Tree Physiology 35, 1035–1046
doi:10.1093/treephys/tpv067
Research paper
Stand density, tree social status and water stress
influence allocation in height and diameter growth
of Quercus petraea (Liebl.)
Raphaël Trouvé1,2,3, Jean-Daniel Bontemps1,2, Ingrid Seynave1,2, Catherine Collet1,2
and François Lebourgeois1,2
1AgroParisTech,
Centre de Nancy, UMR 1092 INRA/AgroParisTech Laboratoire d’Étude des Ressources Forêt Bois (LERFoB), 14 rue Girardet, 54000 Nancy, France; 2INRA,
Centre de Nancy-Lorraine, UMR1092 INRA/AgroParisTech Laboratoire d’Étude des Ressources Forêt Bois (LERFoB), 54280 Champenoux, France; 3Corresponding author
([email protected])
Received December 1, 2014; accepted June 22, 2015; published online July 31, 2015; handling Editor Annikki Mäkelä
Even-aged forest stands are competitive communities where competition for light gives advantages to tall individuals, thereby
inducing a race for height. These same individuals must however balance this competitive advantage with height-related mechanical and hydraulic risks. These phenomena may induce variations in height–diameter growth relationships, with primary dependences on stand density and tree social status as proxies for competition pressure and access to light, and on availability of local
environmental resources, including water. We aimed to investigate the effects of stand density, tree social status and water stress
on the individual height–circumference growth allocation (Δh–Δc), in even-aged stands of Quercus petraea Liebl. (sessile oak).
Within-stand Δc was used as surrogate for tree social status. We used an original long-term experimental plot network, set up in
the species production area in France, and designed to explore stand dynamics on a maximum density gradient. Growth allocation was modelled statistically by relating the shape of the Δh–Δc relationship to stand density, stand age and water deficit. The
shape of the Δh–Δc relationship shifted from linear with a moderate slope in open-grown stands to concave saturating with an
initial steep slope in closed stands. Maximum height growth was found to follow a typical mono-modal response to stand age.
In open-grown stands, increasing summer soil water deficit was found to decrease height growth relative to radial growth, suggesting hydraulic constraints on height growth. A similar pattern was found in closed stands, the magnitude of the effect however
lowering from suppressed to dominant trees. We highlight the high phenotypic plasticity of growth in sessile oak trees that
further adapt their allocation scheme to their environment. Stand density and tree social status were major drivers of growth
allocation variations, while water stress had a detrimental effect on height in the Δh–Δc allocation.
Keywords: competition, drought, increment, plasticity, trade-off, water availability.
Introduction
Plants are highly plastic organisms (­Sultan 2000) that may
adapt their morphology to their local environment to maximize
resource acquisition (­Bloom et al. 1985, ­Ågren et al. 2012,
­Poorter et al. 2012) and face bio-physical constraints. Accordingly, they need to arbitrate between different growth allocation
strategies impacting their status over the longer term, and
­ artition newly acquired assimilates among plant compartments
p
to gain better access to limiting resources and, eventually, competitive advantages over their neighbours (­Poorter et al. 2006).
As the upper stratum of closed forest canopy intercepts most
radiations (­Weiner 1990, ­Pacala et al. 1996), a strong incentive
is given to height growth over diameter growth in tree communities where competition is established (­King 1990, ­Falster and
© The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]
1036 Trouvé et al.
Westoby 2003). This incentive is particularly strong for suppressed individuals, which experience the highest degree of
competition. Resulting from this race for light, suppressed trees
are typically more slender than their dominant counterparts
(­Deleuze et al. 1996, ­Sumida et al. 1997, ­2013, ­Seki et al.
2013). On the opposite side of the density gradient, in lower
density stands, preferential allocation to height growth provides
no competitive advantage over neighbouring trees. Accordingly,
open-grown trees represent an empirical maximum in terms of
bulkiness (­Krajicek et al. 1961, ­Hasenauer 1997).
Advantages related to higher height usually balance with higher
mechanical constraints—since decreasing allocation to stem
thickening leads to a higher risk of mechanical damages
(­McMahon 1973, ­King 1990), higher hydraulic constraints and a
higher risk of disruption of water transport (­Ryan and Yoder
1997, ­Ryan et al. 2006, ­Kempes et al. 2011). As a result, species
growing in drier environments are relatively thicker-stemmed than
those growing in moister sites (­Wang et al. 2006, ­Lines et al.
2012, ­Chave et al. 2014). Similar patterns of variation have been
observed within species (­Callaway et al. 1994, ­Méndez-Alonzo
et al. 2008), but, to our knowledge, none of these studies was
performed in a temperate area.
Patterns of biomass allocation between stem height and diameter have most often been studied from static height–­diameter
relationships, and seldom from changes in height–diameter relationships with time or from the relationship between height
growth and diameter growth. Since allocation patterns can vary
over time, static relationships will integrate multiple effects of
past growth conditions over the whole tree lifespan, which make
them difficult to interpret when past growth conditions have not
been constant in time. Analysing the relationship between height
growth and diameter growth should thus enhance our understanding of height and diameter growth processes, their determinants and their interactions.
In the present study, we aimed to explore the effects of stand
density, tree social status and water stress (soil water content
(SWC), soil water deficit (SWD) and vapour pressure deficit
(VPD)) on the allocation of growth to height versus diameter in
trees. We also aimed to provide a robust empirical model to
quantify the combined effects of these different factors on
growth. We based our study on Quercus petraea Liebl. (sessile
oak), a light-demanding species likely to display a strong res­
ponse to changes in neighbour competition (­Jack and Long
1991) with regard to height–circumference growth (Δh–Δc)
allocation, and also the second largest broadleaved growing
stock in France with 281 million m3 (­IFN 2013). In order to
explore the largest range of Δh–Δc allocation with respect to
light availability, we used a network of silvicultural experiments
sampled over sessile oak production area (­Bédénaux et al.
2001) and covering a full density gradient ranging from opengrown to self-thinning stands. Water stress has been shown to
be an important climatic driver for both radial (­Lebourgeois et al.
Tree Physiology Volume 35, 2015
2004, ­Friedrichs et al. 2009, ­Mérian et al. 2011) and height
growth (­Bergès and Balandier 2010). While many studies have
analysed the relationship between water stress and radial or
height growth in isolation, a gap remains in the knowledge on
the influence of water stress on the Δh–Δc allocation.
Three specific hypotheses were tested: (Hypothesis 1) opengrown trees allocate less to height growth relative to radial
growth than do trees grown in closed-canopy stands; (Hypothesis 2) allocation to height growth relative to radial growth is
higher in suppressed trees than in dominant trees; and (Hypothesis 3) water stress reduces allocation to height growth relative
to radial growth.
Materials and methods
Experimental data
The study focused on sessile oak (Q. petraea Liebl.) as one of
the most common broadleaved species in Europe and France
(­Koeble and Seufert 2001, ­IFN 2013), where it plays an important role in the forest economic sector.
Our data originate from a long-term experimental network
belonging to the ‘French data cooperative on forest growth’, a
national incentive between forest institutions designed to explore
the effect of large density gradients, from open-grown tree to
self-thinning stand situations, on forest dynamics of even-aged
stands (­Bédénaux et al. 2001). Each site corresponds to a set
of experimental plots (0.36 ha) of the same age (ranging from
11 to 42 years in the experimental network), measured every
4 years and experiencing contrasted thinning regimes defined
by a target relative density index (RDI, ­Reineke 1933) scenario.
Stand thinning was carried out once per measurement period
and at the beginning of the period (i.e., just after measurement),
when the relative stand density of the plot was above the target
relative density defined in its thinning regime. When the relative
density was below the target density, no thinning was performed.
Trees selected for thinning were evenly spread among diameter
classes. As is common practice for even-aged oak forests in
France, stands have been naturally regenerated (­Huffel 1927,
­Jarret 2004). In the network of experiments, we selected sites
old enough to have at least two consecutive measurements. The
six selected sites cover the plains of Northern France (Figure 1)
and are representative of sessile oak in its production area. In all
selected plots, the target relative density was held constant in
time. Table 1 provides general information on the selected sites.
Dendrometric variables
At each measurement date, individual tree circumference was
measured with a measuring tape. Two cases occurred: when
<1000 trees per plot were present, all trees were numbered and
their circumference was measured; otherwise a statistical inventory was conducted (usually in young self-thinning stands). This
statistical inventory consisted of 30 rectangular subplots of
and latitude of the study site are shown below site name.
min and max range (inside parentheses) per trial. T and P are yearly mean and sum values, respectively. Soil water content, SWD and VPD are mean summer values.
3Min and max range of the studied variable among different plots of the same site at the start and at the end of the experiment.
4Soil water holding capacity (SWHC) for a soil down to a depth of 1 m. Soil water holding capacity represents the maximum amount of water that a given soil can hold for plants use. They are GIS interpolation
of NFI data extracted from ­Piedallu et al. (2011).
2Averages,
1Longitude
11.5 (11.4–11.6) 810 (808–810) 28 (26–31) 33 (32–34) 7.0 (6.4–7.3)
95
0.34–0.81 0.12–0.8
142–1796
16–17 17–18 33–44 40–58 589–2486
42
38
464
4
0.36
2
2.7046–46.6645
40 (37–44) 5.2 (4.9–5.8)
10.7 (10.6–10.8) 858 (786–915) 15 (7–20)
66
0.43–0.89 0.31–0.95
377–1966
13–14 16–18 29–36 42–55 1090–2946
39
31
799
5
0.36
3
845 (829–873) 32 (26–40) 31 (23–39) 5.8 (5.4–6.7)
10.3 (9.8–10–9)
102
0.15–0.83 0.17–1.06
128–2674
12–17 19–26 37–74 496–5518
9–11
29
17
971
4
0.36
4
801 (801–801) 56 (56–56) 27 (27–27) 4.9 (4.9–4.9)
10.4 (10.4)
127
0.05–1.03 0.05–1.03
359–30,775 359–30,775
7–14
7–14
5–6
5–6
11
11
260
4
0.36
1
703 (615–800) 16 (10–22) 53 (41–67) 5.8 (4.6–7.7)
11.5 (11–12)
104
0.04–0.96 0.09–1.20
16–44 599–49,424 138–13,326
6–8
7–11
4–5
23
11
1183
5
0.36
4
130
End
0.04–0.58 0.10–0.88
Start
End
Start
End
24–49 532–19,400 126–4171
5–9
Start
End
Start
8–12
Range3
Range3
4–6
26
14
698
4
3
0.36
Grosbois
1996
2.9933–46.5022
Montrichard 1995
1.1789–47.3748
Moulins2005
Bonmoulins
0.5124–48.6955
Parroy
1996
6.6554–48.6701
Reno-valdieu 1997
0.6757–48.5289
Tronçais
2001
Range3
Range3
N
(stems ha−1)
Cg
(cm)
Ho
(meters)
Number
Age
of
(years)
individual
height
increment
Start End
Starting Mean Number
date
plot
of plots
size per trial
(ha)
Number
of
growth
periods
per site
Dendrometrical variables
Trial description
Trial1
Table 1. Dendrometrical and environmental description of the experimental sites.
fixed length (in-between two silvicultural racks, from 5 to 10 m),
each of them wide enough (from 1 to 4 m) to contain ∼15 trees
and for which circumferences at breast height were measured
(see Appendix A available as Supplementary Data at Tree
­Physiology Online).
At each measurement date, individual tree height was measured on 60 trees evenly spread along the circumference distribution established for each plot. Height measurements were
done using a telescopic pole where height was < 12 m and with
a hypsometer (mean of two diametrically opposed measurements) when height was > 12 m. As mortality among trees is
significant in these young stands, part of the subsample used for
height measurement was renewed at each measurement period.
Circumference and height increments were calculated from two
subsequent measures on the same tree.
For each site, stand age was estimated at the installation of the
experimental plots. Eight dominant trees were selected and cored
at 30 cm above the soil, and tree age was estimated by counting
ring numbers. In the study, stand age during each measurement
period was set to the age of the stand at the beginning of the
4-year-period. Relative density index (RDI, dimensionless),
expressing the current density (N, in stems ha−1) relative to the
threshold self-thinning density (Nmax, in stems ha−1) at the current
quadratic mean diameter (dg, in cm), was used to express plot
stand density on a relative scale. Relative density index was calculated as RDI = N/Nmax, using Nmax = 125,242/dg1.566 from ­Le Goff
et al. (2011), so that RDI = N ⋅ dg1.566/125,242. Thinning ­intensity
RDI
(dimensionless)
Figure 1. Geographical location of the experimental sites in Northern
France. Large black circles indicate sessile oak sites, while small grey
points represent the distribution of pure stands of sessile oak according
to NFI data. Grey shading on the map indicates elevation, with white
shading indicating sea level and black shading indicating elevation above
2500 m.
SWHC4 T
(mm)
(°C)
Environmental variables2
P
(mm)
SWC
(mm)
SWD
(mm)
VPD
(hPa)
11.2 (10.9–11.8) 762 (728–794) 50 (40–59) 28 (21–37) 6.8 (5.9–7.6)
Crowding and water stress on height–diameter growth 1037
Tree Physiology Online at http://www.treephys.oxfordjournals.org
1038 Trouvé et al.
(TI) in each plot and period was calculated as a ratio between the
RDI removed during thinning and the RDI before thinning.
Climatic data
Data on monthly precipitation (P) and monthly mean temperature (T) were obtained for each site, year and month from the
Safran spatial climatic analysis (­Quintana-Seguí et al. 2008,
­Vidal et al. 2010). We further calculated VPD as an index of
atmospheric evaporative demand (see Appendix B available as
Supplementary Data at Tree Physiology Online), SWC as an
index of belowground water availability potential and SWD as an
index of water stress (see Appendix C available as Supplementary Data at Tree Physiology Online). These indices of water
availability are often jointly used in process modelling (­Dufrêne
et al. 2005, ­Waring and Landsberg 2011, ­Meinzer et al. 2013)
and are expected to be better indicators of the influence of climate on tree growth than raw climatic data (­Lebourgeois et al.
2013, ­Piedallu et al. 2013). Monthly climatic data were then
averaged (except P data, which were summed) by season for a
given year, and averaged by growth period in-between two successive measurement dates.
Modelling growth allocation
Height growth was modelled as a function of radial growth at
1.30 m. Due to the size hierarchy among trees prevailing in
even-aged stands, radial increment within stands is considered a
good proxy of tree social rank (­Ford 1975, ­Dhôte 1994), as
shown in Appendix D available as Supplementary Data at Tree
Physiology Online. In Figure 2, individual height increments were
plotted as a function of individual circumference increments at
1.30 m. In stands of medium to high density, height growth was
well represented by a saturating function of radial growth intersecting the origin (Figure 2), whereas the relationship was linear
in stands with lower RDI. Noticeably, no data with zero radial
increment could be observed in stands with lowest RDI, so that
height increments at the intercept cannot be extrapolated.
Mitscherlich (or monomolecular) function (Eq. (1)) is a simple saturating function able to approximate patterns exhibited
in Figure 2. It comprehends two parameters: α1 as the asymptotic height growth rate (cm year−1), and β1 as a shape parameter that represents how ‘fast’ the asymptote is reached
(year cm−1), α1 ⋅ β1 being the slope at the origin. The general
model follows:
∆h = α1 × (1 − exp(− β1 × ∆c )),
(1)
where Δh is the mean height growth per year of a given tree
during one period and Δc its mean annual circumference growth
at 1.30 m during the same period.
A three-step modelling approach was used to assess the
effects of stand and climatic variables on Eq. (1):
Step 1: The objective was to split the observed variation in the
parameters of Eq. (1) according to the different levels of the
Tree Physiology Volume 35, 2015
Figure 2. Height growth as a function of circumference growth for
stands of contrasting density. Light dots represent open-grown stands
(RDI < 0.4) while dark dots represent medium to dense stands
(RDI > 0.4). Bolded black lines are penalized cubic regression splines fit,
and bold dashed lines are quantile penalized cubic regression splines fit
on the 10th and 90th quantile range.
experimental design (site, plot, period). As the dataset has a
hierarchical structure with measurement periods nested within
plots, themselves nested within site, a Mitscherlich equation with
nested ‘site’, ‘plot’ and ‘period’ random effects introduced on
both α1 and β1 was fitted by maximum likelihood on the whole
dataset (Eq. (2)). The ‘site’ random effect can be interpreted in
terms of variations in age and environmental conditions (soil and
climate) among sites, while the ‘plot’ random effect can be interpreted in terms of RDI treatments and residual micro-site variations. The ‘period’ random effect can be interpreted as changes
in age within site (stand ageing) and variations in climatic conditions between periods. The model is therefore:
∆hi = (α1, s, pl , p ) × (1 − exp(−( β1, s, pl , p ) × ∆ci )) +
εi
~N( 0 ,σ2 )
α1, s, pl , p = α1 +
a1, s
+
b1, s
+
~N( 0 ,σ2α ,s )
β1, s, pl , p = β1 +
~N( 0 ,σ2β ,s )
a1, s, pl
~N( 0 ,σ2α ,s ,pl
b1, s, pl
)
~N( 0 ,σ2β ,s ,pl )
+ a1, s, pl , p
~N( 0 ,σ2α ,s ,pl ,p )
+
(2)
b1, s, pl , p ,
~N( 0 ,σ2β ,s ,pl ,p )
where Δhi and Δci are individual height and circumference
growth for tree i. α1 and β1 are fixed parameters to be estimated,
a1 and b1 are random variables following Gaussian distributions
with 0 mean and variance σ2 (~N(0,σ2)), whose subscript (‘s’/
‘s,pl’/‘s,pl,p’) indicate the hierarchical levels of the sampling
design (‘site’/‘plot within site’/‘period within plot within site’)
they are associated with, and whose variances are also estimated in the procedure. Gaussian d
­ istribution for both the error
Crowding and water stress on height–diameter growth 1039
ε and random variables as well as their independence
were assumed (­Pinheiro and Bates 2000). By summing up
the fixed coefficient and the individual estimates for the random
effects, we obtained 73 estimates of α1,s,pl,p and of β1,s,pl,p
(one for each combination of site, plot and period):
α1,s,pl,p = α1 + a1,s + a1,s,pl + a1,s,pl,p and β1,s,pl,p = β1 + b1,s + b1,s,pl + b1,s,pl,p.
Step 2: The objective was to detect variables influencing the
Δh–Δc relationship. We used multiple ordinary least square
(OLS) regression to regress the two series of parameters α1,s,pl,p
and β1,s,pl,p obtained previously against stand variables (age,
RDI, TI) and seasonal water-related variables (P, SWC, SWD, VPD)
(Eqs (3) and (4)). To take into account possible non-linearities
and interactions in the predictor effects, second-degree polynomials and first-order interactions were tested. Variable selection
was performed by a forward stepwise procedure minimizing the
Akaike information criterion (AIC, ­
Burnham and Anderson
2002). New variables were added to the model when they
reduced the AIC by at least two points and were significant
(P-value <0.05). Ordinary least square models were thus:
α1,s,pl ,p = α1′ + Xα A + εα , (3)
β1,s,pl ,p = β1′ + Xβ B + ε β ,
(4)
where α1′ and β1′ are intercept parameters, Xα and Xβ are predictor matrices (age, RDI, TI, seasonal P, SWC, SWD, VPD, including
second-degree polynomials for each predictor and first-order
interactions between predictors), A and B are associated parameter vectors to be estimated and εα and εβ are additive error
terms assumed to follow Gaussian distributions with constant
variance and independent errors. To measure the respective
contribution of the different predictors in the model, a semipartial R2 was computed for each of them. For each predictor,
the semi-partial R2 was computed by subtracting the R2 of the
full model without the predictor from the R2 of the full model.
Step 3: The objective was to build an integrated model
describing the relationship between height and radial growth at
the tree level. A height growth model (latter referred as ‘integrated’ model, Eq. (5)) structured on the Mitscherlich equation
(Eq. (2)) and incorporating the multiple regression models of
α1,s,pl,p and β1,s,pl,p parameters (Eqs (3) and (4)) into the equation was therefore fitted. The model was defined as follows:
∆hi = (α1,s,pl ,p + Xα A)
× (1 − exp(−( β1,s,pl ,p + Xβ B) × ∆ci )) +
εi
~N( 0 ,σ2 )
α1,s,pl ,p = α1 +
a1,s
+
b1,s
+
~N( 0 ,σα2 ,s )
β1,s,pl ,p = β1 +
~N( 0 ,σ2β ,s )
a1,s,pl
+ a1,s,pl ,p
b1,s,pl
+ b1,s,pl ,p ,
~N( 0 ,σα2 ,s ,pl )
~N( 0 ,σ2β ,s ,pl )
(5)
~N( 0 ,σα2 ,s ,pl ,p )
~N( 0 ,σ2β ,s ,pl ,p )
where Xα and Xβ are predictor matrices selected in step 2, A and
B are parameter vectors to be estimated, while other symbols
have the same signification and rely on the same assumptions as
in Eq. (2).
In order to assess the reduction in the variance of random
effects (‘site’, ‘plot’, ‘period’) when introducing deterministic
effects of the previous predictors (Eq. (5)), the random effects
were kept in the model. Model goodness-of-fits at different hierarchical levels of random effects were measured by pseudo-R2,
defined as the squared correlation between observed and predicted values at different levels of random effects (­Martin-Benito
et al. 2011, ­Aertsen et al. 2014): R2fixed was calculated from predictions of the model with fixed terms only, while R2s/R2s,pl/R2s,pl,p
were calculated from predictions of the model including the fixed
terms plus the ‘site’/‘site and plot’/‘site, plot and period’ random
effects. Potential effects of individual tree size (individual circumference and height) on the height growth model were tested by
analysing the relationships between model residuals and tree size.
No obvious pattern was observed (see Appendix E available as
Supplementary Data at Tree Physiology Online).
To quantify the effects of each predictor on the Δh–Δc relationship, several model predictions were performed, where the
value of the predictors were changed one at a time. For each
predictor, extreme (5 and 95% quantiles) and central (interquantile) values were used. Non-studied variables were fixed at
their interquantile value.
Statistical analyses were performed using the R software
(­R Development Core Team 2012), and non-linear mixed-effects
models were fitted using the ‘nlme’ function (­Pinheiro and Bates
2000).
Results
Modelling step 1
Results from fitting Eq. (2) to the data are summarized in Table 2.
The model with fixed-effects showed a poor fit (R2fixed = 15%).
Introduction of a ‘site’ random effect, mainly associated with variation in α1 (asymptote, coefficient of variation CV σα,s/α1 = 14%)
as compared with β1 (slope, CV σβ,s/β1 = 0.2%), only slightly
improved the amount of variation accounted for by the model
(R2s = 19%). In contrast, the ‘plot’ random effect, mainly associated with variation in β1 (CV σβ,s,pl/β1 = 59%) greatly improved
the variation accounted for by the model (R2s,pl = 40%). The
‘period’ random effect revealed variation in both parameters α1
and β1 and further improved the model (R2s,pl,p = 52%). Predictions of Eq. (2) that included the ‘site’, ‘plot’ and ‘period’ random
effects were unbiased (see Appendix F available as Supplementary Data at Tree Physiology Online).
Modelling step 2
Table 3 displays results from the multiple regression analyses of
the parameter estimates (α1,s,pl,p and β1,s,pl,p fits obtained from
Tree Physiology Online at http://www.treephys.oxfordjournals.org
1040 Trouvé et al.
Table 2. Characteristics of the fitted Eqs (2) and (6). N = 4375.
Equations
Eq. (2)
Parameter
Unit
α1
α2
α3
β1
β2
β3
cm year−1
cm year−2
cm year−3
year cm−1
year cm−1
year cm−1 mm−1
Random effects2
σα,s
σα,s,pl
σα,s,pl,p
σβ,s
σβ,s,pl
σβ,s,pl,p
cm year−1
cm year−1
cm year−1
year cm−1
year cm−1
year cm−1
Goodness-of-fit3
R2fixed
R2s
R2s,pl
R2s,pl,p
%
%
%
%
Fixed parameters1
Predictor
Age
Age2
RDI
RDI × summer SWD
Eq. (6)
Estimate
P-value
Estimate
P-value
46.9
–
–
1.28
–
–
<0.01
–
–
<0.01
–
–
30.95
2.2
−0.053
0.032
3.51
−0.032
<0.01
<0.01
<0.01
0.69
<0.01
<0.01
6.44
1.13
7.55
0.002
0.76
0.4
1.81
0.004
6.62
0.13
<0.001
0.19
15
19
40
52
35
40
40
51
1Estimate
of the fixed parameters.
deviation of the nested random effects.
3Pseudo R2 associated with different levels of random effects.
2Standard
Table 3. Multiple regression on the two parameters series α1,s,pl,p and β1,s,pl,p. N = 73.
Response
Predictors
Estimate
Unit
SE
P-value
R2 variable alone (%)
Semi-partial R2 (%)
α1,s,t,p
Intercept
Age
Age2
39.76
1.101
−0.024
cm year−1
cm year−2
cm year−3
6.06
0.516
0.01
<0.01
0.04
0.02
12
12
β1,s,t,p
Intercept
RDI
Summer SWD
RDI × summer SWD
−0.131
3.43
0.008
−0.037
year cm−1
year cm−1
year cm−1 mm−1
year cm−1 mm−1
0.31
0.47
0.007
0.011
<0.01
<0.01
0.25
0.01
63.2
1.2
31.2
23.1
0.6
4.9
Eq. (2)) against stand and climatic variables (Eqs (3) and (4)).
Model of α1,s,pl,p showed a low goodness-of-fit (R2 = 12%). It
displayed a mono-modal response to age with a maximum at
23 years (see Appendix G available as Supplementary Data at
Tree Physiology Online). Alternatively, we also tested for an
effect of dominant height (Ho) on α1,s,pl,p. The correlation
between stand age and Ho in our dataset was very high
(R = 0.92). Age could be replaced with Ho with only a minor
reduction in goodness-of-fit (R2 of 9%), in which case α1,s,pl,p
displayed a mono-modal response to Ho with a maximum at
9.5 m. The model of β1,s,pl,p had a R2 of 70% and displayed a
strong positive response to RDI, as well as a slight negative
response to summer SWD that increased in amplitude with RDI
(see Appendix G available as Supplementary Data at Tree
­Physiology Online). Other predictors (TI, T, P, SWC, VPD) were
discarded during model selection steps and were therefore not
included in the final multiple regression models.
Tree Physiology Volume 35, 2015
R2 (%)
12
70.7
Modelling step 3
The integrated model of height growth is presented in Eq. (6)
and Table 2. As the effect of summer SWD alone was not significant and decreased the goodness-of-fit, it was not maintained
into the integrated model. All other fixed terms were significant
and associated parameter estimates in Eq. (6) were similar
(Table 2) to those in Eqs (3) and (4) (Table 3), except for the
modal effect of age on the asymptote parameter, more acute in
the integrated model (see Appendix G available as Supplementary Data at Tree Physiology Online). With the exception of the
‘period’ random effect on the asymptote (σα,s,pl,p), standard deviations associated with ‘site’, ‘plot’ and ‘period’ random effects
were drastically reduced in Eq. (6) compared with that of Eq. (2)
(Table 2). Hence, the deterministic terms associated with stand
age, RDI and summer SWD successfully accounted for variations
in the shape of the Mitscherlich function that were initially
described by the random effects. Predictions of Eq. (6) that
Crowding and water stress on height–diameter growth 1041
included the ‘site’, ‘plot’ and ‘period’ random effects were
un­biased (see Appendix F available as Supplementary Data at
Tree Physiology Online).
SWD on the height growth of trees with high circumference
growth appeared to be more acute in low density stands than in
medium (and high, not shown) density stands (Figure 5c).
∆hi = (α1, s, pl , p + α 2 × age + α 3 × age2 )
× (1 − exp(−( β1, s, pl , p + β2 × RDI + β3 × RDI
× summer SWD) × ∆ci )) +
Discussion
εi
~N( 0 ,σ2 )
α1, s, pl , p = α1 +
a1, s
+
b1, s
+
~N( 0 ,σ2α ,s )
β1, s, pl , p = β1 +
~N( 0 ,σ2β ,s )
a1, s, pl
+ a1, s, pl , p
b1, s, pl
+
~N( 0 ,σα2 ,s ,pl )
~N( 0 ,σ2β ,s ,pl )
(6)
~N( 0 ,σα2 ,s ,pl ,p )
b1, s, pl , p
~N( 0 ,σ2β ,s ,pl ,p )
Figure 3 shows the predictive accuracy of the fixed-effects in Eq.
(6) with regard to the shape of the Δh–Δc relationship for contrasted contexts of stand age and RDI. Predictive accuracies of
Eq. (6) for contrasted contexts of RDI and summer SWD were
further explored in Figure 4.
Figure 5 displays the simulated effects of stand age, RDI and
summer SWD on the shape of the Δh–Δc relationship. The monomodal response curve of maximum height growth to stand age
(Figure 5a) and the flattening of the Δh–Δc relationship with
decreasing RDI (Figure 5b) and increasing summer SWD
(­Figure 5c) are clearly visible. The negative effect of ­summer
This research allowed us to quantify the combined effects of
ageing, stand stocking and water stress on the trade-off
between height and circumference growth for even-aged sessile oak stands. Since tree social rank strongly relates to withinstand radial growth, Δc was used as surrogate for tree social
status. Equation (6) provided a simple and convenient way to
represent these influences on the shape of the Δh–Δc relationship (­Figures 2–5), and revealed accurate model predictions.
The shape of the relationship between height growth and circumference growth ranged from linear with a moderate slope in
low density stands, to concave saturating with an initial steep
slope in high density stands: open-grown trees invested proportionally less in height growth than dominant trees in closed
stands (Hypothesis 1), while in closed stands, suppressed
trees invested proportionally more in height growth than dominant trees (Hypothesis 2). High summer SWD was found to
decrease allocation to height growth relative to radial growth in
open-grown stands and in closed stands (Hypothesis 3), except
Figure 3. Height growth as a function of circumference growth for contrasting stand density treatment and age. Relative density index treatments are
represented in different columns (RDI range for each column is shown in parentheses), while sites, period and age are in rows. Solid black lines are
predictions from Eq. (6) with fixed-effect only, while dashed lines are predictions from Eq. (6) including site, plot and period level random effects. Note
that sites and periods selected in this figure are suitably representative of the whole dataset.
Tree Physiology Online at http://www.treephys.oxfordjournals.org
1042 Trouvé et al.
Figure 4. Height growth as a function of circumference growth from successive periods with contrasting summer SWD on the Montrichard site. Relative
density index treatments are represented in different columns (RDI range for each column is shown in parentheses). Solid lines are predictions from
Eq. (6) with fixed-effect only. Black points and lines are from a period (2003–07, 19-year-old stand in 2003) of high summer SWD (67 mm) while
light grey dots and lines are from a period (2007–11, 23-year-old stand in 2007) of medium summer SWD (43 mm). Note that only a few combinations of sites and periods had successive summer SWD contrasted enough to illustrate our model as in this figure.
for dominant trees in the latter ones. In addition, the asymptote
of the Δh–Δc relationship and consequently height growth of
dominant trees was found to follow a mono-modal response to
stand age.
Height and radial growth allocation in open-grown
stands
In open-grown stands, the relationship between height growth
and radial growth followed a fairly linear pattern. The regular
pattern confirms the homogeneous behaviour of open-grown
trees, and underlines the absence of growth allocation differentiation among trees in such stands. Yet, there still remains a large
dispersion of radial increments within a stand, likely to result
from genetic differences, local micro-site variations or initial size
differences that occurred in the regeneration phase and then
amplified over stand development.
Open-grown trees also had a much lower height growth than
dominant trees in closed stands (Figures 2 and 5b). Since there
is almost no competition for light in open-grown stands, there is
no clear adaptive advantage to prioritize height growth at the
expense of radial growth. Furthermore, open-grown trees usually
have larger crown and leaf areas than their closed-stand counterparts (­Hasenauer 1997). This increased leaf area may induce
hydraulic and mechanical constraints, both of which have been
shown to favour radial growth at the expense of height growth.
The increased water flux requirement due to greater leaf area is
usually balanced with an increased sapwood area (­Shinozaki
et al. 1964, ­Long et al. 1981, ­Whitehead et al. 1984), supplied
by additional radial growth at the expense of height growth.
Open-grown trees are also more exposed to wind bending stress,
also shown to stimulate radial growth at the expense of height
growth (­Brüchert and Gardiner 2006, ­Meng et al. 2006).
Height and radial growth allocation in closed stands
In agreement with previous studies (­Deleuze et al. 1996,
­Sumida et al. 2013), we found that suppressed trees show
Tree Physiology Volume 35, 2015
higher investment in height growth relative to circumference
growth than dominant trees. This may be interpreted as ‘a race
for light’, where suppressed individuals maximize their height
growth to remain in the upperstorey. However, this preferential
allocation to height growth may not suffice to keep pace with the
dominant trees (Figure 5). Trees not able to follow the height
growth rate of dominant trees should therefore move to suppression status and would eventually die.
We also found evidence for a maximum height increment in
dominant trees, as shown by the saturation of the Δh–Δc curve.
For these dominant trees, an increase in growth potential
appeared to be systematically allocated to Δc, while allocation to
Δh remained constant. Dominant trees emerge from the canopy
and, as such, are less limited by light resources than suppressed
trees. Nonetheless, they still experience lateral competition for
light (­Harja et al. 2012), and need to grow in height at least as
fast as suppressed and intermediate trees to remain dominant.
This phenomenon may explain both the saturating shape of the
Δh–Δc relationship and the higher investment in Δh than in opengrown trees. In addition, hypothesized hydraulic and mechanical
constraints that were considered for open-grown trees are also
likely to affect these canopy emerging individuals. Nevertheless,
effects of mechanical and hydraulic constraints on Δh–Δc allocation can hardly be disentangled in studies where stand density is
the primary explanatory factor. Examining changes in growth allocation along large gradients of water stress intensity would be
necessary to highlight the importance of trade-offs between
height growth and maintenance of hydraulic conductance.
Effect of summer SWD on growth allocation
Water stress was found to reduce allocation to height growth
relative to radial growth for all trees in open-grown stands. Sustained sapwood growth may be particularly important for sessile
oaks in water-stressed periods, as they transport much of their
water in the most recently produced vessels of the sapwood
(­Granier et al. 1994).
Crowding and water stress on height–diameter growth 1043
et al. 2014) of suppressed and intermediate trees benefit more
from lower water stress conditions than dominant trees do
(­Figure 5c), favourable water conditions are likely to slow down
the process of social rank regression that occurs when individuals cannot keep up with the height growth rate of d
­ ominant
trees. From our model, it would also seem that the effect of
water stress on height growth was less acute in dominant trees
growing in closed stands than in open-grown trees (Figure 5c).
This might stem from the larger crown of open-grown trees,
which increase their tree-level water demand and in turn their
sensitivity to water stress (­McDowell et al. 2006, ­D’Amato et al.
2013). While these conclusions are restricted to the model calibration range, it would be interesting to further investigate
whether they hold in a larger climatic context.
Effect of ageing on growth allocation
Figure 5. Schematic representation of the effect of the predictors from
Eq. (6) on the shape of the Δh–Δc relationship. For each predictor, 5 and
95% extremes and interquantile values were simulated, while non-­
studied variables were fixed at their interquantile value. (a) Effect of
increasing stand age. (b) Effect of increasing RDI. (c) Effect of increasing
summer SWD. Dashed lines show the relationship for low RDI (0.1).
In closed stands, the trend of suppressed trees to favour
height growth over radial growth was lowered when summer
water stress was higher. This result is in agreement with multiple
limitation theory (­Bloom et al. 1985, ­Rubio et al. 2003, ­Ågren
et al. 2012), which states that plants adjust their morphology in
order to increase the acquisition of the most limiting resource,
i.e., light for suppressed trees. No evidence for an effect of water
stress on growth allocation of dominant trees in closed stands
was identified, which conflicts our Hypothesis 3. This result
might stem from a deeper and denser root penetration than in
suppressed trees (­Le Goff and Ottorini 2001, ­Bolte et al. 2004)
and additional mechanical risks to taller-than-average trees that
occur regardless of summer water stress levels (­McMahon
1973). Since both height growth and radial growth (­Trouvé
Although the experiment is a rather recent one, and it was not
intended to highlight ageing patterns, we observed an effect of
stand age on growth allocation. The asymptote of the Δh–Δc
relationship and therefore the height growth of dominant trees
were found to follow a mono-modal curve in response to stand
age, culminating at ∼23 years. This shape is similar to the early
effect of age on height growth that has been found in both
open-grown (­Ek 1971, ­Mäkelä and Sievänen 1992) and closed
stands (­Bontemps and Duplat 2012). Note that the quadratic
term (Eq. (6)) only provides a local approximation for the phenomenon considering that our dataset only covers young to
middle-aged stands. In the literature, the growth decline trend at
the right outermost part of the mono-modal curve usually slows
down for older stands (­Zeide 1993). Since the same monomodal curve of height growth in response to stand age has been
observed for both open-grown and closed-stand trees, the age
at which height growth rate reaches its maximum is more likely
to be related to ontogenetic development than reflecting competition onset as an emergent property of canopy closure around
this age (­Smith and Long 2001).
Our analysis was restricted to young to middle-aged trees,
and included a transient phase, characterized by a maximum in
terms of height growth. It remains uncertain whether our results
would extrapolate to older and larger trees. Indeed, we would
expect mechanical (­McMahon 1973) and hydraulic constraints
(­D’Amato et al. 2013) to gain more importance in older trees
than in younger trees, which are strongly dependent on light
availability. In addition, as more tissues become inert within the
tree, its ability to modify its shape through differential allocation
is likely to reduce with its size, reducing its morphological capacity to respond to environmental changes.
Conclusions
Each year’s growth allocation can be seen as an opportunity for
a tree to alter its morphology and improve its resource a­ cquisition.
Tree Physiology Online at http://www.treephys.oxfordjournals.org
1044 Trouvé et al.
Competition for light makes it beneficial to expand height to its
mechanical and hydraulical limits, while dry conditions make it
beneficial to have thicker-stemmed individuals, thus lowering
hydraulic resistance and embolism risks. This article adds further
evidence of the high phenotypic allocation plasticity of trees, and
illustrates how competition for light and water will cause inevitable departure from universal scaling laws (­Enquist 2002). It
would be interesting to conduct investigations on the effects of
shade tolerance on allocation plasticity in species with different
requirements for light (­Bormann 1965, ­Jack and Long 1991,
­Poorter et al. 2006).
While empirical and ecophysiological modellers are increasingly aware of the effects of environmental factors on tree
growth allocation (­Epron et al. 2012, ­Bravo-Oviedo et al. 2014,
­Doughty et al. 2014), no consensus has yet been reached on
the underlying mechanisms (­Le Roux et al. 2001, ­Mäkelä
2012), and process modellers still often resort to robust empirical models to predict allocation balance (­Davi et al. 2009,
­Mäkelä 2012, ­Guillemot et al. 2014). Models to predict the joint
effects of management and climate on all aspects of tree growth
are a prerequisite to adapting forest management to climate
change (­Mäkelä et al. 2000, ­Landsberg 2003) and studies of
growth allocation patterns are required to establish such models.
Supplementary data
Supplementary data for this article are available at Tree Physiology
Online.
Acknowledgments
We thank all workers who have been involved in setting up and
maintaining the permanent research plot network as well as in
the data collection. We would like to thank the two anonymous
reviewers for their helpful comments, which helped us to
improve the manuscript.
Conflict of interest
None declared.
Funding
The thesis grant of R.T. was funded by the French National Forest Office and the French Ministry for Forests, Agriculture and
Fisheries. R.T. was also funded by the French Research Agency
(ANR) through the ‘Oracle’ project (CEP&S call, 2010). Data
originate from the French data cooperative on forest growth, a
Scientific Interest Group set up and managed by AgroParisTech,
INRA, Irstea and the French National Forest Office, with sustaining funds from the French Ministry for Forests, Agriculture and
Fisheries.
Tree Physiology Volume 35, 2015
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