between trees (see Fig. 1e–g for a graphical representation of this approach). Because sample sizes varied considerably among species (n=10–22,835 trees per species), we subset the data by randomly selecting 10 trees per species prior to model fitting. Without this step, well-sampled species would dominate the signal of the regression and skew the values of the residuals. This randomization step was repeated 100 times, and for each species we then calculated the mean value of the residuals across all model runs as a measure of size-standardized H, CD, and CAR (hereafter H_RESID, CD_RESID and CAR_RESID).

Quantitatively, the two approaches gave very similar results (Supplementary Fig. 1). However, the second method based on model residuals is better suited to comparing species that exhibit contrasting growth trajectories or vary in their size at maturity, as it integrates data across all observed tree sizes instead of focusing on a single point of comparison (e.g., D=30 cm, which could correspond to a small tree for some species and a very large one for others). For subsequent analyses, we therefore focus on comparing values of H_RESID, CD_RESID and CAR_RESID across species, but to aid the interpretation of results, we also report values of H_D=30, CD_D=30 and CAR_D=30. Note that both of these approaches overlook plasticity in allometric scaling relationships within species. This is partly because previous work based on the Tallo database has shown that allometric variation along environmental gradients is twice as pronounced among species as it is within them2 – prompting us to focus on identifying drivers of species-level differences in crown architecture. But it also reflects the fact that for many species in our analysis we have insufficient data to appropriately model intraspecific variability (314 species were measured at a single site and <20% were sampled widely enough to characterise their architectural plasticity along environmental gradients2).

Environmental data
To understand how environmental conditions shape variation in H_RESID, CD_RESID and CAR_RESID among tree species, we used the geographic coordinates of individual trees to assign attributes related to climate, competition, and disturbance (see Supplementary Table 2 for full details on sources of environmental data). These environmental predictors were chosen based on previous work suggesting they play an important role in shaping tree crown allometry by constraining plant hydraulics, growth and competition (Table 1). Importantly, they were also selected as they were not strongly correlated with one another (Supplementary Fig. 3), allowing their effects to be teased apart in subsequent analyses. In addition to the environmental predictors described below, trees were also assigned to one of seven biome classes based on the classification used by the Terrestrial Ecoregions of the World database92.

For climate, we focused on the effects of mean annual temperature (MAT, °C), precipitation seasonality (mm,) and aridity (unitless index). MAT and precipitation seasonality were obtained from the WorldClim2 database at a resolution of 30 arc-seconds93. Aridity was instead calculated as the ratio between potential evapotranspiration (PET, mm) and mean annual precipitation (MAP, mm), where MAP was obtained from WorldClim2 while PET was derived from the Global Aridity Index and Potential Evapotranspiration Climate Database at 30 arc-second resolution94. This is the inverse of how aridity is often expressed94, but has the advantage of being easier to interpret as larger values of the aridity index correspond to drier conditions95.

As a proxy for local competitive environment, we used estimates of tree cover derived from MODIS at 15-arcsecond resolution for the year 200896, which broadly overlaps with the period when the majority of the allometric data were collected. We chose this approach as for most trees we lacked information on stand-level attributes commonly used to characterise competition, such as basal area or stem density16,33. However, for a subset of sites across which these field data were available, we found good agreement between MODIS-derived estimates of tree cover and stand basal area (Supplementary Fig. 4), suggesting satellite estimates of tree cover provide a reliable indicator of competitive environment.

As indicators of disturbance, we focused on wind speed and fire risk. Specifically, we used the ERA5-Land data to calculate the maximum wind gust speed experienced by each tree between 2010–2020. To quantify exposure to fire, we calculated the mean burned area fraction between 2001–2010, as estimated from MODIS in the Global Fire Emissions Database97. Note that we also tried to assess the impacts of snow accumulation on tree crowns, but found that estimates of snow cover duration derived from MODIS were strongly correlated with MAT (ρ=−0.80; Supplementary Fig. 3), and were therefore not considered in subsequent analyses.

For each of the 1914 species that met the minimum sampling criteria described previously, we then calculated mean values of aridity, MAT, precipitation seasonality, tree cover, maximum wind gust speed and burned area fraction across all sampled trees. Each species was also assigned to a unique biome based on the terrestrial ecoregion in which they were recorded most frequently98.

Functional trait data
To test how variation in H_RESID, CD_RESID and CAR_RESID among tree species relates to other key plant functional traits, we compiled data on wood density (g cm-3), leaf nitrogen content (mg g−1), specific leaf area (SLA, mm2 mg−1) and seed mass (g) from multiple sources (Supplementary Table 3). This includes the TRY plant trait database99, the Botanical Information and Ecology Network (BIEN) database100, the global wood density database101, the Royal Botanic Gardens Kew seed information database, the AusTraits database102, the China plant trait database103, the Terrestrial Ecosystem Research Network (TERN), as well as selected publications36,77,104–107. These four functional traits were chosen as previous work suggests they may covary with crown size and shape through their influence on whole-plant growth, size, hydraulics, and mechanical stability33,36,37,75,76,79 and have been measured for numerous tree species.

To obtain species-level mean values for each trait, we first grouped together individual records by site (based on shared geographic coordinates) and then species108. For species where no individual-level records could be sourced, species-level values reported in the literature were used instead if available. Of the 1914 tree species for which we estimated H_RESID, CD_RESID, and/or CAR_RESID, we obtained wood density estimates for 1572 species (82%), leaf nitrogen content for 1085 (57%), SLA for 1120 (59%), and seed mass for 1108 (58%).

Mapping the spectrum of crown architectural types and its distribution across woody biomes
To characterise the range of crown forms that tree species can assume and better understand how these vary among woody biomes, we used estimates of H_RESID, CD_RESID and CAR_RESID to determine how species cluster into architectural types based on their height, crown size, and shape1. To do this, we first calculated the correlation between H_RESID and CD_RESID to determine how tightly constrained these two axes of crown architecture are across the 1309 species where both had been measured. A strong positive correlation would indicate that species that are taller for a given stem diameter also tend to have larger crowns and vice versa. Conversely, a weak correlation between H_RESID and CD_RESID would suggest that when standardized by size, tree species are able to adopt a wide range of crown architectural forms, from tall and narrow to short and wide.

We then grouped species into one of nine crown architectural types: (1) short and narrow, (2) narrow, (3) tall and narrow, (4) short, (5) medium-sized, (6) tall, (7) short and wide, (8) wide, and (9) tall and wide species. Species were assigned to groups based on their H_RESID and CD_RESID values and whether these fell in the lower quartile, interquartile range, or upper quartile of data (see Fig. 2a for a visual representation). Note that CAR_RESID was not used to group species, as any differences in CAR_RESID among species can be directly attributed to ones in H_RESID and CD_RESID. To determine the degree to which crown forms are adapted and confined to specific environments, we quantified the relative frequency of each architectural type across different biomes. To support this analysis, we also used one-way ANOVAs to compare mean values of H_RESID, CD_RESID, and CAR_RESID among species from different biomes.

Evolutionary history and its fingerprint on crown architecture
To determine whether crown architectural traits exhibit phylogenetic signal, we mapped H_RESID, CD_RESID, and CAR_RESID onto the Smith & Brown (2018) phylogeny of seed plants and calculated Pagel’s λ as a general test of phylogenetic signal for each crown attribute109,110. A λ value of 0 indicates no phylogenetic signal, while a value of 1 corresponds to a trait that has evolved according to Brownian motion, indicating strong phylogenetic signal109. Pagel’s λ was calculated using the phytools package111, which uses a likelihood ratio test to determine whether λ is significantly different from 0. Because tests of phylogenetic signal are sensitive to errors in the phylogeny, such as those associated with branch lengths110, only species that were a direct match to those in the time-calibrated phylogeny were retained for subsequent analyses (1225 species for H_RESID, 870 for CD_RESID and 868 for CAR_RESID; Supplementary Table 1).

To complement λ – which provides a global test of phylogenetic signal across the entire phylogeny – we also explored how H_RESID, CD_RESID and CAR_RESID varied among clades within the phylogeny. Specifically, we used one-way ANOVAs fit without an intercept to identify families and genera where species’ mean H_RESID, CD_RESID and CAR_RESID values are significantly greater or smaller than zero. For this purpose, we only retained families and genera represented by at least five species in our dataset (n=63 families and 86 genera for H_RESID, and n=56 families and 60 genera for CD_RESID and CAR_RESID).

Effects of climate, competition, disturbance and functional traits on crown architecture
To quantify the effects of climate, competition, and disturbance on tree crown architecture, we modelled variation in H_RESID, CD_RESID and CAR_RESID among species as a function of aridity, MAT, precipitation seasonality, tree cover, maximum wind gust speed, and burned area fraction using multiple regression. Models also included an interaction term between aridity and MAT to test whether the effects of low water availability on tree height, crown size, and shape would be strongest in hotter environments65, as well as a binary variable testing for systematic differences in H_RESID, CD_RESID, and CAR_RESID between angiosperms and gymnosperms9,33,38.

To determine whether H_RESID, CD_RESID and CAR_RESID also vary in relation to species’ functional traits, we then fit separate models in which either wood density, leaf nitrogen content, SLA or seed mass was added to the multiple regression alongside the environmental predictors described above. Note that models including functional traits as predictors were restricted to the subset of species for which trait data were available (see Supplementary Table 1 for details).

Prior to model fitting, both aridity and seed mass were log-transformed to linearise relationships between response and predictor variables. All continuous predictor variables were then centred and scaled by subtracting the mean and dividing by 1 standard deviation, while the binary variable grouping species into major evolutionary clades was coded as −1 for gymnosperms and 1 for angiosperms. This allowed us to directly compare the effect sizes of different predictors both within and across models based on their regression coefficients. To ensure model coefficients were not affected by collinearity among predictors, we calculated variance inflation factors for all models to confirm they were all ≤ 2.

To account for non-independence among species due to shared evolutionary history, regression models were fit using phylogenetic generalised least squares (PGLS)112. PGLS models were fit using the gls function in the nlme package113, where the correlation structure among species was captured using Pagel’s λ as implemented by the corPagel function in the ape package114. A phylogenetic tree capturing evolutionary relationships among species was generated using the V.PhyloMaker package115, which uses a comprehensive time-calibrated phylogeny of 79,881 seed plant species as a backbone116. Model R2 values that account for the phylogenetic structure of the data were calculated using the rr2 package117.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors provide a robust and extensive analysis of the global distribution of 3 key structural traits in trees by assembling a massive database of individual trait measurements. They use this dataset to test the sensitivity of traits to environmental factors and search for evidence of phylogenetic signatures. Overall, the work is very thorough and brings together years of work from the field in a novel and informative way, while providing support for many generalized hypothesized trait sensitivities in a wide range of species. This is the type of information that could greatly improve a range of tree growth models, vegetation models, remote sensing, and radiative transfer models moving forward. These very same approaches are being applied (as alluded to in the discussion) in the Global TLS Database (global-tls.net) and this creates a nice structure for similar analyses of 3D tree traits.\nThe work is novel and builds on decades of field measurements across most major forest biomes. The work is an excellent contribution to the field of macro ecology and will help inform aspects of plant scaling relationships and sensitivities to climate.\nIn general, the authors are careful to not draw definitive conclusions about the generalized trends they found in the data, but rather offer substantial evidence for each claim to support the major observations regarding plant trait sensitivity. The one area of the work that probably needs a bit more discussion is the role of uncertainty and variation in the findings. Some of the analyses do not explicitly incorporate uncertainty or variation in the estimates. Since the approaches here rely on averaged remotely sensed climate estimates, we can expect there is a bit more uncertainty in the final estimates than reported. That said, I think the authors are taking a reasonable approach and adding propagated and quantified uncertainty estimates are unlikely to change the final findings.\nI see no issues regarding data analysis, interpretation or conclusions. In general, the authors had a robust analysis approach that provided insight on the specific hypotheses tested. As stated above, a structured approach to uncertainty propagation would be appreciated, but would be unlikely to change the overall findings of the study.\nThe methodology is sound and the approaches are in line with expectations for this type of study. My one suggestion would be for the authors to incorporate uncertainty in the analyses more explicitly. For instance, (if I’m not mistaken) the mean of specific climate/ecosystem variables was used for entire species, when these species may exist across a range of growing conditions. In other words, variance exists that may be important in species that are generalists and exist in many places. Enough detail is provided for the methods to be reproduced and code for the analysis is provided. I hope the authors will publish the final cleaned and assembled dataset for others to use.\nThe following line-by-line comments were noted while reviewing:\nLine 223: A nice, simple introduction that is concrete.\nLine 231: Succinct explanation that covers the main applications to remote sensing and vegetation models. Great.\nLine 243: Solid summary of the main research on this topic.\nLine 266: Excellent sample size. The presented figure of the distribution of sample locations should be colored to show number of samples per aggregate unit. This would be a more transparent way of showing the distribution of individual trees in the dataset. It would also be useful to show the aggregate number of samples as a distribution over the latitude and longitude of the global map. The second suggestion is less essential, but would provide some more understanding of the data distribution that the presence / absence map as it is shown now.\nLines: 275-284 Will this compiled and standardized database be made available somewhere? The location should be cited.\nLines 299-311I appreciate taking different analysis approaches, but this first one seems a bit arbitrary and it's unclear if it necessarily adds anything useful (compared to the second approach) to the analysis. Maybe introducing this section with a justification for why this simpler approach is used.\nLines: 360 Please provide detail on why 2008 was chosen as the baseline year.\nLine 373: For each of these species have you reported the mean and standard deviation of your estimates (e.g. mean and standard deviation of precipitation for a single species, etc.)? If not please report them in a table in the supplement. This will provide an estimate of the uncertainty / variation across species (especially those species that exist in many different growing environments).\nLine 1104: It would be helpful if the colors were ordered as shown in the legend on the top of the figure. For instance, group all purple, grey, and yellow/red into a block. The colors and orders of colors are seemingly grouped by the \"low, med, high\" groupings, but I'm not sure if this is easiest for interpretation of the proportions of each class in each biome.\nLooking forward to seeing the published version of this work!\nAtticus Stovall\n(Remarks on code availability)\nI was able to download and run the majority of the code provided. No README was included but the comments were helpful for understanding the different analysis sections. I was unable to evaluate any of the tree-level analysis because these data were not provided, but I imagine the dataset is quite large.", "reviewer_2": "This a timely article and it seeks to answer urgent questions on tree allometry. However, authors need to clarify the data analysis.\n-What are the noteworthy results?\nTree heights were constrained by light competition and water availability while exposure to wind and fire constrained crown size.\n- Will the work be of significance to the field and related fields? How does it compare to the established literature? If the work is not original, please provide relevant references.\nYes. It is unclear whether reported scaling exponents conformed to theoretical predictions. Given the large dataset, it will be interesting to investigate if scaling exponents of the various allometries tested are in line with existing theoretical predictions such as the stress similarity model, metabolic scaling theory, geometric similarity model.\n- Does the work support the conclusions and claims, or is additional evidence needed?\nYes once the corrections are made\n- Are there any flaws in the data analysis, interpretation and conclusions? - Do these prohibit publication or require revision?\nMaybe. Allometry parameters can widely vary with regression techniques. What was the rationale for using log-transformed data? Secondly, selection of allometric models follows a common scientific procedure where different models are experimented and tested, and various indices/coefficient (such R, adjustedR2, RMSE, AIC or BIC, etc.) used in selecting the model that best fits or explains variances in the data. I am seriously questioning how the authors arrived at opting for the log-log regression model. If this model performance was better than other models considered in your analysis? What other models were considered and assessed? These details are necessary to understand the analysis and information reported. I am questioning whether there might be other models which could have fitted the data better than the log-log regression model?\nWhat are the merits of the transformed log-log model? Why did it perform better in explaining variance in the data used for your analyses? I am curious if the log-log model best explained the allometry of all the tree species in this study? Can you provide supporting information or discussions to clarify this?\nIn general, SMA estimates of lines summarizing relationship between two variables are superior to ordinary least square linear regression and have been advocated in the literature because residual variance is minimized in both the X and Y dimensions rather than in the Y dimension only. When comparing regressions, differences can occur in either exponent of a (Y intercept) and/or b (regression slope). If b differs among species, species with larger b will have greater increase in Y per increment of X. If a differs, but b does not, species with larger a will have a consistently larger amount of Y at any given value of X (Kohyama and Hotta, 1990; Sposito and Santos, 2001). Authors should clarify how the ordinary least square regression was suitable for the analysis.\n- Is the methodology sound? Does the work meet the expected standards in your field?\nYes\n- Is there enough detail provided in the methods for the work to be reproduced?\nyes\n(Remarks on code availability)", "reviewer_3": "Review of The global spectrum of tree architecture\nJucker et al. provide and analyze a prodigious dataset on the global relationship of tree height (H), crown diameter (D), and crown aspect ratio (D/H) to climate, disturbance, competition, other functional traits, phylogeny and each other. Height and height scaling relationships appear to be most strongly affected by water availability and competition; crown width, by exposure to disturbance by wind or fire. Some lineages had unusual crown forms apparently tied more to phylogeny than environment.\nThis is an important paper that quantifies and crystallizes several patterns evident, in many cases, to natural historians for decades if not centuries. The global nature of the database, the extraordinary range of plots, species, and evolutionary lineages assessed, the sound statistical frameworks (in most cases) employed to analyze the data, and the conclusions reached will likely make this paper a touchstone for years to come. The authors are to be congratulated.\nHowever, as currently written, the manuscript has two central, interrelated flaws: a lack of a conceptual framework to predict or account for patterns in tree height, diameter, and crown aspect ratio, and a failure to cite some centrally important papers that provide such a framework. These flaws must be addressed.\nSpecifically, the authors should first cite Givnish et al. 2015 (Ecology 95: 2991-3007, Determinants of maximum tree height in Eucalyptus species along a rainfall gradient in Victoria, Australia) AND briefly summarize their general model relating maximum tree height to climate, soil fertility, and disturbance, to the allometry of allocation to wood vs. leaves with height, and to vertical stratification of environmental conditions with height above the ground. That paper shows a strong relationship of tree height to climatic moisture supply relative to demand, as quantified by P/Ep (mean annual precipitation divided by pan evaporation) – which is closely related to the aridity index used by Jucker et al. – and argues for its generality, albeit modulated by differences in temperature, latitude, soil fertility, and disturbance. These theoretical and empirical findings are directly relevant to the subject of the current paper, and they really must be cited – not as a content-less superscript, but for specific predictions and statistical relationships obtained along a substantial climatic gradient. Those earlier findings are directly relevant to what is arguably the most important conclusions of the current paper. • Given that the authors tie global variation in height and crown aspect ratio (tied to height) to leaf nitrogen content and specific leaf area, they should also cite Givnish et al. 2015 for both their model predictions and findings of such relationships in their Eucalyptus study … and for the climatic and edaphic drivers of variation in leaf N and SLA. They might also consider citing Smith et al. 2023 (Nature Communications 14: 7173, Ecophysiological adaptations shape distributions of closely related trees along a climatic moisture gradient) that detail shifts in 50 functional traits, as well as height growth, mass growth, and survival in 10 species of Eucalyptus grown in common gardens along the same gradient. That paper shows that species differences in many of those traits are heritable and largely accord with economic models to maximize rates of height growth.\nSecond, the authors should cite King 1981 (Oecologia 51: 351-356, Tree dimensions: Maximizing the rate of height growth in dense stands) and Givnish 1995 (Plant stems: biomechanical adaptations for energy capture and influence on species distributions. Pp. 3-49 in B. L. Gartner (ed.), Plant Stems: Physiology and Functional Morphology. Chapman and Hall, New York). These papers explain why the ratio of tree crown width to height should converge on a specific value in crowded stands. The first paper presents a quantitative model for the optimal allocation of energy between crown and bole; the second shows that the optimal value of that ratio corresponds to crown width increasing in proportion to crown height (i.e., crown width/height ratio is constant) and accounts for the observed relationship in fully stocked (crowded) stands documented by O’Neill & DeAngelis 1981 (Pp. 411-449 in DE Reichle (ed), Dynamic Properties of Forest Ecosystems, Cambridge University Press) and used by Givnish 1986 (Journal of Theoretical Biology 119: 139-146, Biomechanical constraints on self-thinning in plant populations) to provide the first mechanistic explanation for the -3/2 power thinning law in plants. Givnish 1995 provides an extensive table of predictions for how difference aspects of crown form should vary with environmental conditions. Arguments for broader crowns relative to height in shade-adapted trees are presented, as well as supporting data from an extensive dataset on North American champion trees.\nThird, while the authors’ statistical approaches are generally sound, I note two weaknesses that they should either justify or redress: (A) In studies involving allometric variation (e.g., between crown height and width), Type I regression models that minimize the residual variance of the dependent variable based on relationships to independent variables – i.e., ordinary linear regressions, as employed here) are often viewed as inappropriate, given that there is no clearly distinction between dependent and independent variables. Type II regressions, which minimize the residual variance about the regression in both the x- and y-directions, have generally been employed in such cases. The authors should justify their use of Type I regression or replace it with Type II regression. I am not sure whether a Type II version of generalized linear models is available however, and so they may have to use the current version of GLM for those (important) analyses. (B) It’s generally recognized that phylogenetic regression – which accounts for relationships among species, and thus the non-independence of data points – should be used in comparative studies like those at the heart of this paper. I recommend that the authors should at least present phylogenetic regressions that complement their traditional regressions, even if they rely mainly on the latter. They already have relationships in hand for many of their study species, as shown by Figure 3.\nFourth, I strongly recommend that the authors revise Figure 3 so as to increase its impact, by (A) stretching it vertically a bit, to give better resolution of individual branches, and then (B) using maximum likelihood mapping to colorize branches to visualize the evolution of tree height, crown width, and crown aspect ratio. Widely available R packages by Liam Revell can be used for this task.\nThomas J. Givnish\nHenry Allan Gleason Professor of Botany\nWilhelm Hofmeister Professor of Botany\nUniversity of Wisconsin-Madison\n(Remarks on code availability)"}, "author_response": "Comment: The authors provide a robust and extensive analysis of the global distribution of 3\nkey structural traits in trees by assembling a massive database of individual trait\nmeasurements. They use this dataset to test the sensitivity of traits to environmental factors\nand search for evidence of phylogenetic signatures. Overall, the work is very thorough and\nbrings together years of work from the field in a novel and informative way, while providing\nsupport for many generalized hypothesized trait sensitivities in a wide range of species. This\nis the type of information that could greatly improve a range of tree growth models, vegetation\nmodels, remote sensing, and radiative transfer models moving forward. These very same\napproaches are being applied (as alluded to in the discussion) in the Global TLS Database\n(global-tls.net) and this creates a nice structure for similar analyses of 3D tree traits. The work\nis novel and builds on decades of field measurements across most major forest biomes. The\nwork is an excellent contribution to the field of macro ecology and will help inform aspects of\nplant scaling relationships and sensitivities to climate.\nResponse: Thank you very much for your kind words and for reviewing our paper.\nComment: In general, the authors are careful to not draw definitive conclusions about the\ngeneralized trends they found in the data, but rather offer substantial evidence for each claim\nto support the major observations regarding plant trait sensitivity. The one area of the work\nthat probably needs a bit more discussion is the role of uncertainty and variation in the findings.\nSome of the analyses do not explicitly incorporate uncertainty or variation in the estimates.\nSince the approaches here rely on averaged remotely sensed climate estimates, we can\nexpect there is a bit more uncertainty in the final estimates than reported. That said, I think the\nauthors are taking a reasonable approach and adding propagated and quantified uncertainty\nestimates are unlikely to change the final findings.\nResponse: The issue of variability and plasticity within species is an important one that we\nshould have addressed more directly in the previous version of the manuscript. We agree that\nthis is important both from a methodological standpoint (uncertainty propagation) and an\necological one (i.e., what drives variability and plasticity in crown architectural traits within\nspecies?). First, it’s important to clarify why we decided to focus our analysis on differences in\ncrown architecture among species. Our motivation stems from previous work where we\nshowed that variability in crown architecture among trees is predominantly driven by\ndifferences between species rather than plasticity within them (see Case Study 2 in Jucker et\nal. 2022 GCB). This is why we chose to focus explicitly on characterising the crown\narchitecture of a large number of tree species (nearly 2000) distributed across all biomes, as\nprevious work on this topic has focused either on comparing a small number of temperate\nspecies (10-20) across multiple sites (e.g., Lines et al. 2012 GEB) or a slightly larger number\nof species (100-200) sampled at single site in the tropics (e.g., Iida et al. 2011 FEcol). We\nhave made sure to better articulate this motivation in the revised manuscript (L646-650).\nThe reason why we then chose to limit our analysis to exclusively look at differences between\nspecies (ignoring variability within them) has to do with the nature of our data. Specifically,\nmany species in our analysis have insufficient data to appropriately quantify intraspecific\nvariability in both their architecture and climatic envelopes: 314 species (~16%) were\nmeasured at a single site and only 342 species (<20%) were sampled widely enough to\ncharacterise their architectural plasticity along environmental gradients (the latter are the\nsubset we analysed for Case Study 2 in Jucker et al. 2022 GCB). Any estimates of variability\nand uncertainty we provide would be strongly influenced by differences in sample size among\nspecies (which as we highlight in the paper vary from 10 to 22,835 individuals per species). In\nrevising the paper, we have made sure to more clearly highlight this limitation (L650-653).\nIn terms of our methodology, one thing we did do to explicitly mitigate uncertainty linked to\nwithin-species variability is to only retain samples from a species’ dominant biome (i.e., in\ncases where a species was recorded in multiple biomes, we only kept data from the biome\nwhere it was found most frequently; see L594-597 for details). As you suggested, for each\nspecies we have now also calculated the standard deviations of the various environmental\npredictors used in our analysis. These are reported in the updated species-level data frame\n(species_data.csv) that we have provided as part of the data and code archive accompanying\nour paper. However, we caution on overinterpreting these standard deviation values, as for\nmany species they will considerably underestimate the true range of environmental conditions\nwithin which they can grow.\nFinally, to better integrate the question of within-species variability in our paper, we have added\na new section to the discussion (L536-554) where we highlight this as an important area for\nfuture research. Here, in addition to highlighting some of the limitations of our data to address\nthe questions of intraspecific variability, we have also made an effort to highlight several\nconcrete future research questions which would complement and build on our findings.\nComment: I see no issues regarding data analysis, interpretation or conclusions. In general,\nthe authors had a robust analysis approach that provided insight on the specific hypotheses\ntested. As stated above, a structured approach to uncertainty propagation would be\nappreciated, but would be unlikely to change the overall findings of the study.\nResponse: Thank you, we are pleased that overall the methodology and the interpretations\nwe draw from our results come across as robust. See our previous response for how we have\naddressed the issue of intraspecific variability in our analysis.\nComment: The methodology is sound and the approaches are in line with expectations for\nthis type of study. My one suggestion would be for the authors to incorporate uncertainty in\nthe analyses more explicitly. For instance, (if I’m not mistaken) the mean of specific\nclimate/ecosystem variables was used for entire species, when these species may exist\nacross a range of growing conditions. In other words, variance exists that may be important in\nspecies that are generalists and exist in many places.\nResponse: We agree and as mentioned above we now provide estimates of environmental\nvariability for each species as part of the data and code archive accompanying our paper.\nComment: Enough detail is provided for the methods to be reproduced and code for the\nanalysis is provided. I hope the authors will publish the final cleaned and assembled dataset\nfor others to use.\nResponse: Thank you. We have revised the data and code archive accompanying our paper\nto include all data necessary to calculate the species-level estimates reported in our main\nanalysis. We note however, that these are just a subset of the larger Tallo database, which\nincludes additional tree-level records not included in our present analysis (e.g., trees from\nspecies with fewer than 10 individuals within a given biome, or trees where species IDs were\nmissing). The Tallo database is permanently archived on Zenodo\n(https://zenodo.org/records/6637599).\nComment: Line 223: A nice, simple introduction that is concrete.\nResponse: Thank you!\nComment: Line 231: Succinct explanation that covers the main applications to remote sensing\nand vegetation models. Great.\nResponse: Thank you, we are pleased these applications came across clearly.\nComment: Line 243: Solid summary of the main research on this topic.\nResponse: Thank you!\nComment: Line 266: Excellent sample size. The presented figure of the distribution of sample\nlocations should be colored to show number of samples per aggregate unit. This would be a\nmore transparent way of showing the distribution of individual trees in the dataset. It would\nalso be useful to show the aggregate number of samples as a distribution over the latitude\nand longitude of the global map. The second suggestion is less essential, but would provide\nsome more understanding of the data distribution that the presence / absence map as it is\nshown now.\nResponse: Thank you and great suggestion. We have revised the map in Fig. 1 so that the\ncolour of the grid cells reflects the number of samples acquired from each location.\nComment: Lines: 275-284 Will this compiled and standardized database be made available\nsomewhere? The location should be cited.\nResponse: Yes, this will be archived on Zenodo and we have provided a link to the DOI in the\nrevised manuscript (note the archive will be made public following the review of this paper).\nAs noted above, these are just a subset of the larger Tallo database, which includes additional\ntree-level records not included in our present analysis. The Tallo database is already\npermanently archived on Zenodo (https://zenodo.org/records/6637599).\nComment: Lines 299-311I appreciate taking different analysis approaches, but this first one\nseems a bit arbitrary and it's unclear if it necessarily adds anything useful (compared to the\nsecond approach) to the analysis. Maybe introducing this section with a justification for why\nthis simpler approach is used.\nResponse: We agree that the first approach is more arbitrary than the second, but felt it was\nvaluable to retain both methods as they are complementary. In particular, the first method\nwhere height, crown diameter and crown aspect ratio are estimated for a tree of fixed size (D\n= 30 cm in our case) has been used extensively in previous studies (e.g., Iida et al. 2011\nFEcol; Lines et al. 2012 GEB; Poorter et al. 2012 PlantEcol; Jucker et al. 2022 GCB) –\nmeaning readers will be familiar with this approach. It also has the advantage that that the\npredicted values of height, crown diameter and crown aspect ratio are in units that are easily\ninterpretable (e.g., meters), making it much simpler for readers to get a sense of the magnitude\nof the effects we report. Ultimately as we show in Supplementary Fig. 1 the two methods give\nnearly identical results, so we preferred to report both for the benefit of the reader.\nComment: Lines: 360 Please provide detail on why 2008 was chosen as the baseline year.\nResponse: We chose this year as it corresponds with the period in which most of the\nallometric data were collected (although we do note that exact dates are not known for all our\nrecords). We have clarified this in the text.\nComment: Line 373: For each of these species have you reported the mean and standard\ndeviation of your estimates (e.g. mean and standard deviation of precipitation for a single\nspecies, etc.)? If not please report them in a table in the supplement. This will provide an\nestimate of the uncertainty / variation across species (especially those species that exist in\nmany different growing environments).\nResponse: Agreed. As mentioned above these are now reported in the updated species-level\ndata frame (species_data.csv) that we have provided as part of the data and code archive\naccompanying our paper.\nComment: Line 1104: It would be helpful if the colors were ordered as shown in the legend\non the top of the figure. For instance, group all purple, grey, and yellow/red into a block. The\ncolors and orders of colors are seemingly grouped by the \"low, med, high\" groupings, but I'm\nnot sure if this is easiest for interpretation of the proportions of each class in each biome.\nResponse: This is a great suggestion, we have updated the figure accordingly!\nComment: Looking forward to seeing the published version of this work! Atticus Stovall\nResponse: Thank you!\nComment: Reviewer #1 remarks on code availability: I was able to download and run the\nmajority of the code provided. No README was included but the comments were helpful for\nunderstanding the different analysis sections. I was unable to evaluate any of the tree-level\nanalysis because these data were not provided, but I imagine the dataset is quite large.\nResponse: We have now provided a README file to accompany the data and core archive,\nas well as tree-level data and code used to estimate the species-level parameters reported in\nthe main text.\nReviewer #2\nComment: This a timely article and it seeks to answer urgent questions on tree allometry.\nHowever, authors need to clarify the data analysis.\nResponse: Thank you for reviewing our paper, we are pleased you enjoyed it.\nComment: What are the noteworthy results? Tree heights were constrained by light\ncompetition and water availability while exposure to wind and fire constrained crown size.\nResponse: Thank you, we are pleased the key results were easy to distil.\nComment: Will the work be of significance to the field and related fields? How does it compare\nto the established literature? If the work is not original, please provide relevant references.\nYes. It is unclear whether reported scaling exponents conformed to theoretical predictions.\nGiven the large dataset, it will be interesting to investigate if scaling exponents of the various\nallometries tested are in line with existing theoretical predictions such as the stress similarity\nmodel, metabolic scaling theory, geometric similarity model.\nResponse: This is a good observation, but the reason why we did not present this analysis\nhere is that it has been carried out previously using the entire Tallo database (see Case Study\n1 in Jucker et al. 2022 GCB).\nComment: Does the work support the conclusions and claims, or is additional evidence\nneeded?\nYes once the corrections are made\nResponse: Thank you.\nComment: Are there any flaws in the data analysis, interpretation and conclusions? Do these\nprohibit publication or require revision? Maybe. Allometry parameters can widely vary with\nregression techniques. What was the rationale for using log-transformed data? Secondly,\nselection of allometric models follows a common scientific procedure where different models\nare experimented and tested, and various indices/coefficient (such R, adjustedR2, RMSE, AIC\nor BIC, etc.) used in selecting the model that best fits or explains variances in the data. I am\nseriously questioning how the authors arrived at opting for the log-log regression model. If this\nmodel performance was better than other models considered in your analysis? What other\nmodels were considered and assessed? These details are necessary to understand the\nanalysis and information reported. I am questioning whether there might be other models\nwhich could have fitted the data better than the log-log regression model?\nResponse: This is a very good point and something we should have dealt with in more detail\nin the previous version of our paper. Conceptually, the advantage of the log-log model (i.e., a\npower-law) lies in its simplicity and the fact that it has a long history of being used to study\nallometry, thus directly linking our work to a large body of existing literature). However, we fully\nagree that testing the appropriateness of the log-log is something we should have done more\nformally before adopting it for our analysis. This is especially true for modelling height–\ndiameter scaling relationships, where previous work has suggested that other functional forms\n(particularly saturating ones like the Michaelis-Menten functions) may provide a better fit to\nthe data. To test this we used a subset 754 of well sampled species in our datasets (minimum\nsample size = 50 trees per species; minimum stem diameter range = 30 cm). For each species\nwe took a random subset of 50 individuals to ensure species with larger sample sizes would\nnot dominate the signal. We then used the same approach described in the main text to\nestimate HRESID and HD=30 for each species using both a power-law and a Michaelis-\nMenten function. We found that both estimates of HRESID (ρ = 0.97) HD=30 (ρ = 0.93) derived\nfrom a power-law and a Michaelis-Menten function were strongly correlated (see\nSupplementary Fig. 2). This indicates that the choice of functional form used to model the\nscaling relationship had little to no effect on our results. Moreover, of the two functional forms\nthe power-law model fit the data considerably better (based on both RMSE and AIC). This was\ntrue both when modelling the entire dataset together to estimate HRESID (RMSE = 5.4 m and\n5.8 m for power-law and Michaelis-Menten, respectively) and when accounting for variation in\nallometric scaling relationships among species to estimate HD=30 (RMSE = 3.5 m and 3.9 m\nfor power-law and Michaelis-Menten, respectively). Based on this we opted to model height–\ndiameter relationships using a power-law function. This model comparison is provided in\nSupplementary Fig. 2 and discussed in the Methods section of the revised paper. We have\nalso provided R code to replicate this comparison as part of the data and code archiving\npackage uploaded alongside our paper.\nComment: What are the merits of the transformed log-log model? Why did it perform better\nin explaining variance in the data used for your analyses? I am curious if the log-log model\nbest explained the allometry of all the tree species in this study? Can you provide supporting\ninformation or discussions to clarify this?\nResponse: See our response above about this point. As mentioned, we have now compared\nthe log-log height–diameter model to an alternative saturating function, and found that the log-\nlog model actually fit the data best. Note that we did not perform this comparison for the scaling\nrelationships between crown diameter–diameter and crown diameter–height, as here the\nliterature is much more in agreement on the appropriateness of a log-log model to capture\nthese relationships (e.g., see Loubota Panzou et al. 2020 GEB; Shenkin et al. 2020 Front. For.\nGlob. Change; Jucker et al. 2022 GCB), and no obvious alternative candidate models have\nbeen proposed.\nComment: In general, SMA estimates of lines summarizing relationship between two\nvariables are superior to ordinary least square linear regression and have been advocated in\nthe literature because residual variance is minimized in both the X and Y dimensions rather\nthan in the Y dimension only. When comparing regressions, differences can occur in either\nexponent of a (Y intercept) and/or b (regression slope). If b differs among species, species\nwith larger b will have greater increase in Y per increment of X. If a differs, but b does not,\nspecies with larger a will have a consistently larger amount of Y at any given value of X\n(Kohyama and Hotta, 1990; Sposito and Santos, 2001). Authors should clarify how the\nordinary least square regression was suitable for the analysis.\nResponse: This is another aspect we should have clarified better in methods. As the reviewer\ncorrectly points out, there is a lot of debate in the allometry literature about the appropriateness\nof ordinary least squares (OLS) regression as opposed to model II type approaches such as\nstandardised major axis (SMA) regression for modelling allometric scaling relationships. It is\ntherefore important to justify why we chose one approach over the other. In our case this\ncomes down to the objective of the analysis and whether the models are being used to\nestimate scaling coefficients or generate predictions. When estimating scaling coefficients\n(i.e., the slope of the log-log regression), then SMA regression is typically the preferred choice.\nHowever, the goal of our analysis was not to compare species based on their scaling\ncoefficients, but instead to use the models to generate predictions of height, crown area and\ncrown aspect ratio that we could then use to compare species. In this case, the advice is to\nalways use OLS regression. This point is nicely summarised by Pierre Legendre, who\ndeveloped the user guide and statistical package for model II regression in R: “When the\npurpose of the study is not to estimate the parameters of a functional relationship, but simply\nto forecast or predict values of y for given x’s, use OLS in all cases” (see recommendation 6\nhere: https://cran.r-project.org/web/packages/lmodel2/vignettes/mod2user.pdf). We have\nnow explicitly justified our modelling choice in the methods of the revised paper (L614-616).\nComment: Is the methodology sound? Does the work meet the expected standards in your\nfield?\nYes\nResponse: Thank you.\nComment: Is there enough detail provided in the methods for the work to be reproduced?\nYes\nResponse: Thank you again for reviewing our paper and for the helpful feedback!\nReviewer #3\nComment: Jucker et al. provide and analyze a prodigious dataset on the global relationship\nof tree height (H), crown diameter (D), and crown aspect ratio (D/H) to climate, disturbance,\ncompetition, other functional traits, phylogeny and each other. Height and height scaling\nrelationships appear to be most strongly affected by water availability and competition; crown\nwidth, by exposure to disturbance by wind or fire. Some lineages had unusual crown forms\napparently tied more to phylogeny than environment.\nResponse: Thank you for reviewing our paper.\nComment: This is an important paper that quantifies and crystallizes several patterns evident,\nin many cases, to natural historians for decades if not centuries. The global nature of the\ndatabase, the extraordinary range of plots, species, and evolutionary lineages assessed, the\nsound statistical frameworks (in most cases) employed to analyze the data, and the\nconclusions reached will likely make this paper a touchstone for years to come. The authors\nare to be congratulated.\nResponse: Thank you for the kind words, we are very pleased you enjoyed the paper.\nComment: However, as currently written, the manuscript has two central, interrelated flaws:\na lack of a conceptual framework to predict or account for patterns in tree height, diameter,\nand crown aspect ratio, and a failure to cite some centrally important papers that provide such\na framework. These flaws must be addressed.\nResponse: We fully agree that the relationships and predictions we test in our paper need to\nbe well anchored to the existing literature if our study is to provide a comprehensive overview\nof the drivers that shape the crown architecture of trees. We really appreciate the suggestions\nfor improving this aspect of our work and have incorporated them into our revision (see\nresponses below for details).\nComment: Specifically, the authors should first cite Givnish et al. 2015 (Ecology 95: 2991-\n3007, Determinants of maximum tree height in Eucalyptus species along a rainfall gradient in\nVictoria, Australia) AND briefly summarize their general model relating maximum tree height\nto climate, soil fertility, and disturbance, to the allometry of allocation to wood vs. leaves with\nheight, and to vertical stratification of environmental conditions with height above the ground.\nThat paper shows a strong relationship of tree height to climatic moisture supply relative to\ndemand, as quantified by P/Ep (mean annual precipitation divided by pan evaporation) – which\nis closely related to the aridity index used by Jucker et al. – and argues for its generality, albeit\nmodulated by differences in temperature, latitude, soil fertility, and disturbance. These\ntheoretical and empirical findings are directly relevant to the subject of the current paper, and\nthey really must be cited – not as a content-less superscript, but for specific predictions and\nstatistical relationships obtained along a substantial climatic gradient. Those earlier findings\nare directly relevant to what is arguably the most important conclusions of the current paper.\nGiven that the authors tie global variation in height and crown aspect ratio (tied to height) to\nleaf nitrogen content and specific leaf area, they should also cite Givnish et al. 2015 for both\ntheir model predictions and findings of such relationships in their Eucalyptus study … and for\nthe climatic and edaphic drivers of variation in leaf N and SLA. They might also consider citing\nSmith et al. 2023 (Nature Communications 14: 7173, Ecophysiological adaptations shape\ndistributions of closely related trees along a climatic moisture gradient) that detail shifts in 50\nfunctional traits, as well as height growth, mass growth, and survival in 10 species of\nEucalyptus grown in common gardens along the same gradient. That paper shows that\nspecies differences in many of those traits are heritable and largely accord with economic\nmodels to maximize rates of height growth.\nResponse: Thank you for this, it is really helpful both in terms of framing the analysis of\nvariation in tree height along aridity gradients, but also relating this back to other functional\ntraits such as leaf nitrogen content. We have now incorporated Givnish et al. 2015 into the\ntext, including highlighting it the introduction and citing it as a key reference supporting our\npredictions outlines in Table 1. We have also refer back to it at several points in the discussion,\nciting it as a key example supporting our findings about how investment in height growth varies\nalong aridity gradients and how we might expect this to covary with investment in leaf nitrogen.\nComment: Second, the authors should cite King 1981 (Oecologia 51: 351-356, Tree\ndimensions: Maximizing the rate of height growth in dense stands) and Givnish 1995 (Plant\nstems: biomechanical adaptations for energy capture and influence on species distributions.\nPp. 3-49 in B. L. Gartner (ed.), Plant Stems: Physiology and Functional Morphology. Chapman\nand Hall, New York). These papers explain why the ratio of tree crown width to height should\nconverge on a specific value in crowded stands. The first paper presents a quantitative model\nfor the optimal allocation of energy between crown and bole; the second shows that the\noptimal value of that ratio corresponds to crown width increasing in proportion to crown height\n(i.e., crown width/height ratio is constant) and accounts for the observed relationship in fully\nstocked (crowded) stands documented by O’Neill & DeAngelis 1981 (Pp. 411-449 in DE\nReichle (ed), Dynamic Properties of Forest Ecosystems, Cambridge University Press) and\nused by Givnish 1986 (Journal of Theoretical Biology 119: 139-146, Biomechanical\nconstraints on self-thinning in plant populations) to provide the first mechanistic explanation for the -3/2\npower thinning law in plants. Givnish 1995 provides an extensive table of predictions for how\ndifference aspects of crown form should vary with environmental conditions. Arguments for\nbroader crowns relative to height in shade-adapted trees are presented, as well as supporting\ndata from an extensive dataset on North American champion trees.\nResponse: Again, thank you for highlighting this important work. We agree that it’s really\nimportant to link our finding back to earlier work that set the foundations for our current\nunderstanding the biophysical constraints that shape tree architecture. The papers by King\n1981 and Givnish 1995 are particularly relevant to the opening two paragraph of the\nintroduction, where we provide a broad overview of the various constraints that trees operate\nunder when expanding their crowns both vertically and horizontally. We have also incorporated\nthem in Table 1, where they help support our hypotheses about how we might expect tree\nheight and crown width to vary in relation to competition for light with neighbours. Finally, they\nhelp support several of our key findings, and we have therefore refereed to them specifically\nin the revised discussion.\nComment: Third, while the authors’ statistical approaches are generally sound, I note two\nweaknesses that they should either justify or redress: (A) In studies involving allometric\nvariation (e.g., between crown height and width), Type I regression models that minimize the\nresidual variance of the dependent variable based on relationships to independent variables\n– i.e., ordinary linear regressions, as employed here) are often viewed as inappropriate, given\nthat there is no clearly distinction between dependent and independent variables. Type II\nregressions, which minimize the residual variance about the regression in both the x- and y-\ndirections, have generally been employed in such cases. The authors should justify their use\nof Type I regression or replace it with Type II regression. I am not sure whether a Type II\nversion of generalized linear models is available however, and so they may have to use the\ncurrent version of GLM for those (important) analyses. (B) It’s generally recognized that\nphylogenetic regression – which accounts for relationships among species, and thus the non-\nindependence of data points – should be used in comparative studies like those at the heart\nof this paper. I recommend that the authors should at least present phylogenetic regressions\nthat complement their traditional regressions, even if they rely mainly on the latter. They\nalready have relationships in hand for many of their study species, as shown by Figure 3.\nResponse: Thank you for highlight both of these points. Relating to point (A) about the\nappropriateness of Type I vs Type II regression, we agree that we should have better justified\nour choice for the former. As the reviewer correctly points out, there is a lot of debate in the\nallometry literature about the appropriateness of Type I regression (e.g., ordinary least\nsquares, OLS) as opposed to Type II approaches such as standardised major axis (SMA)\nregression for modelling allometric scaling relationships. It is therefore important for us to\njustify why we chose one approach over the other. In our case this comes down to the objective\nof the analysis – specifically whether the models are being used to estimate scaling\ncoefficients or generate predictions. When estimating scaling coefficients (i.e., the slope of the\nlog-log regression), then SMA regression is typically the preferred choice. However, the goal\nof our analysis was not to compare species based on their scaling coefficients, but instead to\nuse the models to generate predictions of height, crown area and crown aspect ratio that we\ncould then use to compare species. In this case, the advice is to always use OLS regression,\nespecially as the structure of our models requires incorporating random effects which are not\nsupported by SMA. This point is nicely summarised by Pierre Legendre, who developed the\nuser guide and statistical package for model II regression in R: “When the purpose of the study\nis not to estimate the parameters of a functional relationship, but simply to forecast or predict\nvalues of y for given x’s, use OLS in all cases” (see recommendation 6 here: https://cran.r-\nproject.org/web/packages/lmodel2/vignettes/mod2user.pdf). We have now explicitly justified\nour modelling choice in the methods of the revised paper (L614-616).\nRegarding point (B) about accounting for phylogeny in our analysis, we fully agree and this is\nactually something we have already done by using phylogenetic generalised least squares\n(PGLS) regressions for the main analyses presented in our study (i.e., the results presented\nin Figs 4 & 5 of our paper). We have made sure to make this point clearer in revising our paper\n(see L779-786). We also note that the underlying models used to estimate species-level crown\nattributes also leverage phylogenetic relationships among species by incorporating species,\ngenus and family as nested random effects. This approach is very similar (and in some cases\npreferable) to using PGLS (see here for an in-depth discussion:\nhttps://statmodeling.stat.columbia.edu/2016/02/14/hierarchical-models-for-phylogeny-heres-\nwhat-everyones-talking-about/).\nComment: Fourth, I strongly recommend that the authors revise Figure 3 so as to increase its\nimpact, by (A) stretching it vertically a bit, to give better resolution of individual branches, and\nthen (B) using maximum likelihood mapping to colorize branches to visualize the evolution of\ntree height, crown width, and crown aspect ratio. Widely available R packages by Liam Revell\ncan be used for this task.\nThomas J. Givnish\nHenry Allan Gleason Professor of Botany\nWilhelm Hofmeister Professor of Botany\nUniversity of Wisconsin-Madison\nResponse: We agree that in Fig. 3 the separation between individual branches is hard to see.\nBut unfortunately this is product of the large number of species represented on the\nphylogenies. We attempted to stretch the phylogenies vertically as suggested, but this did not\nhelp resolve this issue, as there are simply too many species. As for suggestion (B), we did\nalso try this in a previous iteration of the figure, but again found that because of the large\nnumber of species it ended up being more confusing that helpful. We were also unsure about\nrepresenting these ancestral reconstructions on the phylogenies, as they are not the focus of\nour analysis and we felt they may confuse the reader. We therefore opted to keep Fig. 3 as is,\nbut thank the reviewer for their helpful suggestions on how to improve it further."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The revisions in the current version of the paper addressed all of my previous comments. I am satisfied with the current version and believe it is ready for publication. Nice work.", "reviewer_2": "The authors did a fantastic job clarifying their analysis and methods and providing supplementary files. I recommend it should be accepted.", "reviewer_3": "Jucker et al. have responded adequately to most of the reviewers’ comments. Their efforts are, in general, to be applauded.\nHOWEVER, they have failed to respond to my central criticism – that they need to provide a simple conceptual framework for ecological trends in tree height and crown width vs. height. Worse, their rebuttal letter misrepresents what they actually did in editing the manuscript. The manuscript text must be changed. As detailed below, the changes needed are minimal – rewriting three sentence – but crucial.\nTo quote their letter on two key points:\n1. “COMMENT: Specifically, the authors should first cite Givnish et al. 2015 (Ecology 95: 2991-3007, Determinants of maximum tree height in Eucalyptus species along a rainfall gradient in Victoria, Australia) AND briefly summarize their general model relating maximum tree height to climate, soil fertility, and disturbance, to the allometry of allocation to wood vs. leaves with height, and to vertical stratification of environmental conditions with height above the ground. That paper shows a strong relationship of tree height to climatic moisture supply relative to demand, as quantified by P/Ep (mean annual precipitation divided by pan evaporation) – which is closely related to the aridity index used by Jucker et al. – and argues for its generality, albeit modulated by differences in temperature, latitude, soil fertility, and disturbance. These theoretical and empirical findings are directly relevant to the subject of the current paper, and they really must be cited – not as a content-less superscript, but for specific predictions and statistical relationships obtained along a substantial climatic gradient. Those earlier findings are directly relevant to what is arguably the most important conclusions of the current paper. \nGiven that the authors tie global variation in height and crown aspect ratio (tied to height) to leaf nitrogen content and specific leaf area, they should also cite Givnish et al. 2015 for both their model predictions and findings of such relationships in their Eucalyptus study … and for the climatic and edaphic drivers of variation in leaf N and SLA. They might also consider citing Smith et al. 2023 (Nature Communications 14: 7173, Ecophysiological adaptations shape distributions of closely related trees along a climatic moisture gradient) that detail shifts in 50 functional traits, as well as height growth, mass growth, and survival in 10 species of Eucalyptus grown in common gardens along the same gradient. That paper shows that species differences in many of those traits are heritable and largely accord with economic models to maximize rates of height growth."}, "author_response": "Response: Just to briefly clarify, we did in fact cite Givnish et al. 2015 in the introduction. It is one of the key papers we highlight in Table 1, which though currently located at the end of the manuscript will appear in print in the introduction where it first mentioned. We also cite this paper in the discussion, where we mention its findings explicitly in the context of Australian forests. To avoid any confusion we have now also cited the paper in the main text of the introduction as well (ref 44 in the revised manuscript).\nResponse: Thank you for clarifying these points. We have adapted the suggested text and incorporated it into both the revised introduction (L232–238) and discussion (L453–455). In both cases we have taken care to explicitly cite Givnish et al. (2014). In particular, this section of the introduction now reads:\nFor instance, in arid climates woody biomass allocation tends to shift away from height growth and towards crown expansion to limit the risk of hydraulic failure and maximise energy capture, resulting in trees that are shorter for a given diameter and have wider crown profiles. Conversely, when water and nutrients are non-limiting to photosynthesis, strong competition for light leads to greater investment in height growth and relative allocation of carbon to woody tissues, pushing trees closer to their structural and hydraulic safety margins.\nResponse: Note again that both of these papers were in fact cited throughout our revised manuscript, including the main text of the introduction, Table 1 and the discussion (they are Refs 32 and 7, respectively). As mentioned above we have now amended the introduction to explicitly mention the prediction that trees should invest more (in relative terms) in crown expansion vs height growth in dry, open environments (as suggested in Point 1).\nResponse: Thank you for clarifying this point, we have revised the text as suggested. This now reads as follows:\nMoreover, higher leaf nitrogen content should lead to greater photosynthetic rates and investment in height growth – as found previously along a rainfall gradient in Australia"}]

Decision letter