LETTER Testing metabolic ecology theory for allometric scaling of tree size, growth and mortality in tropical forests Helene C. Muller-Landau, 1 * Richard S. Condit, 2 Jerome Chave, 3 Sean C. Thomas, 4 Stephanie A. Bohlman, 5 Sarayudh Bunyavejchewin, 6 Stuart Davies, 2 Robin Foster, 7 Savitri Gunatilleke, 8 Nimal Gunatilleke, 8 Kyle E. Harms, 2,9 Terese Hart, 10 Stephen P. Hubbell, 2,11 Akira Itoh, 12 Abd Rahman Kassim, 13 James V. LaFrankie, 14 , Hua Seng Lee, 15 Elizabeth Losos, 16 Jean- Remy Makana, 17 Tatsuhiro Ohkubo, 18 Raman Sukumar, 19 I-Fang Sun, 20 Nur Supardi M. N., 21 Sylvester Tan, 22 Jill Thompson, 23 Renato Valencia, 24 Gorky Villa Mun ˜ oz, 24 Christopher Wills, 25 Takuo Yamakura, 26 George Chuyong, 27 Handanakere Shivaramaiah Dattaraja, 19 Shameema Esufali, 8 Pamela Hall, 2,28 Consuelo Hernandez, 24 David Kenfack, 29 Somboon Kiratiprayoon, 30 Hebbalalu S. Suresh, 19 Duncan Thomas, 31 Martha Isabel Vallejo 32 and Peter Ashton 33 Abstract The theory of metabolic ecology predicts specific relationships among tree stem diameter, biomass, height, growth and mortality. As demographic rates are important to estimates of carbon fluxes in forests, this theory might offer important insights into the global carbon budget, and deserves careful assessment. We assembled data from 10 old- growth tropical forests encompassing censuses of 367 ha and > 1.7 million trees to test the theory’s predictions. We also developed a set of alternative predictions that retained some assumptions of metabolic ecology while also considering how availability of a key limiting resource, light, changes with tree size. Our results show that there are no universal scaling relationships of growth or mortality with size among trees in tropical forests. Observed patterns were consistent with our alternative model in the one site where we had the data necessary to evaluate it, and were inconsistent with the predictions of metabolic ecology in all forests. Keywords Asymmetric competition, demographic rates, forest dynamics, light availability, metabolic theory of ecology, resource competition theory, tree allometry. Ecology Letters (2006) 9: xxx–xxx 1 Department of Ecology, Evolution and Behavior, University of Minnesota, 1987 Upper Buford Circle, St Paul, MN 55108, USA 2 Smithsonian Tropical Research Institute, Unit 0948, APO-AA, 34002-0948, USA 3 Laboratoire Evolution et Diversite ´ Biologique UMR 5174, CNRS/UPS, ba ˆ timent IVR3, Universite ´ Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France 4 Faculty of Forestry, University of Toronto, 33 Willcocks St, Toronto, ON, Canada 5 Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, USA 6 Research Office, National Parks Wildlife and Plant Conservation Department, 61 Paholyothin Road, Chatuchak, Bangkok 10900, Thailand 7 The Field Museum, 1400 S. Lake Shore Drive, Chicago, IL 60605-2496, USA 8 Department of Botany, Faculty of Science, University of Peradeniya, Peradeniya 20400, Sri Lanka 9 Department of Biological Sciences, Louisiana State University, 202 Life Sciences Building, Baton Rouge, LA 70803-1715, USA 10 Wildlife Conservation Society, International Programs, 185th St. and Southern Blvd, Bronx, NY 10460, USA Ecology Letters, (2006) 9: xxx–xxx doi: 10.1111/j.1461-0248.2006.00904.x Ó 2006 Blackwell Publishing Ltd/CNRS. No claim to original US government works
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L E T T E RTesting metabolic ecology theory for allometric
scaling of tree size, growth and mortality in tropical
forests
Helene C. Muller-Landau,1*
Richard S. Condit,2 Jerome
Chave,3 Sean C. Thomas,4
Stephanie A. Bohlman,5 Sarayudh
Bunyavejchewin,6 Stuart Davies,2
Robin Foster,7 Savitri
Gunatilleke,8 Nimal Gunatilleke,8
Kyle E. Harms,2,9 Terese Hart,10
Stephen P. Hubbell,2,11 Akira
Itoh,12 Abd Rahman Kassim,13
James V. LaFrankie,14, Hua Seng
Lee,15 Elizabeth Losos,16 Jean-
Remy Makana,17 Tatsuhiro
Ohkubo,18 Raman Sukumar,19
I-Fang Sun,20 Nur Supardi
M. N.,21 Sylvester Tan,22 Jill
Thompson,23 Renato Valencia,24
Gorky Villa Munoz,24 Christopher
Wills,25 Takuo Yamakura,26
George Chuyong,27 Handanakere
Shivaramaiah Dattaraja,19
Shameema Esufali,8 Pamela
Hall,2,28 Consuelo Hernandez,24
David Kenfack,29 Somboon
Kiratiprayoon,30 Hebbalalu S.
Suresh,19 Duncan Thomas,31
Martha Isabel Vallejo32 and Peter
Ashton33
Abstract
The theory of metabolic ecology predicts specific relationships among tree stem
diameter, biomass, height, growth and mortality. As demographic rates are important to
estimates of carbon fluxes in forests, this theory might offer important insights into the
global carbon budget, and deserves careful assessment. We assembled data from 10 old-
growth tropical forests encompassing censuses of 367 ha and > 1.7 million trees to test
the theory’s predictions. We also developed a set of alternative predictions that retained
some assumptions of metabolic ecology while also considering how availability of a key
limiting resource, light, changes with tree size. Our results show that there are no
universal scaling relationships of growth or mortality with size among trees in tropical
forests. Observed patterns were consistent with our alternative model in the one site
where we had the data necessary to evaluate it, and were inconsistent with the
� 2006 Blackwell Publishing Ltd/CNRS. No claim to original US government works
among sites (Fig. 3). Among small individuals, mortality
decreased as diameter increased in all 10 tropical forests;
however, among large individuals, it variously continued to
decrease as diameter increased, ceased to change signifi-
cantly with diameter or increased with diameter. These
changes were reflected in changes in the exponents relating
mortality to diameter, which were larger for large individuals
than for small individuals at nine of 10 sites, with significant
differences at eight sites. Among large individuals, mortality
exponents were not significantly different from zero in five
of 10 sites, were significantly positive at three sites, and
significantly negative at two sites (Table 3). In general,
mortality patterns were less well approximated by power
functions than were growth patterns, even among small
individuals or large individuals alone.
The scaling of mortality rates with diameter was clearly
inconsistent with metabolic ecology predictions at all sites,
while consistent with our resource scaling alternative where
it could be evaluated. Specifically, the exponents relating
mortality to diameter for all individuals combined and for
small individuals alone were significantly different from the
)2/3 value predicted by metabolic theory (M11): the
exponents were significantly smaller at the driest site
Mudumalai, and significantly larger at all other sites
(Table 3). The values of the mortality exponent for small
individuals in Panama in both census intervals ()0.33 and
)0.26) were much closer to, and not significantly different
from, the prediction for this site based on the scaling of
resource availability ()0.19).
D I S C U S S I O N
Assessing metabolic ecology theory for tropical forests
The predictions of metabolic ecology theory regarding the
scaling of height, biomass, diameter growth and mortality
with tree diameter were all rejected for tropical forests.
Given that our alternative predictions based on the scaling
of resource availability were closer to the observed values
and were not rejected, we conclude that the implicit
(a)
0.02
0.05
0.10
0.20
0.50
1.00 (b) (c)
(d)
0.02
0.05
0.10
0.20
0.50
1.00 (e) (f)
Diameter (cm)
Dia
met
er g
row
th (
cm y
–1)
Dia
met
er g
row
th (
cm y
–1)
Dia
met
er g
row
th (
cm y
–1)
(g)
0.02
0.05
0.10
0.20
0.50
1.00
1 2 5 20 100
Diameter (cm)
(h)
1 2 5 20 100
Diameter (cm)
(i)
1 2 5 20 100
Mudumalai
Barro Colorado
Yasuni
Huai Kha KhaengIturi
Pasoh
La Planada
Lambir
Sinharaja
Figure 2 Mean absolute diameter growth rates as a function of diameter for all trees in 10 tropical forests. Vertical lines show 95% CI based
on bootstrapping over 50 · 50-m subplots. Thick dashed lines show power-function fits to the full data sets; thick solid lines show separate
fits to small (< 20-cm diameter) and large (‡ 20-cm diameter) individuals. When there are two intercensus intervals at the same site, the earlier
one is shown in black and the later one in grey. In the case of the Ituri site in the Congo, the results for the Edoro study area are in black and
those for the Lenda study area are in grey. Sites are ordered by increasing dryness. The fitted parameters are given in Table 3.
Testing metabolic ecology in tropical forests 9
� 2006 Blackwell Publishing Ltd/CNRS. No claim to original US government works
assumption of metabolic ecology that the scaling of gross
photosynthetic rates depends only on the scaling of the
potential for resource capture and redistribution (M3) is
faulty. Photosynthesis of tropical trees is commonly limited
by light availability (Chazdon & Pearcy 1986; Pearcy et al.
1994; Graham et al. 2003), and competition for light among
terrestrial plants is strongly size asymmetric (Weiner 1990).
This asymmetry and the resulting changes in light availability
with size need to be considered in order to understand the
scaling of gross photosynthetic rate with plant size in closed
canopy forests. The scaling predicted by metabolic ecology
may yet prove a good approximation for individual trees
grown in the absence of competition, and in systems in
which high mortality severely reduces competition. How-
ever, it cannot begin to explain variation in growth rates
found over the eight orders of magnitude variation in
individual biomass between understory saplings and canopy
trees within a forest.
Table 3 Results of power-function fits of absolute diameter growth rates and mortality rates to tree diameter in 10 tropical forests
Site
Census
interval
Data
set Ngrow Nmort Growth exponent (c) Mortality exponent (b)
Difference in
exponents (c ) b)
Sinharaja 1995–2000 All 170 955 195 627 0.679 (0.643 to 0.706)* 0.125 (0.043 to 0.175)* 0.554 (0.48 to 0.627)*
Small 164 889 188 555 0.687 (0.651 to 0.721)* )0.195 () 0.249 to ) 0.152)* 0.882 (0.8220 to 0.941)*
Large 6066 7072 0.539 (0.347 to 0.658)* 0.726 (0.367 to 0.959)* ) 0.187 () 0.521 to 0.147)*
La Planada 1997–2003 All 76 610 108 751 0.344 (0.302 to 0.407) ) 0.400 () 0.500 to ) 0.358)* 0.744 (0.655 to 0.832)*
Small 72 760 104 107 0.488 (0.462 to 0.514)* )0.558 ()0.596 to )0.522)* 1.045 (1 to 1.091)*
large 3850 4644 )0.205 ()0.452 to 0.122)* 0.399 ()0.329 to 0.804)* )0.603 ()1.238 to 0.032)*
Yasuni 1997–2004 All 115 827 146 941 0.645 (0.607 to 0.670)* )0.024 ()0.120 to 0.018)* 0.669 (0.592 to 0.745)*
Small 111 441 141 461 0.613 (0.583 to 0.644)* )0.335 ()0.380 to )0.289)* 0.949 (0.894 to 1.003)
large 4386 5480 0.618 (0.428 to 0.746)* 0.537 (0.046 to 0.853)* 0.081 ()0.353 to 0.514)*
Lambir 1992–1997 All 305 712 335 457 0.584 (0.567 to 0.600)* )0.213 ()0.269 to )0.161)* 0.797 (0.741 to 0.854)*
Small 294 450 323 502 0.620 (0.596 to 0.645)* )0.189 ()0.227 to )0.158)* 0.809 (0.766 to 0.852)*
Large 11 262 11 955 0.483 (0.395 to 0.557)* )0.462 ()0.744 to )0.138) 0.945 (0.631 to 1.258)
Pasoh 1990–1995 All 275 766 315 665 0.640 (0.621 to 0.657)* )0.103 ()0.159 to )0.063)* 0.743 (0.692 to 0.794)*
Small 267 926 306 925 0.747 (0.733 to 0.763)* )0.320 ()0.353 to )0.293)* 1.067 (1.034 to 1.101)*
Large 7840 8740 0.360 (0.265 to 0.438) )0.038 ()0.333 to 0.205)* 0.397 (0.115 to 0.68)*
1995–2000 All 263 845 310 004 0.677 (0.644 to 0.699)* )0.079 ()0.143 to -0.047)* 0.756 (0.701 to 0.811)*
Small 256 001 300 929 0.636 (0.615 to 0.658)* )0.303 ()0.334 to )0.277)* 0.94 (0.904 to 0.975)*
Large 7844 9075 0.554 (0.365 to 0.664)* 0.295 ()0.023 to 0.479)* 0.259 ()0.033 to 0.551)*
Barro
Colorado
1990–1995 All 192 091 235 745 0.680 (0.652 to 0.701)* )0.216 ()0.280 to )0.175)* 0.897 (0.839 to 0.954)*
Small 186 080 227 990 0.776 (0.751 to 0.799)* )0.329 ()0.365 to )0.297)* 1.105 (1.064 to 1.147)*
Large 6011 7755 0.275 (0.128 to 0.39) )0.193 ()0.541 to 0.046)* 0.468 (0.146 to 0.789)*
1995–2000 All 182 607 221 136 0.674 (0.651 to 0.692)* )0.217 ()0.278 to )0.177)* 0.891 (0.837 to 0.945)*
Small 175 866 213 315 0.673 (0.652 to 0.695)* )0.264 ()0.298 to )0.231)* 0.937 (0.898 to 0.976)*
Large 6741 7821 0.357 (0.23 to 0.452) )0.171 ()0.488 to 0.066)* 0.528 (0.229 to 0.826)*
Ituri-Edoro 1995–2000 All 136 613 152 827 0.751 (0.719 to 0.771)* )0.017 ()0.096 to 0.029)* 0.768 (0.701 to 0.836)*
Small 134 302 150 284 0.817 (0.782 to 0.848)* )0.197 ()0.281 to )0.144)* 1.015 (0.939 to 1.091)
Large 2311 2543 0.351 (0.165 to 0.478) 0.770 (0.499 to 1.224)* )0.418 ()0.813 to )0.023)*Ituri-Lenda 1995–2000 All 114 849 127 684 0.705 (0.671 to 0.727)* )0.236 ()0.328 to )0.171)* 0.941 (0.857 to 1.025)
Small 112 029 124 711 0.625 (0.582 to 0.668)* )0.38 ()0.484 to )0.316)* 1.005 (0.91 to 1.099)
Large 2820 2973 0.401 (0.247 to 0.528) 0.290 ()0.024 to 0.876)* 0.111 ()0.36 to 0.583)*
Huai Kha
Khaeng
1993–1999 All 52 949 75 573 0.202 (0.179 to 0.222)* )0.591 ()0.635 to -0.523)* 0.792 (0.732 to 0.852)*
Small 45 499 67 021 0.135 (0.108 to 0.162)* )0.926 ()0.974 to )0.881)* 1.062 (1.008 to 1.116)*
Large 7450 8552 0.213 (0.127 to 0.295)* )0.666 ()0.823 to )0.242) 0.879 (0.577 to 1.181)
Mudumalai 1992–1996 All 13 665 17 479 )0.259 ()0.377 to -0.194)* )1.175 ()1.319 to )1.111)* 0.916 (0.777 to 1.054)
Small 5443 8494 )0.485 ()0.598 to )0.367)* )1.027 ()1.144 to )0.922)* 0.541 (0.381 to 0.701)*
Large 8222 8985 )0.268 ()0.842 to 0.001)* 0.015 ()0.604 to 0.479)* )0.283 ()0.969 to 0.403)*
1996–2000 All 13 556 15 284 )0.032 ()0.076 to 0.004)* )0.901 ()1.064 to )0.793)* 0.869 (0.727 to 1.01)
Small 5094 6374 )0.422 ()0.495 to )0.34)* )0.805 ()0.936 to )0.612) 0.383 (0.204 to 0.562)*
Large 8462 8910 0.442 (0.250 to 0.572) 0.144 ()0.577 to 0.606)* 0.298 ()0.315 to 0.912)*
Separate fits were performed for data sets including all individuals, small individuals (< 20-cm diameter), and large individuals (‡ 20-cm diameter). Ngrow and
Nmort are the numbers of individuals included in the growth and mortality fits respectively. CI (95%) on the fitted exponents are based on 1000 bootstaps over
50 · 50-m subplots.
*Indicates values that are significantly different from the predictions of metabolic ecology theory (1/3 for the growth exponent, )2/3 for the mortality
exponent, 1 for the difference in exponents). When the exponents for small and large stems are significantly different, those estimates are boldface; when they
are not significantly different, the estimate for all stems is in boldface. Plots are ordered in increasing dryness (Table 1).
10 H. C. Muller-Landau et al.
� 2006 Blackwell Publishing Ltd/CNRS. No claim to original US government works
Taken together, the results suggest that one or both of
the assumptions that tree growth and mortality rates scale
with gross and mass-specific photosynthetic rates, respect-
ively (M9 and M11), must also be rejected for the forest as a
whole, although they may be appropriate for understory
individuals. No matter what the scaling of photosynthetic
rates with size, this combination of assumptions means that
the difference between the exponents of growth and
mortality (c ) b) should be exactly one (M12). For all trees
combined and especially for large individuals alone, the
difference between the growth and mortality exponents was
significantly > 1 in all but one closed-canopy forest (Ituri-
Lenda, Table 3). Thus, there does not exist any scaling of
photosynthesis with size that can reconcile these patterns
with the assumptions that tree growth and mortality rates
scale with gross and mass-specific photosynthetic rates
respectively. We hypothesize that these deviations result
mainly from strong size dependence of some mortality
threats independent of resource availability and photosyn-
thetic rates (Coomes et al. 2003). Size-dependent changes in
allocation to reproduction may also contribute to this
pattern (Thomas 1996; Wright et al. 2005). Among small
individuals in closed-canopy forests, in contrast, the
difference between growth and mortality exponents is
generally close to 1, although still significantly different
from one for most sites (Table 3). This suggests that for
trees in the understory, growth and mortality may scale with
photosynthesis approximately as hypothesized in metabolic
ecology theory; this idea is further supported by the success
of our alternative predictions for below-canopy individuals
that incorporate these assumptions regarding the relation-
ship of growth and mortality to photosynthesis, while
changing assumptions regarding how photosynthesis scales
with size.
Both basic metabolic ecology theory and the variation
upon it that we present here treat all individuals within the
forest as identical in terms of demographic parameters and
underlying physiological processes. These theories thus
ignore ontogenetic and interspecific variation, and essen-
tially average over it in making their predictions. Explicit
consideration of known size-dependent changes in main-
tenance costs could lead to better predictions for biomass
growth (Kooijman 2000). Several authors have already
begun to consider how ontogenetic changes in maintenance
costs might be incorporated into metabolic ecology theory
(West et al. 2001); what we need now is a synthesis that
considers interspecific as well as intraspecific variation in
maintenance with size. There is abundant evidence that
tropical tree species show large differences in stem allometry
(O’Brien et al. 1995), photosynthesis (Kitajima 1994) and
wood density (Muller-Landau 2004), as well as in onto-
genetic variation in physiology and allometry (Poorter et al.
0.002
0.0050.0100.020
0.0500.1000.200
0.5001.000
0.002
0.0050.0100.020
0.0500.1000.200
0.5001.000
Diameter (cm)
Mor
talit
y ra
te (
y–1)
Mor
talit
y ra
te (
y–1)
Mor
talit
y ra
te (
y–1)
0.002
0.0050.0100.020
0.0500.1000.200
0.5001.000
1 2 5 20 100
Diameter (cm)
1 2 5 20 100
Diameter (cm)
1 2 5 20 100
(a) (b) (c)
(d) (e) (f)
(g) (h) (i) Mudumalai
Barro Colorado
Yasuni
Huai Kha KhaengIturi
Pasoh
La Planada
Lambir
Sinharaja
Figure 3 Mean mortality rates as a function of
diameter for all trees in 10 tropical forests.
Vertical lines show 95% CI based on boot-
strapping over 50 · 50-m subplots. Thick
dashed lines show power-function fits to the
full data sets; thick solid lines show separate fits
to small (< 20-cm diameter) and large (‡ 20-cm
diameter) individuals. When there are two
intercensus intervals at the same site, the earlier
one is shown in black and the later one in grey.
In the case of the Ituri site in the Congo, the
results for the Edoro study area are in black and
those for the Lenda study area are in grey. Sites
are ordered by increasing dryness. The fitted
parameters are given in Table 3.
Testing metabolic ecology in tropical forests 11
� 2006 Blackwell Publishing Ltd/CNRS. No claim to original US government works
2003; Bohlman & O’Brien 2006). Thus, it is not surprising
that there is considerable interspecific variation in demo-
graphic rates (Condit et al. 1993, 1995). It is likely that both
interspecific differences and ontogenetic changes within a
given species are important influences on the observed size-
dependent patterns in growth and mortality for the forest as
a whole, and that a complete understanding of patterns
within and across sites will eventually require explicit
consideration of such variability.
Significance and future directions
The results presented here indicate that, despite qualitative
similarities in some patterns, there are no universal scaling
relationships of photosynthetic rates, growth rates, or
mortality rates with size among trees in forests. Instead,
there are significant quantitative differences in the allometric
scaling of demographic rates among forests, differences that
our work suggests are related proximally to among-site
variation in tree allometries and the scaling of light
availability. Of course, the scaling of light availability within
forests itself depends on the tree size distribution (Denslow
& Guzman 2000; Montgomery & Chazdon 2001), which
can be derived from the growth and mortality functions in
old-growth forests (Kohyama et al. 2003). Likewise, the
height and crown allometries of trees reflect plastic
responses to resource availability as well as ecological
sorting and natural selection of species for success within
the local resource competition environment (Iwasa et al.
1985; King & Maindonald 1999; Poorter et al. 2003;
Kitajima et al. 2005). Ultimately, we would like to not only
explain size distributions in terms of growth and mortality,
and growth and mortality in terms of allometries and light,
but also all of these patterns simultaneously from more
fundamental physiological and physical characteristics of
trees and sites.
We hypothesize that the key factor for understanding
variation in demographic rates among forests is the degree
to which large individuals can monopolize resources versus
the degree to which their abundance and resource mono-
polization are limited by other factors such as lethal
disturbances (Coomes et al. 2003) or relatively more
symmetric resource competition (Stoll et al. 2002). Among-
site variation in growth and mortality is greatest between
closed and open canopy forests. In open canopy forests, the
abundance of large trees is below its theoretical maximum –
in the two forests here because of the effects of fire and
elephants on the recruitment and mortality rates of large
trees (Sukumar et al. 2005). Where the densities of large trees
are limited and canopies are consequently more open,
competition for resources is likely to be relatively more
symmetric as small individuals have more access to
resources. Major disturbances, such as fires and cyclones,
that are important causes of large tree mortality and thus of
canopy openings in many forests occur over large areas at
long time intervals. Thus, it will take many years to
accumulate enough data to understand the frequencies of
such disturbances and accurately estimate long-term average
mortality and growth rates as a function of size.
A mechanistic explanation for size-dependent patterns of
tree growth and mortality is not only a fundamental
challenge in forest ecology, but also a problem of
considerable applied significance. Given the large role of
tropical forests in the global carbon cycle, it is important to
understand how increases or decreases in tree photosyn-
thetic rates because of carbon fertilization, nitrogen depos-
ition, increased temperature or other global forcings might
ultimately affect forest dynamics, and thereby net carbon
fluxes (Cramer et al. 2004; Wright 2005). A better mechan-
istic understanding of the processes governing tree growth
and mortality rates and their changes with tree size will shed
light not only on geographical variation in these patterns
today, but on how future forests are likely to change.
A C K N O W L E D G E M E N T S
We thank Joe Wright, Steve Pacala, Bert Leigh and three
anonymous referees for helpful comments on the manu-
script. We gratefully acknowledge the contributions of the
many dedicated people and generous funders that have
made possible the forest dynamics plot data sets upon which
this research is based. We especially thank the US National
Science Foundation for funding the workshop at which this
study was initiated (DEB-9806828). HCM thanks the
University of Minnesota and the National Center for
Ecological Analysis and Synthesis (a centre funded by
NSF and the state of California) for support.
R E F E R E N C E S
Baker, T.R., Swaine, M.D. & Burslem, D. (2003). Variation in
tropical forest growth rates: combined effects of functional
group composition and resource availability. Perspect. Plant Ecol.
Evol. Syst., 6, 21–36.
Bohlman, S.A. & O’Brien, S.T. (2006). Allometry, adult stature and
regeneration requirements of 65 tree species on Barro Colorado