Crown plasticity enables trees to optimize canopy packing in mixed-species forests
Tommaso Jucker, Olivier Bouriaud and David A. Coomes
Supporting information
Appendix S1 | Estimating crown volume of individual trees ................................................ 2
Appendix S2 | Predicted canopy packing .............................................................................. 5
Appendix S3 | Canopy packing models ................................................................................. 6
Accounting for non-target species ..................................................................................... 6
Model selection .................................................................................................................. 6
Appendix S4 | Crown expansion and light interception ........................................................ 9
Crown vertical and lateral expansion ................................................................................. 9
Vertical stratification in species tree heights ................................................................... 10
Relating crown volume and light interception ................................................................. 10
Appendix S5 | The influence of shade tolerance on canopy packing .................................. 12
[1]
Crown plasticity enables trees to optimize canopy packing in mixed-species forests
Tommaso Jucker, Olivier Bouriaud and David A. Coomes
Appendix S1 | Estimating crown volume of individual trees
The volume of a tree’s crown can be estimated in the same way that the volume of a solid of
revolution is calculated. For a given curve determined by an equation of the form y = αxβ,
rotating the curve around the x axis will outline a solid whose shape will depend on β (Fig.
S1). If β = 1, the solid will take the shape of a cone, β < 1 results in convex shape (i.e.,
paraboloid) which becomes increasingly cylindrical as β approaches 0, while β > 1 outlines a
concave object (i.e., neiloid).
Fig. S1 | Schematic representation of the crown profile of a tree, where H corresponds to the height at the top of
the tree, CD is the depth of the crown, CRmax is the crown’s maximum radius (assumed to be at the crown’s
base) and CRh is the crown radius at a given height h from the base of the crown. The volume of the crown is
estimates in the same way as that of a solid of revolution, where the crown profile is rotated around the height
axis to give a 3D object. The shape of the crown is determined by a function of the form y = αxβ which describes
how crown radius changes along the height of the crown (red section of the crown profile).
The volume of the solid between points a and b along the x axis is given by:
𝑏
𝑉𝑜𝑙𝑢𝑚𝑒 = ∫𝑎 𝜋 𝑦 2 𝑑𝑥
(1)
In the same way, a tree’s crown volume (CV) can be approximated by:
2
𝐻
𝐶𝑉 = ∫𝐻−𝐶𝐷 𝜋 (𝑓(ℎ)) 𝑑ℎ
(2)
where H is the height of the tree, CD the depth of the crown, and f(h) describes how the tree’s
crown radius (CRmax) changes along the height of the crown. The function which predicts the
crown radius at a given height h along the crown (CRh) was obtained from Caspersen et al.
(2011) and is:
𝐶𝑅ℎ = 𝐶𝑅𝑚𝑎𝑥 (
𝐶𝐷−ℎ 𝛽
𝐶𝐷
)
(3)
[2]
Crown plasticity enables trees to optimize canopy packing in mixed-species forests
Tommaso Jucker, Olivier Bouriaud and David A. Coomes
where CRmax is the crowns maximum radius, which for the purposes of this study is assumed
to be at the base of the crown, and β is the shape parameter which determines the curvature of
the crown. At the base of the crown h = 0, and therefore CRh = CRmax, while at the top of the
crown h = CD and CRh = 0. Substituting f(h) with equation (3) gives:
2
𝐶𝐷−ℎ 𝛽
𝐻
𝐶𝑉 = 𝜋 ∫𝐻−𝐶𝐷 (𝐶𝑅𝑚𝑎𝑥 (
𝐶𝐷
) ) 𝑑ℎ
(4)
Deriving equation (4) gives:
𝐻
𝐶𝐷−ℎ 2𝛽
2
𝐶𝑉 = 𝜋 𝐶𝑅𝑚𝑎𝑥
∫𝐻−𝐶𝐷 (
𝐶𝐷
)
𝑑ℎ
ℎ
𝐶𝑉 = 𝜋
𝐶𝑉 = −
𝐶𝑉 = −
𝐶𝑉 = −
𝐶𝑉 =
𝐶𝐷(1− )
𝐻
𝐶𝐷
2
𝐶𝑅𝑚𝑎𝑥
∫𝐻−𝐶𝐷 (−
2𝛽+1
2
𝜋 𝐶𝑅𝑚𝑎𝑥
𝐶𝐷
2𝛽+1
2
𝜋 𝐶𝑅𝑚𝑎𝑥
𝐶𝐷
2𝛽+1
2
𝜋 𝐶𝑅𝑚𝑎𝑥
𝐶𝐷
2𝛽+1
ℎ
) 𝑑ℎ
(6)
]
(7)
𝐻−𝐶𝐷
2𝛽+1
((1 − 𝐶𝐷)
𝐶𝐷 2𝛽+1
(− (𝐶𝐷)
2𝛽+1
2𝛽+1 𝐻
[(1 − 𝐶𝐷)
𝐻
(5)
(1 −
) ≡ −
2
𝜋 𝐶𝑅𝑚𝑎𝑥
𝐶𝐷
𝐻−𝐶𝐷 2𝛽+1
𝐶𝐷
)
2
𝜋 𝐶𝑅𝑚𝑎𝑥
𝐶𝐷
2𝛽+1
)
(8)
(−1)
(9)
(10)
2𝛽+1
Estimating the shape parameter β requires measuring a tree’s crown radius at successive
height intervals in order to reconstruct its crown profile. As these data were not available for
our study species, we instead relied on published estimates of β available for 250 North
American tree species (Purves et al. 2007). We first filtered the species list by excluding taxa
that belong to a different genus to those found in our study. We then grouped the remaining
species into conifers and broadleaves, and averaged their β estimates to obtain mean values
for each of the two functional groups. Details on how to calculate a species’ β value can be
found in the supporting information of Purves et al. (2007).
Ideally we would have preferred to directly measure both the inter- and intra-specific
variation in β (as opposed to using published estimates). However, this would have required
taking measurements of crown radius at multiple heights along the crown for each tree,
something which we were unable to do given the large sample sizes of the present study (≈
13000 trees). Nonetheless, we expect equation (10) to provide an adequate approximation of
each trees’ CV, as most of the inter-tree variation in CV is driven by the numerator of the
equation (i.e., CRmax and CD, both of which were measured for all trees). Evidence of this can
be seen when looking at the distribution of β values reported in Purves et al. (2007), where
[3]
Crown plasticity enables trees to optimize canopy packing in mixed-species forests
Tommaso Jucker, Olivier Bouriaud and David A. Coomes
95% of species have β values which range between 0.26 to 0.44 (calculations based on the
subset of species used to estimate β for conifers and broadleaves in this study). Using
equation (10) we can compare the effect of the variability in β on CV estimates versus the
effect of inter- and intraspecific variation in CRmax and CD (e.g., values reported in Table S4).
Even when assuming the extremes of the distribution in β values (i.e, differences in CV when
β = 0.26 vs β = 0.44), the effect of β on CV is much smaller than that of inter- and
intraspecific variation in either CRmax or CD (Fig. S2).
Fig. S2 | Comparison of the effects of variation in β on crown volume versus that of variation in (a) crown
radius and (b) crown depth. Equation (10) was used to generate crown volume estimates in which (a) crown
radius was allowed to vary within the 95% range of observed values in the data while crown depth was kept at
the mean (9.5 m) and (b) in a scenario in which crown depth varied along the 95% range of the data and crown
radius was kept at the mean (2.4 m). This was repeated for β values at both extremes of the spectrum (β = 0.26
in red and β = 0.44 in black). In both cases, variation in crown dimensions had a much larger impact on crown
volume than variation in β.
Caspersen, J. P., Vanderwel, M. C., Cole, W. G. & Purves, D. W. (2011) How stand
productivity results from size- and competition-dependent growth and mortality. PLoS ONE,
6, e28660.
Purves, D. W., Lichstein, J. W. & Pacala, S. W. 2007 Crown plasticity and competition for
canopy space: a new spatially implicit model parameterized for 250 North American tree
species. PLoS ONE, 2, e870.
[4]
Crown plasticity enables trees to optimize canopy packing in mixed-species forests
Tommaso Jucker, Olivier Bouriaud and David A. Coomes
Appendix S2 | Predicted canopy packing
To test whether canopy packing increases with diversity as a consequence of vertical
stratification or as a result of changes in crown allometries at the species level, we used field
data to develop regression models aiming to explain the primary drivers of changes in CV
among trees (Table S1).
Table S1 | Comparison of regression models aiming to explain variation in CV among trees. The AIC of the
best fitting model (M4) is shown in bold. Species richness and plot basal area are abbreviated to SR and BA,
respectively. An interaction term was fitted in order to allow CV~DBH relationships to vary among species.
Model
Structure
M0
M1
M2
M3
M4
log (CV) ~ log (DBH)
AIC
log (CV) ~ log (DBH) x Species identity
log (CV) ~ log (DBH) x Species identity + BA
log (CV) ~ log (DBH) x Species identity + SR
log (CV) ~ log (DBH) x Species identity + BA + SR
30400
22152
22015
22045
21900
We found that tree size explains much of the variation in CV among trees (R2=0.81 for M1 in
Table S1). Based on the relationship between CV and DBH, we predicted the CV of each tree
in the dataset, using these values to obtain a measure of predicted canopy packing at the plot
level. Predicted canopy packing values were strongly related to those obtained from field
measurements (Fig. S3a). However, we found that the influence of species richness of canopy
packing weakened when considering predicted as opposed to observed values (see main text
and Fig. S3b). The reason for this is that trees exhibit crown plasticity, tending to have larger
crown in mixed stands and decreased CV in plots with high basal area. The strong influence
of both species richness and basal area on CV is confirmed by the fact that models which
account for these two factors significantly outperform ones that do not (Table S1).
Fig. S3 | Predicted vs observed canopy packing values. In panel (a) the relationship is shown for each country,
with the dashed line corresponding to a 1:1 relationship. In panel (b) separate lines are fitted to plots in each
species richness level, highlighting a progressively larger difference between observed and predicted canopy
packing (i.e., observed > predicted) when going from monocultures to mixtures with 4 or more species.
[5]
Crown plasticity enables trees to optimize canopy packing in mixed-species forests
Tommaso Jucker, Olivier Bouriaud and David A. Coomes
Appendix S3 | Canopy packing models
Accounting for non-target species
Canopy packing models were fitted to a subset of the total FunDivEUROPE plot network
(199 of the 209 plots). Ten plots were excluded from the analyses as they contained too high
a proportion of non-target trees within the stand (Fig. S4): 6 in Poland, 3 in Germany and 1 in
Romania. The criteria used to exclude plots was based on proportion of total canopy volume
belonging to non-target trees (>20% in excluded plots). Plots with a high proportion of nontarget trees were excluded as we did not have sufficient allometric data to model the crown
volume of non-target species. This precluded us from robustly teasing apart vertical
stratification effects from those of crown plasticity for these plots, as this requires substituting
measured CV with predicted values from models to tease out the effects of crown plasticity.
Nonetheless it should be noted that analyses performed on the entire dataset led to almost
identical results to those performed on the subset of the data which we present in the main
document.
Fig. S4 | Scatter plot of canopy volume estimates for each plot (in 1000 m3) based on all trees within the stand
and only accounting for target species. Dashed line corresponds to a 1:1 relationship. Points falling to the right of
red line (n = 10) correspond to plots in which non-target species make up > 20% of the total canopy volume.
These were excluded from the analyses presented in the main document.
Model selection
To determine the importance of species richness as a predictor of canopy packing and to
gauge the appropriate level of model complexity, a number of alternative mixed effects
models of canopy packing were fitted and compared using AIC (Table S2). Models included
different combinations of three predictors: species richness, plot basal area (to account for the
fact that plots with a greater density of trees are expected to have greater total canopy
volume) and country (to account for the fact that baseline canopy packing values vary among
forest types; treated a random effect in the model).
[6]
Crown plasticity enables trees to optimize canopy packing in mixed-species forests
Tommaso Jucker, Olivier Bouriaud and David A. Coomes
Table S2 | Comparison of mixed-effects models of canopy packing. The AIC of the best fitting model (M7) is
shown in bold. Species richness and plot basal area are abbreviated as SR and BA, respectively. Model structure
follows lme4 syntax in R, where (1 | Country) indicates that country is included as a random effect, which is
normally distributed and affects the intercept, while (SR | Country) corresponds to a varying slope and intercept
model (i.e., testing whether the effects of species richness on canopy packing varies among countries).
Model
M0
M1
M2
M3
M4
M5
M6
M7
M8
Structure
logit (Canopy packing) ~ (1 | Country)
logit (Canopy packing) ~ SR + (1 | Country)
logit (Canopy packing) ~ BA + (1 | Country)
logit (Canopy packing) ~ SR + BA + (1 | Country)
logit (Canopy packing) ~ SR + (SR | Country)
logit (Canopy packing) ~ SR + BA + (SR | Country)
logit (Canopy packing) ~ BA + (BA | Country)
logit (Canopy packing) ~ SR + BA + (BA | Country)
logit (Canopy packing) ~ SR + BA + (BA | Country) + (SR | Country)
AIC
369.8
365.0
335.7
331.5
368.9
335.5
318.7
309.4
315.4
We chose basal area as a descriptor of stand structure in the models as it correlates strongly
with both the mean size of trees within plots and the total number of stems within a stand
(Fig. S5).
Fig. S5 | Scatter plots of (a) stand basal area and quadratic mean stem diameter (ρ = 0.74; P < 0.0001) and (b)
quadratic mean stem diameter and total number of stems within a plot (ρ = –0.77; P < 0.0001). Relationships are
plotted on a logarithmic scale.
For a given level of complexity (e.g., M1 vs M0), models which included a species richness
term always outperformed ones that did not. However, models which included a random
slope term for species richness were not supported (i.e., M4 vs M1 and M8 vs M7). This
suggests that although canopy packing values vary among forest types, the effect of species
richness on canopy packing does not (Fig. S6).
[7]
Crown plasticity enables trees to optimize canopy packing in mixed-species forests
Tommaso Jucker, Olivier Bouriaud and David A. Coomes
Fig. S6 | Relationship between canopy packing (logit transformed) and species richness for each site. Fitted
relationships were obtained from a mixed-effects model in which the effect of species richness on canopy
packing was allowed to vary across sites (i.e., random slope effect). Variation in slope among sites was minimal
in the model (± 0.02 from the overall slope of 0.12).
Overall, the best performing model (the results of which are presented in the main text)
included both the effects of species richness and plot basal area on canopy packing, with the
effect of plot basal area on canopy packing varying among countries (M7). Species richness
and plot basal area were only weakly correlated (Fig. S7), suggesting that collinearity should
not affect parameter estimates in the models.
Fig. S7 | Relationship between plot basal area and species richness across the entire plot network (black fitted
line), and for each site separately (see figure legend for colour coding). Pearson’s correlation coefficients (ρ)
between plot basal area and species richness, both within and among countries, were weak: ρ = 0.13 across all
plots, with a minimum in Spain (-0.16), and a maximum in Poland (0.21) .
[8]
Crown plasticity enables trees to optimize canopy packing in mixed-species forests
Tommaso Jucker, Olivier Bouriaud and David A. Coomes
Appendix S4 | Crown expansion and light interception
Crown vertical and lateral expansion
Increased crown volume (CV) can be the result of one of two processes: trees can either
expand their crown laterally by increasing their crown radius (CRmax) and/or vertically by
increasing their crown depth (CD). To determine whether changes in CV where primarily
driven by changes in CRmax or CD, we modelled the two crown architectural components
separately. In addition to this, we also tested whether tree height (H) – diameter (DBH)
scaling relationships varied in response to species richness:
log (CRmax) ~ log (DBH) + SR + BA + (log (DBH) | Species identity)
(11)
log (CD) ~ log (H) + SR + BA + (log (H) | Species identity)
(12)
log (H) ~ log (DBH) + SR + BA + (log (DBH) | Species identity)
(13)
Across species, both CRmax and CD increased significantly in response to species mixing,
suggesting that increased crown volume of trees in mixture is the result of both a lateral and
vertical expansion of the crown (Table S3). Interestingly, CD increased even though trees
became significantly shorter (for a given diameter) when growing in mixture (Table S3). The
fact that tree in mixture allocate less carbon to height growth vs diameter increment suggests
that species mixing is alleviating competition for light among neighbouring trees (Jucker et
al. 2014). In addition to species richness, plot basal area also had a strong influence on crown
morphology (Table S3). In general, trees growing in densely packed stands are taller and
have slimmer crowns that are less deep.
Table S3 | Regression models testing the effects of species richness and plot basal area on crown radius, crown
depth, tree height and crown light interception (equations 11-13 and 15).
Equation
Response variable
11
Crown radius
12
Crown depth
13
Tree height
15
Light interception
Predictor
Slope (CI95)
Species richness
Plot basal area
Species richness
Plot basal area
Species richness
Plot basal area
Species richness
0.0351 (0.0057)
-0.0035 (0.0007)
0.0282 (0.0058)
-0.0092 (0.0007)
-0.0252 (0.0040)
0.0068 (0.0005)
0.0664 (0.0175)
Plot basal area
-0.0166 (0.0022)
[9]
Crown plasticity enables trees to optimize canopy packing in mixed-species forests
Tommaso Jucker, Olivier Bouriaud and David A. Coomes
Vertical stratification in species tree heights
Table S4 | Mean and maximum height (H), crown depth (CD) and crown radius (CR) of each study species.
Maximum values correspond to the 99th percentile of the data for each allometric measurement.
Study site
Finland
Germany
Italy
Poland
Romania
Spain
Species name
Mean H
Max H
Mean CD
Max CD
Mean CR
Max CR
Betula pendula
18.1
Picea abies
16.3
24.8
9.7
16.7
2.3
4.0
24.3
11.5
19.5
2.2
3.5
Pinus sylvestris
17.8
24.5
8.0
12.9
2.2
3.5
Acer pseudoplatanus
20.8
33.9
9.6
23.0
2.6
7.2
Fagus sylvatica
21.1
37.0
12.8
27.1
3.2
7.0
Fraxinus excelsior
25.8
38.7
9.3
23.5
2.6
7.0
Picea abies
21.4
35.5
10.9
23.7
2.2
5.0
Quercus petraea
30.8
37.6
16.5
26.4
4.5
7.0
Castanea sativa
14.9
22.1
8.2
16.9
2.1
4.5
Ostrya carpinifolia
14.8
24.2
6.2
15.4
1.8
4.3
Quercus cerris
19.1
29.3
9.2
20.0
2.8
7.0
Quercus ilex
13.3
22.9
8.0
18.4
2.3
7.0
Quercus petraea
18.0
27.9
9.6
19.5
2.9
8.4
Betula pendula
31.8
38.3
14.1
21.6
3.8
7.1
Carpinus betulus
20.8
30.5
13.7
23.3
3.5
8.0
Picea abies
25.6
38.5
15.9
28.3
2.7
5.0
Pinus sylvestris
32.7
39.6
11.1
19.0
3.5
6.0
Quercus robur
29.6
40.3
15.4
24.5
4.0
8.1
Abies alba
26.7
40.1
11.5
26.4
2.1
4.2
Acer pseudoplatanus
26.3
35.5
11.2
20.3
2.5
5.0
Fagus sylvatica
25.4
39.9
12.9
24.5
2.7
6.0
Picea abies
28.3
43.5
14.6
30.5
2.1
4.0
Pinus nigra
11.3
19.5
5.9
11.7
2.4
5.0
Pinus sylvestris
12.8
21.2
5.6
11.4
2.2
6.6
Quercus faginea
7.5
14.0
4.5
9.8
1.4
4.0
Quercus ilex
4.8
10.4
3.1
6.5
1.3
3.3
Relating crown volume and light interception
Crown volume is considered a good proxy of a tree’s ability to intercept light (Binkley et al.
2013). Nevertheless, even a tree with a large crown may exhibit slow growth if neighbouring
trees cast it in shade. To determine whether crown volume estimates effectively capture the
extent to which a tree is able to intercept light, we used field data to calculate a light
interception (LI) index for each tree using the approach developed by King et al. (2005):
𝐿𝐼 = 𝐶𝑃𝐴 × 𝐶𝐼 2
(14)
where CPA is the crown projected area of each tree (in m2; calculated using the crown radius
measurements taken in the field) and CI is the crown illumination index, which scores each
[10]
Crown plasticity enables trees to optimize canopy packing in mixed-species forests
Tommaso Jucker, Olivier Bouriaud and David A. Coomes
tree on a scale of 1 to 5 based on exposure to direct sunlight (Clark & Clark 1992).
Suppressed crowns with no direct access to light receive a CI score of 1, trees exposed only
to lateral light are assigned to class 2, trees experiencing overhead light on a portion of their
crown are scored as 3, crowns with complete access to overhead light belong to class 4, while
fully exposed dominant crowns are assigned to class 5. Crown volume was found to be a
strong predictor of light interception (Fig. S8).
Fig. S8 | Relationship between light interception and crown volume for all tree in the plot network (axes are on
a log-log scale). Tree species are grouped by country.
In addition to this, we also tested whether light interception varied in relation to species
richness by fitting a linear mixed-effects model of:
log (LI) ~ log (DBH) + SR + BA + (log (DBH) | Species identity)
(15)
As was found for crown volume, this revealed that light interception increased significantly
in response to species richness (Table S3).
Binkley, D., Campoe, O. C., Gspaltl, M. & Forrester. D. I. 2013 Light absorption and use
efficiency in forests: Why patterns differ for trees and stands. Forest Ecol. Manag., 288, 5–13.
Clark, D.A. & Clark, D.B. 1992 Life history diversity of canopy and emergent trees in a
neotropical rain forest. Ecol. Monogr., 62, 315–344.
Jucker, T., Bouriaud, O., Avacaritei, D., Danila, I., Duduman, G., Valladares, F. & Coomes,
D. A. 2014 Competition for light and water play contrasting roles in driving diversity–
productivity relationships in Iberian forests. J. Ecol., 102, 1202–1213.
King, D. A., Davies, S. J., Nur Supardi, M. N. & Tan, S. 2005 Tree growth is related to light
interception and wood density in two mixed dipterocarp forests of Malaysia. Func. Ecol., 19,
445–453.
[11]
Crown plasticity enables trees to optimize canopy packing in mixed-species forests
Tommaso Jucker, Olivier Bouriaud and David A. Coomes
Appendix S5 | The influence of shade tolerance on canopy packing
To test whether mixtures which include species with a greater range of shade tolerance (i.e.,
mixtures of shade tolerant and light demanding species) are able to partition aboveground
space most efficiently we calculated a metric of functional diversity in shade tolerance
(FDshade) for each plot. To do so we made use of a continuous measure of shade tolerance
developed by Niinemets & Valladares (2006) which has since been widely used in forest
ecology (e.g., Kunstler et al. 2011). Estimates of shade tolerance were obtained for each
species from Appendix A in Niinemets & Valladares (2006) and are reported in Table S5.
Table S5 | Shade tolerance index for each species in the FunDivEUROPE plots (± standard errors) as reported
in Appendix A of Niinemets & Valladares (2006). Low values identify light demanding species, while high
values indicate species with a greater degree of shade tolerance. Estimates were available for all species with the
exception of Quercus faginea (†), for which a genus-level mean was used.
Species name
Shade tolerance
Abies alba
Acer pseudoplatanus
Betula pendula
Carpinus betulus
Castanea sativa
Fagus sylvatica
Fraxinus excelsior
Ostrya carpinifolia
Picea abies
Pinus nigra
Pinus sylvestris
Quercus cerris
Quercus faginea†
Quercus ilex
Quercus petraea
Quercus robur
4.60 ± 0.06
3.73 ± 0.21
2.03 ± 0.09
3.97 ± 0.12
3.15 ± 0.23
4.56 ± 0.11
2.66 ± 0.13
3.94 ± 0.18
4.45 ± 0.50
2.10 ± 0.43
1.67 ± 0.33
2.55 ± 0.11
2.51 ± 0.07
3.02 ± 0.19
2.73 ± 0.27
2.45 ± 0.28
To calculate the diversity in shade tolerance of each plot (FDshade) we used Rao’s quadratic
entropy index (de Bello et al. 2010). For a given plot, we calculated FDshade as:
𝐹𝐷𝑠ℎ𝑎𝑑𝑒 = ∑𝑆𝑖𝑗 𝑑𝑖𝑗 𝑝𝑖 𝑝𝑗
(15)
where S is the number of species in the plot (species richness), dij is the distance between the
species pair i and j, weighted by the relative abundance pi and pj of the two species (estimated
on the basis of relative basal area within a plot). The dissimilarity between species (dij) is
quantified using a multivariate functional distance matrix based on Euclidean distance.
FDshade was calculated using the dbFD function in the R package FD.
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Crown plasticity enables trees to optimize canopy packing in mixed-species forests
Tommaso Jucker, Olivier Bouriaud and David A. Coomes
FDshade emerged a strong predictor of canopy packing (Fig. S9), with plots that included
species with a greater range in shade tolerance exhibiting more efficient use of aboveground
space (P = 0.0004; Slope and 95% confidence intervals = 0.50 ± 0.27).
Fig. S9 | Relationship between canopy packing (logit transformed) and FDshade (a measure of the diversity in
shade tolerance of species within a plot) across the FunDivEUROPE network. The red line corresponds to the fit
of a linear model, with the shaded region marking the 95% confidence intervals of the regression line.
Niinemets & Valladares. 2006 Tolerance to shade, drought, and waterlogging of temperate
northern hemisphere trees and shrubs. Ecol. Monogr., 76, 521–547.
de Bello, F., Lavergne1, S., Meynard, C.N., Lepš, J. & Thuiller, W. 2010 The partitioning of
diversity: showing Theseus a way out of the labyrinth. J. Veg. Sci., 21, 992-1000.
Kunstler et al. 2011. Effects of competition on tree radial-growth vary in importance but not
in intensity along climatic gradients. J. Ecol., 99, 300–312.
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