Southern Forests: a Journal of Forest Science
ISSN: 2070-2620 (Print) 2070-2639 (Online) Journal homepage: http://www.tandfonline.com/loi/tsfs20
Coarse root–shoot allometry of Pinus radiata
modified by site conditions in the Western Cape
province of South Africa
H Pretzsch , P Biber , E Uhl & P Hense
To cite this article: H Pretzsch , P Biber , E Uhl & P Hense (2012) Coarse root–shoot
allometry of Pinus radiata modified by site conditions in the Western Cape province
of South Africa, Southern Forests: a Journal of Forest Science, 74:4, 237-246, DOI:
10.2989/20702620.2012.741794
To link to this article: http://dx.doi.org/10.2989/20702620.2012.741794
Published online: 16 Nov 2012.
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Southern Forests 2012, 74(4): 237–246
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SOUTHERN FORESTS
ISSN 2070-2620 EISSN 2070-2639
http://dx.doi.org/10.2989/20702620.2012.741794
Coarse root–shoot allometry of Pinus radiata modified by site conditions
in the Western Cape province of South Africa
Downloaded by [University Library Technische Universität München] at 03:37 30 November 2015
H Pretzsch*, P Biber, E Uhl and P Hense
Chair for Forest Growth and Yield, Technische Universität München, Hans-Carl-von-Carlowitz-Platz 2, 85354 Freising,
Germany
* Corresponding author, e-mail: [email protected]
The relationship between root and shoot growth and how it is modified by chronic or episodic drought stress is so
far not well understood. Allometric partitioning theory (APT) supposes a constant root–shoot allometry. Optimal
partitioning theory (OPT) assumes that plants’ root growth is enhanced under water limitation. However, recent
studies show that fine and coarse roots react differently. This paper draws attention to the root–shoot allometry of
adult Monterey pines (Pinus radiata D.Don) and its dependency on site conditions in South Africa. For assessment
of the root–shoot-diameter relationship as an allometric relationship in general and for comparison with APT we
used a sample of nine radiata pines from Jonkershoek and three maritime pines (Pinus pinaster Aiton) from Napier.
In order to test for a site-dependency of the root–shoot allometry we sampled increment cores from stem and coarse
roots of 48 radiata pines along a gradient from moist to dry sites in the Western Cape province. Tree ring analysis
revealed an allometric relationship between root diameter (dr) and shoot diameter (ds) (ln(dr)  a  dr,ds  ln(ds)).
Despite strong variation of the allometric exponent dr,ds we found a systematic deviation from 1.0 as would be
predicted by APT. We also found dr,ds to decrease with drought stress, which is contradictory to both APT and OPT.
However, on sites with more pronounced drought stress we detected greater allometric factors a. We hypothesise
that fine root growth, and also fine root mortality, is higher on dry sites. On these sites coarse roots seem to be less
necessary for matter transport compared with moist and fertile sites. On the latter, fine roots are less ephemeral and
require larger coarse roots for transport. We conclude that combined root shoot tree ring analyses have the potential
for improving understanding and modelling ecosystems and better assessment of forest functions such as resource
use efficiency, stand stability and belowground carbon storage.
Keywords: allometric partitioning theory, APT, biomass partitioning, optimal partitioning theory, OPT, root–shoot ratio, structural plasticity,
tree ring analysis
Introduction
How the relationship between root and shoot growth
develops in the long term and how it is modified by chronic
or episodic drought stress is so far not well understood. In
this study, we analyse and model the coarse root–shoot
dynamics by methods of allometric research. The allometric
equation offers an appropriate approach to describe the
size development of a plant and the relationship of one
plant dimension to another as, for example, root versus
shoot diameter.
The optimal partitioning theory (OPT) and the allometric
biomass partitioning theory (APT) are two alternative
theories that recently have been advanced to describe
the allocation in plants (Müller et al. 2000, Niklas 2004,
Coyle et al. 2008, Pretzsch 2009, Price et al. 2010,
Pretzsch and Dieler 2012, Pretzsch et al. 2012). Their
different concepts become obvious by their assumptions on the behaviour of the allometric parameters a
and . According to APT, resource allocation patterns
between different organs change solely with plant size
(i.e. allometrically) being insensitive to the variation in the
local environmental conditions (Müller et al. 2000, Enquist
and Niklas 2001). This means that parameter a can be
modified by environmental factors, resource supply or
growth, whereas the allometric exponent  is assumed to
be constant and to have overarching validity. In contrast,
OPT states that a plant always invests into improving the
access to the currently limiting factor. If, for example, the
limiting factor is light or water, the plant invests in shoot
or root growth, respectively (Bloom et al. 1985). With
regard to the parameters of the allometric equation, this
implies that both exponent  as well as the normalisation
factor a can be modified by environmental conditions in
space and time.
If we assume that environmental factors and resource
supply modify allometric exponents at all, then this is most
probable for the relationship between root and shoot. For
maximising their fitness, plants are supposed to partition
resources and allocate biomass to organs in a way that
remedies limitations to biomass production. This concept
should also become obvious in the dynamics of root–
shoot growth, as root growth should be increased when
belowground resources (water and nutrients) are limiting
and shoot growth when aboveground resources (light
and CO2) are scarce. This behaviour is assumed to be
Southern Forests is co-published by NISC (Pty) Ltd and Taylor & Francis
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238
responsible for the wide variation of the root–shoot ratio
under different site conditions (Keyes and Grier 1981,
Comeau and Kimmins 1989).
This paper draws attention to the root–shoot allometry of
adult Montery pine (Pinus radiata D.Don) and to a lesser
extent of Maritime pine (Pinus pinaster Aiton) applying
combined coarse root–shoot increment boring. Although
the natural range of Monterey pine is limited to a few
thousand hectares in California and Mexico, it represents
one of the most important artificially cultivated tree species
on the globe, mainly in the Southern Hemisphere (Roy
1966). In particular, high growth rates and volume production even on poorer sites foster the commercial interest for
the tree species. Natural growing conditions are classified
as seasonal and humid with annual precipitation ranging
from 380 to 890 mm. A considerable amount of precipitation comes as fog. Under these conditions Monterey pine
grows on both fine dune sands, high in silica content as
well as on calcareous sandy loams derived from a marine
deposit (Roy 1966). Tree height depends on soil quality
and can reach up to 38 m within its natural range. In South
Africa top heights of 47 m have been measured. Only on
drier sites P. radiata grows in pure stands. In mixed stands
it is associated with other conifers and hardwoods. Boles
show little taper in general, and crown structure depends
on stand density and tree age. In open stands irregularly
and heavily branched crowns occur. The root system’s
development starts with pronounced growth of tap roots
in early years. But tap root growth is soon replaced by a
strong growth of lateral coarse roots, which generally
remain shallow and reach extensions up to 12 m from the
stem base (Roy 1966).
Although P. pinaster is of Mediterranean origin, a mean
annual precipitation demand between 800 and 1 000 mm
indicates a preference for oceanic growing conditions. In
South Africa the species is successfully cultivated relatively
close to the coast. In contrast to P. radiata it retains its tap
root growth throughout its life and even lateral coarse roots
tend to grow into deeper levels.
Analysis of tree-ring chronologies based on sampling
of cross-sectional discs along stems and root systems
has been used for assessing whole-tree resource allocation under differing climatic conditions (Drexhage et al.
1999, Krause and Eckstein 1993) or after insect outbreaks
(Krause and Morin 1999). These analyses concentrated on ring-width variations or structural changes on a
macroscopic level. The selection of cross-sectional discs
from adult trees, however, is related with several methodological difficulties, such as restriction to use of individuals
felled by windstorms or after felling and following mechanical uprooting and excavation of the root system (Bolte et al.
2004). The combined coarse root–shoot increment boring
used in this study is based on the methodology successfully
tested in a pilot study by Nikolova et al. (2011) in temperate
forests and Pretzsch et al. (2012) in boreal forests. With
this study we extend the methodology to an ecological
gradient in the Mediterranean climate of the Western Cape
province in South Africa. The main tree species of interest
is Monterey pine, which shows easily measurable year
rings in the stem and coarse roots, but a small sample of
Maritime pine was analysed as well.
Pretzsch, Biber, Uhl and Hense
Increment cores taken from the stem and from the
coarse roots were used for retrospective analysis of coarse
root–shoot dynamics. We draw attention to the following
questions:
(1) are coarse root and stem diameters coupled by a
log-linear allometric relationship?
(2) does root–shoot allometry lie in a narrow corridor
around dr,ds  1.0 as predicted by the APT?
(3) does coarse root–shoot allometry change along a stress
gradient from dry to moist sites as assumed by the OPT?
Materials and methods
Study site
The study was based on two different data sets that were
established during two collection periods. To test the feasibility
of root–shoot analyses with different pine species and in order
to detect a possible log-linear allometric relationship between
coarse root and shoot diameters analyses, characteristics
from nine individuals of Monterey pine, collected from three
different compartments at Jonkershoek and from three individuals from Maritime pine collected in Napier, were used (data
set 1) in 2008. The analysis of these samples showed, that
tree rings are much easier to identify, measure and synchronise in the case of Monterey pine. Maritime pine often showed
narrow or missing rings, especially on roots. In view of these
difficulties and concerning the small sample size, we only
display the results of Maritime pine and focus the further
analysis on Monterey pine.
To cope with the question of site effects on root–shoot
allometry, a second data set using 48 Monterey pine
AFRICA
SOUTH
AFRICA
B40
L34
Cape Town
South
Africa
19°30ƍ E
WESTERN CAPE
A71
M6a
M4
M36e
G35
E3b
M9
34° S
Napier
0
55 km
Figure 1: Geographical position of the sampling locations and plots
(hollow triangles indicate locations of data set 1, filled triangles
indicate those of data set 2)
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Southern Forests 2012, 74(4): 237–246
239
individuals from eight different locations covering a gradient
from dry to moist site conditions was established (data
set 2) in 2010. Figure 1 displays the geographical positions
of the single plots used for data sets 1 and 2.
The plots for data set 2 were established on areas of
Mountain to Ocean Forestry (MTO) that are partly used
as long-term monitoring plots. To classify the water supply
status, records of precipitation and temperature from
nearby weather stations were used. Information about
the soil type provided an estimation of the water retention
capacity. In addition, topographic specifics such as hillside
situation were integrated to distinguish five relative water
supply classes among the used plots. The evaluation
was supported by experts from Stellenbosch University
(B du Toit, pers. comm., 2011). Table 1 gives an overview
of the dominant soil type, climatic conditions and water
supply class. Climate data were obtained from weather
stations close to the plots.
Sampling and measurements
All selected trees in both data sets were dominant, without
any damage and not neighbouring with one another within
a stand to avoid dependencies between the samples.
From all trees diameter at breast height (girth tape)
and total height (Haglöf Vertex ultrasonic hypsometer)
were measured.
Concerning increment boring we built upon standard
techniques described by Pretzsch (2009) and Nikolova et
al. (2011). Two cores were taken at breast height on each
sample tree’s stem from the north and east. In addition,
three (data set 1) and two to five (data set 2) of the largest
lateral roots per tree were partly excavated from the soil
and cored at a distance of about 30–50 cm from their offset
at the trunk. This distance was determined according to
Krause and Morin (1995), who found the number of missing
or discontinuous rings in roots to increase with increasing
distance between coring position and trunk edge. On the
other hand, this also takes into account that Monterey
pine tends to form elliptical root cross-sections very close
to the trunk with the largest radius being perpendicular to
the forest floor (Roy 1966). To further minimise bias by
non-circular root cross-sections we took two increment
cores per root each at 45° to the plumb-line (Figure 2) in
the case of data set 1. In the case of data set 2 an additional
core was taken vertically from above. With all increment
cores we attempted to hit the pith in order to trace back the
increment as far as possible. The diameter of each sampled
root was measured twice, vertically and horizontally, at the
sampling point with a calliper.
All increment cores were polished on a grinder using
sandpaper with 80–120 grits. The tree-ring widths were
measured with a universal plane table type 2 after Johann
(Biritz GmbH 2012).
All year ring series of any single root were synchronised against each other and averaged root-wise but also
tree-wise in order to produce one time-series representative
for the root growth patterns of the respective tree (Cook and
Kairiukstis 1992). The resulting series was then synchronised against the previously synchronised stem cores from
the same tree. Series with absent tree rings were excluded
from further analysis. In addition, we removed the very early
years with juvenile growth from the analyses, as in these
years the trajectories of the root–shoot development can
deviate considerably from the log-linear course that prevails
in the later development phase.
In the following sections we refer to single trees from
data set 1 with abbreviations composed of the location’s
initial and tree number (e.g. J1 means tree number 1 from
Jonkershoek). Adding ‘S’ or ‘R’ we indicate whether a growth
series comes from a stem (shoot) or a root, respectively (e.g.
N1R2 means root number 2 from tree number 1 sampled in
Napier). When we refer to a tree-wise averaged root series,
a root number is not added (e.g. N1R is the average root
growth series from tree number 1 from Napier). In order to
have a clear connection to the term ‘root–shoot allometry’, we
hereafter consistently use the term ‘shoot’ for a tree’s stem.
90°
90°
Figure 2: Schematic illustration of location of sampling increment
cores from the stem and two main roots (cf Pretzsch et al. 2012)
Table 1: Site conditions for the plots of data set 2
Variable
Kluitjieskraal
B40
Mean annual precipitation (mm)
676
Mean annual temperature (°C)
–
Soil type
Sandy
loam
Water supply class
Very dirty
Grabouw
M9
739
17.0
Sandy
loam
Dry
Location
La Motte
Grabouw
La Motte
A71a
G13a
L34
857
1200
838
18.4
–
18.5
Sand/sandy Sandy loam/ Fine sandy
loam
sandy clay
loam
Medium
Medium
Medium
Grabouw
E3b
1036
15.7
Sand
Moist
Jonkershoek Grabouw
M6a
G35
1069
940
16.5
17.1
Sandy loam/
Loamy
sandy clay
sand
Moist
Very moist
240
Pretzsch, Biber, Uhl and Hense
Grabouw
E3b
P. radiata
6
23–27
37.1–47.7
24.1–26.7
5.39
0.19–23.54
21(3–4)
11–27
6.5–26.1
1.96
0.07–10.43
La Motte
L34
P. radiata
6
17–19
28.8–36.0
19.3–22.1
7.14
1.59–36.62
21(2–4)
12–19
8.6–17.2
2.35
0.43–9.59
Grabouw
M9
P. radiata
6
23–28
38.0–43.4
27.3–29.1
6.73
1.54–17.28
22(3–5)
16–28
7.3–22.0
2.0
0.16–6.98
La Motte
A71a
P. radiata
6
19–26
34.9–50.7
24.2–31.1
6.85
1.79–31.31
25(3–5)
10–26
4.6–27.2
2.38
0.18–13.01
Grabouw
G13a
P. radiata
6
21–24
41.9–49.7
31.9–37.1
7.44
1.08–20.72
23(2–4)
10–24
6.9–30.8
2.77
0.15–14.53
Allometric equations (questions 1 and 2)
Supposing x and y quantify the size of two different
plant dimensions, their growth x′ (dx/dt) and y′ (dy/dt) is
related to the size x and y as y′/y   x′/x. More common
are integrated (y  ax ) or logarithmic representations
(ln y  ln a    ln x ). Latter equations address the relative
change of one plant dimension, dy/y (e.g. the relative
root growth) in relation to the relative change of a second
plant dimension dx/x (e.g. the relative shoot growth). Pairs
of size measurements (e.g. x  stem diameter, y  root
diameter) taken from n different individuals or from n
subsequent measurements of the same individual over
time provide xi,i  1…n and yi,i  1…n. After logarithmic transformation of the bivariate size data (ln(xi), ln(yi)), linear regression techniques yield the parameters a and  of ln y  ln a
  ln x. The allometric exponent  can be perceived as
a distribution coefficient for the growth resources between
organs y and x. When x increases by 1%, y increases by
%. The allometric factor a is a species-specific normalisation constant and reflects growth form and environment
(Sackville Hamilton et al. 1995). It differs, for example,
significantly between herbaceous and woody plants.
Minimum–maximum per tree is specified in parentheses
Species
Number of shoots analysed
Number of counted tree rings
Diameter (cm)
Tree height (m)
Year ring width – mean (mm)
Minimum–maximum (mm)
Number of roots analysed1
Number of counted root rings
Root diameter (cm)
Year ring width – mean (mm)
Minimum–maximum (mm)
Regression model for site-dependent allometry (question 3)
In order to test root–shoot allometry for site dependency with
data set 2, we formulated the following regression model:
1
P. pinaster
3
39–89
34.0–47.7
16.0–19.3
1.9–4.0
0.3–18.2
9(3)
17–45
19.3–34.8
0.9–2.2
0.2–7.8
Kluitjieskraal
B40
P. radiata
6
16–21
30.4–36.1
16.0–19.9
7.33
0.78–20.42
20(3–4)
15–21
7.1–18.8
1.42
0.19–6.16
Napier
Jonkershoek
M6a, M4,M36e
P. radiata
9
9–34
19.4–40.4
11.1–29.2
3.0–16.2
1.1–30.6
27(3)
6–24
8.5–15.8
0.7–10.9
0.3–36.0
Variable
Table 2: Sample tree and root characteristics for data sets 1 and 2
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Jonkershoek
M6a
P. radiata
6
20–34
34.9–49.4
24.7–27.9
4.81
0.71–16–20
20(2–4)
11–34
6.4–21.4
1.27
0.15–5.97
Grabouw
G35
P. radiata
6
20–25
43.9–54.6
29.8–39.1
6.69
2.00–13.64
18(2–3)
12–25
10.9–26.5
2.66
0.24–14.07
The trees in data set 1 cover a considerable range of
ages, shoot diameters and an even broader range of
mean, minimum and maximum ring widths (Table 2). On
average, the root age is lower than the shoot age with the
root diameters being smaller than the corresponding shoot
diameters at 1.3 m. However, the mean, minimum and
maximum ring widths of the roots are not very different from
the respective shoots’ values. For data set 2, counted year
rings of shoots vary between 16 and 34 (Table 2). Similarly,
measured year rings of roots range from 10 to 34. Here too,
root diameters are clearly smaller compared to the shoot
diameters. Plot mean root increment varies between 1.27
and 2.77 mm y−1 and mean shoot increment accounts for
4.8 to 7.4 mm y−1.
ln(drijkt)  a0  a1·ln(dsijkt) a2·wateri  a3·ln(dsijkt)·wateri  ijkt (1)
In this model, the indices i, j, k and t stand for plot, tree,
root and year, respectively. dr and ds are the root diameter
and the shoot diameter (in cm). The site variable water is
a transformation of the five water supply classes into the
numeric values 1, 2, 3, 4 and 5, where 1 and 5 represent
the driest conditions and the best water supply, respectively. This very simple coding, which implies equal
distances between subsequent levels of water supply,
proved to be superior – by Akaike information criterion
(AIC) based model comparisons as proposed by Burnham
and Anderson (2004) – compared to any other available
site indicators and was thus included in the final model as
shown above.
Clearly, because of the time series character of the data,
the errors  are not uncorrelated. We used an ARMA(p, q)
model (Pinheiro and Bates 2000, Zuur et al. 2009) for
description of the serial correlation of the errors:
Southern Forests 2012, 74(4): 237–246
p
H ijkt
dr,ds  a1  a3· water. If a2 or a3 differ from zero significantly,
this would suggest a dependency of the intercept or the
allometric exponent from water supply, respectively.
As a more descriptive complement to this formal analysis,
we fitted the generic allometric model from equation 3
separately for each root with ordinary least squares
(OLS) regression, which means several regressions for
each tree. For the estimated ln(a) and dr,ds we visualised
their empirical density functions based on kernel density
estimates (Sheather and Jones 1991) for the whole set and
separately by water supply level.
q
¦M
m 1
m
˜ H ijk t m ¦ T n ˜ K ijk t n K ijkt
(2)
n 1
where  and  are parameter vectors of length p and q to
be estimated, and  is i.i.d. noise. Thus, autocorrelation is
described on individual-root level. Introducing random effects
that express correlation on different nesting levels (plot,
subplot, tree and root) always weakened model performance
in terms of the AIC compared to the combination of equations
1 and 2. As this indicated weak dependencies, especially
among the different roots of a given tree, only the temporal
autocorrelation on root level was taken into account.
The whole model was fitted by optimising the maximum
likelihood criterion. Residuals were assessed visually for
normality, homogeneity and absence of autocorrelation as
proposed by Pinheiro and Bates (2000).
Conceptually, the model is a special case of the allometric
relationship:
ln(dr)  ln(a)  dr,ds·ln(ds)
Results
Shoot and coarse root radial growth of Monterey pine
and maritime pine trees (data set 1, questions 1 and 2)
Figure 3 exemplarily shows the course of annual ring
width over tree age as measured at shoots and roots in
Jonkershoek (Figure 3a and b) and Napier (Figure 3c
and d) for three selected trees from each location. We
observe a clear ontogenetic drift with high increments
in the juvenile state and decreasing growth rates with
progressive aging.
(3)
where the intercept ln(a) and the allometric exponent
 are site dependent, so that ln(a)  a0  a2· water and
(a)
RADIAL INCREMENT (ir mm yí1)
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241
(b)
Pinus radiata
14
14
12
12
10
10
8
8
6
6
4
4
2
2
5
10
15
20
(c)
25
10
Pinus radiata
5
Pinus pinaster
20
30
40
50
60
(d)
70
80
Pinus pinaster
7
6
4
5
3
4
3
2
2
1
1
5
10
15
20
25
10
20
30
40
50
AGE (y)
Figure 3: Annual radial increment (ir) over age for shoots J7S–J9S (a) and N1S–N3S (b) and roots of the sample trees J7R1–J9R2 (c) and
N1R1–N3R2 (d)
242
5
Pretzsch, Biber, Uhl and Hense
(a)
Jonkershoek
5
4
(b)
Napier
4
In(a) = í0.3
3
In(dr)
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3
In(a) = í1.3
In(a) = í0.3
2
2
In(a) = í2.3
In(a) = í1.3
1
1
In(a) = í2.3
0
0
3.0
3.5
4.0
4.5
5.0
5.5
In(ds)
3.0
3.5
4.0
4.5
5.0
5.5
Figure 4: Relationship between root diameter (dr) and stem diameter (ds) in double-logarithmic scale for the trees (a) J1-9 and (b) N1-3
from data set 1. Shown are the observed trajectories (grey lines) and corresponding straight (black) lines fitted with OLS regression. Dashed
reference lines represent the allometry expected for geometric similitude with dr,ds  1 and different intercepts ln(a)
The root–shoot diameter allometry in double logarithmic
scale for the trees in Jonkershoek and Napier is illustrated in
Figure 4. The dashed reference lines represent trajectories
as would be expected for dr,ds  1 (i.e. for geometric similitude) with different intercepts ln(a). Obviously, in most cases
the slopes are steeper than 1, in other words the relative
growth rate of the root diameters is higher than the one of
the corresponding shoot diameter.
Linear OLS regression for the allometric relationship ln(dr)
versus ln(ds) (equation 3) yields slopes of dr,ds  0.48 – 1.99
for the trees in Jonkershoek and dr,ds  2.04 – 2.65 for
Napier. On average the slope amounts to dr,ds  1.51 in
Jonkershoek and dr,ds  2.44 in Napier. This result means
that a diameter growth of 1% is coupled with a main root
growth of 1.5% in Jonkershoek and 2.4% in Napier. In most
cases the OLS slopes are significantly steeper (p  0.05) than
a slope of dr,ds  1, which would be expected for a proportional growth of root versus shoot (geometric similitude). The
relationships obtained with OLS for the trees J1 to J9 are,
respectively, ln(dr)  −3.442  1.382 ln(ds), ln(dr)  −5.011 
1.812 ln(ds), ln(dr)  −4.056  1.577 ln(ds), ln(dr)  −1.055 
0.933 ln(ds), ln(dr)  −4.318  1.711 ln(ds), ln(dr)  −3.606 
1.371 ln(ds), ln(dr)  −5.457  1.664 ln(ds), ln(dr)  −3.135 
1.382 ln(ds), and ln(dr)  −5.722  1.831 ln(ds).
Root–shoot allometry in dependence on site conditions
(data set 2, question 3)
Based on the preliminary study with data set 1, altogether
48 Monterey pine trees with 157 roots were sampled and
analysed as described in the previous section. The root-byroot OLS regressions according to equation 3 yielded ln(a)
values between −31.6 and 2.5, and dr,ds values between
0.1 and 9.2. Figure 5 shows the empirical frequency distribution of both parameters and reflects a high variability of
the allometric parameters, but distinct modes of their distributions, and a significant deviation of the mode of dr,ds from
the assumption of dr,ds  1 according to allometric theory
(McCarthy and Enquist 2007). In order to test for the mode’s
deviation from dr,ds  1, we bootstrapped 5 000 samples
of dr,ds with n  157 from the original sample, generated a
kernel density estimate (Sheather and Jones 1991) for each,
and found its mode. From the 5 000 resulting modes 95%
lay between 0.52 and 0.74 around a mean of 0.63. More
complicated bootstrap algorithms that took into account the
nested data structure, i.e. several dr series for one ds series
per tree, produced virtually the same result, indicating no
relevant correlation between the time series on tree level.
Table 3 presents the parameter estimates for the fitted
model from equation 1 combined with the autocorrelation
model as denoted in equation 2. All parameter estimates
differ significantly from zero with p  0.001. The ARMA
autocorrelation model performed best with p  1 and q  3,
resulting in one element of  and three elements for .
Although 1 (Table 3) is close to 1, which could indicate a
non-stationary autocorrelation process, residual inspection
did not reveal any such problems.
Surprisingly, a3 is greater than zero, which indicates that
the allometric exponent dr,ds increases with increasing
water supply, taking values between 0.20 and 0.55. This is,
however, counteracted by a2  0, which shows an intercept
reduction with better water supply. Seemingly, trees on dry
sites start with a higher dr/ds ratio whereas trees on sites
with better water supply start with a lower ratio, but show a
higher relative investment into root growth.
Southern Forests 2012, 74(4): 237–246
(a)
243
Slope
(b)
0.8
mode = 0.63
95% confidence bounds (bootstrapped)
reference = 1
DENSITY
0.6
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Intercept
0.20
0.15
0.4
0.10
0.2
0.05
0.0
0.00
mode = 0.24
0
1
2
D dr,ds
3
4
í10
í8
í6
í4
í2
In(a)
0
2
Figure 5: Empirical probability density (kernel density estimate) of the allometric exponent dr,ds (a) and the long-term allometric factor
ln(a) (b) resulting from separate OLS fits for each ln(dr)–ln(ds) time series of 48 trees with 157 roots sampled along a drought gradient (data
set 2). The modes of the density functions are dr,ds  0.63 and ln(a)  0.24, respectively. The dotted vertical lines include the bootstrapped
95% confidence interval for the mode of dr,ds. The dashed vertical line marks the reference value dr,ds  1, which indicates that the mode
dr,ds is significantly smaller than 1
Table 3: Parameter estimates and standard errors for the fitted
model from equation 1 in combination with equation 2
Parameter
a0
a1
a2
a3

1


Estimate
1.8928***
0.1077***
−0.3199***
0.0882***
0.9850
0.6137
0.3199
0.7062
Standard error
0.1482
0.0310
0.0514
0.0117
*** Significance level of p  0.001
Figure 6 illustrates this result by comparing the model
predictions with the observed trajectories. Albeit the observations show a broad variation, the trend becomes evident
even visually. Obviously, the drier sites show a higher level
but flatter slopes and thus have thicker roots at the same
diameters compared to better sites. At large diameters,
however, the lines cross, and the dr/ds ratio becomes
increasingly greater on the sites with higher water supply.
The empirical distributions for ln(a) and dr,ds obtained from
fitting equation 3 root-wise support this result as well (Figure
7). Their modes show the same trend and magnitudes as
indicated by the parameter estimates for a2 and a3 from
equation 1. Remarkably though, the variation seems to
increase for both parameters with increasing water supply.
Discussion
Potentials and limitations of the applied methods
Insights into root growth and root–shoot relationships are
facilitated by combined root–shoot analysis using increment
boring. They deliver useful information about root–shoot
allometry of mature trees without exhausting root excavations, which are often hardly possible or feasible (Ammer and
Wagner 2002). The coarse roots as well as the stem certainly
represent only a part of the belowground and aboveground
growth of trees. Fine root and branch growth can differ
considerably in amount and dynamic from the coarse organs
(see e.g. Zerihun and Montagu 2004, Coyle et al. 2008).
Thus the analysed allometric relationships represent only a
portion of the root–shoot dynamics (Santantonio et al. 1977).
However, stem and coarse roots represent a substantial part
of these dynamics, and have a structural–functional relationship with the smaller tree organs, as the latter ensure the
supply and arrangement of the former.
A promising approach might be the combination of
the presented coarse root–shoot sampling by increment
boring with traditional total root excavations. This bears the
potential to upscale from coarse root attributes to total root
information. In addition, it would be a basis for an efficient
scaling from easily accessible tree variables such as
diameter and height to otherwise little available and difficultto-access root quantitative variables.
The method presented in this study enables intraindividual analysis of the root–shoot dynamics. Most other
244
Pretzsch, Biber, Uhl and Hense
20
dr (cm)
íí
5
í
0
+
++
Water supply
íí
í
0
+
++
2
1
10
5
20
50
ds (cm)
Figure 6: Observed dr–ds trajectories of 48 trees with 157 roots sampled along a drought gradient (data set 2) and model predictions (fitted
equation 1, black lines) in double-logarithmic scale. Water supply levels range from very dry (--) to very moist (++) conditions, respectively
1.0 (a)
íí
í
0
+
++
0.8
DENSITY
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10
1.0
Water supply
mode = 0.33
mode = 0.68
mode = 0.72
mode = 0.83
mode = (b)
íí
í
0
+
++
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
Water supply
mode = 1.07
mode = í
mode = 0.05
mode = í
mode = í
0.0
0
1
2
D dr,ds
3
4
í10
í5
0
In(a)
5
10
Figure 7: Empirical probability density (kernel density estimate) of the allometric factors and slopes of 48 trees with 157 roots sampled along
a drought gradient (data set 2). (a) Allometric factor ln(a) and (b) allometric exponent dr,ds as obtained from fitting equation 3 root-wise.
Empirical density functions (standardised to maximum  1) are plotted for the water supply levels from very dry (--) to very moist ()
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Southern Forests 2012, 74(4): 237–246
related studies are based on inter-individual sampling and
evaluation (e.g. Weiner and Thomas 1992). Typically, roots
of a number of individuals are excavated and weighed or
measured as well as stems and branches. The advantage
is that larger parts of the root and shoot system can be
integrated in the study, as the trees are harvested. However,
these sampling procedures are destructive, disable the
compilation of time series of root–shoot growth and substitute an artificial time series for a real time series. Such a
substitution of intra-individual for inter-individual records
invites to confound differences in root–shoot allometry
because of relative size, competitive status and microsites
with real allometric effects caused by matter partitioning.
Previous studies of the long-term trajectory of the root–
shoot growth in temperate forests of Central Europe
(Nikolova et al. 2011) and boreal forests of Canada (Pretzsch
et al. 2012) tested the combined root–shoot increment boring
methods and evaluation procedure, which we used here for
studying root–shoot dynamics in the Mediterranean climate
of the Western Cape province. With future studies we want to
extend our investigations to a broader number of species and
a more expanded site spectrum.
Relevance for ecological theory
Without chronic or episodic water stress fine roots are less
ephemeral and maintain a more voluminous coarse root
system for matter exchange with the shoot. In contrast,
under scarce and variable water supply fine root growth
can be enhanced by water limitation but also interrupted
by severe episodic drought stress (Meier and Leuschner
2008a, 2008b). This higher fine root growth and turnover on
dry sites requires obviously thinner coarse roots because
the matter flow between fine roots and the stem is lower
and less continuous. This might explain our findings that
the allometric exponent for coarse root growth is considerably lower on dry compared to moist sites. We hypothesise that the variation in root structure is more triggered
by resource supply than by mechanical forces (wind
and slope). The latter will most probably result in similar
tendencies of root structure development even if sites
differ in water regime. This belowground allocation pattern
is analogous to the higher matter investment into leaves
instead of branches and stem biomass when trees grow
under light limitation (Shipley and Menziane 2002). Such
a counteracting dynamic of fine, in relation to coarse,
root growth results in structural plasticity and guarantees a highly efficient resource exploitation (Weiner 2004).
Zerihun and Montagu (2004) also consider that changes
of belowground biomass to aboveground biomass ratios
is mainly caused by changes in fine root biomass being
smaller under fertilised conditions.
The interpretation of our results is corroborated by other
works that found values of dr,ds  2–3 on rather moist sites
in Central European temperate forests (Nikolova et al.
2011), dr,ds  1.5–2.0 in more water-limited boreal forests
(Pretzsch et al. 2012), in comparison with dr,ds  0.3–0.8
in the rather dry forest in the Mediterranean climate of
the Southern Cape. This generally rather broad range of
allometric exponents might be more narrow in clonal forests
(Stovall et al. 2011). In other words, investment in coarse
roots decreases from well-water-supplied to water-limited
245
sites. We hypothesise that fine root allometry would behave
inversely. Coarse and fine root biomass together (mr) in
relation to shoot mass (ms) may follow the OPT or scale
as mr,ms  1.0 and thus follow the APT. However, coarse
root–shoot diameter allometry as observed here deviates
from both the APT and OPT. Thus, the finding that coarse
roots in relation to the shoot grow less on dry sites and
more on moist sites is counterintuitive at first sight and in
contradiction to the OPT, but may be plausible when fine
root dynamics are considered in addition.
Practical relevance
The revealed principles and functions could be useful for
estimation of species-specific and site-specific biomass
and carbon sequestration depending on easily accessible
variables such as the tree diameter and rough information
about water supply. Coarse roots represent the majority
of the living belowground biomass in forests, whereas fine
roots are more ephemeral. Combined coarse root–shoot
sampling can contribute to developing site-dependent
biomass functions or expansion factors. This may be an
important contribution for a more accurate estimation of
belowground biomass and carbon storage in forest stands
and carbon balance of forest ecosystems.
Conclusions
Based on combined coarse root–shoot increment boring,
tree ring analysis and allometric evaluation on 57 Monterey
pine and three maritime pines, we conclude that combined
coarse root–shoot increment boring, tree ring analysis,
and subsequent growth-course analysis by methods of
allometry is feasible and provides valuable insights into
root–shoot relationships of adult trees. The revealed coarse
root–shoot allometry is remarkably variable and part of the
variability can be explained by the trees’ water supply. The
high variability of the allometric scaling of root versus shoot
and its decrease with dryness contradicts both the APT and
OPT. However, we hypothesise that incorporation of fine
root state and dynamics into the root–shoot relationship
may yield a closer correspondence of the trees’ behaviour
with the APT and OPT. For upscaling from coarse roots to
the total root, our sampling method might be extended to
more roots per tree or be combined with root excavations
and ingrowth core approaches.
Acknowledgement — Thanks are due to BMBF and NRF for
providing the funds for climate change research and cooperation between Germany and South Africa (project FORSIM,
# SUA 08/041). The study was also supported by EU-mobility
funding (project Climate-Fit Forests, FP7 Marie Curie IRSES,
GA 295136). We also thank Mark February and Klaus von Schirp
for assisting with sampling in the field, Petia Nikolova, Simon
Springer and Christian Zang for support of the increment core
and data analysis, Ulrich Kern for the graphical artwork, and the
reviewers for critical comments.
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