Research Paper
Analysis of Competition Effects in Mono- and Mixed Cultures
of Juvenile Beech and Spruce by Means of the Plant Growth
Simulation Model PLATHO
S. Gayler1, T. E. E. Grams2, A. R. Kozovits2, 3, J. B. Winkler1, G. Luedemann2, and E. Priesack1
1
2
Institute of Soil Ecology, GSF – National Research Center for Environment and Health, Ingolstädter Landstraße 1, 85764 Neuherberg, Germany
Ecophysiology of Plants, Department of Ecology, Technische Universität München, Am Hochanger 13, 85354 Freising-Weihenstephan, Germany
3
Present address: Departamento de Ecologia, Universidade de Brasília, caixa postal 04457, Brasília-DF, 70919-970, Brazil
Received: October 4, 2005; Accepted: February 8, 2006
Abstract: Inter- and intra-specific competition between plants
for external resources is a critical process for plant growth in
natural and managed ecosystems. We present a new approach
to simulate competition for the resources light, water, and nitrogen between individual plants within a canopy. This approach
was incorporated in a process-oriented plant growth simulation
model. The concept of modelling competition is based on competition coefficients calculated from the overlap of occupied
crown and soil volumes of each plant individual with the occupied volumes of its four nearest neighbours. The model was parameterised with data from a two-year phytotron experiment
with juvenile beech and spruce trees growing in mono- and
mixed cultures. For testing the model, an independent data set
from this experiment and data from a second phytotron experiment with mixed cultures were used. The model was applied to
analyse the consequences of start conditions and plant density
on plant-plant competition. In both experiments, spruce dominated beech in mixed cultures. Based on model simulations, we
postulate a large influence of start conditions and stand density
on the outcome of the competition between the species. When
both species have similar heights at the time of canopy closure,
the model suggests a greater morphological plasticity of beech
compared with spruce to be the crucial mechanism for competitiveness in mixed canopies. Similar to the experiment, in the
model greater plasticity was a disadvantage for beech leading
to it being outcompeted by the more persistent spruce.
Key words: Fagus sylvatica, Picea abies, plant density, competitiveness, competition intensity, plasticity.
Introduction
Competition between plants for light, water, and nutrients is a
critical process for plant growth in natural and managed ecosystems (Kropff and van Laar, 1993; Aerts, 1999). However, the
mechanisms of inter- and intra-specific competition are not
yet well understood.
Plant Biol. 8 (2006): 503 – 514
© Georg Thieme Verlag KG Stuttgart · New York
DOI 10.1055/s-2006-923979 · Published online May 11, 2006
ISSN 1435-8603
In particular, for agricultural systems, numerous empirical regression models have been developed that statistically describe yield loss due to crop-weed competition, based on one
or more parameters (e.g., plant density, relative leaf area) (Wilson and Wright, 1990; Kropff and Lotz, 1993; Kim et al., 2002).
These general parameters were obtained by fitting model outcomes to results from field experiments. However, these empirical models are unable to account for the effect of changing
soil and climatic conditions and their parameters are highly
specific to the site and year of the experiments (Grant, 1994).
But, there is some evidence that mechanisms of competition
strongly depend on external factors, such as nutrient availability or changing climatic conditions. For example, in habitats
with high nutrient availability, plants compete mainly for light
and thus high growth rates and a large specific leaf area are
successful strategies of competition. Conversely, in nutrientpoor environments a more efficient long-term nutrient economy is essential (Aerts, 1999; Schippers and Kropff, 2001). In
process-oriented models that describe the influence of external factors on plant growth, competition between plant species is simulated as the distribution of growth-limiting factors
in the canopy and the efficiency in capturing resources. There
is a high variability of simulation concepts for grasslands, agriculture, and forestry in the degree to which physiological functions and morphological structures of plant individuals are
considered in representing mechanisms of competition (Kiniry
et al., 1992; Lafolie et al., 1999; Schippers and Kropff, 2001;
Porté and Bartelink, 2002).
Many models simulate aboveground competition by dividing
the canopy into horizontal layers with different proportions
of morphological elements such as leaves or internodes (Kropff
and van Laar, 1993; Grant, 1994; McDonald and Riha, 1999;
Wohlfahrt et al., 2001; Ittersum et al., 2003). Similar concepts
exist to model belowground competition for water and nutrients, where roots belonging to different individuals are either completely mixed (Adiku et al., 1996) or fully separated
(Kiniry et al., 1992). Those models consider the whole canopy
as a homogeneous medium and neglect individual plant architecture and the arrangement of plant individuals within
the canopy. Therefore, they are not suitable for analysis of
the effect of plant arrangement on competition. In general,
individual-based plant population and community models
with an explicit spatial arrangement of the structures have a
lower accuracy in physiological process simulation (Grote and
Pretzsch, 2002). If models aim at size variation in crowded
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Plant Biology 8 (2006)
plant populations, they are often solely based on allometric relations and neglect plant physiology completely (Garcia-Barrios et al., 2001; Weiner et al., 2001). Similarly, individualbased functional-structural models reproduce plant architecture in great detail but are based on rather simple assumptions
with respect to physiological processes (Perttunen et al., 1998;
Genard et al., 2000; Kurth, 2000; Birch et al., 2003; Eschenbach, 2005; Renton et al., 2005).
Within the framework of the research project SFB607 (Matyssek et al., 2005), the generic, process-based model PLATHO
was developed to simulate growth of both herbaceous plants
and juvenile trees, depending on climatic conditions and availability of external resources such as light, water, and nitrogen
(Gayler and Priesack, 2003). This simulation model is based on
concepts of common monoculture models from agronomy and
forestry (Jones and Kiniry, 1986; Hoffmann, 1995; Bossel, 1996;
Gayler et al., 2002; Wang and Engel, 2002; Ittersum et al.,
2003) and, in addition, includes several new approaches to
simulate C and N allocation to plant organs and plant internal
biochemical pools. Moreover, a new approach was developed
to estimate competition effects between individual plants.
The calculation of light, water, and nutrient capture is based
on competition coefficients that result from the overlap of occupied crown and soil volumes of each individual plant with
its four nearest neighbours. Thus, PLATHO allows the analysis
of competition mechanisms with regard to plant spatial arrangement and the availability of external resources without
restrictions to the level of detail in the simulation of physiological processes.
The aims of the present work were: (i) to develop a new modelling approach to simulate competition mechanisms between
plants; (ii) to parameterise the plant growth model PLATHO
for the specific conditions of a phytotron experiment with juvenile beech (Fagus sylvatica) and spruce (Picea abies) trees;
(iii) to test the model output using results of two experiments
with respect to aboveground biomass distribution between
these species in the mixed culture; and (iv) to analyse the consequences of the proposed competition mechanisms on tree
growth under varying start conditions and plant densities.
Materials and Methods
Plant growth conditions
This simulation study is based on data which were collected in
two experiments that were carried out from 1998 until 2000
(Experiment A) and from 2001 until 2003 (Experiment B)
within phytotrons maintained by the GSF – National Research
Centre for Environment and Health in Neuherberg, Germany.
In spring 1998, two-year-old seedlings of European beech (Fagus sylvatica L.) and three-year-old Norway spruce (Picea abies
[L.] Karst.) of uniform height (about 0.2 m) were transplanted
into containers (0.7 × 0.4 × 0.3 m; volume: 84 l) filled with untreated forest soil (dystric cambisol, Ah-B horizon). Twenty
trees (arranged in rows of 4 × 5 individuals) were planted into
containers, resulting in plant densities typical for the natural
offspring of both species in the field (71 plants per m2). Eight
containers comprised 1 : 1 beech/spruce mixtures and 4 containers each contained monocultures of spruce or beech. Being
aware of potential edge effects, data were collected only from
the six central individuals of each container.
S. Gayler et al.
For one year prior to the phytotron study, plants were kept in
two climate-controlled greenhouse chambers under ambient
or elevated (ambient + 300 ppm) CO2 concentrations. For the
following two growing seasons (1999 and 2000), plants were
transferred into four walk-in phytotrons (two with ambient
and two with elevated CO2) maintained by the GSF. Six study
plants per species, CO2 concentration and type of competition
(i.e., intra- or interspecific competition) were held in one phytotron. This experimental set-up was independently reproduced in a parallel phytotron.
In the phytotrons, the climate conditions measured at the top
of the canopy of a nearby forest were reproduced. During
the winter months, plants were placed into open-top chambers outdoors, where corresponding CO2 regimes were maintained. Soil moisture of each container was monitored continuously by tensiometers (Model T5, UMS, Munich), triggering
irrigation with deionized water whenever soil water tension
reached 350 hPa. Fertilization (1 l of double-concentrated
Hoagland solution [Hoagland and Arnon, 1950]) was applied
six and eight times during the growing seasons 1999 and
2000, respectively. For details on the phytotrons, experimental
design and climate conditions see Payer et al. (1993) and Kozovits et al. (2005 a, b). Three years later, a second experiment
with one year younger trees (Experiment B) was carried out
in the same phytotrons (Luedemann et al., 2005). Again, competition effects in mixed cultures of juvenile beech and
spruce were investigated. Plant growth conditions in phytotrons (climate, fertilization) of control trees in experiment B
corresponded to the mixed containers under ambient CO2 of
experiment A and were used for model testing.
The simulation model
PLATHO simulates the growth of individual plants grown in
monoculture and mixed canopies, considering phenological
development, photosynthesis, water and nitrogen uptake by
roots, biomass growth and respiration and senescence, as well
as distribution of leaf area and root length. Allocation of C and
N to structural biomass, reserves, and defensive compounds is
dependent on plant internal availabilities of these resources. C
and N availability depends on environmental factors such as
soil properties and fertilization rates. 1 ≤ i ≤ I plant individuals
can be simulated simultaneously. Each individual can differ in
starting biomass, ecophysiological parameters (e.g., assimilation rate or optimal nitrogen concentration), or in species (e.g.,
coniferous or deciduous). Plant individuals are positioned in a
rectangular grid with periodical boundary conditions neglecting possible boundary effects within the phytotrons. The arrangement of individuals and the distance between the individuals can be defined by the user. Thus, the model can be used
to simulate canopies of identical individuals with and without
intra-specific competition as well as canopies of individuals
that differ in physiological properties, size, or species (intraor inter-specific competition). In the following, we present
the relevant algorithms for the simulation of intra- and interspecific competition effects. For detailed and complete documentation of the PLATHO model, including all process descriptions and equations, see Gayler and Priesack (2003).
Modelling Competition between Beech and Spruce
Plant Biology 8 (2006)
Plant morphology
The occupied crown and soil volumes of each individual are
defined as a cylinder with flexible height to diameter proportions. As a first approximation, the diameter of this cylinder is
assumed to be the same above and below ground. The circular
basal area of the cylinder is restricted by the radius, which is
limited to the distance between two plants. The above- and belowground parts of the plant are divided into N and L simulation discs, respectively. The symbols used for the description
of occupied crown and soil volume are shown in Fig. 1. The vertical distribution of leaf area and root length within each cylinder is described by means of species-specific, rotationally
symmetric distribution functions, each defined by a single
form parameter (Fig. 2).
The calculation of the root system morphology is adapted from
the CERES model (Jones and Kiniry, 1986; Ritchie et al., 1987;
Villalobos and Hall, 1989). Actually formed biomass of roots is
converted into root length using a species-specific root length
factor and is subsequently distributed to the different soil discs
depending on temperature, moisture, and nitrogen conditions
in the soil. Reduction functions relating to these factors are
taken from the SPASS model (Wang, 1997). Beyond the concept
of root system simulation, PLATHO considers belowground
competition for space sequestration between neighbouring individuals by competition factors CRLD (l) [-] (equation 4). The
actual loss of root biomass due to rhizodeposition and senes-
Fig. 1 Geometry and symbols used for calculating plant morphology.
H (m) denotes the actual height of the plant, zR (m) is the actual depth
of the root system. N simulation discs are considered above-ground
and L discs below-ground. h (m) is the height over the ground and z
(m) the depth in the soil. Aplant (m2) is the basal area of the cylinder,
r (m) is the radius of the cylinder.
Fig. 2 Two overlapping plant cylinders representing (a) a beech tree and (b) a spruce
tree. Gray values and solid lines indicate the
vertical, rotationally symmetric density distributions of leaf area and root length within the
cylinder. The species specific form parameters pL (0 ≤ pL ≤ 1) and pR (0 < pR ≤ 1) denote
the relative height of the maximal leaf area
density and the relative depth of the maximal
root length density, respectively.
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Plant Biology 8 (2006)
S. Gayler et al.
cence is converted into root length and subsequently subtracted from the root biomass in the root discs. The dieback of roots
occurs preferably in soil layers with unfavourable moisture
and nitrogen conditions. The actual root surface in the soil disc
l is calculated from the root length in this disc, the density of
root tissue, and the specific root length.
HDmax. If there is no competition for light (CL = 0), plants are assumed to pursue stem diameter growth until their minimum
height to diameter ratio, HDmin [-], has been reached. A plant
individual without light competition grows at HD = HDmin.
Competition coefficients
with
The overlap of the occupied space of neighbouring plants determines the competition intensity of the individuals. Therefore, at each time step, light competition coefficients, CL, i [-],
between plant i and its four nearest neighbours j = 1, …, 4, were
calculated from the overlap of the crown volumes:
hd1 ¼
4
P
CL;i ¼
LAIj Cij min 1; Hi Hj
j¼1
4
P
LAIj
(1)
j¼1
with
Cij ¼
Aij
;
Aplant;i
where LAI [-] is the leaf area index, H (m) is the plant height,
Aplant (m2) is the basal area of the plant cylinder and Aij (m2) is
the overlap of the basal areas of the respective plant cylinders
of plants i and j. Cij equals zero, if there is no overlap. In each
soil disc l the actual competitive situation of each individual
is calculated in relation to its resource capture capacity for
water, CW [-], nitrogen, CN [-], and in relation to belowground
space occupation, CRLD (l) [-]:
CW;i ðlÞ ¼
aR;i ðlÞ W;i
4
P
aR;i ðlÞ W;i þ
aR;j ðlÞ W;j Cij
(2)
dH dWS
4
1 hd1 2 hd1
¼
C
;
1
þ
min
C
L
L;crit
dt
dt S D2S
3
3
(5)
HD HDmin
:
HDmax HDmin
In equation 5 dWS /dt (kg d–1) denotes the actual growth rate
of the stem biomass, where ρS (kg m–3) and DS (m) are the density of stem tissue and the stem diameter, respectively. For
every simulation time step, the relative growth rate of the
cylinder diameter, DC (m), describing the occupied volume of
a plant, is proportional to the relative growth rate of DS. The
proportionality factor depends on actual HD and a parameter
ξCS [-] (ξCS ≥ 1) that describes the morphological plasticity of a
plant species (equation 6). If ξCS equals 1, the relative change
of DC equals DS . At ξCS ≥ 1 the relative increase of DC is greater
than the relative increase in DS , if the actual HD is lower than
the mean of Hmax and Hmin (lower competition intensity). Conversely, if HD exceeds the mean of Hmax and Hmin (high competition intensity), the relative increase of DC is lower than the
relative increase in DS:
dDC dDS
1
1
¼
2 hd2 1 þ
CS
CS
DC
DS
(6)
with
HDmax HD
:
hd2 ¼
HDmax HDmin
j¼1
Radiation absorption and leaf photosynthesis
aR;i ðlÞ N;i
CN;i ðlÞ ¼
4
P
aR;i ðlÞ N;i þ
aR;j ðlÞ N;j Cij
(3)
j¼1
8
>
>
>
<
lR;i ðlÞ þ
4
P
j¼1
lR;j ðlÞ Cij
9
>
>
>
=
; 0:1 ;
CRLD;i ðlÞ ¼ max 1 >
>
KRL Aplant ðzl zl1 Þ
>
>
>
>
:
;
(4)
where aR, i (l) (m2) and lR, i (l) (m) are the surface and the length
of roots from plant i in soil disc l, ζW, i (cm3 m–2 d–1) and ζN, i
(g m–2 d–1) are the uptake capacities of roots for water and nitrogen and zl (m) is the depth of soil disc l. The root length
density is limited to a maximum of KRL = 3 · 104 m m–3 (Adiku
et al., 1996).
Plant height growth
The calculation of the increment in plant height H (m) (equation 5) is an extension of the concept presented by Bossel
(1996). Under competition for light (CL > 0), plants are assumed
to grow in height until the maximal plant height to stem diameter ratio, HDmax [-], is reached. The actual increase of plant
height to stem diameter ratio, HD [-], depends on CL. If CL exceeds a critical value CL, crit , only stem height growth occurs.
If HDmax has been reached, new growth will continue at HD =
The light distribution profile in the canopy was simulated according to the method of Kropff and van Laar (1993). To consider the competitive situation of each plant, this approach
was extended to account for shading by neighbours. Attenuation of irradiance is estimated by means of Lambert-Beer’s law.
The irradiance intensity, ΦL (h) (W m–2), at height h (m) of plant
i was calculated as
L;i ðhÞ ¼ L;0 ð1 Þ
0
exp@ki LAIcum;i ðhÞ 4
X
1
Cij kj LAIcum;j ðhÞA;
(7)
j¼1
where ΦL, 0 (J m–2 s–1) is the irradiance over the canopy, LAIcum
(m2 [leaf] m–2 [ground]) is the cumulative leaf area index,
counted from the top of the plant downwards, ρ [-] is the reflection coefficient of the whole canopy, k [-] is the light extinction coefficient, and Cij gives the competition coefficients between plant i and its neighbours j (equation 1). The response
of leaf gross photosynthesis per unit leaf area to irradiance
and leaf internal CO2 concentration are calculated following
the approach of Farquhar and von Caemmerer (Farquhar et al.,
1980; von Caemmerer and Farquhar, 1981). Leaf internal CO2
concentrations were estimated from atmospheric CO2 concentrations and the simulated aperture of the stomata. In order to
consider the effect of water availability and leaf nitrogen con-
Modelling Competition between Beech and Spruce
Plant Biology 8 (2006)
centration on potential assimilation rate, Apot (μmol [CO2] m–2
s–1], a minimum factor for both effects was used (Jones and
Kiniry, 1986; Hoffmann, 1995):
Apot ¼ Amax min ’H2 O ; ’N ;
(8)
where Amax (μmol [CO2] m–2 s–1) is the light saturated assimilation rate in the case of no water deficiency and optimal nitrogen supply to leaves, ϕH2O = Tact/Tpot describes the actual aperture of stomata, where Tact and Tpot (cm3 d–1) are the actual
and potential transpiration, and
act min
’N ¼
opt min
(9)
describes the relation between leaf nitrogen concentration and
assimilation rate, where νact , νopt , and νmin (kg [N] kg–1 [dm])
are the actual, optimal, and minimal leaf nitrogen concentrations in relation to photosynthesis.
Carbon allocation to biochemical pools
The model considers four main biochemical pools: 1) assimilates, as glucose equivalents, potentially available for growth,
respiration, or defence; 2) reserves, that can be mobilized if
required; 3) defence-related compounds; and 4) structural
biomass. Flux rates between these pools depend on both the
actual plant internal carbon and nitrogen availability and the
actual demand for maintenance processes, growth, and defence. At each time step (0.01 – 0.1 d), all pools are updated
separately for each individual. Increase in the assimilate pool
results from photosynthesis and retranslocation from storage
organs or dying biomass, whereas the assimilate pool is decreased by growth, respiration, and defence. All conversion
processes are calculated in units of glucose using biochemical
information on energetics and stoichiometry of the dominant
reaction pathways. The procedure of simulating carbon allocation to these four main pools is described in Gayler et al.
(2004) for young apple trees. For beech and spruce, we assume
the same hierarchy of C allocation to these pools. In a subsequent step, assimilates allocated to the pool of structural biomass are partitioned to the different organs of the plant. In this
simulation study, the compartments fine roots, leaves, and
wood are considered, where wood is further subdivided into
coarse roots, stem, and branches. The conversion efficiencies
for glucose into structural biomass are estimated from the biochemical composition of plant organs (Penning de Vries et al.,
1989; Thornley and Johnson, 1990; Poorter, 1994). For a detailed description of the calculation of allocation rates see Gayler and Priesack (2003).
Uptake of water and nitrogen
The method used to calculate actual rates of water and nitrogen uptake is an extension of the concept used in CERES models (Jones and Kiniry, 1986; Villalobos and Hall, 1989; Wang,
1997). Water uptake is assumed to equal transpiration, which
is either limited by root conductance for water uptake, by soil
resistance for water transport, or by climatic conditions. Root
conductance is expressed by the maximal water uptake rate
per unit root surface, ζW (cm3 m–2 d–1). The maximal water uptake, qW, max, i (l) (cm3) during one simulation time step Δt (d)
from soil disc l under plant i is determined by the total surface
of roots in this disc and the respective maximal uptake rates.
Besides roots of plant i, also roots of the four next neighbouring plants (j = 1, …, 4) can be present in this disc. The fractions
of root surfaces of the neighbours that meet disc l under plant i
are calculated from the actual root area distribution and the
competition factors Cij (equation 1):
0
qW;max;i ðlÞ ¼ @aR;i ðlÞ W;i þ
4
X
1
aR;j ðlÞ W;j Cij A t:
(10)
j¼1
In equation 10, aR, i (l) (m2) is the root surface of plant i in soil
disc l. If the water content in soil layer l decreases below field
capacity, qW, max, i (l) will be reduced by limited water transport
to the roots. If the soil water content equals the permanent
wilting point, no water uptake is possible. Climatic conditions
limit transpiration if potential water uptake from all soil discs
of plant i will be greater than potential transpiration Tpot (cm3),
which depends among other factors on air temperature, humidity, wind speed, and the radiation balance at the soil surface. Tpot was estimated using the model of Penman and Monteith (Monteith, 1981). In this case, actual water uptake from
each disc is reduced by the same factor. Actual transpiration,
Tact, i (cm3), of plant i is calculated as the sum of the total water
uptake from all soil discs l under plant i by all plants present in
these discs, qW, act, i (l) (cm3), multiplied by the respective water
competition factor, CW, i (l) (equation 2):
Tact;i ¼
L
X
qW;act;i ðlÞ CW;i ðlÞ:
(11)
l¼1
Actual nitrogen uptake of a plant is limited by the nitrogen
availability in the soil, by the nitrogen uptake capacity of the
roots or by the actual plant nitrogen demand that results from
the nitrogen requirement for growth and for compensating N
deficiencies in plant organs. Nitrogen uptake is simulated in
analogy to Tact, i (equation 11), replacing the water competition
factors CW, i (l) with the nitrogen competition factors CN, i (l)
(equation 3) and ζW, i in equation 10 with the maximal nitrogen uptake rate per unit root surface, ζN, i (g m–2 d–1). The nitrogen allocation between plant organs is governed by their actual sink strengths, which are estimated from the differences
between optimal and actual nitrogen concentrations in each
organ. The changes in organ N content result from incorporation of new nitrogen, translocation of mobile nitrogen between
organs, and nitrogen losses due to senescence.
Simulation of soil water and nitrogen relations
The plant growth model PLATHO is implemented as part of the
development tool Expert-N (Baldioli et al., 1995; Stenger et al.,
1999). Expert-N consists of several modules for simulating different processes in the soil-plant-atmosphere system that can
be coupled in various combinations. This simulation study was
carried out by coupling PLATHO with the soil water transport
modules from the model HYDRUS (Simunek et al., 1998) and
with modules for nitrogen transport and turnover from the
model LEACHN (Hutson and Wagenet, 1992).
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Plant Biology 8 (2006)
Assessment of plant biomass, model parameterisation,
and simulations
Experiment A was started in spring 1998. In March and September 1999, biomass (dry mass) of leaves, stems, and axes of
the six central individuals of each container was assessed.
Stem and branch biomass were determined volumetrically by
measuring the diameters and lengths of the shoot axes. Biomass to volume relation (measured on comparable plants)
was used to convert measured volumetric data into shoot biomass. At the end of August 2000, the six central individuals
from each container were harvested. For each tree, biomass
(dry mass) of leaves, branches, and stem was determined directly. The root biomass of two (randomly chosen) out of the
six central plants was estimated quantitatively as described in
Liu et al. (2004). For details on the assessment of plant biomass, see Kozovits et al. (2005 a). A significant reduction in
aboveground biomass between trees grown in monoculture
and mixed culture could be observed for beech under ambient
and elevated CO2 conditions at p < 0.05. Aboveground biomass
of spruce was significantly increased in the mixed culture under elevated CO2. Because of uncertainties in root biomass estimation and the small root sample size, significant differences
between mono- and mixed culture in belowground biomass
could be observed only for beech trees under elevated CO2.
For this reason, belowground biomass measurements were
only used for parameterisation of allocation patterns, whereas
the calibration procedure and model tests are related to the
aboveground biomass data set.
Initial biomass of trees in experiment B were estimated in
April 2002 by harvesting 2 containers and measuring biomass
(dry mass) of roots, branches, and stem, and leaves of the six
central individuals from each container (Luedemann et al.,
2005). In September 2002 and September 2003 (end of the experiment), further containers were harvested and biomass of
plant organs of the central individuals were measured.
To separate experimental data for model testing from data for
model parameterisation, the data set was split in two parts.
Data from experiment A measured on plants grown under ambient CO2 and on plants grown in monocultures under elevated
CO2 were used for the parameterisation, whereas data measured on plants grown in mixed cultures under elevated CO2
as well as data from experiment B (mixed cultures, ambient
CO2) were used for model testing. In PLATHO, elevated atmospheric CO2 concentration affects only the estimation of potential assimilation rate Amax, which is calculated using the photosynthesis model of Farquhar and von Caemmerer (Farquhar et
al., 1980). The parameterisation of the PLATHO model was carried out in three steps. In a first step, as many parameter values
as possible were taken from measurements. All parameters required by the leaf photosynthesis model were assessed twice
per vegetation period for sun and shade leaves of beech and
for current and older needles of spruce. In addition, the following measured data were used as model parameters: specific
leaf area, specific length of fine roots, maximal and minimal
stem height to stem diameter ratio, minimal and optimal nitrogen concentration limits in different plant organs, allometric coefficients for the partitioning of structural biomass to
stem, branches, and coarse roots, as well as threshold values
of temperature sums for the simulation of bud break and leaf
senescence.
S. Gayler et al.
In a second step, missing parameter values were adopted from
other plant growth simulation models (Penning de Vries et al.,
1989; Thornley and Johnson, 1990; Hoffmann, 1995; Bossel,
1996). These parameters are: maximal growth rates of total
plant biomass, light extinction coefficients, potential translocation rates between biochemical pools, and uptake capacities
of roots for water and nitrogen.
Finally, in a third step, the remaining species-specific plant
parameters for beech and spruce (maxima of leaf area and
root length distributions, morphological plasticity) were fitted
to the plant biomass of the calibration data set measured under ambient CO2. The parameters were varied simultaneously
within reasonable limits in order to minimise the root mean
square error RMSE defined by Loague and Green (1991). RMSE
provides a percentage term of the difference between model
predictions and observations, proportioned against the mean
observed value. Its optimal value is zero, which is obtained if
simulated values agree with all measurements. RMSE was calculated using all measured aboveground plant organ biomass
during both vegetation periods as well as total plant biomass
at the end of the experiment.
The simulation runs reproducing experiment A were started
with measured values for biomass of branches and stems. Biomass start values of fine roots, coarse roots and needles were
estimated from branch and stem biomass by means of allometric relations. Initial biomass of fine and gross roots in the simulation runs reproducing experiment B were also estimated
from allometric relations. In all cases, mean values of the six
central individuals per container in the experiments were
used. In this way, monoculture simulations considered canopies as composed of identical individuals. In simulations for
mixed cultures, each beech individual was surrounded by four
identical spruce individuals and vice versa, each spruce individual was surrounded by four identical beech trees.
Results and Discussion
Model calibration
Fig. 3 compares the simulated dynamics of different biomass
compartments with measured data for beech and spruce individuals in monocultures under ambient atmospheric CO2. The
model reproduces the typical growth dynamics of trees: early
in the vegetation period, fine roots and leaves grow. Growth of
the woody compartments (stem and branches) follows as soon
as leaf expansion is largely finished. Senescence of beech
leaves starts at the beginning of autumn. Fine roots and spruce
needles are subject to a continuous loss and regeneration process.
The simulated and measured biomass of single organs and total aboveground biomass are compared in Fig. 4 for beech and
spruce grown in monocultures under ambient and elevated
CO2 conditions and in mixed cultures under ambient CO2 conditions (experiment A). After model calibration, the simulation
results fit well to the measured values at the organ level, with
RMSE = 0.18 (%/100) for roots, 0.21 for stem and branches, and
0.15 for leaves and for total aboveground biomass after two
vegetation periods with RMSE = 0.095. However, the simulations of total aboveground biomass after two vegetation periods of monocultures under ambient CO2 are in better agree-
Modelling Competition between Beech and Spruce
Plant Biology 8 (2006)
Fig. 3 Simulated (lines) growth dynamics of the plant organ biomass
compartments from the beginning of experiment A (May 1999) until
the end of the experiment in August 2000 for beech (a) and spruce
(b) individuals, respectively, grown under ambient atmospheric CO2.
Symbols (means ± SE) represent measured biomass.
Fig. 4 Simulated versus measured biomass of (a) single plant organs
(2 vegetation periods) and (b) total aboveground plant biomass at the
end of experiment A of individual beech and spruce in mono- and
mixed culture (calibration data set). The straight lines indicate the ideal
1 : 1 relation.
ment with measured data than under elevated CO2, because
the simulated promotion of beech growth under elevated
atmospheric CO2 was not confirmed by the experiment. But
overall, the results of the model calibration show that the
model is able to reproduce the observed effect on the growth
of beech and spruce in mixed culture. Similar to the experiment, growth of beech is lowered in mixed culture compared
with monoculture, whereas growth of spruce benefits slightly
from the mixed culture.
single organ biomass during two vegetation periods and total
aboveground biomass at the end of the experiments with
beech and spruce are shown in Fig. 5. Again, the simulations
of total aboveground biomass after two vegetation periods reproduce the observed effect that spruce out-competes beech
in mixed culture. However, the strong effect of mixed culture
on beech under elevated CO2 (experiment A) is somewhat underestimated by the model (Fig. 5 b). A 50 % decline in aboveground biomass in mixed culture compared to monoculture
was simulated for beech, but a decline of 60 % was measured
in the experiment. The underestimation of the competition effect results in a 40 % overestimation of the observed biomass of
beech under elevated CO2 by the model. As in the experiment,
the simulated spread between beech and spruce under ambient CO2 is lower than under elevated CO2. In experiment B the
trees were slightly smaller than in experiment A. Thus, competition effects were established only during the second vegeta-
Test of reliability of model predictions
To test the model behaviour, a second data set, which was not
used in the model parameterisation procedure, was applied.
The test data set consists of data from experiment A (mixed
cultures under elevated CO2) and the data from experiment B
(mixed cultures, ambient CO2). Simulated versus measured
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S. Gayler et al.
Fig. 6 Effect of plant density on simulated aboveground plant biomass after two vegetation periods of individual beech (circles) and
spruce (triangles), which were grown in mono- (closed symbols) and
mixed cultures (open symbols) under atmospheric ambient CO2. The
dotted line indicates the plant density in the experiment (71 plants
m–2).
Start values
tion period. Nevertheless, RMSE = 0.11 was achieved for total
aboveground biomass, while at the organ level the accuracy
of the model was lower but still satisfactory (RMSE = 0.35 for
roots, 0.30 for stem and branches, and 0.43 for leaves).
First, we tested if the better growth of spruce in the mixed container during two vegetation periods is only a transient effect.
We therefore extended the simulation over a period of five
years. Starting with values for plant biomass taken from the
experiment A, i.e., 3-year-old beech versus 4-year-old spruce,
the five-year simulations predict that, in monocultures, beech
can still synthesise more biomass than spruce. However, in
mixed culture, beech growth is increasingly reduced in contrast to the biomass development of its competitor spruce,
which out-competes beech so strongly that, after three vegetation periods, beech growth has nearly ceased. This situation
changes completely if start conditions of beech are changed
to the measured data after the first experimental year, i.e.,
4-year-old beech versus 4-year-old spruce trees. In this case,
already after the second vegetation period, beech is advantaged compared to spruce and now out-competes spruce in
the following years. The critical point seems to be which species occupies a dominant position at the time of canopy closure. An individual plant is in an advantageous position if its
potential light assimilation determined by plant height, leaf
area distribution, and carbon fixation rate is higher than that
of neighbouring plants. The high relevance of this dominance
is a typical outcome of asymmetric aboveground competition
(Weiner and Fishman, 1994; Weiner et al., 2001).
Analysis of model behaviour
Plant density
The model test shows the ability of the model to reasonably reproduce the growth of beech and spruce in mono- and mixed
cultures for the given experimental conditions. Therefore, the
analysis of the model features that generate advantageous
spruce growth in the mixed canopy under the given conditions
may provide insight to understand processes and mechanisms
of competition between juvenile beech and spruce trees. The
model analysis in the following sections is related to the experimental conditions of experiment A.
The results of the previous section, together with the fact that
in this experiment beech is the faster-growing species, suggest
that plant density should also affect competition in mixed
cultures. Therefore, we ran simulations for mono- and mixed
cultures using plant densities from 20 – 120 plants m–2 (see
Fig. 6). All other input quantities, including the start values of
plant biomass, remained unchanged and corresponded to the
experiment. The simulation runs extend over two vegetation
periods, analogous to the duration of the experiment. At lower
Fig. 5 Simulated versus measured biomass of (a) single plant organs
(2 vegetation periods) and (b) total aboveground plant biomass at the
end of experiments A and B of individual beech and spruce in mixed
culture (test data set). The straight lines indicate the ideal 1 : 1 relation.
Modelling Competition between Beech and Spruce
Fig. 7 Effect of plant density on the relative sensitivity coefficient
(RSC) of the model parameter ξCS of beech related to the simulated ratio between aboveground plant biomass of beech and spruce trees after two vegetation periods grown in mixed cultures. RSC is calculated
following Janssen (1994) and gives the relative variation of a model
output quantity with respect to the relative variation of a model parameter. The dotted line indicates the plant density in the experiment
(71 plants m–2).
plant densities, beech out-competes spruce, because beech
plants can grow for a longer time without competing for resources with neighbouring individuals. When the canopy
closes and competition for light increases, beech is in a dominant position in relation to spruce. Conversely, at high plant
densities, competition for light starts earlier and spruce is not
overgrown by beech until canopy closure. At a critical plant
density of about 40 plants m–2 spruce will dominate over
beech.
Morphological plasticity
The dominant position at the time of canopy closure is not,
however, solely responsible for the advantage of spruce in
mixed containers under the given experimental conditions.
An important mechanism of competition between the species
reveals the importance of parameter ξCS that was introduced
to describe the morphological plasticity of a plant species to
occupy space (see equation 6). From the experimental observations (Grams et al., 2002; Kozovits et al., 2005 b) and from
literature (Muth and Bazzaz, 2002), a greater morphological
plasticity was expected for beech. Correspondingly, best fit parameters are ξCS = 1.72 for beech and ξCS = 1.05 for spruce. Simulations showed that, if we assume the same morphological
plasticity for both beech and spruce, the critical plant density
where spruce can dominate over beech would shift to higher
values. Under the experimental conditions with a plant density of 71 plants m–2, a ξCS of 1.05 for both species results in a
nearly balanced situation after two vegetation periods. Simulated plant growth in mixed cultures is highly sensitive to
variations in ξCS for a range of plant densities from about 50 to
80 plants m–2 (Fig. 7). Under low and very high plant densities,
the relative dominance achieved at canopy closure is the decisive factor. In monocultures, variation of ξCS has only a minor
effect on biomass growth over two vegetation periods for both
species. Thus, the greater morphological plasticity of beech is a
Plant Biology 8 (2006)
disadvantage compared to spruce under the experimental conditions with homogeneous resource availability, because the
more flexible beech avoid competition with the more persistent spruce. However, field experiments with mixed canopies
of adult trees show that the flexibility of beech can also be a
competitive advantage if resources are heterogeneously distributed. Due to their greater flexibility in crown architecture,
hardwoods are more successful than conifers in foraging for
the patchily distributed resource, light, in disturbed situations
with forest gaps (Muth and Bazzaz, 2002). Physiological flexibility is also important for successful exploitation of patchily
distributed belowground resources (Hodge, 2004). In order to
use our model for analysing the effect of spatially variable resource supply on space occupation and hence on resource uptake, the simplistic representation of occupied crown and soil
volumes by means of cylinders in the PLATHO model has to be
substituted for a more realistic, non-circular modelling of
plant morphology. In addition, PLATHO has to be linked to a
3D soil model, similar to the approach realised in the 3DMIPS
model (Biondini, 2001).
Belowground space occupation
Water and nitrogen fluxes in the soil were simulated, considering uptake by roots, transport processes in the soil and nitrogen mineralisation. The resulting distributions of water and
nitrogen govern the distribution of newly formed root biomass
in the soil (section “Plant morphology”). Consequently, the
model predicts effects of belowground competition on vertical
root distribution. In Fig. 8, the simulated vertical root distributions of juvenile beech and spruce after two vegetation periods
in the mono- and mixed culture of experiment A are presented,
together with field observations carried out in pure and mixed
stands of adult beech and spruce in Lower Austria (Schmid,
2002). In the latter study, the fine root systems of 55 – 65year-old trees were characterised to a soil depth of 80 cm. The
model simulation for juvenile trees (Fig. 8 a) predicts that, in
the monoculture, both species preferentially occupy the upper
soil layers, where nutrient availability is highest. In mixtures,
a clear relocation of beech roots to deeper soil layers is simulated and mean root depth zM shifts from 11.5 to 13.8 cm,
whereas spruce persists in the upper layers (zM shifts from
8.5 to 6.6 cm). Because root distribution was not measured
in the container experiments A and B, this simulated effect
could not be verified, but corresponds with field observations
(Schmid, 2002). Similar to simulation for juvenile trees, in this
study fine roots of adult beech occupied deeper soil layers in
the mixed stand (zM = 28.4 cm) compared to the pure stand
(zM = 19.7 cm), whereas fine roots of spruce were shifted to upper soil layers in the mixed stand (zM = 7.4 cm) compared to the
pure stand (zM = 15.0 cm).
Because the field situation is not directly comparable with the
conditions of the container experiments, here the simulation
results only function as a working hypothesis which will be
tested in future work.
Conclusions
The study shows that the plant growth simulation model
PLATHO can be applied to analyse mechanisms of competition
in dense canopies of young beech and spruce trees, due to its
ability to consider the arrangement of plant individuals and
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S. Gayler et al.
Fig. 8 (a) Simulated vertical root length
density distribution and mean root depth after two vegetation periods of juvenile beech
(circles) and spruce (triangles) grown in
mono- (closed symbols) and mixed cultures
(open symbols) under ambient CO2-conditions (experiment A). (b) Vertical root length
density distribution and mean root depth
measured in adult beech (circles) and spruce
(triangles) stands in Lower Austria. Pure
stands are indicated by closed symbols,
mixed stands by open symbols (data from
Schmid, 2002).
morphological parameters, as well as effects of plant external
resource availabilities, on species-specific growth processes.
The model simulations demonstrate that the start values of
plant biomass and the density of the canopy are the most important factors affecting aboveground competition in mixed
canopies of juvenile beech and spruce trees. In addition, the
simulated effect of mixture on vertical root distribution, which
correspond to field observations on adult trees, stresses the
importance of belowground competition. However, if neither
of the species has a dominant position at the moment of canopy closure, the greater morphological plasticity of beech is a
strong disadvantage compared to spruce. In accordance with
experimental findings (Grams et al., 2002; Kozovits et al.,
2005 b), the parameter ξCS that describes the morphological
plasticity of a plant species, seems to be the most important
model parameter for explaining the dominance of spruce in
the mixed containers under the given experimental conditions.
Acknowledgements
The investigation was funded by the Deutsche Forschungsgemeinschaft “DFG” as the SFB 607 “Growth and Parasite Defence” – Competition for Resources in Economic Plants from
Forestry and Agronomy, Projects B5 and C2. A. R. K. and G. L.
were sponsored by a fellowship from DAAD/CAPES.
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S. Gayler et al.
S. Gayler
Institute of Soil Ecology
GSF – National Research Center for Environment and Health
Ingolstädter Landstraße 1
85764 Neuherberg
E-mail: [email protected]
Editor: H. Rennenberg