The dependency of the size-growth relationship of Norway spruce (Picea abies [L.] Karst.) and European beech (Fagus sylvatica [L.]) in forest stands on long-term site conditions, drought events, and ozone stress

Abstract

Against a backdrop of increasing climate change, the effects of site conditions, drought events and ozone stress on the size-growth
relationship in Norway spruce (Picea abies [L.] Karst.) and European beech (Fagus sylvatica [L.]) stands are analyzed. The size-growth relationship is represented by a straight line defined by intercept and slope
of a simple linear equation with stem diameter at height 1.30m as independent variable and annual stem diameter increment
at height 1.30 as dependent variable. On the basis of 64 long-term experimental plots dating back to 1871 and representing
an ecological gradient from fertile to poor sites, it is shown that poorer sites exhibit shallower slopes of the linear size-growth
relationships than fertile sites. Annual measurements of the size-growth relationship, including the extremely dry years of
1976 and 2003, also showed that lower stand growth rates result in shallower size-growth relationship slopes. By comparing
stands with and without experimental twice-ambient ozone exposure between 2000 and 2007, it was found that ozone stress can
significantly reduce the slope of the size-growth relationship. This indicates that limiting site condition, whether acute
or chronic in nature, distinctly reduces the superiority of tall trees, and that a lower degree of resource limitation increases
the steepness of the size-growth relationship. The causes for this behavior and the consequences for stand dynamics, silvicultural
treatment and prognostication by models are discussed.

KeywordsSize-asymmetric growth–Diameter increment–Competition–Resource partitioning–Limitation–Allocation principle–Stand structure

Full text

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ORIGINAL PAPER
The dependency of the size-growth relationship of Norway spruce
(Picea abies [L.] Karst.) and European beech (Fagus sylvatica [L.])
in forest stands on long-term site conditions, drought events,
and ozone stress
Hans Pretzsch•Jochen Dieler
Received: 17 September 2010/Revised: 8 October 2010/Accepted: 21 October 2010/Published online: 11 November 2010
? The Author(s) 2010. This article is published with open access at Springerlink.com
Abstract
change, the effects of site conditions, drought events and
ozone stress on the size-growth relationship in Norway
spruce (Picea abies [L.] Karst.) and European beech (Fa-
gus sylvatica [L.]) stands are analyzed. The size-growth
relationship is represented by a straight line defined by
intercept and slope of a simple linear equation with stem
diameter at height 1.30 m as independent variable and
annual stem diameter increment at height 1.30 as depen-
dent variable. On the basis of 64 long-term experimental
plots dating back to 1871 and representing an ecological
gradient from fertile to poor sites, it is shown that poorer
sites exhibit shallower slopes of the linear size-growth
relationships than fertile sites. Annual measurements of the
size-growth relationship, including the extremely dry years
of 1976 and 2003, also showed that lower stand growth
rates result in shallower size-growth relationship slopes. By
comparing stands with and without experimental twice-
ambient ozone exposure between 2000 and 2007, it was
found that ozone stress can significantly reduce the slope of
the size-growth relationship. This indicates that limiting
site condition, whether acute or chronic in nature, distinctly
reduces the superiority of tall trees, and that a lower degree
of resource limitation increases the steepness of the size-
growth relationship. The causes for this behavior and the
consequences for stand dynamics, silvicultural treatment
and prognostication by models are discussed.
Against a backdrop of increasing climate
Keywords
increment ? Competition ? Resource partitioning ?
Limitation ? Allocation principle ? Stand structure
Size-asymmetric growth ? Diameter
Introduction
The principles of resource and biomass growth distribution
between neighboring trees in a stand and the change of this
distribution due to stress are important factors when scaling
up from individual tree to stand and ecosystem dynamics.
However, while the allocation principles at an individual
plant level have been well documented and studied (e.g.,
Niklas 1994; Landsberg 1986; Ma ¨kela ¨ and Hari 1986) and
the growth dynamics at a stand level are well described on
the basis of the average tree (e.g., Assmann 1970; Oliver
and Larson 1996; Pretzsch 2010), insight into the resource
and growth distribution between the trees of a stand or
cohort and its dependency on site conditions is still limited
(Schwinning and Weiner 1998). Analysis at an individual
plant level, considering allocation principles and plant
responses under stress, can produce evidence of a stress
response. However, far reaching conclusions on the rele-
vance of such reactions and the performance at a stand
level require further research into tree interactions, com-
petition and possible compensation effects between trees
under stress. The reaction pattern of stands or cohorts is
more than just an individual tree response and, thus, cannot
be inferred from trees growing solitarily in greenhouses
(Matyssek et al. 2005).
The insight into the dependency of the size-growth
relationship from environmental conditions is of particular
interest because tree growth and stand dynamics are
increasingly affected by trends of changing growing con-
ditions (Spiecker et al. 1996) and stress events (Jentsch
Communicated by U. Luettge.
H. Pretzsch (&) ? J. Dieler
Chair for Forest Growth and Yield Science,
Technische Universita ¨t Mu ¨nchen, Munich, Germany
e-mail: hans.pretzsch@lrz.tum.de
123
Trees (2011) 25:355–369
DOI 10.1007/s00468-010-0510-1

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et al. 2007; Matyssek and Sandermann 2003; Pretzsch et al.
2010). The effects of site conditions, disturbances and
stress events on tree as well as stand growth as a whole
have frequently been analyzed empirically (Schweingruber
et al. 1986; Ro ¨hle 1987), summarized (Pretzsch 1999), and
prognosticated by models (Bugmann et al. 1997; Pretzsch
et al. 2008). The reaction pattern of individual tree growth
spans from growth acceleration, where the former limita-
tion is remedied (Pretzsch 1999), to gradual decreases of
vitality by long-term deposition (Elling 1993), abrupt
growth losses (Utschig 1989) or even die-back (Ro ¨hle
1987). The reaction pattern at a stand level is corre-
spondingly wide,site-dependent
pp. 543–550), and subject to considerable variation
between stands. Growth rates may increase on formerly
poor sites, or sites with decreasing air pollutants (Miel-
ika ¨inen and Timonen 1996). Sites which become water
limited or suffer from absorption of long-range emissions
or summer drought show severe declines in growth (Bei-
erkuhnlein and Foken 2008). Numerous investigations
have thus contributed to a sound understanding of tree
growth and of cumulative stand growth rates in dependence
on trees species, site conditions and types of stress.
In contrast, the understanding of the distribution of
resources and growth between competing individuals in a
stand is still rather limited. Depending on the respective
limiting factor (e.g., light, water, nutrients) the division of
resources between individuals in a stand may be entirely
size asymmetric, whereby the larger plants receive all the
contested resources. The opposite, borderline case is a
completely symmetric division of resources, in which all
plants, irrespective of size, obtain the same amount of
resources. Within these two scenarios, Schwinning and
(Pretzsch 2009,
Weiner (1998) distinguish between partial size-symmetric,
perfect size-symmetric and partial size asymmetric distri-
bution of resources. As resource distribution between
individuals is difficult to measure, but assumed to be pro-
portional to the absolute growth rate, the size-growth
relationship is used as a proxy for the size-resource rela-
tionship (e.g., Hara 1993; Pretzsch and Biber 2010;
Wichmann 2001, 2002; Weiner 1990). The stem diameter
increment (id = absolute growth rate in a defined period,
such as 1 year) was thus plotted against stem diameter
(d = diameter at tree height 1.30 m) at the beginning of
the respective period. Figure 1 displays a set of linear (lines
1, 3, 4, and 5) and non-linear (lines 2, 6) size-growth
relationships (adapted from Weiner 1990). A steeper slope
indicates higher growth rates and favored resources supply
of tall trees in the stand. The case of complete size-
asymmetry, indicated by a line parallel to the y-axis
(slope = ?; a sub-cohort of large plants receives all
growth), is solely of academic interest and not integrated in
Fig. 1. Note that all relationships in Fig. 1a are linear.
However, only line 4 represents a linear and proportional
increase of absolute growth rate with increasing size,
meaning only in this case is the relative growth rate equal
for all individuals.
Complete symmetry (Fig. 1a, line 1) means that growth
and resources, which competitors receive, are independent
of their size. Tendency towards complete symmetry (line 1)
or partial size-symmetry (Fig. 1a, line 3; Fig. 1b, line 2) is
assumed to prevail under limitation by below-ground
resources (water and mineral nutrients), as they are difficult
to preempt by larger individuals (Kuijk et al. 2008). Partial
or strong size-asymmetry (Fig. 1a, line 5; Fig. 1b, line 6)
means that larger individuals obtain a disproportionately
(a)
(b)
Fig. 1 Hypotheses on the relationship between plant size (repre-
sented by stem diameter d at height 1.30 m) and absolute growth rate
(represented by annual stem diameter increment id at height 1.30 m).
a Different linear relationships between plant size and growth and
b non-linear relationships between size and growth. Line 1 represents
the more theoretical case of complete symmetric size-growth
relationship where all plants receive the same budget of growth
irrespective of their size. Line 2 displays non-linear concave size-
symmetry where growth increases degressively with size. Line 3
reflects partial size-symmetry where growth increases linearly with
size. Line 4 represents perfect size-symmetry and means that the
amount growth increases proportionally with size. Line 5 stands for
partial size-asymmetry where growth increases linearly with size.
Finally, line 6 represents non-linear convex size-asymmetry as the
growth increases progressively with size
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higher share of resources and growth. This mode of size-
growth relationship can be expected on rich sites where
light is the limiting factor of tree growth and, as a vectorial
resource, preemptible by the larger individuals (Canell and
Grace 1993; Weiner and Thomas 1986).
A number of studies show that the mode of competition
and the size-growth relationship can change spatially along
ecological gradients (Hara 1993; Pretzsch and Biber 2010)
as well as temporally with stand development (Thomas and
Weiner 1989; Weiner and Thomas 1986). Other studies
have revealed a change from size-symmetric competition
in dry years when below-ground resources are scarce, to
size-asymmetry in moist years when light becomes the
limiting factor (Wichmann 2001).
On long-term experimental plots in forest stands, the
manner in which chronic and acute limiting site conditions
affect the size-growth relationship between neighboring
trees was analyzed in this study. Norway spruce (Picea
abies [L.] Karst.) and European beech (Fagus sylvatica
[L.]) were analyzed, as they represent the most important
species for Central European forestry (Bundesministerium
fu ¨r Erna ¨hrung and Landwirtschaft und Verbraucherschutz
2005; FAO 2005). Specifically, the following three ques-
tions were addressed:
(i)On the basis of 64 long-term experimental plots,
dating back to 1871 and representing an ecological
gradient from excellent to poor sites, we question
how the site index affects the size-growth relation-
ship within the stands.
Using the size-growth relationship between 1972 and
2007, including the extremely dry years 1976 and
2003 we ask how whole stand growth rate and
whether conditionsaffect
relationship.
On the basis of a dataset of the Kranzberg ozone
fumigation experiment (Matyssek et al. 2010)
between 2000 and 2007 we scrutinize how the
size-growth relationships in stands is affected by
ozone exposure.
(ii)
the size-growth
(iii)
Materials and methods
The analysis of the size-growth relationship is based on the
diameter at breast height as the independent size variable
(Fig. 1, x-axis). As the dependent variable (Fig. 1, y-axis),
the mean periodical annual diameter increment was used
for the long-term plots (i) and the current annual diameter
increment was used for analyzing the effect of weather
conditions and ozone-effects (ii and iii). Throughout the
text the term ‘‘size-growth relationship’’ is used when we
refer to the growth partitioning between trees in a stand in
general, while we use the term ‘‘diameter–diameter incre-
ment relationship’’ when we address the methodological
approach and variables which we used to study the growth
partitioning principle. The following three sections outline
the samples and methods used to answer questions (i), (ii)
and (iii).
The approach to question (i) was as follows: Long-term
experimental plots were selected from pure stands of
Norway spruce and European beech in the lowland and
sub-alpine forests in the German states of Bavaria and
Rhineland Palatinate. The following 12 experiments were
used for Norway spruce: Sachsenried 3, Ottobeuren 8,
Eglharting 72, 73, Denklingen 84, Mitterteich 101, Fich-
telberg 227, Feuchtwangen 261, Eurach 605, Sachsenried
607, Weißenburg 613, and Wackersdorf 619. For European
beech, the following four experiments were used: Mit-
telsinn 25, Hain 27, Starnberg 91, and Mitterteich 101. All
are spacing or thinning experiments and they comprise a
number of plots with different stand densities set by initial
spacing and/or continuous thinning. The names indicate the
experiment’s locations and their numbers in the network of
long-term experiments established in forests in Germany
since 1871. Most of them are well-known and frequently
quoted experiments for other research into forest science
(e.g., Assmann 1970; Pretzsch 2009). As this analysis
requires the size-growth relationship and its dependency on
limiting factors, experiments which represent a broad range
of site conditions were selected. In order to understand and
eliminate the effect of stand age and stand density on the
size-growth relationship, a robust sampling method ensur-
ing sufficient representation of stand age and stand density
was employed. Exclusively plots free of mixture and
unwanted disturbances (e.g., bark beetle, ice-breakage, and
wind-throw) were included. By choosing plots with a
sample size of more than 50 trees and successive survey
periods covering lengths [5 years, a robust database for
the subsequent statistical analysis of the size-growth rela-
tionship was ensured.
Table 1 summarizes the number of experiments and
plots, the year of establishment, survey period, site con-
ditions, and growth characteristics. The year of establish-
ment ranges between 1871 in case of the oldest thinning
experiments in European beech and 1988 in case of the
newer combined spacing and thinning experiments in
Norway spruce. The spectrum of site conditions is char-
acterized by the range of maximum height (ho) that
Norway spruce and European beech achieve at an age of
100 years.
The analysis of the size-growth relationship is based on
the relationship between the diameter at breast height (d in
mm) at the beginning of the growth period and the mean
annual diameter increment (id in mm) within the period. In
order to assign each of the d–id relationships to one of the
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six basic relationships shown in Fig. 1, the d–id value pairs
were fitted by both of the following models:
id¼ a0þ a1? d þ e
id¼ b0þ b1? d þ b2? d2þ e:
with id increment in diameter (mm); d diameter (mm); a0–
a1and b0–b2, regression coefficients; e random error.
When b2in Eq. 2 differs significantly from zero, it is
evident that the relationship is non-linear and we can dis-
tinguish two different outcomes; a positive b2, which
indicates a more than proportional increase (Fig. 1b, line
6), and a negative b2, which indicates a less than propor-
tional increase of increment with size (Fig. 1b, line 2).
b2= 0 indicates a linear d–id relationship, represented by
Eq. 1. In this case, four distinctly different linear arche-
types can be distinguished (Eq. 1): a1 not significantly
different from zero indicates a complete symmetric size-
growth relationship (Fig. 1a, line 1). Perfect size-symmetry
occurs when a0is close to 0, forming a straight line through
the origin (Fig. 1a, line 4). A less than proportional
increase of increment with size (Fig. 1a, line 3) is indicated
by a0[0 and a more than proportional increase (Fig. 1a,
line 5) is indicated by a0\0. Each of the analyzed size-
growth relationships was assigned to one of the six basic
curve types.
The vast majority of the d–id curves proved to be linearly
increasing for all four species (Fig. 1a, lines 3, 4, or 5).
Non-linear, less than proportional increases (Fig. 1b, line 2)
occurred in 12% of Norway spruce and 1% of European
beech cases, while non-linear, more than proportional
ð1Þ
ð2Þ
increases (Fig. 1b, line 6) occurred in 6% of Norway spruce
and 1% of European beech cases. In 2% of Norway spruce
and 1% of European beech cases the d–id relationship ran
parallel with the x-axis (Fig. 1a, line 1). Since the d–id
relationship followed a straight line in 82% of Norway
spruce and 98% of European beech cases (Fig. 1a, lines 3,
4, or 5), all relationships were fitted with the simple linear
model (Eq. 1). This meant that a minority of non-linear
diameter–diameter increment relationships were fitted with
a straight line in order to maintain consistency in the sub-
sequent analyses.
The application of a linear model should be taken into
consideration when interpreting the results, even in cases
where a non-linear model might seem more appropriate.
When compared with predictions of the linear model, the
share of the growth of the larger trees is higher in the upper
range of the a1parameter (Eq. 1), and lower than predicted
in the lower range. This shows that the results of the linear
fit represent somewhat conservative estimations of the
relative share of growth and resources of the large trees
when compared with their smaller neighbors.
The slope defined by the coefficient a1from Eq. 1 is
subsequently arranged as dependent on available stand
characteristics (Eq. 3).
a1¼ c0þ c1? hoþ c2? SDI þ c3? dqþ e
The signs and absolute values of the parameters c1, c2
and c3reveal how site quality ho(m), stand density SDI
(N ha-1) and stage of stand development dq (cm)
determine the growth distribution among individuals. In
order to scrutinize the impact of site conditions on the slope
ð3Þ
Table 1 Essentials of the long-
term experiments (applied for
answering question i): year of
establishment differs between
1871 in case of the oldest and
1988 in case of more recently
established experiments.
Minimum, maximum, mean and
standard deviation of stand age
(age), height of the quadratic
mean diameter of the 100 tallest
trees per hectare (ho), stand
density index (SDI), quadratic
mean diameter of the stand (dq),
and mean annual diameter
increment of the quadratic mean
diameter tree (idq). Site index ho
refers to yield table Assmann
and Franz (1963) for Norway
spruce and Schober (1967) for
European beech
VariableNorway spruceEuropean beech
Number of experiments (sum) 124
Year of establishment (range)1887–19881871–1966
Number of plots per experiment (range) 2–13 2–5
Number of survey periods (sum) 28698
Height above sea level (m)
Mean annual temp. (?C)
Mean annual precip. (mm year-1)
380–830400–645
5.9–8.05.5–7.5
668–1,204893–1,080
Number of observations54,88813,192
Age (±SD) (years)61.8 (±25.0) 99.0 (±36.4)
Age min–max (years)16–11943–169
hoat age 100 mean (±SD) (m)
hoat age 100 min–max (m)
SDI mean (±SD) (trees ha-1)
SDI min–max (trees ha-1)
35.7 (±6.1) 33.0 (±4.5)
19.5–48.727.5–38.0
1,056 (±286) 704 (±138)
283–1872434–950
dqmean (±SD) (mm)
dqmin–max (mm)
idqmean (±SD) (mm)
idqmin–max (mm)
239.3 (±95.0)271.9 (±112.1)
47.8–496.9 94.1–564.4
2.97 (±1.57)2.17 (±0.76)
0.30–11.950.62–5.28
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of the diameter–diameter increment relationship, the yield
characteristics, specifically dominant height at age 100 (ho)
(a proxy for site quality), stand density index (SDI)
(Reineke 1933; Pretzsch and Biber 2005), and quadratic
mean stand diameter (dq) were specified for each plot and
survey. Thus in creating this model and including dq, the
well-known fact that the slope of the size-growth
relationship decreases with increasing average tree size
was taken into consideration (Prodan 1965, pp. 474–476).
In order to keep the decimal places of parameters c0to c3
low, the independent variables (ho, SDI and dq) were
divided by 1,000 before being applied in the regression.
The approach to question (ii) was as follows: In order to
analyze the effect of alternating annual growing conditions
and drought on the size-growth relationship, the long-term
experimental plot FRE 813/1, which is not included in the
dataset applied for question (i), was selected. The number
behind the slash in FRE 813/1 means that we deal with plot
1 of experiment FRE 813.
The experimental plot FRE 813/1 is located at
11?3904200E, 48?2501200N, in the ecological region descri-
bed by Kreutzer and Foerst (1978) as Tertiary Hill Country,
Upper Bavarian Hill Country (‘‘Wuchsbezirk 12.8, Ober-
bayerisches Tertia ¨rhu ¨gelland’’), in the southern region of
the German state of Bavaria, near the town of Freising and
approximately 35 km northeast of Munich (Pretzsch et al.
1998). At an altitude of 490 m, the stand stocks on para-
brown soil, based on loess and tends to pseudo-gley. The
potential natural vegetation would be a Galio-odorati-
Fagetum association, dominated by European beech
(Pretzsch and Schu ¨tze 2009). Daily observations of pre-
cipitation (P, mm) and temperature (T, ?C) were collected
by the German Weather Service (Deutscher Wetterdienst,
DWD) from the Weihenstephan-Du ¨rnast weather station.
The respective climate conditions are shown in Table 2 and
Fig. 5.
The plot is part of the Kranzberg crane experiment, and
details are published by, among others, Matyssek et al.
(2010), Pretzsch et al. (1998) and Werner and Fabian
(2002). The experimental design comprises pure stands of
Norway spruce and European beech and, separated by a
stand section in which both species are mixed. From the
three subplots (pure spruce, pure beech and mixed spruce/
beech) the pure stands, which represent very good to
excellent site conditions for both species, are used. The
pure Norway spruce and European beech plots used in this
experiment are best suited to the agenda of this study, as
records of annual diameter and diameter increment for the
period 1972–1980 (retrospectively with increment cores)
and 1999–2007 (monitored continuously by permanently
installed and monthly read girth tapes at 1.30 m stem
height; annual increment in diameter is represented by the
difference of two consecutive January measurements) are
readily available. The two time periods include the extre-
mely dry years of 1976 and 2003. The ages at the end of the
measurementperiodin 2007
56 ± 2 years for Norway spruce, and 66 ± 4 years for
European beech. For more characteristics of the samples
see Table 2.
For each of the years covered in this study, the d–id
relationship was fitted by a linear regression
weredetermined as
id ¼ e0þ e1? d þ e
with id, diameter increment in mm at height 1.30 m; d,
diameter in mm at height 1.30 m and the regression coef-
ficients e0and e1for further evaluation. By continuing with
regression coefficients e0and e1in Eq. 4, we deviate from
the alphabetical order to avoid confusion of parameters d0
or d1with diameter d. In order to analyze whether any
interdependency between the size-growth relationship and
the annual growing conditions exists, two types of inde-
pendent analyses were carried out.
In the first analysis, the annual stand volume growth was
used as a proxy for the annual growing conditions. Due to
the short length of the analyzed growth periods it was not
necessary to correct for any age trend. The regression
coefficient e1of the size-growth relationship was regressed
on the annual stand growth rate in volume (ivol,
m3ha-1year-1)
ð4Þ
e1¼ f0þ f1? ivol þ e
as it represents the overall stand level productivity, and the
slope e1indicates how this growth is partitioned among the
trees. In order to keep the decimal places of parameters f1
low the independent variable ivol was divided by 100
before inserting into the regression.
In the second step, the dependency of the slope of the
diameter–diameterincrement
weather characteristics such as precipitation (P, mm year-1),
temperature (T, ?C) and deduced variables such as potential
evapotranspiration (pET, mm year-1) and climate water
balance (CWB, mm year-1) during growing season was
analyzed using the Pearson correlation. The significance
and mode of statistical relationship between these inde-
pendent variables and e1indicate how annual d–id rela-
tionships depend on annual climate conditions. In addition,
an attempt was made to identify any relationship between
the annual slopes of the d–id relationship and the climate
variables by pairwise comparisons using the Pearson cor-
relation and the Gleichlaeufigkeit score (GLK) (Eckstein
and Bauch 1969). GLK values close to 1 indicate that the
two time series follow the same pattern in terms of their
annual trends, while lower GLK values indicate less syn-
chronicity between the compared time series. GLK scores
were calculated using the R software package ‘‘dplR’’ (R
development Core Team 2009). In order to reveal any
ð5Þ
relationshipon annual
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