Tree Physiology 20, 399–406
© 2000 Heron Publishing—Victoria, Canada
Effects of stand composition and thinning in mixed-species forests: a
modeling approach applied to Douglas-fir and beech
H. H. BARTELINK
Department of Environmental Sciences, Group of Silviculture and Forest Ecology, Wageningen Agricultural University, P.O. Box 342, 6700 AH
Wageningen, The Netherlands
Received October 13, 1998
Summary Models estimating growth and yield of forest
stands provide important tools for forest management. Pure
stands have been modeled extensively and successfully for decades; however, relatively few models for mixed-species
stands have been developed. A spatially explicit, mechanistic
model (COMMIX) is presented that simulates growth of
mixed-species forest stands, and takes account of the effects of
management on stand dynamics.
Previously, it was shown that COMMIX satisfactorily reproduced the development of monospecific stands. In the
present study, the model was used to simulate growth and
yield in mixed stands differing in the proportions of species
present. The concept of a “replacement series” was used to
compare productivities of the mixed stands. The model was
also used to analyze effects of thinning regimes and stand
composition on productivity. Model simulations indicate that
productivity of a mixed stand will generally be intermediate
between the productivities of monospecific stands of the contributing species. However, stand composition, and especially
thinning regime, will strongly affect stand productivity. The
simulations are discussed with reference to the effects of resource partitioning, canopy stratification, complementarity,
spatial pattern, crown dynamics, and phenology on the growth
and yield of mixed stands. The study highlights the value of
using mechanistic approaches to predict mixed stand development in relation to management regime.
Keywords: distance-dependency, growth, management, mixed
stands, productivity, replacement series, simulation, yield.
more sophisticated approach is represented by the model of
Pretzsch (1992), which simulates growth of individual trees
within a forest stand; however, growth calculations are based
on descriptive relationships with tree stem diameter (dbh),
which restricts the ability to take account of the effects of environmental conditions.
Generally, empirical approaches lack the flexibility to deal
with the wide range of potential species combinations, management regimes, and site-dependent interactions that occur in
mixed stands. A causal approach would appear to offer advantages over a descriptive approach (cf. Lavigne 1992, Burkhart
and Tham 1992). Mechanistic or process-based approaches
have been successfully used to simulate growth of monospecific stands (e.g., Mäkelä and Hari 1986, Mohren 1987,
Nikinmaa 1992). A mechanistic model can be used to simulate
responses to silvicultural treatments that have never been performed in practice. Moreover, process-based models provide
mechanistic understanding of, and insights into, tree grow and
forest dynamics.
A mechanistic model, COMMIX, which simulates growth
of mixed-species forest stands (Bartelink 1998b), was used to
estimate the response of mixed-forest growth and development to specific silvicultural treatments and stand compositions. The mixed Douglas-fir (Pseudotsuga menziesii (Mirb.)
Franco) and beech (Fagus sylvatica L.) forest type, which is
prevalent in The Netherlands and Germany, was used as a
case-study. This type of mixed stand allows investigation of both
the interactions between a coniferous and a broad-leaved species,
and the importance of species-specific features like growth pattern and crown features on growth and competition.
Introduction
Models estimating growth and yield of forest stands provide
important tools for forest management. Pure stands have been
modeled extensively, resulting in yield tables for different
species on a range of sites (e.g., Jansen et al. 1996). In contrast,
systematic research on stand dynamics of mixed forests is
lacking and relatively few models for mixed-species stands
have been developed (cf. Pretzsch 1992, Burkhart and Tham
1992). One approach has involved the use of competition indices (e.g., Holmes and Reed 1991); however, such empirical relationships between growth and tree or stand characteristics
are applicable only to a limited range of growing conditions. A
Material and methods
The COMMIX model
The model COMMIX (COMpetition in MIXed stands) is a
process-based, tree-level, distance-dependent model of forest
growth. In the model, individual trees are characterized by the
dry weights of their biomass components (fine roots, coarse
roots, stem, branches, foliage), the dimensions of stem and
crown, and the position (x,y,z) of the stem foot. COMMIX was
developed on the basis of three main assumptions: (1) radiation is crucial for growth—radiation (light) absorbed by a tree
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BARTELINK
strongly determines tree growth rate, and competition for radiation among stand members determines stand development
(Landsberg 1986, Cannell 1989); (2) the dry matter production
of a tree is related to the radiation it absorbs, according to the
radiation-use efficiency (RUE) concept (Monteith 1977,
Cannell 1989); and (3) the partitioning of dry matter growth
among the biomass components is dependent both on tree state
and growing conditions (e.g., site), and is largely determined
by the need to maintain structural balances (Mäkelä 1986,
Cannell and Dewar 1994). Water and nutrient relations were
not included in this modeling study: growing conditions are
considered to be optimal for the particular study sites, i.e.,
well-drained, acid brown podsolic soils on ice-pushed
preglacial deposits. COMMIX differs from other processbased models of mixed forests in its spatial detail (vertically
and horizontally explicit), in the way growth is calculated
from estimated radiation absorption rates, and in the way dry
matter partitioning is accounted for.
Four steps can be distinguished in the dynamic simulation.
Step 1 involves the interception of radiation by a tree. Radiation attenuation is spatially explicit in COMMIX. Calculation
of interception by individual forest trees is based on the geometrical characteristics of the radiation, the locations of the
trees in the stand, and the foliage characteristics of each tree.
Stem and branch intercepting areas are ignored; it is assumed
that there is always foliage between the source of radiation and
the woody components. Foliage reflection and transmission
are ignored. Assuming a uniform distribution of foliage area
within a crown, the relationship between radiation regime, leaf
characteristics, and radiation extinction is described by the
Lambert-Beer equation:
I l = I 0 exp( −( K / sin(β)) LADl )
(1)
where Il is irradiance at depth l (along the ray direction) in the
canopy (W m –2), I0 is irradiance outside the canopy (W m –2),
K is an extinction coefficient, β is the ray inclination, LAD is
leaf area density (m 2 m –3), and l trajectory length, i.e., distance
penetrated by the ray inside the crown (m).
To calculate absorption, a grid is defined on the forest floor;
virtual beams are described, starting from the grid points, and
heading in a direction determined by the orientation of the radiation (van Kraalingen, 1989). The beam is assigned a width
equal to the grid cell size. When the center of the beam intersects a crown, the beam cross-sectional area perpendicular to
the beam direction (β) is determined. The distance penetrated
in the crown determines the attenuation rate. The difference
between irradiance input and irradiance passing through the
crown (in W m –2) multiplied by the beam cross-sectional area
gives an estimate of the amount of radiation absorbed by that
part of the crown (see Bartelink 1997).
In The Netherlands, about 50% of the radiation is from diffuse sky conditions (Spitters et al. 1986). For the present application, all radiation was considered to be diffuse. Mean annual
amount of photosynthetically active radiation (PAR) was derived from the weather station in Wageningen, The Netherlands (5°40′ E, 51°58′ N).
Step 2 in the dynamic simulation involves conversion of the
amount of absorbed photosynthetically active radiation
(APAR) into an amount of dry matter. A potential pitfall in
process-based models of forest growth is the lack of information on maintenance requirements (Cannell 1989, Cannell and
Dewar 1994). To avoid this in COMMIX, the concept of radiation-use efficiency (RUE) is applied to calculate growth
rates. Based on the annual amount of absorbed radiation
(APAR), the total amount of dry matter produced (net primary
production NPP) is estimated directly, by assuming a linear relationship between APAR and NPP (Monteith 1977, Cannell
1989). The RUE estimates were derived from Bartelink et al.
(1997).
Step 3 in the dynamic simulation involves partitioning of
the dry matter (i.e., growth) among the different biomass components. The theoretical concepts underlying assimilate allocation, or dry matter partitioning, have been summarized by
Cannell and Dewar (1994). Unfortunately, most of these concepts are unsuitable for forest modeling studies aimed at practical applications, because many of the parameters are still
unknown (Cannell 1989, Cannell and Dewar 1994). In COMMIX, a dynamic approach was used to simulate dry matter
partitioning, based on the concept of maintaining structural
balances (Valentine 1985, Mäkelä 1986). Partitioning among
tree parts was determined by physiological or mechanical interdependencies, or both (Mäkelä 1986). A suitable procedure is
first to divide the plant into parts that differ in function, and to
identify the phenomena that determine or constrain the allocation
or partitioning of dry matter among them (Cannell and Dewar
1994). In COMMIX, the following relationships were used: (1)
an empirical relationship describing height development over
time; (2) a mechanistic relationship between sapwood area and
foliage area (pipe-model); (3) a mechanistic relationship between
fine root and foliage biomass; (4) an allometric relationship between stem diameter at breast height, height and branch biomass;
and (5) an allometric relationship between stem diameter at
breast height and root biomass. During the growth process, a
structural balance between the different organs must be maintained. This requirement introduces a formal relationship between the time dependence of partitioning and distribution (see
Bartelink 1998a).
Step 4 in the dynamic simulation involves updating tree biomass status (integration) and calculating changes in tree structure. After growth and turnover rates are calculated,
integration takes place, resulting in new biomass amounts and
tree states. The principal time-step of the model is one year.
The loss rates of the biomass components are assumed to be
proportional to the amounts of biomass. Natural tree death is
induced by an unbalanced tree structure; trees with a
height/diameter ratio (h/dbh ratio) greater than 150 (cm cm –1)
have an increased probability of wind-throw. Trees can also be
cut (see below). For the surviving stand members, the new
biomass amounts are calculated based on growth rates, and the
crown size is updated.
With respect to management in COMMIX, different thinning rules can be chosen. In this study, thinning from above
(“crown thinning” or “high thinning”) was applied: to benefit
TREE PHYSIOLOGY VOLUME 20, 2000
MODELING MIXED-SPECIES FORESTS
the best trees, the strongest competitors are removed, i.e., the
second-largest trees (in terms of diameter).
Model simulations
To investigate model performance, simulation estimates were
compared with field data. Because data on long-term dynamics
of mixed stands are scarce, model validation was carried out using monospecific Douglas-fir and beech stands (Bartelink
1998b). Simulation results were compared with yield tables
(Jansen et al. 1996). Thinning regimes included in the yield tables
(in terms of basal area to be removed) were applied in the model
runs.
For Douglas-fir, the yield table data conformed well to the
results of simulated low thinning in the first decades. However, there were differences between table and model estimates in older stands. The higher estimates with the model
compared with the yield table in older stands are in accordance
with the findings of Schoonderwoerd and Daamen (1995),
who reported that the yield table underestimates growth rates
in stands older than approximately 40 years.
The simulated beech stand initially grew faster than described by the yield table, but slowed down with increasing
stand age. Simulated stand productivity decreased as stand age
increased, which could be attributed to the opening up of the
canopy. The thinning intensity indicated by the yield table is
large compared with the estimated basal area increment.
These discrepancies could be associated with uncertainties
and errors in the data and assumptions used to build the yield
table. The table is largely based on Swedish and German tables, because of the lack of permanent sample plots in The
Netherlands (Jansen et al. 1996).
Based on the results of the analysis of monospecific stand
dynamics, model performance was considered satisfactory,
and COMMIX was considered suitable for the study of mixed
stand dynamics (Bartelink 1998b). In the present study, COMMIX was used to investigate the effects of stand composition
and thinning regime on growth and yield. An overview of the
main species parameters is given in Table 1. The initial values
of the tree biomass components and the structural variables are
listed in Table 2.
To enable comparisons of simulation results, the model was
run with several stand compositions that together form a replacement series (de Wit 1960, Kelty 1992) (Equation 2). In a
sequence of stand compositions, the share of one species is
gradually increased until a monospecific stand of species A is
completely replaced by a monospecific stand of species B.
Five mixtures differing in species shares were used; in terms
of basal area, the proportion of Douglas-fir amounted respectively 100, 75, 50, 25 and 0%. The relative yields of Douglas
fir and beech were defined as:
RYD = YDmix / YDmono
RYB = YBmix / YBmono,
(2a)
where YDmix and YBmix are the yields of Douglas-fir and beech
in the mixture (m 3 ha –1), and YDmono and YBmono are the yields in
401
Table 1. Main species-specific parameters used in COMMIX (after
Bartelink 1998b). In addition, empirical parameters are applied to describe the allometry between tree diameter at breast height (dbh; 1.30
m above the forest floor), dbh and branch biomass, dbh and coarse
root biomass, dbh and crown dimensions, and dbh, height and bole
volume. Values of these parameters can be found in Bartelink (1998a).
Parameter
Unit
Douglas-fir
Beech
Radiation-use efficiency
Fine root/foliage ratio
Leaf angle distribution
zontal
Specific leaf area
Wood basic density
Crown form
soid
Foliage age classes
Sapwood rings
Foliage loss coefficient
Turnover branches
Turnover coarse roots
Turnover fine roots
Turnover sapwood
Pipe-model ratio
g MJ –1
kg kg –1
–
1.1
0.35
Spherical
1.2
2.0
Hori-
m 2 kg –1
kg m –3
–
5.63
450
Cone
17.20
550
Ellip-
–
–
Year –2
Year –1
Year –1
Year –1
Year –1
m 2 (foliage)
m –2 (sapwood)
5
20
0.20
0.03
0.03
0.75
0.05
16
1
100
1.00
0.03
0.03
0.75
0.01
10
monoculture (m 3 ha –1), respectively. The relative total yield
was defined as:
RYT = RYD + RYB.
(2b)
Two thinning regimes were also defined. In Thinning Regime
I, thinning intensity (expressed as a fraction of the standing
basal area) was the same as used in the yield table (the “default” thinning regime). High thinning was the method of thin-
Table 2. Tree components distinguished in the COMMIX model and
the initial values of the variables. Biomass amounts are dry weights.
Foliage area is one-sided (i.e., projected area). Tree diameter (dbh) is
measured at breast height (1.30 m above the forest floor).
Tree characteristic
Unit
Beech
Douglas-fir
Tree age
Foliage biomass
Branch biomass
Stem biomass
Fine-root biomass
Coarse-root biomass
Sapwood area
Year
kg
kg
kg
kg
kg
m2
0.0040
m2
cm
m
m
m
20
8.00
7.10
48.90
2.80
10.90
0.0110
20
0.75
2.16
7.70
1.50
1.56
45.0
14.3
12.9
1.45
5.5
12.9
7.2
7.0
0.85
0.5
Foliage area
Stem diameter
Tree height
Crown radius
Crown base height
402
BARTELINK
ning applied, in accordance with current forestry practice.
Because beech is generally believed to be at a disadvantage in
this mixture type, Thinning Regime II was defined so that the
thinning intensity in beech was fixed at only 5% of the standing basal area, whereas for Douglas-fir the thinning fraction
increased from 1.0 times the default fraction (i.e., the yield table values) at Age 20, to 1.5 times the default fraction at Age
70.
Simulated stands comprised 400 (20 × 20) trees. Initial planting distance was 2.5 m, based on Douglas-fir stand densities. Although monospecific beech stands will have a higher density,
planting distance was kept constant to avoid additional variability
that could hamper comparison of the simulation results. Stand
amounts were calculated based on the sizes of the inner 256 (16 ×
16) trees, to prevent border effects; the outer tree row was not
thinned at all for the same reason. The model was set to simulate
50 years of stand growth, from age 20 to 70.
Figure 2. Simulated development over time of the total stand biomass
for stands with different proportions of Douglas-fir and beech, for
Thinning Regime I. Abbreviations: %dg indicates percentage of
Douglas-fir.
Results
Stand-level results: LAI and biomass
Results obtained under the various stand composition and
thinning regimes are presented in Figures 1 to 4. Figures 1 to 3
show only the results obtained under Thinning Regime I, because relatively little variation between the two thinning
regimes were apparent in the stand-level results.
In Figure 1, the development of leaf area index (LAI) over
time is shown. Leaf area index starts at low values in stands
with a high proportion of beech because, for this species, the
2.5 × 2.5 m planting density used was low; however, differences become less pronounced at greater ages, resulting in
LAIs of 6–7. The mixed stands have the highest LAIs. This is
because a reduction in the contribution of a species to basal
area does not necessarily result in an identical reduction in
LAI. For example, in the stand with 75% Douglas-fir, the
Douglas-fir component is able to develop almost the same LAI
as the Douglas-fir monoculture (not shown): therefore, the additional presence of beech trees in the mixture results in a
higher stand LAI.
Figure 2 presents the total amount of living biomass. Predicted biomass amounts at Age 70 range from 220 Mg ha –1
year –1 in beech stands to 380 Mg ha –1 year –1 in Douglas-fir
stands. Stand composition strongly affects the biomass accu-
Figure 1. Simulated LAI development over time for stands with different shares of Douglas-fir and beech, for Thinning Regime I. Abbreviations: %dg indicates percentage of Douglas-fir.
Figure 3. Simulated development over time of the root/shoot ratio for
stands with different shares of Douglas-fir and beech, for Thinning
Regime I. Abbreviations: %dg indicates percentage of Douglas-fir.
mulation rate, beech-dominated stands have less biomass than
Douglas-fir-dominated stands. This difference can be attributed to the higher net growth rate of Douglas-fir compared
with beech, mainly as a result of (1) more efficient light interception, and (2) lower loss rate, i.e., a lower foliage turnover
rate (Table 1).
Stand composition and thinning regime not only affected stand
Figure 4. Simulated stand volume increment for stands with different
proportions of Douglas-fir and beech, for Thinning Regimes I (a) and
II (b). Abbreviations: % indicates percentage of Douglas-fir.
TREE PHYSIOLOGY VOLUME 20, 2000
MODELING MIXED-SPECIES FORESTS
403
productivity and biomass, but also the distribution of the biomass
among the belowground and aboveground components (Figure 3). The ratio of aboveground to belowground biomass is not
constant over time. Moreover, the ratio varies strongly with stand
composition because it is dependent on partitioning, which differs among species (Bartelink 1998a), and on the turnover of the
biomass components, which is also species-dependent (Table 1).
The largest changes in the ratio appeared in the monospecific
beech stand.
Stand composition and thinning regime also affected stand
volume increment (m 3 ha –1 year –1). Figures 4a and 4b show that,
after reaching a maximum, stand volume increment slowly decreases to about 14 and 9 m 3 ha –1 year –1 in the monospecific
Douglas-fir and beech stand, respectively. Yields of the mixed
stands lie somewhere in between.
Stand-level results: relative and absolute yield
Figure 5 presents the relative yields (RYB, RYD, and RYT) of
beech and Douglas-fir in the two scenarios. The yield of
Douglas-fir in the mixed stand is higher than the yield of a
monospecific Douglas-fir stand. However, when thinning intensities in beech are lower than the default-thinning regime (Figure 5b), the RY of Douglas-fir in mixtures with a low proportion
of Douglas-fir is less than 1.0, and the RYT exceeds 1.0.
Absolute yields for the various scenarios are presented in
Figure 6. Obviously, absolute yield of the mixture for all stand
Figure 6. Estimated absolute yield of the stands over a 50-year period
for Thinning Regimes I (a), and II (b). The dashed lines show the expected yield if intra- and inter-specific interactions were equivalent;
i.e., no advantage of mixing would exist. Solid lines represent the
model estimates: deviations from the dashed lines indicate that interaction between the species occurs.
compositions and thinning regimes is less than the sum of the
fractions of the monospecific stands of the contributing species. Over the 50-year simulation period, it appears that productivity of the monospecific Douglas-fir stand is equal to or
higher than that of both the monospecific beech and the mixed
stands (Figure 6). Figure 6a shows that, in stands with a low
proportion of Douglas-fir, the productivity of Douglas-fir is
lower than could be expected from its basal area share in the
mixture. However, in stands with initially more than 40% of
the basal area consisting of Douglas-fir, the opposite is the
case. The productivity of beech, in contrast, is lower than
could be expected from its proportion of basal area, except in
stands with few Douglas-fir trees and hardly any thinning in
beech (Figure 6b). Increasing the thinning intensity in
Douglas-fir leads to a higher yield, mainly because of a higher
yield of the beech fraction in the mixture.
Tree-level results: diameter distributions
Figure 5. Estimated relative yield (RY) for the stands, based on the
stem volume production over a 50-year period, for Thinning Regimes
I (a) and II (b). The lower-left to upper-right solid line represents the
yield of the Douglas-fir trees in the mixture (RYD), the upper-left to
lower-right solid line represents the beech yield (RYB), and the horizontal solid line is the (mixed) stand total yield (RYT). The dashed
lines show the expected yield if intra- and inter-specific interactions
were equivalent, i.e., no advantage of mixing would exist. The position of the individual stands on the x-axis depends on their proportion
(in terms of basal area) of Douglas-fir.
Both thinning intensity (compare between thinning regimes)
and initial stand composition (compare stand compositions
within one thinning regime) affect the diameter distribution of
the stand at Age 70. Figures 7 and 8 show the results of the
50-year run for Thinning Regimes I and II, respectively. Figure 7 shows that, for Douglas-fir, mean dbh increases and dbh
range decreases as the proportion of beech increases. The
highest dbh variability (at Age 70) is achieved in the
monospecific beech stand. For beech, an increasing proportion of Douglas-fir results in a decreasing mean dbh and a
smaller dbh range. Roughly the same pattern can be observed
TREE PHYSIOLOGY ON-LINE at http://www.heronpublishing.com
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BARTELINK
Figure 7. Relative diameter
frequency distributions of
beech (open) and Douglas-fir
(solid), for Thinning Regime I.
Relative diameter frequency
distributions after 50 years of
growth (Age 70), for the five
initial stand conditions (a–e).
The x-axis shows the dbh class
(cm), and the y-axis shows the
relative frequency in the stand.
in Figure 8.
Comparing Thinning Regimes I and II reveals that, for
Douglas-fir, increased thinning intensity of Douglas-fir (Thinning Regime II) results in (1) larger diameters in stands with a
low share of beech; and (2) smaller diameters in mixtures with
a large share of beech, compared with the stand structures arrived at in Thinning Regime I. For beech, the reduced thinning
intensities in both beech and Douglas-fir (Thinning Regime II)
lead to a higher stem number and, consequently, a lower mean
dbh and a smaller dbh range.
Discussion
Patterns of LAI, biomass and productivity
The reason for the relatively high LAI of the mixed stands is
that the ratio between a species’ LAI and its basal area depends
on stand composition. Figure 1 also indicates that a higher LAI
can be maintained in mixed stands than in monocultures, suggesting that mixed stands intercept more light and hence reach
higher growth rates. However, the latter suggestion is not confirmed by other results of this study (see Figure 5). Generally,
simulated LAI and biomass amounts are in agreement with
values mentioned in other studies (e.g., Cannell 1982,
Bartelink 1998b). Productivity (Figure 4) shows the same
trends and order of magnitude as the yield table for monospecific stands (Jansen et al. 1996).
Biomass accumulation rate appeared to depend on stand
composition (Figures 2 and 3). This is because species-specific characteristics, such as allocation or partitioning patterns
and loss rates, strongly affect dry matter accumulation and distribution. Models using dry matter distribution patterns as a
target-distribution for growth allocation should take both age
(or biomass) and composition of the species into account
when estimating the root/shoot ratio of a forest stand.
Relative and absolute yield
Generally, the productivity of beech is low compared to its
share in the basal area of the mixed stand. From the simulation
for Thinning Regime I in Figure 5a, for example, it follows
that the productivity of beech is significantly lower (the solid
line) than could be expected from its proportion in the mixture
(dashed line), whereas the opposite was found for Douglas-fir.
In contrast, the simulation for Thinning Regime II in Figure 5b
reveals that, in stands with a low proportion of Douglas-fir, the
productivity of Douglas-fir is lower than could be expected
from its basal area share in the mixture. This is probably a result of differences in crown shape. The ellipsoidal beech
crowns are able to compete successfully for radiation in stands
containing only a few cone-shaped Douglas-fir tree crowns.
Based on the simulations in Figure 5, it appears that some of
the mixed stands are more productive than the sum of the
productivities of each species (RYT exceeds 1.0). However,
apart from relative yields, absolute values should be used to
identify the highest yielding stand in the experimental series.
For example, if one of the species is much more productive in
monoculture than the other, the mixture can have an RYT >
1.0, and yet not exceed the yield of the more productive species in monoculture (cf. Kelty 1992). Figure 6 shows that, although RYT exceeds 1.0 in some mixtures, absolute yield is
lower, implying that the productivity of all simulated stands is
intermediate between the productivities of monospecific
stands of the contributing species. The productivity of a mixed
stand of Douglas-fir and beech will not exceed the yield of a
monospecific Douglas-fir stand; hence, mixing the two spe-
TREE PHYSIOLOGY VOLUME 20, 2000
MODELING MIXED-SPECIES FORESTS
405
Figure 8. Relative diameter frequency distribution of beech
(open) and Douglas-fir (solid),
for Thinning Regime II. Relative diameter frequency distributions after 50 years of growth
(Age 70), for the five initial
stand conditions (a–e). The
x-axis shows the dbh class
(cm), and the y-axis shows the
relative frequency in the stand.
cies does not result in a more efficient use of the resources.
Stand structure
Both thinning and initial stand composition have a strong impact on stand structure and the effect of thinning intensity depends on stand composition (Figures 7 and 8). For example,
the diameter distributions at Age 70 differ greatly among the
scenarios, indicating that silvicultural operations will have serious consequences on final stand structure, and thus the size
distribution of the harvestable timber. In general, Douglas-fir
trees will benefit from mixing with beech because they are
able to outcompete the beech, at least as far as radiation interception is concerned. A small portion of beech will hence
ensure large Douglas-fir diameters; however, this is accompanied by a lower stand productivity; i.e., there is a trade-off between stand productivity and diameter size.
Yield of mixtures versus monocultures
Most of the evidence for interactions between species comes
from studies showing that mixed stands with layered canopies
may intercept light more completely than canopies of a single
species (Kelty and Cameron 1994). This phenomenon, called
“complementarity,” results in reduced competition and more
complete use of a site’s resources. Complementarity contrasts
with “facilitation,” which occurs when the presence of one
species directly benefits another. Both types of interactions
cause yields in mix stands to exceed those in monocultures of
the component species (Kelty and Cameron 1994). Studies in
central Europe show that, on some sites, the productivity of
mixed stands of Norway spruce (Picea abies (L.) Karst.)–beech and white fir (Abies alba Mill.)–beech might
slightly exceed the yield of a monospecific stand, but only
when the proportion of the most productive species is not too
low. Generally, the yield of these mixed stands will be somewhere in between the yields of the two monocultures as observed in the present study (Wiedemann 1950, Assmann 1961,
Kennel 1965, Zimmermann 1988, Kelty 1992, Nusslein
1993).
Limitations to the modeling approach
The model COMMIX was able to reproduce the development
of monospecific stands and could be applied to analyze management consequences for growth, yield and stand composition; however, there are several features of the model that need
to be improved. For example, differences in phenology need to
be included, because phenological differences (e.g., timing of
bud burst and leaf development) among species cause a temporal separation of light interception that strongly affects competitive interrelationships (Kramer 1996).
Crown expansion is currently dependent on stem size (dbh).
Because of the high structural diversity in uneven-aged,
mixed-species stands, it is necessary to link crown dynamics
directly to changes in resource availability. The same arguments hold for height growth, which is currently described by
the empirical Chapman-Richards function. The height growth
potential and the actual height growth of a tree have a large impact on its role and survival, and ultimately on stand structure
and composition.
Dry matter partitioning should be coupled to environmental
conditions to enable dynamic modeling of tree responses to
growing conditions, and to provide mechanistic understanding
of and insights into competition, tree grow, and forest dynamics. It is proposed to incorporate both water-balance and nutrient relationships in the next version of the model. In addition,
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features like natural regeneration and more species need to be
parameterized, to allow simulations of spontaneous forest development on a range of sites.
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