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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-

spondinglywide, 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

(Pretzsch2009,

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

whetherconditionsaffect

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)12 4

Year of establishment (range)1887–1988 1871–1966

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

668–1,204 893–1,080

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)

47.8–496.994.1–564.4

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

measurementperiod in 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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lagged climate effects on growth, lagged Pearson correla-

tions and lagged GLK scores (-5,… ?5) were also

calculated.

The approach to question (iii) was as follows: A subset

of the experimental plot FRE 813/1 was maintained under

ozone fumigation from spring 2000 to the autumn of 2007

(Matyssek et al. 2010), with access by a canopy crane and

scaffolding to study stress effects on adult Norway spruces

and European beeches. The center of the ozone fumigation

was represented by a group of beech trees together with

neighboring spruces. The ozone fumigation was conducted

by means of the Kranzberg Ozone Fumigation Experiment

(KROFEX), representing a free-air methodology of ozone

release (see Werner and Fabian 2002). The size-growth

data from trees under long-term ozone fumigation

(2 9 O3) was applied. Analogously, data from reference

stands with ambient ozone levels (1 9 O3) was collected to

identify any difference in the size-asymmetry of growth

allocation between cohorts with and without additional O3

impact. In contrast to the approach used for question (i) and

(ii), the diameter at breast height (d) was used at the

beginning of the fumigation period, and the periodical

annual diameter increment (id) was used from 2000 to

2007. Table 3 shows the complete dataset used for these

analyses. Stand characteristics are similar to those given in

Table 2, as the trees exposed to 1 9 O3and 2 9 O3con-

ditions are on a plot in the same stand.

In order to reveal any effect of ozone on the species

specific size-growth relationship, an ordinary least square

regression (OLS) was fitted, describing the relationship

between the variables id and d discretely for each distinct

group. For identifying the group affiliation, the effect of

ambient or doubled ozone was included as a dummy var-

iable on the intercept and the slope of the linear model,

which described the diameter–diameter increment rela-

tionship (see Eq. 6). The following model was applied:

id ¼ ðg0þ g1ozoneÞ þ ðg2þ g3ozoneÞ ? d þ e

with diameter increment id (mm), diameter d (mm), ozone

as a factor for the effect of the ozone treatment

(0 = ambient ozone, 1 = double ambient ozone), regres-

sion coefficients g0to g3, and random error e.

Due to the aim of analyzing effects of double ambient

ozone, the group 1 9 O3was set to zero to serve as a

reference. The coefficients, g1 and g3, of each of the

dummy variables, depicted as the ozone variable, represent

ð6Þ

Table 2 Characteristics of the two sampled pure stands of Norway spruce and European beech (applied for answering question ii) shown for the

survey periods 1972–1980 and 1999–2007 separately

Variable Period 1972–1980Period 1999–2007

N. spruce E. beech N. spruceE. beech

Tree number first year (n ha-1) 2,4667868771,374

Mean height first year (m)12.514.8 24.724.3

Stand age first year (year)1735 44 62

Site index hoat age 100 (m)

Number of trees (n)

4535 4535

61 32 5943

Mean diameter (± SD) (mm)148 (±39)143 (±44)277 (±81)223 (±74)

Min–max diameter (mm)

Diameter growth (± SD) (mm year-1)

Min–max diameter growth (mm year-1)

Annual stand growth (± SD) (m3ha-1year-1)

P veg. per. (± SD) (mm year-1)

P year (± SD) (mm year-1)

T veg. per. (± SD) (?C)

T year (± SD) (?C)

pET veg. per. (± SD) (mm year-1)

pET year (± SD) (mm year-1)

CWB veg. per. (± SD) (mm year-1)

CWB year (± SD) (mm year-1)

59–26364–269107–522 81–449

4.8 (±2.0)3.6 (1.8)3.5 (±2.6) 2.1 (±2.0)

0.4–11.2 0.6–10.50.0–14.60.0–9.9

27.9 (±6.0) 25.1 (±4.6)

438 (±101) 440 (±100)

790 (±129) 868 (±163)

14.3 (±0.6)15.7 (±1.0)

7.6 (±0.5) 8.3 (±0.5)

542 (±23) 545 (±54)

790 (±24) 754 (±41)

-104 (±112)-105 (±134)

-7 (±139) 114 (±208)

Besides from stand characteristics sample sizes, growth and climate are reported. Site index horefers to yield table Assmann and Franz (1963) for

Norway spruce and Schober (1967) for European beech. Climate conditions refer to mean annual temperature (T, ?C), precipitation (P,

mm year-1), potential evapotranspiration (pET, mm year-1) and climatic water balance (CWB, mm year-1) during vegetation period (veg. per.)

and per year (year)

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the difference between the double ambient ozone group

and the reference ambient ozone group. Thus g0represents

the intercept for 1 9 O3, g0? g1the intercept for 2 9 O3,

and analogously d2the slope for 1 9 O3and g2? g3the

slope for 2 9 O3. The respective p value reveals the sig-

nificance of the effect of double ambient ozone exposure

on the slope, as well as on the intercept of the size-incre-

ment relationship. This method allows for testing 1 9 O3

treatment against 2 9 O3treatment concerning intercept

and slope simultaneously.

Results

Dependence of the slope of the size-growth relationship

on site conditions

Figure 2 illustrates exemplarily how slopes of size-growth

relationships were extracted from the data of long-term

plots. The size-growth observations and regression lines

are shown for two experimental plots in (a) Norway spruce

and (b) European beech with excellent (SAC 607, MIT

101) and low (EGL 72, MIS 25) site fertility but otherwise

rather similar stand parameters such as quadratic mean

diameter dqand SDI. We restricted the graphical analysis

of the match of observed and modeled size-growth rela-

tionships to these examples as a scatter-plot with all 54,888

respective 13,192 observations for spruce and beech (see

Table 1) proofed to be useless; however, for the following

statistical analysis equivalent data of all experiments and

plots was pooled.

The comprehensive scrutiny of the relationship between

slope of the diameter–diameter increment relationship and

stand characteristics on all plots is based on the following

variables displayed in Table 1: stand age (A), dominant

height at the age of 100 years (ho), SDI as defined by

Reineke (1933) and calculated with the species specific

allometric exponents by Pretzsch and Biber (2005), and

quadratic mean diameter (dq). Regression analysis revealed

a significant effect of ho, SDI and dqon the slope (a1) of the

diameter–diameter increment relationship. Key results of

the analysis are given in Fig. 3 and Table 4; all variables

included in the model were significant to at least

p\0.001. Figure 3 displays the result of the analysis

graphically for (a) Norway spruce and (b) European beech.

The relationship between diameter increment and diameter

is shown to be dependent on the site index (ho) when all

other influencing variables are kept constant. For the

independent variables (SDI, dq) species specific mean

values as given in Table 1 were inserted. Using Eq. 3, the

slope a1was calculated and the respective intercept a0was

derived by rearranging Eq. 1 to a0= idq- a19 dqand

substituting values for idq und dq. The relative growth

distribution among trees of different size is reflected by the

differing slopes of the lines shown in Fig. 3. The steepest

and shallowest lines represent the borderline cases of the

site index range in which all observed size-growth rela-

tionships lie. The lines in between represent the diameter–

diameter increment relationships for stands in the dataset

with average top height (ho= 36 m and ho= 25 m, in the

case of Norway spruce and European beech, respectively).

Size-asymmetry increases with increasing site index for

both species. On poor sites, the relationships indicate a

tendency towards a size-symmetric size-growth relation-

ship. On mediocre and fertile sites perfect size-symmetry

or even size-asymmetry is found. Both species’ range of

size-growth lines includes perfect size-symmetry (lines

through the origin with a0= 0).

Effect of drought on the diameter–diameter increment

relationship

In the first approach for measuring the effect of drought on

the diameter–diameter increment relationship, the annual

stem volume growth per hectare (ivol, m3ha-1year-1) of

the Norway spruce and European beech pure stand FRE

813/1 was used as a proxy variable for the annual growth

conditions. To analyze the size-growth relationship and its

Table 3 Characteristics of the

sample stands under ambient

and double ambient ozone

(applied for answering question

iii)

VariableAmbient ozone (1 9 O3) Double ambient ozone (2 9 O3)

N. spruceE. beech N. spruce E. beech

First/last year of observation 2000/2007 2000/20072000/2007 2000/2007

Number of trees (n)9 11 1425

Mean diameter (± SD) (mm)264 (±77)254 (±68)269 (±98) 236 (±78)

Min–max diameter (mm)

Diameter growth (± SD) (mm year-1)

Min–max diameter growth (mm year-1)

Ozone concentration (± SD) (sum00year-1) 226 (±22)

min–max ozone conc. (sum00year-1)

143–401133–37281–415 133–383

3.4 (±1.5) 2.4 (±2.4) 3.7 (±1.4) 1.5 (±1.9)

2–6 0–72–60–8

344 (±48)

213–280304–455

Trees (2011) 25:355–369 361

123

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dependency on the annual growth conditions, the rela-

tionship between the annual slopes of the diameter–diam-

eter increment relationships and respective annual growth

was linearly fitted. The resulting parameters of the linear

regression (Eq. 5) are reported in Table 5. For the periods

1972–1980 and 1999–2007 a significant increase of the

diameter–diameter increment relationship slope e1 was

found with increasing absolute stand growth rate (ivol)

(Fig. 4). This indicates that Norway spruce (a) and Euro-

pean beech (b) reveal a tendency towards size-asymmetry

(steep slopes of diameter–diameter increment relationship)

in years of high growth rates and rather size-symmetric

size-growth relationship (shallow slopes of the d–id rela-

tionship) in years of low growth rates. The tendency

towards size-asymmetry (steeper slopes) under beneficial

growth conditions and size-symmetry (shallower slopes)

under unfavorable conditions which we revealed along an

ecological gradient (see ‘‘Dependence of the slope of the

size-growth relationship on site conditions’’) obviously

applies also for the temporal change of growth along a time

series with beneficial and unfavorable years.

In the second approach for measuring the effect of

drought on the diameter–diameter increment relationship,

the analysis was repeated, this time making use of the mean

(a)

(b)

Fig. 2 Relationship between diameter and diameter increment for

(a) Norway spruce: Sachsenried 607, plot 7, survey 2001, dq244 mm,

ho40.6 m, SDI 1212 (empty triangles; id = -3.135 ? 0.023 9 d,

R2= 0.593, p\0.001) and Eglharting 72, plot 2, survey 1950, dq

252 mm,

ho

31.4 m,SDI 1316

0.941 ? 0.012 9 d, R2= 0.202, p\0.001) and for (b) European

(filledtriangles; id = -

beech: Mitterteich 101, plot 2, survey 1960, dq305 mm, ho37.1 m,

SDI 733 (empty circles; id = -1.487 ? 0.014 9 d, R2= 0.595,

p\0.001) and Mittelsinn 25, plot 1, survey 1968, dq311 mm, ho

27.5 m, SDI 876 in case of beech (filled circles; id = -

1.418 ? 0.010 9 d, R2= 0.401, p\0.001)

(a)

(b)

Fig. 3 Relationship between stem diameter and diameter increment

for poorest, medium and best site conditions for the species

(a) Norway spruce and (b) European beech. For each species, we

show the diameter–diameter increment relationship for sites with

highest fertility (steepest line), medium fertility (medium line), and

lowest site fertility (shallow line). For both species applies, that the

steepness of the slope, i.e. the asymmetry of the size-growth

relationship increases from poor to fertile sites

362Trees (2011) 25:355–369

123

Page 9

annual temperature (T), precipitation (P), potential evapo-

transpiration (pET), and climatic water balance (CWB) as

independent variables. The climate conditions are shown in

Fig. 5. The correlation between these annual weather

variables was analyzed, along with the slope e1 of the

diameter–diameter increment relationship in the respective

years. Table 6 shows that the effect of high temperature on

the slope is negative, and the effect of high precipitation is

positive regardless of tree species. Although, these rela-

tionships are only partially significant, they do indicate that

sufficient water supply and moderate temperatures increase

the size-asymmetry of growth and resource partitioning in

the stand. By contrast, drought and high temperatures

flatten the d–id relationship and increase the tendency

towards size-symmetric growth and resource partitioning

among the trees in a stand. For spruce the analysis reveals

that it reacts more sensitive to drought as indicated by the

significant correlation between T and slope. In addition,

analysis of the Gleichlaeufigkeit reveals that the year-to-

year agreement between the analyzed slope and P or CWB

is higher than for T or pET. Lagged effects of the corre-

lation (r) or the Gleichlaeufigkeit (GLK), computed by

shifting the climate data (-5,… ?5) were not found.

Correlation and Gleichlaeufigkeit score between the slope

and weather variables in different years are lower.

Figure 6 displays the reaction pattern for the extremely

dry/warm year 1976 in contrast to the rather moist/tem-

perate year 1978. In the case of Norway spruce, the slopes

Table 4 Parameters (± SE) and coefficient of determination for the

linear model (Eq. 3) of slope a1in dependency on top height at age

100 (ho), stand density index according to Reineke (SDI), and qua-

dratic mean diameter (dq)

Parameter VariablesN. spruceE. beech

c0

c1

c2

0.012 (±0.004)0.003 (±0.006)

ho(m)/1,000

SDI (trees ha-1)/

1,000

0.771 (±0.120)0.840 (±0.129)

0.005 (±0.003)0.009 (±0.004)

c3

R2

dq(mm)/1,000-0.093 (±0.008) -0.072 (±0.005)

0.37

\0.001

0.72

\0.001

p value

In order to keep the decimal places of parameters c0to c3low, the

independent variables (ho, SDI and dq) were divided by 1,000 before

being applied in the regression

Table 5 Parameters (± SE) and coefficient of determination for the linear model of slope e1of the annual diameter–diameter increment

relationship in dependency on annual volume increment (ivol) (Eq. 5)

ParametersVariablesN. spruceE. beech

1972–19801999–20071972–19801999–2007

f0

f1

R2

-0.016 (±0.009) -0.006 (±0.010)-0.030 (±0.013)0.002 (±0.004)

ivol (m3ha-1year-1)/100 0.246 (±0.071)0.104 (±0.036) 1.071 (±0.244) 0.058 (±0.015)

0.63

\0.01

0.48

\0.05

0.70

\0.01

0.64

\0.01

p value

In order to keep the decimal places of parameters c1low, the independent variable ivol was divided by 100 before inserting in the regression

(a)

(b)

Fig. 4 Slope of the diameter–diameter increment relationship for

(a) Norway spruce and (b) European beech trees over the annual

stand volume growth (ivol). The OLS fit is separately shown for the

periods 1972–1980 (empty symbols) and 1999–2007 (filled symbols).

The linear regressions are significant at the 0.05 level in case of

spruce and at the 0.01 level in case of beech, respectively

Trees (2011) 25:355–369 363

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(a)(b)

Fig. 5 Annual

mm year-1), potential evapotranspiration (pET, mm year-1) and

climatic water balance (CWB, mm year-1) during growing season

meantemperature(T,

?C),precipitation(P,

recorded by the DWD weather station Weihenstephan/Du ¨rnast.

Climate conditions are presented for the observation periods

(a) 1972–1980 and (b) 1999–2007

Table 6 Pearson correlation

coefficient r and

Gleichlaeufigkeit GLK

calculated between the slope e1

of the annual diameter–diameter

increment relationship and the

annual climate variables during

growing period (May–

September)

•r is significant at the 0.1 level

* r is significant at the 0.05

level

Climate variables Pearson correlation r

Gleichlaeufigkeit GLK

Slopeid, d

N. spruceE. beech

1972–19801999–20071972–19801999–2007

T (?C)

r

-0.704*-0.597*-0.087-0.465

GLK0.3750.250

0.666•

0.500

0.631•

0.250

0.593•

P (mm year-1)

r

0.144

GLK0.5000.8750.6250.625

pET (mm year-1)

r

-0.150-0.678*-0.184-0.444

GLK 0.3750.1250.500

0.604•

0.375

0.578•

CWB (mm year-1)

r

0.1590.703*

GLK 0.500 0.875 0.6250.625

(a)

(b)

Fig. 6 Annualdiameter–diameterincrementrelationshipinyearswith

contrasting climate conditions for (a) Norway spruce and(b) European

beech. Year 1976 (filled symbols; OLS fit: Norway spruce

1.368 ? 0.004 9 d, p[0.05, European beech -0.683 ? 0.024 9 d,

p\0.001) represents an extremely dry year whereas 1978 (empty

symbols; OLS fit: Norway spruce 2.139 ? 0.021 9 d, p\0.001;

European beech -1.156 ? 0.031 9 d, p\0.001) is characterized by

excellent growing conditions

364Trees (2011) 25:355–369

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of the diameter–diameter increment relationship in 1976

and 1978 are significantly different at the level p\0.05,

whereas European beech shows no significant change.

Hence, spruce reveals a change in its mode of size-growth

relationship; after a rather shallow slope in the dry/warm

year 1976, which indicated size-symmetry, the allocation

pattern changes within 2 years towards a far more size-

asymmetric size-growth relationship in 1978.

Effect of ozone fumigation on the diameter–diameter

increment relationship

The comparison between mean periodic diameter incre-

ment of trees with and without ozone fumigation yields

neither a different intercept nor a different slope for Nor-

way spruce (Fig. 7a). In the case of European beech, ozone

fumigation results in a significantly shallower slope

(slope1?O3g3

the diameter–diameter increment relationship (Fig. 7b).

The difference is significant to the level p\0.05. This

indicates that ozone stress reduces the growth of dominant

European beeches more than their smaller neighbors; so the

latter are the relative winners of the ozone stress. The

straight line representing the size-growth relationship

changes from size-asymmetry under ambient ozone expo-

sition (1 9 O3) to size-symmetry under ozone stress

(2 9 O3).

Finally, the combined effect of summer drought and

ozone on the annual diameter–diameter increment rela-

tionship was analyzed for 2003. Figure 8 shows the annual

diameter increment over the initial diameter of trees

ð Þ ¼ 0:033; slope2?O3g3þ g4

ðÞ ¼ 0:011)of

exposed to 1 9 O3and 2 9 O3conditions in 2003. Again,

it was found that ozone fumigation reduces the slope

considerably, which is equivalent to a shift from size-

asymmetric to a more size-symmetric size-growth rela-

tionship under combined drought and ozone stress in 2003.

Norway spruce shows a stronger flattening of the slope

under ozone fumigation than European beech. For spruce,

the flattening of the slope is significant (Fig. 8a) whereas

beech shows no significant change (Fig. 8b; Table 7). This

suggests that spruce reacts more sensitively to 2 9 O3in

years with poor water supply than beech. Figure 8a dis-

plays one high value of diameter increment (11.2 mm). At

first glance this value seems to suggest a possible outlier.

However, as the diameter increments are based on monthly

read records of permanent increment tapes, it was possible

to correlate this annual increment against the increment in

the previous and successive years and verify its accuracy.

Discussion

The results of this study contribute to the theory of resource

and growth partitioning in tree communities, as well as to a

better understanding of the structural stand dynamic of

forest stands under different growing conditions. Similar

analyses are available to some degree for herbaceous

stands (Canell and Grace 1993; Mu ¨ller et al. 2000; Weiner

and Thomas 1986), somewhat more scarcely so for juvenile

woody stands (Ammer 1996; Hara 1993; Kuijk et al. 2008;

Thomas and Weiner 1989; Weiner and Thomas 1986) and

are extremely limited for mature forest stands (Wichmann

(a)

(b)

Fig. 7 Mean annual diameter increment in the O3fumigation period

2000–2007 over initial diameter without ozone fumigation (1 9 O3:

empty symbols) and with double ambient ozone fumigation (2 9 O3:

filled symbols) for (a) Norway spruce and (b) European beech trees.

The diameter–diameter increment relationship is represented by thin

lines in case of 1 9 O3,and by bold lines in case of 2 9 O3. The OLS

fit (Eq. 6) yielded in id99-07= (1.238 - 2.182 9 ozone) ? (0.008 ?

0.005 9 ozone) 9 d99

(p\0.05)

(-6.254 ? 5.210 9 ozone) ? (0.033 - 0.002 9 ozone) 9 d99 (p\

0.001) for beech. In case of beech the effect of ozone on intercept and

slope is significant at the level 0.05

forspruce andid99-07=

Trees (2011) 25:355–369365

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2001, 2002). In this study, forest stands which were under

survey for decades to centuries were analyzed, where the

growth of individuals had been measured continually

without affecting the stand growth and structure in the

course of taking the measurements. The stands cover a

broad range of ages, stand phases and site conditions, and

are selected along an ecological gradient for question (i), to

reflect a time series for question (ii), and with differing

stress conditions for question (iii).

In all three reported evaluations the slope of the rela-

tionship between size and size growth shows a clear

dependence on the prevailing limitation. The general

reaction pattern, which can be assumed as a preliminary

working hypothesis, is shown schematically in Fig. 9. On

poor sites under drought or ozone stress the slope is shal-

low, indicating that the difference between the growth of

small and tall trees is smaller than on fertile sites or on sites

without stress. In stands with unfavorable growing condi-

tions, size growth increases at a rate less than proportional

to plant size. Under mediocre site conditions size growth

increases proportionally to tree size, resulting in size-

symmetry. Optimal resource supply results in dispropor-

tional increase of size growth with tree size, i.e. size-

asymmetric size-growth relationship (Fig. 9).

(a)

(b)

Fig. 8 Annual diameter increment in 2003 over initial diameter of

(a) Norway spruce and (b) European beech trees without ozone

fumigation (1 9 O3: empty symbols) and with double ambient ozone

fumigation (2 9 O3: filled symbols). The OLS fit of the diameter–

diameter increment relationship is represented by thin lines in case of

1 9 O3,and by bold lines in case of 2 9 O3. For statistical results see

Table 7

Table 7 Fit of the model for the diameter–diameter increment relationship (Eq. 6) for Norway spruce and European beech in the dry year 2003

ParametersVariablesN. spruceE. beech

Value (± SE)

p value Value (± SE)

p value

g0

g1

g2

g3

R2

-5.613 (±1.604)

\0.01

\0.05

\0.001

\0.01

-2.893 (±1.308)

\0.05

[0.05

\0.01

[0.05

Ozone4.988 (±1.889)

1.742 (±1.416)

d (mm) 0.028 (±0.005)0.016 (±0.005)

Ozone

-0.020 (±0.006)-0.007 (±0.005)

0.50 0.41

The effect of double ambient ozone is considered by the bivariate factor ozone (0 = 1 9 O3; 1 = 2 9 O3)

Fig. 9 Effect of resource limitation on the relationship between size

and growth in schematic representation

366Trees (2011) 25:355–369

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This general reaction pattern is in accordance with,

among others, the empirical findings of Wichmann (2001,

2002) in adult forest stands, Kuijk et al. (2008) for tree

dominated communities in the succession phase, and

Thomas and Weiner (1989) and Weiner and Thomas

(1986) for herbaceous stands, as well as by model scenarios

from Hara (1993) for forest stands. In terms of the com-

bined effect of ozone and drought stress, our results match

the findings of Lo ¨w et al. (2006), who shows that drought

counteracts the impact of O3in adult beech by stomatal

closure.

For causal explanation it is speculated that under

favorable site conditions and without additional stress,

dominant trees profit disproportionally as they make use of

their privileged access to light. By pre-empting light they

raise their own growth rate and impede the growth of their

smaller neighbors. In contrast, under unfavorable condi-

tions, where growth is restricted by limitation of water or

mineral nutrient supply, by drought or by ozone stress,

dominant trees can make less use of their superior position.

For this reason, the relationship between size and size

growth becomes less pronounced. In the sense of Dar-

winian fitness, the relative advantage over competitors

rather than the absolute growth rate is decisive for success

under selective pressure and fitness. Hence, the analyzed

relationship between size and size growth is an indicative

proxy for competitiveness, as it explicitly reflects this rel-

ative difference between the growth of small and large

members of a community.

The relationship between plant size and resource supply

(water, light, mineral nutrients) is of particular interest but

difficult to measure accurately. Therefore, we used the

distribution of diameter increment among the trees in a

stand and the relationship between diameter and diameter

increment (intercept, slope, linearity or non-linearity of the

size-growth relationship) as a proxy for the size-resource

relationship. This analysis of the size-growth relationship

represents a first step towards an explanation of site-

dependency of the biomass and resource distribution

between the trees of a stand. The inference from size-

growth relationship to size-resource relationship requires

further investigation (Schwinning and Weiner 1998).

Long-term experiments, especially when covering various

site conditions, can provide considerable information for

further research in this area. In herbaceous plant popula-

tions, where most of the empirical and theoretical research

exists to date, it is rarely possible to measure the spatial

occupation of individuals and to record growth of survivors

and losses of individuals accurately without greatly dis-

turbing them and the stand structure (Thomas and Weiner

1989; Weiner and Thomas 1986). By contrast, the partic-

ular spatial dimension of forests provides a unique oppor-

tunity to analyze the individual plant growth, biomass

distribution between trees of different size and their

mortality.

Thereasonforapplyingthediameter–diameterincrement

relationshipinsteadof volume increment-tree volumeisthat

the former method’s values are directly derived from mea-

surement, while volume increments and volume are derived

variables and subject to the inaccuracies in the chosen form

factors and height measurements. Hara (1993) states that

both the growth and size-structure dynamics of stem diam-

eter and stem volume are almost parallel, which is also

expressed by the proportional relationship between the rel-

ative growth rates of diameter and volume, id/d ? 3 ffi

increment in volume/volume (Prodan 1965, pp. 455–456).

So far, in this study the site conditions are reflected by

factors such as the stand site index and the degree of stress

impact by the amount of annual stand volume growth.

These factors are represented by proxy variables, as direct

measurements of site variables were not available for most

of the long-term plots. Furthermore, the mode of compe-

tition is indicated by the size [d]-growth [id] relationship

rather than by the resource distribution between the plants.

Conclusions

The consequences of these findings concern silvicultural

treatment: improved resource supply leads to a steeper

slope of the relationship between size and size growth, and

a lower relative share of resources that the subdominant

and understory trees can utilize for growth. This means that

the slope also reflects the structural diversity of a stand:

Shallow relationships between size and size growth on poor

sites indicate rather similar growth conditions for small and

tall members of the population. Steep slopes indicate that

dominant neighbors consume much more of the available

resource than their smaller neighbors, and this superiority

of the dominate trees can increase self-thinning in the

understory. Under ceteris paribus conditions (same stand

density, age etc.) structural diversity increases when

resource supply becomes scarce (Assmann 1970). On rich

sites, such as those with dominating light limitation,

growth can be more easily concentrated on a limited

number of selected trees. However, on poor sites under-

story trees still grow at a rate proportional to their size, and

vertical structure is more stable on such latter sites. On

these sites, water and nutrients are the limiting factors and

restrict the competition and superiority of dominant trees,

which is overwhelming on rich sites.

The dependency of the size-growth relationship on the

prevailing limitation also applies to the modeling of com-

petition: As long as models are developed and applied for a

narrow range of site conditions the limitation and the mode

of competition and size-growth relationship also varies

Trees (2011) 25:355–369367

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within a small range so that the prognosis of growth,

growth reaction after thinning or underplanting is realistic.

However, as future models should be applicable for a

broader range of site conditions (Pretzsch et al. 2008), such

as for predicting growth reactions on thinning, under-

planting, fertilization on different sites and possibly also

for predicting growth reaction under climate change (shift

from light limitation to below-ground resource limitation),

then it seems important to differentiate between different

modes of competition and size-growth relationships. In

light of these results, a generalization of the function for

the growth reduction in individual-tree models is not

appropriate (Pretzsch and Biber 2010). Compared to rich

sites, individuals of similar size which are impacted by the

same competition index (CI) still grow better on poor sites.

Thus, the so far site independent reduction function applied

in individual-tree models (e.g., Biging and Dobbertin 1995)

requires site-dependency. For this reason, an improvement

of existing growth models and a more flexible algorithm

for reduction of the potential growth by considering dif-

ferent trajectories of modifier-CI relationships depending

on the mode of competition is recommended.

Acknowledgments

Lu ¨ttge, Rainer Matyssek, and anonymous reviewers for their helpful

comments on the manuscript. The research was supported by Deut-

sche Forschungsgemeinschaft by funding the Sonderforschungsber-

eich SFB 607 ‘‘Growth and Parasite Defense’’ and by the Bavarian

State Ministry for Nutrition, Agriculture and Forestry funding the

project W 07 ‘‘Long-term experimental plots for forest growth and

yield research’’. Thanks are also given to the German Weather Ser-

vice (Deutscher Wetterdienst, DWD) and Ulrich Kern for the

graphical artwork. All of the experiments conducted in this study

complied with the current applicable German laws.

The authors would like to thank Ulrich E.

Open Access

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medium, provided the original author(s) and source are credited.

This article is distributed under the terms of the

References

Ammer Ch (1996) Konkurrenz um Licht—Zur Entwicklung der

Naturverju ¨ngung im Bergmischwald. Forst. Forschungsber.

Mu ¨nchen, Forstwiss. Fak. der Univ. Mu ¨nchen, Nr. 158, 211 p

Assmann E (1970) The principles of forest yield study. Pergamon

Press, Oxford 506

Assmann E, Franz F (1963) Vorla ¨ufige Fichten-Ertragstafel fu ¨r

Bayern. Forstl Forschungsanst Mu ¨nchen, Inst Ertragskd, 104 p

Beierkuhnlein C, Foken Th (2008) Klimawandel in Bayern. Ausw-

irkungen und Anpassungsmo ¨glichkeiten. Bayreuther Forum

O¨kologie, University Bayreuth, vol 113, 501p

Biging GS, Dobbertin M (1995) Evaluation of competition indices in

individual tree growth models. For Sci 41:360–377

Bugmann H, Grote R, Lasch P, Lindner M, Suckow F (1997) A new

forest gap model to study the effects of environmental change on

forest structure and functioning. In: Mohren GMJ, Kramer K,

Sabate ´ S (eds) Impacts of global change on tree physiology and

forest ecosystems. Forestry sciences. Kluwer Academic Pub-

lishers, Wageningen, pp 255–261

Bundesministerium fu ¨r Erna ¨hrung, Landwirtschaft und Verbrauchers-

chutz (2005) Die zweite Bundeswaldinventur—BWI2, Der

Inventurbericht. Bundesministerium fu ¨r Erna ¨hrung, Landwirts-

chaft und Verbraucherschutz, Bonn, 231p

Canell MGR, Grace J (1993) Competition for light: detection,

measurement, and quantification. Can J For Res 23:1969–1979

Eckstein D, Bauch J (1969) Beitrag zur Rationalisierung eines

dendrochronolgischen Verfahrens und zur Rationalisierung

seiner Aussagesicherheit. Forstwissenschaftliche Centralblatt

88:230–250

Elling W (1993) Immissionen im Ursachenkomplex von Tan-

nenscha ¨digung und Tannensterben. AFJZ 48(2):87–95

FAO (2005) Global Forest Resources Assessment 2005. FAO, Rome

Hara T (1993) Mode of competition and size-structure dynamics in

plant communities. Plant Species Biol 8:75–84

Jentsch A, Kreyling J, Beierkuhnlein C (2007) A new generation of

climate change experiments: events, not trends. Front Ecol

Environ 5(7):365–374

Kreutzer K, Foerst K (1978) Forstliche Wuchsgebietsgliederung

Bayerns. Karte 1:1,000,000. Bayerisches Staatsministerium fu ¨r

Erna ¨hrung, Landwirtschaft und Forsten

Landsberg JJ (1986) Physiological ecology of forest production.

Academic Press, New York, p 198

Lo ¨w M, Herbinger K, Nunn AJ, Ha ¨berle K-H, Leuchner M, Heerdt C,

Werner H, Wipfler P, Pretzsch H, Tausz M, Matyssek R (2006)

Extraordinary drought of 2003 overrules ozone impact on adult

beech trees (Fagus sylvatica). Trees 20:539–548

Ma ¨kela ¨ A, Hari P (1986) Stand growth model based on carbon uptake

and allocation in individual trees. Ecol Mod 33:205–229

Matyssek R, Sandermann H (2003) Impact of ozone on trees: an

ecophysiological perspective. Prog Bot 64:349–404

Matyssek R, Agerer R, Ernst D, Munch JC, Oßwald W, Pretzsch H,

Priesack E, Schnyder H, Treutter D (2005) The plant’s capacity

in regulating resource demand. Plant Biol 7:560–580

Matyssek R, Wieser G, Ceulemans R, Renneberg H, Pretzsch H,

Haberer K, Lo ¨w M, Nunn AJ, Werner H, Wipfler P, Oßwald W,

Nikolova P, Hanke D, Kraigher H, Tausz M, Bahnweg G, Kitao

M, Dieler J, Sandermann H, Herbinger K, Grebenc T, Blu-

menro ¨ther M, Deckmyn G, Grams TEE, Heerdt C, Leuchner M,

Fabian P, Ha ¨berle KH (2010) Enhanced ozone strongly reduces

carbon sink strength of adult beech (Fagus sylvatica)—resume

from the free-air fumigation study at Kranzberg Forest. Environ

Pollut 158:2527–2532

Mielika ¨inen K, Timonen M (1996) Growth trends of Scots pine

(Pinus sylvestris, L.) in unmanaged and regularly managed

stands in southern and central Finland. In: Spiecker H,

Mielika ¨inen K, Ko ¨hl M, Skovsgaard JP (eds) Growth trends in

European forests. European Forest Institute, Research Report 5,

Springer, Heidelberg, pp 41–59

Mu ¨ller I, Schmid B, Weiner J (2000) The effect of nutrient

availability on biomass allocation patterns in 27 species of

herbaceous plants. Perspect Plant Ecol Evol Syst 3(2):115–127

Niklas KJ (1994) Plant allometry. University of Chicago Press,

Chicago

Oliver CD, Larson B (1996) Forest stand dynamics. Wiley, New

York, p 520

Pretzsch H (1999) Waldwachstum im Wandel, Konsequenzen fu ¨r

Forstwissenschaft und Forstwirtschaft. Forstw Cbl 118:228–250

Pretzsch H (2009) Forest dynamics, growth and yield. From

measurement to model. Springer, Berlin 664

PretzschH(2010)ZurVerteilungdesZuwachseszwischendenBa ¨umen

eines Bestandes und Abha ¨ngigkeit des Verteilungsschlu ¨ssels von

den Standortbedingungen. Allg Forst J Ztg 181(1/2):4–13

368 Trees (2011) 25:355–369

123

Page 15

Pretzsch H, Biber P (2005) A re-evaluation of Reineke’s rule and

stand density index. For Sci 51:304–320

Pretzsch H, Biber P (2010) Size-symmetric versus size-asymmetric

competition and growth partitioning among trees in forest stands

along an ecological gradient in central Europe. Can J For Res

40(2):370–384

Pretzsch H, Schu ¨tze G (2009) Transgressive overyielding in mixed

compared with pure stands of Norway spruce and European

beech in Central Europe: evidence on stand level and explana-

tion on individual tree level. Eur J Forest Res 128:183–204

Pretzsch H, Kahn M, Grote R (1998) Die Fichten-Buchen-Mis-

chbesta ¨nde des Sonderforschungsbereiches ,,Wachstum oder

Parasitenabwehr?‘‘ im Kranzberger Forst. Forstwisschaftliches

Centralblatt 117:241–257

Pretzsch H, Grote R, Reineking B, Ro ¨tzer T, Seifert S (2008) Models

for forest ecosystem management: a European perspective. Ann

Bot 101:1065–1087

Pretzsch H, Dieler J, Matyssek R, Wipfler P (2010) Tree and stand

growth of mature Norway spruce and European beech under

long-term ozone fumigation. Environ Pollut 158:1061–1070

Prodan M (1965) Holzmeßlehre. JD Sauerla ¨nder’s Verlag, Frankfurt

am Main, 644 p

R Development Core Team (2009) R: A language and environment

for statistical computing. R Foundation for Statistical Comput-

ing, ISBN 3-900051-07-0, Vienna, Austria

Reineke LH (1933) Perfecting a stand-density index for even-aged

forests. J Agr Res 46:627–638

Ro ¨hle H (1987) Entwicklung von Vitalita ¨t, Zuwachs und Biomas-

senstruktur der Fichte in verschiedenen bayerischen Un-

tersuchungsgebietenunter

Walderkrankungen. Forstl Forschungsber Mu ¨nchen 83:122

Schober R (1967) Buchen-Ertragstafel fu ¨r ma ¨ßige und starke

Durchforstung. In: Schober R (1972) Die Rotbuche 1971. Schr

Forstl Fak Univ Go ¨ttingen u Niedersa ¨chs Forstl Versuchsanst 43/

44, JD Sauerla ¨nder’s Verlag, Frankfurt am Main, 333 p

dem Einfluß derneuartigen

Schweingruber FH, Albrecht H, Beck M, Hessel J, Joos K, Keller D,

Kontic R, Lange K, Niederer M, Nippel C, Spang S, Spinnler A,

Steiner B, Winkler-Seifert A (1986) Abrupte Zuwachsschwank-

ungen in Jahrringabfolgen als o ¨kologische Indikatoren. Ber Eidg

Anst forstl Versuchswesen, pp 125–179

Schwinning S, Weiner S (1998) Mechanisms determining the degree

of size asymmetry in competition among plants. Oecologia

113:447–455

Spiecker H, Mielika ¨inen K, Ko ¨hl M, Skovsgaard JP (eds) (1996)

Growth trends in European forests. European Forest Institute,

Research Report 5, Springer, Heidelberg, 372 p

Thomas SC, Weiner J (1989) Growth, death and size distribution

change in an Impatiens Pallida population. J Ecol 77:524–536

Utschig H (1989) Waldwachstumskundliche Untersuchungen im

Zusammenhang mit Waldscha ¨den.

wachstrendanalysefla ¨chen des Lehrstuhles fu ¨r Waldwachstumsk-

unde fu ¨r die Fichte (Picea abies (L.) Karst.) in Bayern. Forstl

Forschungsber Mu ¨nchen 97, 198p

van Kuijk M, Anten NPR, Oomen RJ, van Bentum DW, Werger MJA

(2008) The limited importance of size-asymmetric light compe-

tition and growth of pioneer species in early secondary forest

succession in Vietnam. Oecologia 157:1–12

Weiner J (1990) Asymmetric competition in plant populations.

Trends Ecol Evol 5(11):360–364

Weiner J, Thomas SC (1986) Size variability and competition in plant

monocultures. Oikos 47:211–222

Werner H, Fabian P (2002) Free-air fumigation of mature trees—a

novel system for controlled ozone enrichment in grown-up beech

and spruce canopies. Environ Sci Pollut Res 9:12–117

Wichmann L (2001) Annual variations in competition symmetry in

even-aged Sitka Spruce. Ann Bot 88:145–151

Wichmann L (2002) Competition symmetry. Chapter 7. In: modelling

the effects of competition between individual trees in forest

stands. PhD thesis, University of Forestry, Copenhagen,

pp 67–77

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