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The limits to tree height
George W. Koch
1
, Stephen C. Sillett
2
, Gregory M. Jennings
2
& Stephen D. Davis
3
1
Department of Biological Sciences and the Merriam-Powell Center for
Environmental Research, Northern Arizona University, Flagstaff, Arizona 86011,
USA
2
Department of Biological Sciences, Humboldt State University, Arcata,
California 95521, USA
3
Natural Science Division, Pepperdine University, Malibu, California
90263-4321, USA
.............................................................................................................................................................................
Trees grow tall where resources are abundant, stresses are minor,
and competition for light places a premium on height growth
1,2
.
The height to which trees can grow and the biophysical determi-
nants of maximum height are poorly understood. Some models
predict heights of up to 120 m in the absence of mechanical
damage
3,4
, but there are historical accounts of taller trees
5
.
Current hypotheses of height limitation focus on increasing
water transport constraints in taller trees and the resulting
reductions in leaf photosynthesis
6
. We studied redwoods
(Sequoia sempervirens), including the tallest known tree on
Earth (112.7 m), in wet temperate forests of northern California.
Our regression analyses of height gradients in leaf functional
characteristics estimate a maximum tree height of 122–130 m
barring mechanical damage, similar to the tallest recorded trees
of the past. As trees grow taller, increasing leaf water stress due to
gravity and path length resistance may ultimately limit leaf
expansion and photosynthesis for further height growth, even
with ample soil moisture.
According to the cohesion-tension theory, water transport in
plants occurs along a gradient of negative pressure (tension) in the
dead, tube-like cells of the xylem, with transpiration, water adhesion
to cell walls, and surface tension providing the forces necessary to
lift water against gravity
7
. Height growth may slow if the xylem
tension and therefore leaf water potential (
W
) predicted for great
heights, &22 MPa (ref. 7), reduces sufficiently the positive pressure
(turgor) necessary for expansion of living cells or increases the risk
of xylem cavitation
—
cavitation is the formation of embolisms that
reduce hydraulic conductivity and can cause branch dieback and
plant death
8,9
. Many trees respond to
W
below 21 MPa by decreas-
ing the aperture of microscopic pores (stomata) in leaves through
which water vapour is lost in transpiration and carbon dioxide
(CO
2
) is gained in photosynthesis
10
. Reduced stomatal conductance
can decrease cavitation risk and turgor loss, but it also limits photo-
synthesis. Thus, as trees grow taller, maintenance of favourable
water status might progressively slow height growth by reducing
photosynthetic carbon gain
4,6
.
We accessed the crowns of redwoods to measure water stress and
photosynthesis and to collect samples for laboratory analyses.
Within individual trees, the xylem pressure of small, foliated
branches measured during the dry season (late September to early
October) was strongly correlated with height (Fig. 1a). The gradient
before dawn, when transpiration was negligible, averaged
20.0096 ^ 0.0007 MPa m
21
for five trees over 110 m tall
(R
2
. 0.97, P , 0.0001), nearly identical to the hydrostatic gradi-
ent due to gravity (20.0098 MPa m
21
) as predicted by the cohe-
sion-tension theory
7
. The slope of the xylem pressure–height
relationship was slightly steeper (20.0106 ^ 0.0022 MPa m
21
)at
midday when the evaporative gradient and transpiration were high.
The minimum xylem pressure (that is, maximum tension) recorded
in the highest branches sampled (108 ^ 1.2 m) averaged
21.84 ^ 0.04 MPa. The importance of height per se for water
potential was evident in that nearly two-thirds of the midday
xylem pressure was due to gravity.
Reduced water potential due to soil drought causes a decline in
the turgor of living plant cells that is necessary for cell growth and
leaf expansion
11
. To determine if this also occurs as water potential
declines with height, we estimated turgor at dry-season water
potentials from pressure–volume measurements. Turgor (in MPa)
declined linearly with height, h, as turgor ¼ 2ð0:0074 ^ 0:0004Þh
þð1:30 ^ 0: 07Þ, n ¼ 4 trees, ranging from 0.93 MPa at 50 m to
0.48 MPa at 110 m. At night when xylem pressure increased, the
turgor gradient was less steep, turgor ¼2ð0:0044 ^ 0:0023Þh
þð1:39 ^ 0: 19Þ, and turgor was 0.3–0.4 MPa higher than at
midday.
Given the role of turgor in leaf expansion, its reduction with
height may underlie the distinct vertical gradient in leaf structure in
redwoods (Fig. 2). Leaf shape varied from large and expanded in the
lower crown to small and scale-like at the treetop. We quantified this
variation in terms of the leaf mass:area ratio (LMA, g m
22
), which
increased exponentially over a fourfold range with height (Fig. 1b,
LMA ¼ (37.1 ^ 12.3)exp(0.0260 ^ 0.0030)h,0.88# R
2
# 0.99,
0.0001 # P # 0.003, n ¼ 5 trees). At 112 m, LMA was similar to
the highest published value for terrestrial plants
12
. Height-related
variation in LMA has been attributed to light level in forest
canopies
13,14
. In our study trees, we found that the direct site factor
(DSF), an index of direct solar radiation based on hemispherical
photographs, decreased by 14% of the value at 110 m for a 10-m
decrease in height. Relative to water potential, the influence of
light on LMA was small, however; DSF added only 4% to the
explained variation of within-crown LMA in a multiple regression
analysis including DSF (P ¼ 0.0025) and predawn xylem pressure
(P , 0.0001) as independent variables (adjusted R
2
¼ 0.88, n ¼ 33
samples from five redwoods over 110 m tall). The following obser-
vations (Fig. 3) also support the hypothesis that water relations are
more important than light environment in determining leaf struc-
ture in redwood: (1) leaves of a 2-m-tall epiphytic redwood rooted
in soil near the top of a 95-m-tall redwood were much more
Figure 1 Variation with height in physiological and structural features of redwood trees at
Humboldt Redwoods State Park, California. a, Xylem pressure of small branches
measured at predawn (upper group) and midday (lower group) during September and
October 2000. The upper line is the expected gravitational pressure gradient with the
same y-intercept as the average of the 5 trees. b, Leaf mass:area ratio (g m
22
) of second-
year internodes increases with height. c, Foliar carbon isotope composition (
d
13
C, ‰)
increases with height within the crowns of 5 trees over 110 m tall and among the tops
(filled circles) of 16 trees from 85 to 113 m tall. d, Light-saturated photosynthetic rate per
unit mass (nmol CO
2
g
21
s
21
) decreases with height. The regression line is fitted to data
from six trees. Different symbol types denote different trees and are consistent for a–d.
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expanded than leaves of the host tree in the same light environment,
and (2) when a fallen branch from the upper crown of a tall redwood
was potted in wet soil and allowed to root with the branch exposed
to high light, the new leaves produced were much more expanded
than the existing leaves. It is likely that in very tall trees, components
of water potential, notably turgor, are important determinants of
LMA and related anatomical features, just as they are along soil
moisture gradients
12
.
To assess further the physiological consequences of declining
water potential with height, we measured stable carbon isotope
composition (
d
13
C) and leaf photosynthesis. The
d
13
C value (‰) of
plant tissues expresses the photosynthetic discrimination against
13
CO
2
compared with
12
CO
2
and is a common metric of long-term
water stress, ranging from 220‰ to 234‰ in plants such as
redwood that have the C
3
photosynthetic pathway
15
. When water
stress reduces stomatal conductance, CO
2
concentration in the
intercellular air spaces of leaves (C
i
) declines, and this lessens the
enzymatic discrimination against
13
CO
2
, causing
d
13
C to increase.
In redwood, foliar
d
13
C (‰) was correlated with height (Fig. 1c,
exponential fits of the form
d
13
C þ 31 ¼ b
1
exp(b
0
h), b
1
¼
0:681 ^ 0:434, b
0
¼ 0.033 ^ 0.005, 0.78 # R
2
# 0.94, 0:0001 #
P # 0:002). The highest
d
13
C was always observed at the treetop
and averaged 222.2 ^ 0.6‰ at $110 m. This is the highest
published foliar
d
13
C for tall trees and is close to the apparent
limit for C
3
plants
16–18
. We also found a significant relationship of
d
13
C (‰) to height for the treetop foliage of 13 trees from 85 m
to 110 m tall plus 3 trees taller than 112 m (Fig. 1c,
d
13
C þ 31 ¼ 1.928exp(0.0131 h), R
2
¼ 0.321, P ¼ 0.022, n ¼ 16).
That
d
13
C was higher (less negative) at the tops of trees than at the
same height within tree crowns probably indicates the effect of
shading in reducing foliar
d
13
C (ref. 15). Nonetheless, patterns both
within and among trees demonstrate a strong increase of
d
13
C with
height in redwood, indicative of increasing water stress.
High values of
d
13
C occur when stomatal conductance is strongly
limiting to photosynthesis, as in plants experiencing low water
potentials due to soil moisture stress
15,16
. Rather than soil moisture
stress, however, it is likely that in tall trees the reduction in water
potential due to gravity and path length resistance causes stomatal
conductance to increasingly limit photosynthesis with height
6,19
.
The treetop
d
13
C of about 222‰ corresponds to a flux-weighted C
i
of ,160 p.p.m. during the assimilation of CO
2
into new biomass.
This is similar to the average daily C
i
estimated from our in situ gas
exchange measurements near the tops of two 112-m-tall trees
during autumn (170 ^ 11 p.p.m.). Thus, integrated
d
13
Cand
instantaneous gas exchange indicate that stomatal conductance is
increasingly limiting to photosynthesis with height, as reported for
other conifers up to 65 m tall
19,20
.
Laboratory gas exchange measurements of foliage cut from
different heights and re-hydrated to uniformly high water potentials
enabled us to examine the consequences of height for photosyn-
thesis in the absence of a direct influence of low water potential.
Light-saturated photosynthesis per unit leaf area (P
max,a
)did
notvarywithheight(R
2
¼ 0.012, P ¼ 0.78), averaging
5.6
m
mol CO
2
m
22
s
21
. Photosynthesis per unit leaf mass (P
max,m
)
decreased with height (Fig. 1d, P
max,m
¼ 20.455h þ 55.3,
R
2
¼ 0.88, P ¼ 0.0002), however, indicating a lower potential
photosynthetic return on biomass invested in leaves at greater
heights. The P
max,m
of 110-m foliage was 28% of that at 80 m and
only 16% of that at 50 m. Because light levels decline exponentially
with depth in forest canopies
2
, actual differences in photosynthesis
per unit biomass are probably smaller than indicated by our
Figure 2 Variation in leaf structure with height in redwood. Leaf length and the angle
between the long axis of the leaf and supporting stem segment both decrease with height.
Numbers denote the sample height in m. Scale divisions are cm.
Figure 3 Leaf structure can vary independently of light environment. The upper panel
shows foliage of an epiphytic redwood (expanded, light-green leaves) and adjacent foliage
(unexpanded, darker-green leaves in background) of the host redwood at 95 m in the
same light environment. The lower panel shows the new, more expanded foliage (at
branch tips) that developed next to the existing unexpanded foliage on a detached upper
crown (.90 m) branch after it was rooted in wet soil and kept in high light. Both examples
support the view that variation in light environment explains little of the variation in leaf
structure in redwood (see text).
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measurements at light saturation. Nonetheless, photosynthetic
capacity per unit foliar mass declines with height, and we hypoth-
esize that this results from the observed changes in leaf structure.
High LMA is associated with high tissue density and increased
allocation of biomass to structure, including thicker cell walls
12,21
.
These changes can increase internal resistance to CO
2
diffusion
within leaves
22,23
, reducing photosynthesis and contributing to high
d
13
C values. We speculate that the universal influence of gravity on
water potential gradients in tall trees underlies structural changes in
photosynthetic tissues that, along with increased stomatal regu-
lation, reduce photosynthesis and carbohydrate availability for
height growth.
Our studies of the tallest redwoods reveal gradients in physio-
logical and structural features that support hypotheses of height
limitation due to hydraulic constraints
4,6
. Water potential, turgor,
leaf structure, carbon isotope composition, and photosynthesis all
change with height as they do along gradients of soil moisture stress,
consistent with a general role for water availability in determining
leaf functional traits
12,21
. Height gradients of these variables also
allowed us to address the potential biophysical limit to height in
redwood. To estimate a maximum height in the current environ-
ment barring mechanical damage, we calculated the height at which
the functional variables we examined would reach a limit value
(Table 1).
Low water potential affects growth severely when the formation
of embolisms by cavitation reduces hydraulic conductivity
8
.
Whereas it is not uncommon for shorter trees to operate at water
potentials that cause considerable loss of hydraulic conductivity,
cavitation avoidance may be critical for height growth in tall trees.
Great height may prevent recovery of lost hydraulic function by
embolism dissolution, the standard model for which requires that
xylem pressures rise to within a few tenths of 0 MPa (ref. 24), higher
than is possible in a water column held by tension above a few tens
of metres. Our measurements of xylem vulnerability to cavitation in
upper crown branches (109 m) of five trees over 110 m tall indicate
that loss of hydraulic conductivity begins as xylem pressure drops to
21.9 MPa (Supplementary Information), slightly lower than the
lowest pressure we recorded at the tops of the tallest trees at midday.
The xylem pressure–height relationship (Fig. 1a, Table 1) estimates
a pressure of 21.9 MPa at 122 m, increasing to 132 m for a limit
value of 22.0 MPa. It is likely that lower water potentials and
cavitation do occur in tall redwoods, mature individuals of which
may experience severe droughts during life spans of up to 2,200
years (refs 25, 26). It may be during such episodes that the upper
crown dies back, as evidenced by our observations that nearly all
very tall redwoods have multiple tops, the original leader having
died and been replaced repeatedly.
Surveys of several hundred terrestrial plant species across diverse
biomes report values of LMA from 20 g m
22
for thin planar leaves of
herbaceous species to a maximum of 833 g m
22
for the scale-like
leaves in Juniperus monosperma, a short coniferous tree of arid
regions and, like redwood, a member of the Cupressaceae
12,21
. Using
833 g m
22
as the maximum possible for redwood, the LMA–height
relationship (Fig. 1b, Table 1) estimates a maximum height of
122 m. If the limiting value of LMA is allowed to increase by 10%,
the maximum height increases to 126 m.
For C
3
plants, the apparent limit of foliar
d
13
C is the approxi-
mately 220‰ reported for plants of arid environments
16–18
. The
overall within-crown
d
13
C–height relationship (Fig. 1c, Table 1)
estimates a
d
13
Cof220‰ at 130 m. The sensitivity of this estimate
to the limiting
d
13
C value is low; heights of 134 m and 125 m are
estimated for
d
13
Cof219‰ and 221‰, respectively.
A linear extrapolation of maximum photosynthesis versus height
(Fig. 1d, Table 1) predicts that P
max,m
in saturating light would
decline to 0 at 125 m. Carbon import from elsewhere in the tree may
support early growth of new leaves, but the trend in foliar
d
13
C with
height (Fig. 1c) indicates at most a minor quantitative significance
of carbon subsidies from the lower crown.
Taken together, these height trends in ecophysiological variables
indicate that the maximum height of redwood at our study site in
current environmental conditions is 122 to 130 m. The reduction in
water potential with height reduces leaf expansion and photosyn-
thesis, the latter directly via increased stomatal regulation, as
evidenced by
d
13
C, and indirectly by altering leaf structure
(LMA), which in turn may further constrain carbon balance. Several
additional lines of evidence support a limit to tree height for
redwood that is taller than today’s tallest trees and near the estimates
from our regression analyses. First, our measurements indicate that
the tallest redwoods are growing by up to 0.25 m yr
21
. Second, over
95% of the original old-growth redwood forest has been logged
26
,
and it is likely that redwoods taller than today’s giants were felled
5
.
Third, we analysed the height gradient in foliar
d
13
C reported for
Douglas-fir
20
(
d
13
C ¼ 0.060h 2 27.5, R
2
¼ 0.999, P ¼ 0.005) and
estimated by linear extrapolation that
d
13
C would reach 220‰ at
125 m. Finally, the maximum tree height we predict for redwood
and Douglas-fir is similar to the 126 m of the tallest reliably
measured gymnosperm of the past, a Douglas-fir
5
.
The tallest redwoods today stand in large reserves where intact
forest structure sustains moist conditions and buffers trees against
wind. The trees in this study, which include the first, second, fourth,
sixth and eighth tallest known individuals on Earth, all occur within
the largest contiguous old-growth redwood forest remaining
(Humboldt Redwoods State Park, California), a reserve protecting
89 of the 116 tallest redwoods. (Measurements of redwoods
throughout the species’ range in California have found 116 indi-
viduals over 107 m; C. Atkins and M. Taylor, personal communi-
cation.) At reserves further north and closer to the coast, stronger
storms may explain the lower heights (,100 m), yet similar
relationships of water potential and
d
13
C to height
27
as we observed
in the tallest redwoods. At the drier inland margin of redwood’s
natural distribution in northern California, maximum tree height is
lower (,80 m), yet treetop values of minimum water potential
(21.9 MPa) and maximum
d
13
C(222‰) are similar to those at
110 m in the tallest redwoods. Thus a similar physiological ceiling
may be reached at different physical heights depending on water
availability, with storm damage reducing realized heights at sites
that are otherwise optimal. Tree height should also vary over time as
climate fluctuates, and linking top dieback dates and growth rates to
past climate may reinforce our physiological interpretation of
height limitation. Climate and atmospheric change will affect the
height to which redwoods grow, the outcome depending on the
combined effects of elevated atmospheric CO
2
concentration and
altered temperature and moisture on tree water relations and
carbon balance
28
. A
Table 1 Maximum height predictions for redwood, Sequoia sempervirens
Dependent variable Equation Limit value of dependent variable Maximum height (m)
...................................................................................................................................................................................................................................................................................................................................................................
W
, midday (MPa) W ¼ 20.00973 h 2 0.712 21.9 122
LMA (g m
22
) LMA ¼ 37.43exp(0.0255 h) 833 122
d
13
C(‰)
d
13
C ¼ 0.559exp(0.0229 h) 2 31 220 130
P
max,m
(nmol g
21
s
21
) P
max,m
¼ 20.434 h þ 54.3 0 125
...................................................................................................................................................................................................................................................................................................................................................................
The relationship of physiological and structural variables to height in redwoods at Humboldt Redwoods State Park, California.The equations describe the relationship of the dependent variable to height for
data from all study trees combined. See text for explanations of limit values for dependent variables.
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Methods
Tree access
We accessed tree crowns by shooting arrows trailing filament over branches with a
powerful bow. Rope was then hauled over the branches and climbed via mechanical
ascenders. Access to the treetop was achieved by arborist-style techniques. Heights were
measured by lowering weighted fibreglass measuring tapes from the treetop to average
ground level.
Physiological measurements
Water potential of small branches (#15 cm length) located within 1 to 3 m of the main
trunk was measured using a pressure chamber (PMS Instruments). Measurements of
photosynthesis used a portable photosynthesis system (LI6400, LiCor) with a 2 cm £ 3cm
chamber with red/blue LED light source. Photosynthesis was measured under controlled
conditions: air temperature, 22 ^ 1 8C; CO
2
concentration, 365 ^ 10 p.p.m.; vapour
pressure deficit, 1.2 ^ 0.2 kPa; light, $1,400
m
mol photons m
22
s
21
). Samples used for
laboratory measurements of photosynthesis and pressure–volume relationships were cut
from different heights, then re-cut immediately under water, allowed to re-hydrate
overnight, and then measured. This produced high water potentials (20.6 ^ 0.3 MPa)
and allowed comparisons of photosynthetic capacity without the influence of height-
related variation in water potential. During these measurements, the C
i
values did not
differ significantly in foliage from different heights (239 ^ 16 p.p.m., P ¼ 0.42). Turgor
was estimated by the pressure–volume method
29
.
Morphological measurements
To determine LMA, projected surface areas of 10 second-year internodes from each sample
height were measured using a digital surface-area meter (Delta T Instruments). Samples
were oven-dried at 70 8C, weighed, and mean LMA calculated as g m
22
. Area and mass
measurements included the entire foliated internode.
Stable carbon isotope composition
d
13
C of foliage samples was analysed at the Colorado Plateau Stable Isotope Laboratory
(http://www4.nau.edu/cpsil/). In 2000, second-year internodes were collected at different
heights, dried (70 8C), ground to 40 mesh, and then a subsample was pulverized,
encapsulated in tin, and combusted (CE Instruments NC2100) at 1,000 8C. The resultant
CO
2
was purified and its
13
CO
2
/
12
CO
2
ratio was analysed by isotope-ratio mass
spectrometry (Delta Plus XL, ThermoQuest Finnigan) in continuous-flow mode. The
d
13
C values were expressed as the relative abundance of
13
C versus
12
C compared with a
standard (Pee Dee Belemnite):
d
13
C ¼ (R
sam
/R
std
2 1)1,000‰, where R
sam
and R
std
are
the
13
C/
12
C ratios in sample and standard, respectively. The standard deviation of repeated
measurements of secondary standard material was ,0.1‰ (external precision).
Light environment
Hemispherical photographs were taken directly above leaf sample locations throughout
tree crowns using a digital camera on a self-levelling mount. Photographs were analysed
with WinSCANOPY (v.2002a, Re
´
gent Instruments Inc.) to calculate direct site factor,
which is the average proportion of direct radiation received during the 12-month growing
season.
Received 7 November 2003; accepted 16 February 2004; doi:10.1038/nature02417.
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Supplementary Information accompanies the paper on www.nature.com/nature.
Acknowledgements This work was supported by the Global Forest Society, the Save-the-
Redwoods League, and Northern Arizona University’s Organized Research, and permitted by
Redwood State and National Parks. J. Amthor, S. Burgess, T. Dawson, A. Fredeen, B. Hungate and
H. Mooney provided comments that improved the paper.
Authors’ contributions G.K., S. S. and G.J. conceived and conducted the experiments, and G.K.
and S.S. analysed the data and co-wrote the paper. S. D. and G. K. conducted the xylem cavitation
experiments.
Competing interests statement The authors declare that they have no competing financial
interests.
Correspondence and requests for materials should be addressed to G.W.K.
(george.koch@nau.edu).
..............................................................
Perceived luminance depends
on temporal context
David M. Eagleman
1,2
, John E. Jacobson
2,3
& Terrence J. Sejnowski
2,4
1
Department of Neurobiology and Anatomy, University of Texas, Houston
Medical School, 6431 Fannin Street, Suite 7.046, Houston, Texas 77030, USA
2
Howard Hughes Medical Institute at the Salk Institute for Biological Studies,
10010 North Torrey Pines Road, La Jolla, California 92037, USA
3
Department of Philosophy and
4
Division of Biological Sciences, University of
California at San Diego, La Jolla, California 92093, USA
.............................................................................................................................................................................
Brightness
—
the perception of an object’s luminance
—
arises from
complex and poorly understood interactions at several levels of
processing
1
. It is well known that the brightness of an object
depends on its spatial context
2
, which can include perceptual
organization
3
, scene interpretation
4
, three-dimensional
interpretation
5
, shadows
6
, and other high-level percepts. Here
we present a new class of illusion in which temporal relations
with spatially neighbouring objects can modulate a target
object’s brightness. When compared with a nearby patch of
constant luminance, a brief flash appears brighter with increas-
ing onset asynchrony. Simultaneous contrast, retinal effects,
masking, apparent motion and attentional effects cannot account
for this illusory enhancement of brightness. This temporal
context effect indicates that two parallel streams
—
one adapting
and one non-adapting
—
encode brightness in the visual cortex.
We report here a novel illusion in which temporal relationships
affect brightness perception. Two flashes appeared on either side of
a fixation point: one was brief (56 ms), the other long (278 ms;
Fig. 1a). Observers reported which flash appeared brighter. When
flashes of identical luminance had simultaneous onset, subjects
letters to nature
NATURE | VOL 428 | 22 APRIL 2004 | www.nature.com/nature854
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