Directory UMM :Data Elmu:jurnal:T:Tree Physiology:Vol16.1996:

Tree Physiology 16, 359--365
© 1996 Heron Publishing----Victoria, Canada

Controlling growth and chemical composition of saplings by iteratively
matching nutrient supply to demand: a bootstrap fertilization
technique
D. ALEXANDER WAIT,1,2,3 CLIVE G. JONES2 and MICHAEL SCHAEDLE1
1
2
3

SUNY-College of Environmental Science and Forestry, Syracuse, NY 13210, USA
Institute of Ecosystem Studies, Box AB, Millbrook, NY 12545, USA
Present address: Biological Research Laboratories, Department of Biology, 130 College Place, Syracu
se University, Syracuse, NY 13244, USA

Received October 4, 1994

Summary We developed a fertilization technique that results
in the control, and maintenance at defined rates and levels, of
growth and tissue composition of plants of different sizes and

developmental stages growing at exponential and nonexponential rates in solid media under naturally fluctuating light and
temperature regimes. Clonal cottonwood (Populus deltoides
Bartr.) saplings were grown in sand. Low concentrations of
nutrient solution were added daily at different constant exponentially increasing rates for 20--30 days to produce plants with
different growth rates and tissue nutrient composition. Matching nutrient supply to measured growth demand by bootstrapping, where bootstrapping is the use of an iterative equation
that calculates demand from either actual or desired growth
rates, maintained these differences for 20--40 days. Nutrient
additions controlled growth of saplings with growth rates between 2.0 and 4.0% day −1, heights between 13.9 and 37.5 cm,
dry weights between 0.70 and 3.90 g, leaf nitrogen contents
between 1.2 and 3.9%, and leaf carbon/nitrogen ratios between
42.1 and 12.5. The technique was reproducible in a greenhouse
without temperature, humidity, or light control, and is easily
modified to suit different plant species, plants of various sizes,
and various growing conditions.
Keywords: cottonwood, foliar carbon, foliar nitrogen, growth
rate, nutrition, Populus deltoides, steady-state growth.

Introduction
The effects of soil nutrient availability on plant growth, physiology, tissue chemistry, or stress tolerance are often investigated by experimentally manipulating nutrient supply. Several
approaches have been used including stationary solution culture, bulk fertilization in soil, and supplying nutrients exponentially to solid media (e.g., Timmer et al. 1991, Miller and

Timmer 1994) or exponentially in flowing solution-spray culture (e.g., Ingestad 1982, Asher and Edwards 1983, Ingestad
and Lund 1986).

In stationary solution culture and bulk fertilization, a relatively high concentration of nutrients is added once, or infrequently at the same concentration. Initial nutrient supply
invariably exceeds plant demands, and nutrient concentrations
in tissues are often in surplus relative to requirements (Timmer
et al. 1991) and substantially in excess of those found in the
field (Epstein 1972). Plant demand then begins to exceed
supply as nutrients are used for growth and are not replenished
(Ingestad 1982, 1987). Nutrient stress at various stages of
seedling development (Imo and Timmer 1992) and deficiency
symptoms may then appear that are not commonly seen in
natural systems (Ingestad 1982). Consequently, plant growth
(Ingestad 1982), development, physiology (McDonald et al.
1986) and tissue biochemistry (Waring et al. 1985) fluctuate,
often to a greater extent than found for plants in the field
(Ingestad 1982).
In contrast, exponential additions of nutrients at low concentrations (Ericsson 1981a, 1981b, Ingestad 1982, Asher and
Edwards 1983, Ingestad and Lund 1986) can match nutrient
supply with plant uptake and use over time. In response to

exponential nutrient additions, small seedlings exhibit stable
biochemical composition of tissues during exponential growth
(e.g., Ingestad 1982, Waring et al. 1985). The resultant steadystate growth and nutrition during exponential growth has advantages. Comparisons between plants grown under different
environmental conditions become simplified and more precise
because plant nutrient status and growth rates are stable (Tamm
1964, Linder and Rook 1984, Ingestad and Ågren 1991, 1992,
and see Duarte et al. 1989, Burgess 1990, Cromer and Jarvis
1990, Thorsteinsson et al. 1990). Time- and size-dependent
variations in the tissue content of nutrients and other chemical
characteristics, and luxury consumption of nutrients are reduced, preventing these factors from confounding the interpretation of plant responses to changes in nutrient availability
(Waring et al. 1985, Coleman et al. 1994, Ågren 1994). The
allocation of carbon (C) and nitrogen (N) to growth (Ingestad
and Ågren 1988, 1991) versus defense (Waring et al. 1985,

360

WAIT, JONES AND SCHAEDLE

Larsson et al. 1986) can be readily investigated. Increased
fertilizer-uptake efficiency and outplanting performance of

nursery stock has been achieved (Timmer et al. 1991, Imo and
Timmer 1992, Miller and Timmer 1994).
The use of flowing solution or spray culture to achieve
steady-state growth and nutrition has some disadvantages.
Nutrient flux rates across the root surface are often more rapid
than those found in nature; root development and architecture
are different from that found in soils; the necessary equipment
is expensive; and the size and number of plants that can be
grown are limited (e.g., Ingestad and Lund 1986, Koch et al.
1987). Applying exponentially increasing rates of nutrients to
plants in solid media is problematic because plants will not
always be growing at constant exponential rates (e.g., Braakhekke and Labe 1990, Freijsen and Otten 1993), and therefore,
exponential additions will not maintain steady-state growth
and nutrition.
The theoretical concepts and methodology to maintain
steady-state conditions beyond exponential growth are not
well developed (Friejsen and Otten 1993) for large plants or
plants growing in solid media. The objective of this study was
to develop a steady-state fertilization technique that would
control growth and tissue composition of plants of various

sizes and developmental stages growing at exponential and
nonexponential growth rates in solid media.

Materials and methods
Plant culture
Shoot cuttings from 2-year-old cottonwood (Populus deltoides
Bartr.) saplings (Clone ST109) were rooted in perlite and
grown in sand to a uniform height (10 ± 0.5 cm) and fresh
weight (FW, 2 ± 0.1 g), and then planted in plastic tree tubes
(50 cm height × 10 cm diameter) containing 3 l of deionized
water-washed Mystic White silica sand (bulk density, 1300 kg
m −3). Tree tubes were spaced 12 cm apart within a plywood
rack to minimize shading. Saplings were randomly assigned to
a nutrient addition treatment, and treatments were randomly
distributed within and between racks. Racks were placed on
benches in a greenhouse without humidity, temperature, or
light control at 60% of full sun. Experiments took place at the
Institute of Ecosystem Studies in Millbrook, New York, between June and August.

Nutrient solution composition

Nutrient additions were expressed as the amount of N (mg)
added to pots, with all other nutrients added in constant proportion to N (Table 1). The nutrient proportions used were
similar to those found to be optimal for Betula verrucosa J.F.
Ehrh. (Ingestad 1970), Salix aquatica Smith (Ericsson 1981a,
1981b) and Populus simonii Carr. (Hui-Jun and Ingestad 1984)
with one major modification. Because P. deltoides foliage has
a high calcium (Ca) content (0.8--3.0% dry weight (DW),
Blackmon 1977), the proportion of Ca was increased sixfold
relative to the nutrient proportions used by Ingestad (1970) to
ensure that Ca was not limiting to growth or development.
Pot dynamics
To match nutrient supply with uptake and use, we first determined that nutrients added to a tree tube on a daily basis and
not taken up by the plant would be flushed out at the next
addition, i.e., there would be no net accumulation of nutrients
in the sand that might lead to subsequent oversupply of nutrients.
Based on a 200-ml addition to pots and a measured retention
volume of 80 ± 2.5 ml, nutrient retention as N was measured
in two ways. First, nutrients were added once daily for 16 days
at an exponentially increasing rate of 7.2% day −1, with an
initial N concentration of 0.5 mM (0.56 mg) and a final N

concentration of 1.6 mM (1.8 mg), to five pots without saplings. Leachate was collected from the pots after 3, 6, 9, 13 and
16 days, and its specific conductivity determined with a YSI 33
S-C-T meter. Conductivity of leachate samples (three replicates and 40-ml aliquots per sample) was converted to N
concentration based on a standard curve (N (mM) = 0.0064 ×
conductivity (ohm) − 0.048; r 2 = 0.99, P < 0.001, n = 30). All
but 6 ± 14% of the N added the previous day was recovered in
the leachate, with an estimated retention of 0.06 mg N per
1.0 mg N added. Second, nutrients were added once daily for
8 days at a N concentration of 1.0 mM to five pots without
saplings, and leachate conductivity was determined after 1, 3
and 8 days. Over 95% of the total N added over the 8 days was
recovered in leachate.
These data, along with weekly NO −3 , NH +4 and pH measurements of input and leachate solutions in a preliminary growth
experiment (Wait 1992), indicated that the assumption of no
nutrient retention over time was valid, and that the pH (4.5 to
5.7) was within the range required for growth of cottonwood.

Table 1. Nutrient solution composition.
Element

Mole ratio

Macronutrient salts

Concentration (µM)

Micronutrient salts

Concentration (mM)

N
K
P
Ca
Mg
S

1.00
0.24
0.06

0.50
0.05
0.04

NH4NO3
Ca(NO3)2
CaCl2
MgSO4
MgCl2
KH2PO4
KCl

200
300
200
40
10
60
180

H3BO3
MnCl2
CuSO4
ZnSO4
Na2MoO4
NaCl
FeEDTA

46.0
9.5
0.2
0.8
0.1
50.0
10.0

BOOTSTRAP FERTILIZATION TECHNIQUE

Nutrient addition method
(1) Establishing different growth rates and tissue composition among treatments; nutrient additions for lag phase

growth and exponential growth Deionized water was added
to saplings once daily for 5 days to acclimate plants to pots. A
low concentration of nutrient solution (0.056 mg N) was then
added for 5 days to initiate uniform growth in all treatments.
Nutrients were then added daily at different, but constant,
exponential rates to initiate differences in growth rates and
tissue composition among treatments (Ingestad and Lund
1986). The exponential additions were carried out for 20--30
days until growth rates appeared to separate. Exponentially
increasing addition rates were calculated as in Ingestad and
Lund (1979) and Imo and Timmer (1992, Equations 1 and 2).
The additions were based on the exponential function Nt =
Ns(ert − 1), where Nt is the amount of N to be added in the
number of nutrient applications (t), Ns is the content of N in the
seedlings on any given day, and r is the relative addition rate
required to maintain or increase the N content in the tissue to
a final N content. Thus, Nt − Ns is the amount of N to be added
to allow the N content to increase at the desired relative rate
(Ericsson 1981a), which is a direct function of the relative
growth rate. Therefore, the amount of N needed to maintain a
current N content at a given growth rate can be calculated as
follows:
r = W Ns RGR,

(1)

where W is sapling fresh weight, and RGR is measured or
desired relative growth rate. The initial amount of N in 2.0 gFW
saplings in these experiments was 0.5% FW. The potential
range of RGRs was estimated to be between 1.0 and 6.0%
day −1 (Hui-Jun and Ingestad 1984, Wait 1992).

361

rate or linear rate until the amount of N to add is again
re-estimated. Deciding at what rate to add nutrients will depend on whether the measured growth rate is an exponential or
nonexponential function. Thus, the essence of bootstrapping is
to adjust the amount of N and the addition rate to account for
nonexponential growth, and thereby avoid the over- or undersupply of nutrients that leads to deviations from steady-state
conditions.
Growth experiments
In Experiment 1, 80 saplings were grown for 76 days at one of
four nutrient addition rates (Figure 1a). The initial N mass
added to all treatments was 0.056 mg; the final N mass added
for each treatment was 0.47, 1.12, 3.36 and 5.15 mg for
constant exponential addition rates of 1.5, 3.0, 4.5 and 6.0%
day −1, respectively. Because the nutrient addition rate was
adjusted periodically (Equation 2), treatments were designated
as the average exponential nutrient addition rate (Raavg , mg
mg −1 day −1 or % day −1) over the entire experiment. The Raavg
for the 76 days for each treatment was 2.8, 3.9, 5.4 and 5.8%
day −1, respectively.
In Experiment 2, 60 saplings were grown for 86 days at one
of three nutrient addition rates (Figure 1b). The initial N mass
added to all treatments was 0.056 mg; the final N mass added
for each treatment was 0.54, 2.24 and 4.48 mg for constant
exponential addition rates of 2.0, 4.0 and 6.0% day −1, respectively. The Raavg for the 86 days for each treatment was 2.6, 4.3
and 5.1% day −1, respectively.

(2) Maintaining different growth rates and tissue composition among treatments; iterative, bootstrap, nutrient additions for nonexponential growth Nutrient additions were reestimated from instantaneous shoot elongation rates (cm day −1)
and estimated leaf N concentration (1.0 to 5.0% DW, Hui-Jun
and Ingestad 1984, Hansen et al. 1988) after the initial 20--30
days of constant exponentially increasing additions. The following equation re-estimates the amount of N to add on a given
day to maintain differences in growth rates and tissue composition achieved from exponential additions:
Ng = ∆Ht Np HW,

(2)

where Ng is the amount of N (g) required for the plant to
maintain the current N concentration at the given current
absolute growth rate, ∆Ht is the change in height over time (cm
day −1), Np is the actual or estimated percentage N (N concentration, % DW) in leaves, and HW is a factor that relates height
to weight, estimated from weight = 0.149 × height − 0.998
(1 cm = 0.08 g, r 2 = 0.914, n = 67, P = 0.0001). The value of
HW was determined from 19 harvested saplings between 10
and 40 cm in height and confirmed with 48 saplings harvested
from growth experiments (Wait 1992).
The amount calculated (Ng) is then added at an exponential

Figure 1. Nutrient solution concentration for (a) Experiment 1 and (b)
Experiment 2, expressed as N (mg) added during the experiments.
Proportions of other nutrients relative to N are given in Table 1.
Treatments are designated as Raavg (mg mg −1 day −1), the average
addition rate over the entire experiment.

362

WAIT, JONES AND SCHAEDLE

Growth and foliar chemistry

Results

Height was measured from an acrylic paint mark at the stem
base to the tip of the primary node (stem apex) on eight
saplings per treatment every 2 to 4 days in Experiment 1 and
on 12 saplings per treatment every 7 to 10 days in Experiment 2. On Day 76 in Experiment 1, the saplings measured for
height were harvested. Leaf area was determined with an
LI-3100 area meter (Li-Cor Inc., Lincoln, NE); roots, stems
and leaves were weighed, dried at 35 °C and re-weighed.
Leaves (two per sapling) at or approaching full expansion were
pooled, dried and milled (20 mesh), and analyzed for elemental N and C with a Carlo Erba NA 1500 N/C analyzer and
microwave digested and analyzed for elemental P, K, Ca and
Mg with a Spectro ICP analyzer. In addition, the 12 saplings
per treatment not measured for height in Experiment 1 were
harvested in randomly chosen pairs for determination of foliar
N, RGR (g g −1 day −1), and height/weight ratio through time.
Data analysis
Sapling height was used to calculate instantaneous relative
height growth rate (RHGR, day −1) as follows:
RHGR = (ln(h2) − ln(h1))/(t2 − t1),

(3)

where ln(h2) and ln(h1) are the natural log of plant height at
time t2 and t1, respectively.
The mean daily RHGR in a treatment (RHGRdaily ) plotted
against time was used to visualize the growth rate in a treatment between time intervals (Evans 1972, Poorter 1989a).
Third-order polynomials were fitted to RHGRdaily to derive the
RHGR over time (Hunt 1982, Poorter 1989a, 1989b).
To verify that different nutrient addition rates significantly
affected RHGRdaily , fitted curves to RHGRdaily (fitted to 12 and
8 time intervals in Experiments 1 and 2, respectively) were
analyzed with regression methods as described by Potvin et al.
(1990). Pairwise comparisons of fitted response curves (i.e.,
RHGR) indicated which treatments were statistically different
from each other. The RHGRdaily data were analyzed by repeated measures ANOVA (Potvin et al. 1990) to verify the
results of regression analysis. Stable growth was defined as a
period of time when the rate of change of RHGR was at or near
zero. That is, a plant growing at the same relative (i.e., constant
exponential) or absolute rate over a given time period, where
the rate of change in growth could be increasing, constant, or
decreasing depending on whether growth is described by a
constant exponential, or nonexponential function. Stable
growth was determined by visually inspecting RHGRdaily and
the curves (i.e., slope of line) fit to RHGRdaily, and by calculating the rate of change of growth from the derivatives of the
polynomial (Hunt 1982, Poorter 1989a, 1989b). End point
heights, leaf areas, root/shoot ratios, and tissue nutrient compositions were analyzed by ANOVA. When a significant treatment effect occurred (P < 0.05), pairwise comparisons of
means were made by either the Waller/Duncan method or
t-tests.

Growth rates
Daily nutrient addition treatments (Raavg ) significantly affected RHGR (Table 2). The treatments that differed by more
than 1.5% day −1 in Experiment 1 and by more than 0.8% day −1
in Experiment 2 resulted in statistically significant differences
in RHGR (Table 2). Repeated measures ANOVA of RHGRdaily
indicated that there were significant nutrient addition by time
effects (P < 0.001) in both experiments. By bootstrapping
nutrient additions to account for nonexponential growth, the
mean RHGRdaily was maintained at a stable rate between Days
49 and 76 in Experiment 1 and between Days 65 and 86 in
Experiment 2 (Figure 2, Table 3). Dry matter growth rates
(RGR, g g −1 day −1) were significantly positively correlated to
RHGRdaily over time (df = 19, r 2 = 0.69, P = 0.0001, RGR =
0.717 × RHGRdaily + 3.094 × 10 −4), indicating that RGR was
stable and that height was a good estimate of biomass for these
cottonwood saplings.
Growth characteristics
Saplings grown at high rates of nutrient addition were significantly taller, and had significantly greater biomass, leaf area
and weight (Table 3) than saplings grown at low rates of
nutrient addition. Root/shoot ratios were lower in saplings
grown at high nutrient addition rates than in saplings grown at
low nutrient addition rates (Table 3). Variation in growth characteristics between saplings within a treatment was low, as
indicated by low coefficients of variation (Table 3).
Foliar chemistry
Foliar N was significantly greater in saplings in the high
nutrient addition treatments than in saplings in the low nutrient
addition treatments (Table 3). Foliar C/N ratios declined with
growth rate and were significantly different between each Raavg
treatment except between treatments 5.4 and 5.8% day −1 in
Table 2. Regression analysis of third-order polynomials fitted to
RHGRdaily (from Figure 2) for different average rates of nutrient
addition (Raavg , % day −1). Experiment 1, n = 8 saplings per Raavg ;
Experiment 2, n = 12 saplings per Raavg .
Sources for F-tests (Raavg )

df

P

Experiment 1
Among groups
5.8 versus 5.4
5.8 versus 3.9
5.8 versus 2.8
5.4 versus 3.9
5.4 versus 2.8
3.9 versus 2.8

31,344
9,174
9,174
9,174
9,174
9,174
9,174

< 0.001
> 0.10
< 0.001
< 0.001
< 0.02
< 0.001
> 0.10

Experiment 2
Among groups
2.6 versus 4.3, 5.1
5.1 versus 4.3
4.3 versus 2.6

32,357
31,358
16,238
16,238

< 0.05
< 0.05
> 0.05
< 0.05

BOOTSTRAP FERTILIZATION TECHNIQUE

363

Figure 3. Mean percent nitrogen in leaves harvested over time in
Experiment 1 as a function of the average nutrient addition rate
(Raavg ). Bars are standard errors of the mean.

symptoms (as described by Epstein 1972). Foliar concentrations of Ca and Mg were similar in all Raavg treatments,
whereas foliar concentrations of P and K increased with increasing nutrient supply.
Figure 2. Mean RHGRdaily of saplings grown at different average
nutrient addition rates (see Figure 1). The solid lines (RHGR) are the
fit of third-order polynomials as described by Poorter (1989a). (a)
Experiment 1, n = 8 saplings per treatment; pooled standard deviation
for all treatments was 0.0050 between Days 49 and 76; pairs of Raavg
treatments are shown in separate graphs for clarity. (b) Experiment 2,
n = 12 saplings per treatment; pooled standard deviation for all treatments was 0.0020 between Days 65 and 85.

Experiment 1 (Table 3). Foliar N was significantly correlated
to RHGRdaily (df = 19, r 2 = 0.77, P = 0.0001, N (gDW) = 0.488
× RHGRdaily + 53.255), indicating stable foliar N (Figure 3).
Concentrations of P, K, Ca and Mg were above deficiency
levels in Experiment 1, with no visible nutrient deficiency

Discussion
Constant exponential growth may not occur, or may be of short
duration in plants (Pieters and van den Noort 1985, 1990)
because of self-shading (Ingestad and Lund 1979), a declining
ratio of growing to mature tissue (Pieters and van den Noort
1990), or reproduction (Freijsen and Otten 1993). Therefore,
constant exponential nutrient supply would only be expected
to control growth over limited time periods and plant developmental stages. For example, Ingestad (1982) and Ericsson
(1981a, 1981b) used exponential nutrient supply to control the
growth of small Betula seedlings and Salix ramets during
exponential growth phases. Once growth deviated from expo-

Table 3. Sapling growth and foliar chemistry. Numbers in parentheses are coefficients ofvariation unless otherwise indicated; letters within a row
and experiment indicate significant differences between means (P < 0.05).
Raavg (% day −1)

Experiment 1

Experiment 2

2.8

3.9

5.4

5.8

2.6

4.3

5.1

76 (49--76)
0.019 (20)
13.9 (20) a
1.08 (52) a
0.37 (52) a
54 (50) a
0.90 (28) a

76 (49--76)
0.026 (20)
22.3 (30) b
2.26 (43) b
1.01 (25) b
174 (17) b
0.69 (13) b

76 (49--76)
0.033 (15)
29.5 (11) c
3.69 (30) c
2.77 (5) c
492 (1) c
0.57 (14) c

76 (49--76)
0.039 (13)
37.5 (13) d
5.00 (11) d
3.41 (21) c
610 (3) d
0.48 (8) c

86 (65--86)
0.026 (6)
15.3 (8) a
nd3
nd
nd
nd

86 (65--86)
0.034 (6)
25.9 (5) b
nd
nd
nd
nd

86 (65--86)
0.037 (7)
34.5 (5) c
nd
nd
nd
nd

Foliar chemistry (dry weight basis)
%N
1.2 (2) a
C/N ratio
42.1 (21) a
%P
0.10 (20) a
%K
0.59 (29) a
% Ca
1.3 (18) a

2.4 (2) b
18.8 (16) b
0.16 (18) b
0.85 (22) b
1.5 (23) a

3.2 (1) c
14.5 (1) c
0.26 (23) c
1.50 (16) c
1.6 (18) a

3.7 (11) d
12.8 (2) c
0.42 (23) d
1.80 (8) d
1.6 (17) a

1.9 (4) a
29.5 (9) a
nd
nd
nd

3.2 (2) b
14.9 (3) b
nd
nd
nd

3.9 (1) c
12.5 (2) c
nd
nd
nd

Sapling growth
Days of stable growth1
Stable mean RHGR2
Height (cm)
Total dry weight (g)
Leaf dry weight (g)
Leaf area (cm2)
Root/shoot ratio

1
2
3

Days of stable growth refers to the time period during which the rate of change in growth was constant or essentially zero (see Figure 2).
Stable mean RHGR is the mean RHGRdaily during the days of stable growth.
nd = No data available.

364

WAIT, JONES AND SCHAEDLE

nential, the relationships between relative addition rates, relative growth rates, and relative uptake rates were no longer
constant, and growth and tissue composition could no longer
be controlled. Wait (1992) observed that exponential nutrient
addition rates to cottonwood saplings for over 30 days resulted
in oversupply so that growth and tissue composition were
ultimately not different between treatments, or stable within a
treatment. Conventional, single dose or constant top dressing
fertilization regimes would also not be expected to result in
steady-state growth and nutrition (Imo and Timmer 1992).
Nutrient addition method
Because exponential nutrient additions can lead to oversupply,
and possibly undersupply, of nutrients over time, which would
lead to fluctuations in growth and tissue composition, we
developed an iterative bootstrap fertilization method. This
method takes into account that growth is not a constant exponential function because of plant size, plant developmental
stage, and fluctuations in temperature, light and humidity.
Initially, no or low nutrient concentration additions were
made so that the saplings could adjust to the culture system and
to avoid oversupply of N during the lag phase growth (see
Ingestad and Lund 1986). The negative slope for RHGR for up
to 15 days in both Experiments 1 and 2 (Figure 2) illustrates
this lag phase, or pre-exponential phase of growth. Constant
exponential nutrient addition rates were then made based on
potential, and desired, growth rates and tissue N concentrations (Ingestad and Lund 1986). Separation of RHGRs during
the exponential additions illustrated that nutrient supply was
driving RHGR at different rates (Figure 2). Day to day variations in RHGRdaily occurred (Figure 2) that were most likely
due to fluctuations in light and temperature, and to different
measurement intervals (Poorter 1989a). During the nonexponential phase of growth, iterative bootstrap-calculated additions were used to maintain the differences in RHGRs achieved
by the exponential additions. Bootstrapping re-estimates the
amount of N needed to maintain stable growth and tissue
composition based on actual growth in each treatment. The
re-estimated N amount was then added at a constant exponential or linear rate depending on current growth rates until N was
again re-estimated. For example, every 3--5 days in Experiment 1 and every 7--10 days in Experiment 2 (Figure 1).
Growth and tissue composition
The fertilization method controlled sapling growth, by varying
the supply rate of nutrients, over relatively long time periods
(60+ days) during which exponential and nonexponential
growth occurred (Figure 2). In two independently replicated
experiments, the nutrient addition treatments (Table 2) resulted
in differing sapling relative height growth rates (Figure 2), but
within a treatment, stable height growth rates were maintained
(Table 3) for over 20 days. Foliar N concentration increased
with increasing nutrient addition rate (Figure 3). The patterns
of growth and biomass allocation conformed to those expected
for plants growing at different rates of nutrient supply (Table 3)
(Ingestad 1982, McDonald et al. 1986, Wilson 1988, Ingestad
and Ågren 1991).

Applicability of nutrient addition method
The basic premise of establishing different growth rates and
tissue composition with exponential nutrient additions, and
then maintaining these differences at defined levels throughout
different developmental growth phases with a set of iterative
bootstrap equations is applicable to fertilization experiments
in general. Successful application of the technique to other
plant species would require certain preliminary data. First, the
approximate range of growth rates observed at different developmental stages should be known. Second, the mean and range
of macronutrient concentrations in the leaf tissues or the whole
plant or both at plant sizes of interest should be estimated.
Third, the best nondestructive estimate of dry matter accumulation that can be readily measured (e.g., leaf area, height, or a
combination of both) should be determined. Finally, some
estimate of nutrient retention in the solid medium is needed.
Because the technique helps avoid potentially confounding
effects of uncontrolled fluctuations in resource supply and
demand, it will be useful for studies that require conditions of
steady-state growth and nutrition (see Ingestad and Ågren
1992, Ågren 1994). For example, the technique could be used
to investigate resource allocation to shoot growth versus root
growth, or growth versus other processes such as partitioning
of metabolites to defense. It should also be possible to use the
technique to control resource availability while studying the
effects of multiple types of stress or physical damage.

Acknowledgments
We thank D. Bulkeley for invaluable greenhouse assistance, and J.S.
Coleman and G.M. Lovett for critical comment. Supported by the NSF
(BSR-8817519) (CGJ), the General Reinsurance Corporation (CGJ),
John Simon Guggenheim Foundation (CGJ), the Mary Flagler Cary
Charitable Trust (CGJ) and Sigma Xi (DAW). Contribution to the
program of the Institute of Ecosystem Studies.

References
Ågren, G.I. 1994. The interaction between CO2 and plant nutrition:
comments on a paper by Coleman, McConnaughay, and Bazzaz.
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