Growth responses of neotropical trees to resource
availability and individual condition : an innovative
method using LIDAR canopy height model
Elias Ganivet1 *, Romain Gaspard1 *
Abstract
In complex ecosystems like neotropical forests, it is largely unknown how tree species differ in their response of growth to
resource availability and individual conditions (e.g. size, density...). Previous studies having usually focused on the seedling
or sapling life stage, an understanding of the drivers of tree growth is required to predict changes of community composition
and biodiversity, as well as to apply detailed process-based simulation models to predict forest dynamics when environmental
conditions change. We used a linear mixed effect approach to quantify the impact of light availability and individual conditions
on growth of 134 woody species in a 1 ha plot of lowland tropical rainforest at the Paracou experimental site in French Guiana.
To estimate the light avalability, we used an innovative technique by estimating the illumination of the crown from LIDAR data,
especially from the LIDAR canopy height model (CHM). A program was created to estimate canopy openings at the crown
height of each tree. Results confirm that the annual growth is higher when the tree is well illuminated (high crown illumination),
facing few competition and with high maximum size. Moreover, the most important result is that after a certain age, the
variation of resources influences no longer the growth of trees. Together resource availability and individual conditions only
explained on average 25% of the variation in growth rates, a large part (46%) is explained by mixed effects (species effect).
Thereby other non-investigated additional environmental variables (topography, soil, etc.) may contribute to shaping tree
growth in tropical rainforests.
Keywords
tree growth rate – tropical rainforest – light availability – leaf area index – Dawkins’ index – LIDAR
1 Master Ecologie des Forets Tropicales, UMR ‘Ecologie des Forets de Guyane’, 97379 Kourou Cedex, French Guiana
*Corresponding authors: [email protected] & [email protected]
Introduction
In complex ecosystems like neotropical forests, it is largely
unknown how tree species differ in their response of growth
to resource availability (e.g. light) and individual conditions
(e.g. size, density...). An understanding of the drivers
of tree growth is required to predict likely changes of
species abundance and hence community composition
and biodiversity, as well as to apply detailed process-based
simulation models to predict forest dynamics and carbon
storage under changing disturbance regimes such as logging
or hurricanes.
Tree growth is an important component of demographic
variation among neotropical trees species. It varies widely
in response to individual condition (Dalling et al., 2004;
Herault et al., 2010) and local resource availability (Clark
and Clark, 1999), particularly the light (Denslow, 1987; King
et al., 2005). Light is the most limiting resource in rainforest
at all stages of development (Whitmore, 1996). It is a limiting
factor at low intensity, and too much light or a sudden
change may also alter the development (Lovelock et al.,
1998). Thereby in some tropical forests, canopy openings
are essential for species to grow (Brokaw and Scheiner,
1989). The spatio-temporal variation of light availability
is an important component of species coexistence. The
heterogeneity of light conditions thus contributes to
tropical trees diversity and causes opportunities for niche
differentiation (Ricklefs, 1977). Previous studies have
usually focused on a small number of species (Clark and
Clark, 1992; Davies, 2001; King et al., 2005) and the seedling
or sapling life stage (Turner, 1990; Brown and Whitmore,
1992; Sizer and Tanner, 1999; Poorter and Arets, 2003) but
rarely on adult trees. Nevertheless, a few studies have
included measures of light availability as predictors of tree
growth and they consistently found significant effects for the
majority of species (Sterck and Bongers, 2001; Herault et al.,
2010). In this context, studying the relationship between
growth and light on adult trees appears really significant.
Other studies have simultaneously included measures
of tree size and light availability as predictors of tree
growth, and they consistently found significant effects of
both variables for the majority of species (Davies, 2001;
Uriarte et al., 2004; Rüger et al., 2011). It even appears
that light availability, according to the Dawkins’ index
(Dawkins, 1958), is a better predictor of growth when the
tree size is also included. It also emerges that the maximum
DBH (diameter at breast height) is the first predictor of
Growth responses of neotropical trees to resource availability and individual condition : an innovative method using
LIDAR canopy height model — 2/10
inherent growth rate and growth response (Herault et al.,
2010). Moreover, models of growth response retained three
additional and important predictors: stem architecture
(Rutishauser et al., 2011), mode of germination and wood
density (Baker et al., 2004; Herault et al., 2010). It has
especially shown that tropical trees growth rate decreases
with the density of wood (Rüger et al., 2011).
A further complication in modeling tree growth arises
because growth strategies may change with ontogeny,
with the development history of a tree within its own
lifetime (Clark and Clark, 1999; Poorter et al., 2005). Most
species showed clear hump-shaped ontogenetic growth
trajectories and attained their maximum growth at 60% of
their maximum size, whereas the magnitude of ontogenetic
changes in growth rate varied widely among species
(Herault et al., 2011). A high abundance of such shifts
would profoundly change our current views on the role of
disturbance in the dynamics of tropical trees communities
(Hubbell et al., 1999).
Consequently, it is important to understand how species
differ in their response of growth to resource availability
and individual conditions in species-rich tropical forests.
In this study we modeled this growth with measures of
light availability, tree size and wood density. We used a
linear mixed model (LMM) that provides a more flexible
approach for analyzing data when random effects are
present (Bolker et al., 2009). Moreover, the aim of this study
is also to estimate the trees crown illumination from LIDAR
data, which would be a great novelty in the study of tree
communities in tropical forest.
Materials and methods
growth rate. In total, 433 individuals of 111 species were
included in the analysis. We also excluded trees of the
Arecaceae family present in the plots, due to their lack of
secondary growth.
Estimation of light availability
Dawkins proposes a "crown illumination index" (Dawkins,
1958) that describes the crown position (from crown with
no direct light to emergent crown, Table 1).
Class
Definition
1
No direct light (crown not lit directly either
vertically or laterally)
2
Lateral light (≤10 percent of the projection of the
crown exposed to vertical light, crown lit
laterally)
3
Some overhead light (10-90 per cent of the
vertical projection of the crown exposed to
vertical illumination)
4
Full overhead light (≥90 per cent of the vertical
projection of the crown exposed to vertical light,
lateral light blocked within some or all of the
90°inverted cone encompassing crown)
5
Crown fully exposed to vertical and lateral
illumination within the 90°inverted cone
encompassing the crown
Table 1. Crown illumination index (Dawkins, 1958)
Study site
The study was conducted in the Guyaflux permanent plots
at the Paracou experimental site (5°18’N, 52°55’W), a 5,5 ha
plot of lowland tropical rainforest near Sinnamary, French
Guiana. The climate of the region is equatorial, with two
main seasons: a dry season from August to mid-November
and a rainy season (often interrupted by a short drier
period) from December to April. The annual rainfall in
the vicinity of the station is 3041mm (Gourlet-Fleury
et al., 2004). The floristic composition is typical of
Guianese rainforests (Ter Steege et al., 2003) with dominant
families including Leguminoseae, Chrysobalanaceae,
Lecythidaceae, Sapotaceae and Burseraceae.
Growth data
We analyzed data from the Guyaflux experimental site on a
one ha area (plot 1 & 9). All trees with a diameter at breast
height (dbh) ≥ 10 cm were mapped, identified to species and
measured in 2004 and at least every two years afterwards.
Here we used the census intervals from 2008-2013 and
determined annual circumference growth rate (mm/yr). We
excluded the individuals identified in the census after 2008
because we couldn’t determine a correct circumference
This index is the best estimator of light available for the
crown (Keeling and Phillips, 2007) and a good predictor of
growth rate (Rutishauser et al., 2011).
The evaluation of Dawkins’ index is very
time-consuming and we had no data for 2008. Thereby
we used an innovative method to estimate the index from
LIDAR (Light Detection And Ranging) data. Laser altimetry,
based on the principle of LIDAR technology, allows high
sample density and spatial resolution of the components
of a given space (e.g. soil and canopy). The derived
altimetric models, ground altitude model (GAM) and
canopy altitude model (CAM), give information about the
spatial organization of the different types of vegetation. The
canopy height model (CHM) was obtained by subtracting
the interpolated ground-classified hits (GAM) from the
interpolated vegetation-classified altitudes (CAM, Fig. 1). It
gave the interpolated height of all points in the canopy in
the form of a regularly spaced grid with a 1 m pixel size.
Then, using the R software, we created a program to
assess the openings of the canopy at the crown height of all
trees on the studied site. Inputs needed for the program are
LIDAR data (GAM and CAM)) and height of all trees. The
Growth responses of neotropical trees to resource availability and individual condition : an innovative method using
LIDAR canopy height model — 3/10
Figure 1. Production of the different elevation models
output is an angle between 0°and 90°. This angle represents
the opening of the light cone available for the crown, as the
mean of eight angles calculated in eight directions.
To validate the method, we first evaluated the Dawkins’
index and trees heights in the plot 1 & 9 of the Guyaflux
experimental site. Then, we used heights and LIDAR data
from 2013 to calculate the crown illumination with the
program, and made the comparison with Dawkins’ index
from the field.
Consistent results would then allow the estimation of
the crown illumination in 2008, based on LIDAR data from
2008 and height evaluated in the field on 2013, making the
hypothesis that there is no real change for heights since
2008.
Estimation of competition
To include a competition factor in the model, we used
the variation of Leaf Area Index (LAI) between 2008 and
2013. The LAI of vegetation cover, defined as half of the
total leaf area per unit ground surface area, determines
the productivity of the surface and hence affects the light
availability in the understory. We made the hypothesis that
an increase of the leaf area during the census intervals could
cause more competition for resources (e.g. soil, light...) and
limit growth of trees.
The LAI is annually measured since 2008, with an
indirect method by using a Plant Canopy Analyzer LAI-2000.
This optical instrument measures the amounts of direct
or diffuse light penetrating the canopy at three angles
simultaneously, and hence avoids the need for knowing the
foliage-angle distribution. Because the LAI 2000 measures
the foliage attenuation of the diffuse sky light, the method
requires two simultaneous measures: inside and outside the
vegetation. Moreover, to avoid direct light, measurements
were made during the sunrise with one LAI 2000 fixed at the
top of the flux tower and the second LAI 2000 making the
measurements under the canopy every 10 square meter.
Fifty values of LAI were measured per plot each year,
each time located at different places. We checked the
spatial correlation of the measures for the 2013 data, using
a multiscale second-order neighborhood analysis (Goreaud
and Pélissier, 1999). In case of a spatial correlation, it would
be possible to interpolate the measures in 2008 and in 2013,
and therefore to calculate the LAI variation through time in
all points.
The interpolation method was Inverse Distance
Weighting (IDW), a type of deterministic method for
multivaried interpolation with a known scattered set of
points. The assigned values to unknown points would be
calculated with a weighted average of the values available
at the known points. In order to measure the LAI variation
through time, a ∆LAI (LAI2013-LAI2008) was calculated.
Statistical Analyses
Many biological datasets, such as species within
communities, have multiple strata due to the hierarchical
nature of the biological world. Linear mixed-effects models
(LMMs), also referred to as multilevel/hierarchical models,
and their extension, generalized linear mixed-effects
models (GLMMs), form a class of models that incorporate
Growth responses of neotropical trees to resource availability and individual condition : an innovative method using
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multilevel hierarchies in data. Hence, LMMs and GLMMs
are becoming a part of standard methodological toolkits in
biological sciences (Bolker et al., 2009).
We first described a standard (general) linear model
(LM), defined as:
y i = β0 +
p
X
βh x hi + ²i
wi t h
h=1
²i ∼ N (0, σ2² ) (1)
with y i the response value of individual tree i, x hi the value
for the hth predictor of individual tree i, β0 the intercept, βh
the slope (regression coefficient) of the hth predictor and
²i the error term of individual tree i, which was assumed to
follow a centred normal distribution with variance σ2² .
Then, extending the LM shown in equation 1, we can
fit a linear mixed-effects model with one random factor
(‘species-specific effect’) defined as:
p
X
y i s = β0 +
βh x hi s + αs + ²i s
(2)
h=1
wi t h
αs ∼ N
(0, σ2α )
and
²i s ∼ N
(0, σ2² )
with αs the species-specific effect from a normal
distribution of species-specific effects with mean of
zero and variance of σ2α (between-species variance). As
seen in the previous equations, LMMs have by definition
more than one variance component (in this case two: σ2α
and σ2² ), while LMs have only one (Equations 1).
As a starting point, we introduced a mathematical model
of ontogenetic growth trajectories that has already been
studied (King et al., 2006), as trees size effect. We used the
ratio between the individual DBH and the 95th percentile of
the DBH values in the species population across unlogged
plots at Paracou. Both the ratio and the squared ratio were
included to obtain a flexible enough mathematical form
allowing a monotonic increase, a monotonic decrease or
a humped growth. We also included predictors that could
possibly be relevant for explaining growth, like wood density
and the 95th percentile of the DBH values for the species
(to characterize the growth potential difference of species
within the community). Finally, we added the variables of
ressources availibity, which are the main predictors that we
want to study.
The final growth LMM was constructed as :
with AGR i s the annual growth rate of the individual i
of the focal species s; δp the fitted-model parameters
of the individual condition predictor IC (wood density,
DBH/DBH95, (DBH/DBH95)² and DBH95); γp the
fitted-model parameters of the ressource availability
predictor RA (light and LAI); λp the fitted-model parameters
of the interactions INT ; ωs the species-specific effect and
²i s the fitted-model residuals.
Throughout the data analysis, the Akaike Information
Criterion (AIC) was always used in a stepwise algorithm
to choose the most parsimonious models and to avoid
over-parameterization (Legendre and Legendre, 1998).
Moreover, because R² for mixed-effects have theoretical
problems (e.g. decreased or negative R² values in larger
models) and/or their use is hindered by practical difficulties
(e.g. implementation), two types of R² (marginal and
conditional R²) were calculated (Nakagawa and Schielzeth,
2012). All analyses were performed using the R project
software (http://www.r-project.org/).
Results
Estimation of crown illumination
The result of the estimation of crown illumination is shown
in Figure 2.
Figure 2. Comparaison between measured Dawkins’
index & calculated crown illumnation (degrees
l og (AGR i s + 1) =
µ + (γ1 × R A 1i s + ... + γP × R A Pis )
+ ... + δP × IC iPs )
+ (λ1 × I N Ti1s + ... + λP × I N TiPs )
+ (δ1 × IC i1s
+ ωs + ²i s
wi t h
and
ωs ∼ N (0, σ2ω )
²i s ∼ N (0, σ2² )
(3)
It appears that there is a clear relationship between
the field-evaluated Dawkins’ index and the calculated
crown illumnation. The calculated values systematically
increase with the Dawkins’ index values. In order to test
the significance of these results, we performed a pairwise
Wilcoxon test between all Dawkins’ index class (Table 2).
Most of the tests show a highly significant difference
between Dawkins’ index classes. Two slightly less significant
results, found between Dawkins’ classes 2 and 3, and
Growth responses of neotropical trees to resource availability and individual condition : an innovative method using
LIDAR canopy height model — 5/10
Dawkins’ index
1
2
3
4
2
3
4
5
***
***
***
***
**
***
***
***
***
*
Table 2. Result of a pairwise Wilcoxon test on the
calculated crown illumination (*P < 0.05, **P < 0.01, ***P <
0.001)
(a) 2008
between classes 4 and 5, can be explained by the smaller
differences between the classes. Indeed, field identification
revealed also difficult between these couples of classes.
Nonetheless, these results show that the illumination of the
crown can be approximated from LIDAR data, thus allowing
to have data without going on the field to make Dawkins’
index measures. So we calculated crown illumination for
2008, using LIDAR data from 2008 and height evaluated in
the field on 2013, making the hypothesis that there is no real
change for heights since 2008.
Correlation of LAI measurement and interpolation
The results of the multiscale second-order neighborhood
analysis showed that there is a positive correlation from
12 meters (Fig. 3). This means that there is a dependency
between the LAI of two points spaced of at least 12 meters.
This seems relevant because LAI measures were made with
one value per 10 square meters, which explains the lack of
correlation below 12 meters.
(b) 2013
Figure 4. Evolution of the LAI values on plots 1 & 9 of the
Guyaflux experimental site between 2008 & 2013. A LAI of 3
indicates a low leaf area and a LAI of 11 indicates a high leaf
area.
relation between the ∆LAI and the initial LAI was studied
(Fig. 5). The result shows that the variation of LAI between
2008 and 2013 is strongly related to its initial state (LAI 2008).
Globally, an area initially opened in 2008 (low LAI) will be
more closed in 2013. Areas initially closed stay closed trough
time or have a few re-opening process.
Figure 3. Spatial correlation test
Then, we made an interpolation using Inverse Distance
Weighting (IDW) with data from 2008 and 2013 (Fig. 4). It
was therefore possible to have LAI values for each point of
the area, and so for each tree of the study.
It appears that the forest cover has undergone changes
during the last five years, particularly on the left side that is
more closed in 2013 than in 2008. This canopy closure could
have affected the tree growth. In order to well understand
the parameter that we want to insert in the model, the
Figure 5. Relation between Delta LAI and initial LAI values
Growth responses of neotropical trees to resource availability and individual condition : an innovative method using
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Regarding the correlation between both values (initial
LAI and variation), we chose to include the initial LAI value
in the model as a competition factor and not the variaton
of LAI. We made the hypothesis that a weak LAI in 2008 is
equivalent to a weak competition for resources (e.g. soil,
light...). The absolute growth rate has a direct effect on
the LAI variation, so the interpretation of results could be
complicated. In fact, the growth of a tree results in the
growth of its crown, increasing the amount of leaves and
therefore the value of LAI under the tree.
Growth model
Using Akaike Information Criterion (AIC) in a stepwise
algorithm allowed us to choose the most parsimonious
model starting from the following null model with only
species-specific effect :
Parameters
Estimate
Standard error
µ
γ1
γ2
δ1
δ2
δ3
λ1
λ2
1.034
0.004
0.174
-0.798
-0.071
0.007
-0.003
0.174
0.213
0.002
0.049
0.351
0.165
0.002
0.002
0.049
σ2ω
Marginal R²
Conditional R²
0.0213
0.245
0.467
Table 3. Parameters of the LMM of tree growth
l og (AGR i s + 1) = µ + ωs + ²i s
(4)
wi t h
ωs ∼ N
(0, σ2ω )
and
²i s ∼ N
(0, σ2² )
This led us to remove the wood density predictor, because it
did not bring a better model.
The final growth model was thus constructed as:
l og (AGR i s + 1) =
µ + (γ1 × l i g ht i + γ2 × L AI i )
+ (δ1 × D i s + δ2 × D i2s + δ3 × DB H 95s )
+ (λ1 × D i s × l i g ht i + λ2 × D i s × L AI i )
+ ωs + ²i s
wi t h
and
(5)
ωs ∼ N (0, σ2ω ), ²i s ∼ N (0, σ2² )
µ
¶
DB Hi
Di s =
DB H 95s
with AGR i s the annual growth rate of the individual i of
the focal species s; µ, γ1 , γ2 , δ1 , δ2 , δ3 , λ1 and λ2 the
fitted-model parameters; l i g ht i the crown illumination of
individual tree i, L AI i the LAI under the individual tree
i, DB Hi the diameter at breast height of the individual
tree i, DB H 95s the 95th percentile of the DBH values in
the species s; ω j the species-specific effect and ²i j the
fitted-model residuals.
The value of each parameters is shown in the table 3.
We expected to have opposit signs for δ1 and δ2 but
due to interactions, the effect of DB Hi /DB H 95s is more
complex to interprate. Furthermore, analysis of R² shows
that fixed effects only explained on average 24,5% of the
variation in growth rates, a large part (46%) being explained
by mixed effects (species effect). The predicted values
compared with real AGR (Fig. 6) confirm that null values for
growth can’t be predicted with the model. The model also
underestimates the AGR for trees with a real AGR > 1cm.
Figure 6. Comparison between observed AGR (mm/year)
and model predictions (mm/year
Making a simulation with the model (Fig. 7), we
can interprate results and explain growth regarding each
predictor. The ratio DBH/DBH95 is used as a proxy of the
ontogenetic stage of the tree and had an obvious effect
on AGR. Results confirm that AGR is higher when the tree
is well illuminated (high crown illumination), facing few
competition (low LAI) and with high maximum size (high
DBH95).
In addition, a striking result is that the old trees (close
to their maximum size) are less influenced by resource
availability (crown illumination and LAI predictors) than
younger ones.
Regarding curves of AGR according to resources
availability, two groups of trees can be identified for both
parameters.
Graphic A (Fig. 7) shows that for trees with a good light
availability (crown illumination > 40°), the AGR decreases
Growth responses of neotropical trees to resource availability and individual condition : an innovative method using
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Discussion
Estimation of crown illumination from LIDAR data
One of the main results of this study is the possibility of
estimating the crown illumination (ie the canopy openings)
from the LIDAR canopy height model. Frequently used
in temperate and boreal forests (Brandtberg et al., 2003;
Hopkinson et al., 2006; Chasmer et al., 2006), the LIDAR
technology remains anecdotal for the study of tropical wet
forests. Although some studies in rainforest used LIDAR
data (Drake et al., 2002; Hofton et al., 2002), they were often
limited to estimate the forest structural characteristics (e.g.
ground and canopy altitude model). Therefore the use of
these data to estimate the crown illumination represents a
highly innovative method. Like in the census plot of Barro
Colorado Island, Panama, until LIDAR-mapping data of
the entire 50 ha were available, only methods like Dawkins
crown illumination index or optical instruments were used
to measure how much vegetation was blocking the sky in
the entire forest. Measuring light at every tree in 50-ha plot
involved an important amount of time and labor. Using
this method would allow to save much time and money.
However, the height of each tree is required for the calcul,
and this data collection is also very time consuming. We
used field evaluated values in this study because it was
already available. For forthcoming studies, heights can be
easily evaluated from diameter using an allometry.
Growth model
Figure 7. Simulation (only the fixed effect) of the AGR
(mm/year) versus the ontogenetic stage (DBH/DBH95) of
the tree, with variation of ressource availability and
functional traits selected in the final model: A the Crown
illumination (degrees) with others predictors fixed to
median, B the LAI with others predictors fixed to median
and C the DBH95 (cm) with others predictors fixed to
median. Marginal densities are plotted for each predictors,
with a bandwidth equal to 5% of the amplitude.
with ontogenetic stage. This means that the young trees
grow quickly than the old trees. For trees with few light
available (crown illumination < 40 degrees), the process is
reversed: the AGR increases with ontogenetic stage.
Graphic B (Fig. 7) shows the same kind of process. For
trees who face strong competition (LAI > 5,5), the AGR
increases with ontogenetic stage. On the other side, the
AGR of trees with few competition (LAI < 5,5) decreases with
ontogenetic stage.
Graphic C (Fig. 7) shows that the maximum diameter
does not modify the shape of the curve linking ontogenetic
stage to the AGR, but drives the value of AGR in the way that
they induce a translation of the curve.
This study allowed to disentangle light and individual effects
on growth across a diverse community of tropical tree
species. First of all, it has been suggested that wood density
varied widely across Amazonian trees (Baker et al., 2004), as
well as a high wood density may contribute to lower growth
rate because less volume is produced per unit biomass (King
et al., 2005). For these reasons we chose to include the wood
density in our growth model. However our results show that,
contrary to our expectations and to the results from other
recent studies (Poorter et al., 2008), wood density was not a
good predictor of growth rate.
Nevertheless it appears that light, as well as leaf area,
could be good predictors of growth rate. The results show
that species grew faster at higher light availability and
confirms that light is effectively an important limiting
resource for woody species in natural forests, not only at
the seedling and sapling life stage. In the same way, as
expected, species have higher growth rate when the leaf
surface is low and therefore when there is few competition.
However, a substantial fraction of individual variation in
growth remains unexplained and suggests that other factors
contribute to shaping tree growth in the tropics. Indeed tree
growth is influenced by several non-investigated additional
environmental variables (topography, soil, etc.) and also
by the unique individual history that depends on complex
environmental changes occurring (Herault et al., 2010).
Although, for a majority of species, growth rates
Growth responses of neotropical trees to resource availability and individual condition : an innovative method using
LIDAR canopy height model — 8/10
were well approximated by the power function which
only allows for a monotonic increase or decrease of
growth with diameter, many other studies have validated
a hump-backed response of growth to diameter (Davies,
2001; Kohyama et al., 2003; Uriarte et al., 2004; Coates et al.,
2009; Herault et al., 2010, 2011). It has been especially
shown that most species have a size-dependent growth,
with maximal growth rates attained at intermediate sizes
(Herault et al., 2011). Thus we included in our analysis a
priori the possibility that trees may change their inherent
growth with developmental stages (δ1 and δ2 ). It has
been suggested that the stage for optimal growth rates
may be driven by internal shifts in allocation, affecting the
balance between photosynthesizing and respiring tissue, or
the balance between vegetative growth and reproduction
(Thomas, 1996). However this is not supported by our
results when considering only the effect of ontogenetic stage
on growth. While it was expected to obtain a positive and
negative parameter for δ1 and δ2 , both showes a negative
value (Tab. 3). However it is also important to consider
the interaction mechanism, particularly between crown
illumination, LAI and DB Hi /DB H 95s , which results in a
more difficult interpretation of these values.
The interest of this study is especially to observe
the interaction between light availability and tree size.
Although it has been postulated that tree growth response
to increasing light availability changes with ontogeny
(Baraloto et al., 2005), few data exists to test this hypothesis
for a large number of species.
The analysis of these combined effects on growth
revealed contrasting ecological behaviours when values
of crown illumination or competition remain constant
(Fig. 7). First, when light is scarce, as well as when
competition for resources is high, the growth rates of species
decreased with increasing ontogenic stage. Then, when
light is available and competition for resources is low,
species growth rates increased with the ontogenic stage.
An explanation could be that growth may increase rapidly
with tree size because taller trees have better access to light
and a larger photosynthetic area (Sterck et al., 2003). Upon
attaining the canopy, many species may spread their crown
to further enhance light capture and maximize growth
(Poorter et al., 2006).
Moreover, the most important result is that, regardless
of the availability of resources (and thus competition), older
trees have the same growth rate. This means that after
a certain age, the variation of resources have no longer
influence on the growth of trees. This result is worth
noticing, on the one hand because it has never been studied
in Paracou, and on the other hand because the literature
does not seem to indicate this kind of result. However,
some mechanisms could explain this result. First, trees
of advanced ontogenetic stage have probably had access to
the necessary resources for their growth throughout their
lives. Because they have a size close to their maximum size
and are well balanced to their environment, their growth
will be unaffected by changes in resource availability.
Thereby it has been suggested that at even larger
diameters, growth rates can decrease because constant
biomass investment leads to less overall diameter increment
(Herault et al., 2011). Four other mechanisms could also
contribute to the decline in growth rate at larger sizes: (i)
the respiration load of roots and stems becomes too high
(Ryan and Yoder, 1997); (ii) hydraulic pathways become too
long, leading to water stress and stomatal closure (Koch
et al., 2004); (iii) resources are reallocated to reproduction
(Thomas, 1996); or (iv) trees begin to senesce. The resources
are thus mainly allocated to maintain the tree in the
environment rather than to its growth. Thus its growth
response will be slower than a sapling where resources are
allocated mainly to growth.
Finally this result allows us to distinguish two different
ecological groups already pointed in the literature. First,
understorey and subcanopy species that perform better in
high-light environments when young, probably because
they adjust their light-growth performance with age when
they are most frequently overtopped by canopy and
emergent trees (Herault et al., 2010). The second group
includes canopy emergent trees that may not change
optimum light environments with age but rather overtop all
other trees when larger and thus do not depend on resources
fluctuations for growth (Herault et al., 2010).
Conclusion
This study offers a promising way to model individual
growth of tropical rainforest trees. A key result is that it
seems now possible to characterize the light environment
of a forest from LIDAR data, allowing to save a lot of time.
Our linear mixed effect approach permit to show that
wood density was not a good predictor of growth rate. As
expected it appears that light strongly influences the growth
of neotropical trees. Similarly, as shown by some studies
growth rates and growth responses varied substantially
with tree size. The most striking result remains that old
trees (close to their maximum size) are less influenced by
resource availability than younger ones.
The final growth model has nevertheless shown that
fixed effects only explained on average 24,5% of the
variation in growth rates, a large part is explained by mixed
effects (species effect). Thereby a substantial fraction of
variation in growth remains unexplained and suggests that
other factors, as well as the unique individual history,
contribute to shaping tree growth in the tropics.
It is also important to note that a problem inherent
in highly diverse tropical forests is the low number of
individuals per area of the many rare species (Pitman et al.,
1999). In this study, 67 species were represented by only
one individual, which limits the species effect on the model.
Thereby it could be interesting to extend the study to all
plots of the Paracou experimental site. Because crown
Growth responses of neotropical trees to resource availability and individual condition : an innovative method using
LIDAR canopy height model — 9/10
heights necessary for analysis are not available on all plots,
a growth allometry could be used to estimate them.
Acknowledgments
We thank S.Traissac, B. Herault, M. Aubry-Kientz & E. Allie
for their help in defining the objectives of the study and for
the results analysis. We also thank P. Petronelli, B. Burban,
J.Y. Goret of CIRAD, without whom this study would not
have been possible, for the important field work realized at
Paracou and their assitance on the ground.
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