Allometric Models for Predicting Aboveground Biomass in Two Widespread Woody Plants in Hawaii

Abstract

Allometric models are important for quantifying biomass and carbon storage in terrestrial ecosystems. Generalized allometry exists for tropical trees, but species- and site-specific models are more accurate. We developed species-specific models to predict aboveground biomass in two of the most ubiquitous natives in Hawaiian forests and shrublands, Metrosideros polymorpha and Dodonaea viscosa. The utility of the M. polymorpha allometry for predicting biomass across a range of sites was explored by comparing size structure (diameter at breast height vs. tree height) of the trees used to develop the models against trees from four M. polymorpha-dominated forests along a precipitation gradient (1630-2380 mm). We also compared individual tree biomass estimated with the M. polymorpha model against existing generalized equations, and the D. viscosa model with an existing species-specific model. Our models were highly significant and displayed minimal bias. Metrosideros polymorpha size structures from the three highest precipitation sites fell well within the 95% confidence intervals for the harvested trees, indicating that the models are applicable at these sites. However, size structure in the area with the lowest precipitation differed from those in the higher rainfall sites, emphasizing that care should be taken in applying the models too widely. Existing generalized allometry differed from the M. polymorpha model by up to 88 percent, particularly at the extremes of the data range examined, underestimating biomass in small trees and overestimating in large trees. The existing D. viscosa model underestimated biomass across all sizes by a mean of 43 percent compared to our model. The species-specific models presented here should enable more accurate estimates of biomass and carbon sequestration in Hawaiian forests and shrublands.

Full text

BIOTROPICA 40(3): 313–320 2008 10.1111/j.1744-7429.2007.00383.x
Allometric Models for Predicting Aboveground Biomass in Two Widespread Woody
Plants in Hawaii
Creighton M. Litton1
Department of Natural Resources and Environmental Management, University of Hawai’i at Manoa, 1910 East-West Rd., Honolulu, Hawaii
96822, U.S.A.
and
J. Boone Kauffman
USDA Forest Service, Institute of Pacific Islands Forestry, 60 Nowelo St, Hilo, Hawaii 96720, U.S.A.
ABSTRACT
Allometric models are important for quantifying biomass and carbon storage in terrestrial ecosystems. Generalized allometry exists for tropical trees, but species- and
site-specific models are more accurate. We developed species-specific models to predict aboveground biomass in two of the most ubiquitous natives in Hawaiian forests
and shrublands, Metrosideros polymorpha and Dodonaea viscosa. The utility of the M. polymorpha allometry for predicting biomass across a range of sites was explored
by comparing size structure (diameter at breast height vs. tree height) of the trees used to develop the models against trees from four M. polymorpha-dominated forests
along a precipitation gradient (1630–2380 mm). We also compared individual tree biomass estimated with the M. polymorpha model against existing generalized
equations, and the D. viscosa model with an existing species-specific model. Our models were highly significant and displayed minimal bias. Metrosideros polymorpha
size structures from the three highest precipitation sites fell well within the 95% confidence intervals for the harvested trees, indicating that the models are applicable
at these sites. However, size structure in the area with the lowest precipitation differed from those in the higher rainfall sites, emphasizing that care should be taken in
applying the models too widely. Existing generalized allometry differed from the M. polymorpha model by up to 88 percent, particularly at the extremes of the data
range examined, underestimating biomass in small trees and overestimating in large trees. The existing D. viscosa model underestimated biomass across all sizes by a
mean of 43 percent compared to our model. The species-specific models presented here should enable more accurate estimates of biomass and carbon sequestration
in Hawaiian forests and shrublands.
Key words: Allometry; Dodonaea viscosa; generalized allometric models; Hawaii Volcanoes National Park; Metrosideros polymorpha; nonlinear regression.
THE CYCLING OF CARBON IN FOREST ECOSYSTEMS IS A TOPIC OF
CONSIDERABLE IMPORTANCE WITH rising atmospheric CO2concen-
trations, global climate change, and the poorly defined role that
terrestrial ecosystems play in mitigating or exacerbating these phe-
nomena. In addition, increasing value is being placed on ecosystem
services in forests and carbon cycling is among the most important
of these services. Aboveground biomass—the amount of organic
matter in living and dead plant material—is a critical component
of the carbon cycle in forest ecosystems, providing both short- and
long-term carbon sequestration. Tropical forests, in particular, are
major components of the terrestrial carbon cycle, accounting for
26 percent of global carbon storage in biomass and soils (Dixon
et al. 1994, Geider et al. 2001, Grace 2004). Yet, accurate estimates
of carbon sequestration in tropical forests are lacking for many ar-
eas, due in large part to a paucity of appropriate allometric models
for predicting biomass in species-rich tropical ecosystems (Chave
et al. 2005). Due to the high species diversity in tropical forests,
much attention has been placed on developing generalized allomet-
ric models for tropical trees (Brown 1997, Zianis & Mencuccini
2004, Chave et al. 2005, Pilli et al. 2006). However, the use of
generalized equations can lead to a bias in estimating biomass for
a particular species (Clark et al. 2001, Cairns et al. 2003, Chave
et al. 2004, Litton et al. 2006, Pilli et al. 2006), although recent
Received 3 May 2007; revision accepted 3 September 2007.
1Corresponding author; e-mail: litton@hawaii.edu
approaches incorporating data on wood density hold more promise
(Chave et al. 2005).
In many Hawaiian forests, generalized allometric equations do
not accurately predict aboveground biomass (Litton et al. 2006).
However, because tree diversity is low in Hawaii compared to the
continental tropics, species-specific allometry can be more easily
developed and applied to estimate carbon sequestration in biomass.
Two of the primary woody species in Hawaiian forests and shrub-
lands are Metrosideros polymorpha Gaud. and Dodonaea viscosa Jacq.,
respectively. Both of these species have wide distributions across
extreme climatic gradients, ranging from sea level to >2000 m
(Wagner et al. 1999), and they frequently account for most of
the individuals and biomass in native-dominated areas (Aplet &
Vitousek 1994, Crews et al. 1995, Vitousek 2004, Mueller-
Dombois 2006).
Allometric equations exist for predicting aboveground biomass
in M. polymorpha in Hawaii (Aplet & Vitousek 1994, Raich et al.
1997), and in the pantropical D. viscosa in Hawaii and elsewhere
(Harrington 1979, Aplet et al. 1998). However, the provenance of
the individuals used in the development of these earlier models is
unclear and, therefore, the geographic locality to which the models
are most applicable is largely unknown. Moreover, existing equa-
tions are limited in their utility because they require measurements
of both individual plant basal diameter and total height to predict
biomass. Most inventory studies, in turn, do not commonly mea-
sure these variables but instead measure diameter at breast height
C2008 by The Association for Tropical Biology and Conservation
No claim to original US government works
313
THE JOURNAL OF TROPICAL BIOLOGY AND CONSERVATION

314 Litton and Kauffman
(dbh) and, at times, commercial height for trees, and basal diameter
for shrubs (Chave et al. 2005, Segura & Kanninen 2005). As with
most tropical forests, it is difficult and time consuming to accurately
measure individual tree heights in closed canopies dominated by M.
polymorpha.
Our objectives here were to: (1) develop allometric models
to predict M. polymorpha individual tree foliage, wood, and total
aboveground biomass from measurements of dbh using an existing
data set of harvested trees (Raich et al. 1997); (2) develop allom-
etry from destructive harvest to predict foliage, wood, and total
aboveground biomass for D. viscosa individuals from measurements
of basal diameter; (3) determine if the allometry developed for M.
polymorpha in this study is applicable across the range of climatic
conditions where this species is found, by comparing size structure
relationships (dbh vs. tree height) between trees from which the
equations were developed and trees from each of four sites along
a precipitation gradient (1630–2380 mm); (4) determine if our
species-specific allometry for M. polymorpha differs from existing
generalized equations for tropical trees (Brown 1997, Chave et al.
2005); and (5) determine if the allometry developed for D. viscosa
in this study differs from an existing model developed in Hawaii,
which relies on both basal diameter and plant height (Aplet et al.
1998).
METHODS
Metrosideros polymorpha
ALLOMETRY.—Metrosideros polymor-
pha is a Hawaiian endemic, the only native dominant canopy species
present in wet forests, and one of only two found in mesic forests
(Mueller-Dombois 2006). In mesic to wet forests, M. polymorpha is
the most common pioneer species occupying early-successional sites
and also maintains dominance in later seral communities (Wagner
et al. 1999, Mueller-Dombois 2006), accounting for ≥75 percent
of total canopy coverage across large gradients in climate and sub-
strate age (Crews et al. 1995). In drier forests, M. polymorpha is the
primary pioneer species, but can be replaced by other taxa at later
seral stages (Stemmermann & Ihsle 1993).
A subset of an existing data set of harvested trees, originally an-
alyzed in Raich et al. (1997), was used to develop allometric models
for predicting M. polymorpha foliage, wood, and total aboveground
biomass from dbh. Harvested trees represent a cumulated data set
from the Island of Hawaii, U.S.A. The dbh range of trees com-
prising the data set was 0.3–33.3 cm (Table 1). Details on harvest
locations are not available, but all trees were harvested from the
windward side of the island. We used all trees >1.33 m height and
>0.3cmdbh,reducingtheoriginaldatasetfrom44to30indi-
viduals for leaf and total biomass and to 36 individuals for wood
biomass. For harvested trees, basal diameter was measured in lieu of
dbh. For these trees, we estimated dbh from basal diameter using a
taper equation (r2=0.96) following Raich et al. (1997).
The same 36 harvested trees used to develop the allometric
models were used to develop a dbh versus total tree height curve.
We then randomly sampled dbh and height from a total of 170 trees
TABLE 1. Allometric models for predicting aboveground live biomass in individ-
uals of Metrosideros polymorpha and Dodonaea viscosa in Hawaii.
Dependent variable Na(SE) b(SE) MSE R2
Metrosideros polymorpha
Leaf biomass (kg) 30 0.09 (0.03) 1.45 (0.11) 0.85 0.94
Wood biomass (kg) 36 0.53 (0.21) 2.00 (0.12) 1166.2 0.96
Total tree biomass (kg) 30 0.88 (0.41) 1.86 (0.14) 1178.8 0.95
Dodonaea viscosa
Leaf biomass (g) 20 0.08 (0.10) 2.25 (0.40) 596.0 0.78
Wood biomass (g) 20 0.08 (0.06) 2.63 (0.26) 2396.9 0.93
Total shrub biomass (g) 20 0.13 (0.09) 2.55 (0.21) 2673.1 0.95
Note: Models for all dependent variables are of the form Y=aXbwhere Yis
the dependent variable (kg dry weight for M. polymorpha and g dry weight for
D. viscosa), Xis the predictor variable (dbh (cm) for M. polymorpha and basal
diametes (mm) for D. viscosa), and aand bare constants in the equation. SE
is the asymptotic standard error of the parameter estimate, MSE is the mean
square of the error, and R2is the coefficient of determination. All models were
highly significant (P<0.001).
in four areas along a precipitation gradient in Hawaii Volcanoes Na-
tional Park on the windward side of the Island of Hawaii (Table 2),
and developed separate dbh-height curves for each area. Sites along
the gradient were within 5 km of each other and ranged from a low
of 1630 mm mean annual precipitation (MAP) at 440 m elevation,
to 2380 mm MAP at 815 m. All sites were located on relatively
young (400–750 yr) pahoehoe lava flows (Trusdell et al. 2005). To
determine if the allometric models we developed could be used at
these sites that represent variation in climate and growth form, we
compared the dbh-height curves from each site to the 95% CIs for
TABLE 2. Diameter at breast height versus total tree height models for Met-
rosideros polymorpha trees used to develop the allometric models in
Table 1 (Harvest), four sites across a precipitation gradient in Hawaii
Volcanoes National Park, and all sites combined.
Site dbh range Na(SE) b(SE) MSE R2
Harvest 0.3–33.3 36 21.89 (1.84) 0.071 (0.012) 3.69 0.92
2380 mm 4.7–83.5 25 23.80 (1.54) 0.039 (0.006) 4.62 0.91
1930 mm 4.0–44.0 75 22.82 (1.23) 0.053 (0.005) 3.27 0.84
1730 mm 2.7–60.0 38 15.58 (1.26) 0.045 (0.007) 2.14 0.85
1630 mm 2.5–70.0 32 9.39 (0.44) 0.074 (0.009) 0.81 0.84
All sites 0.3–83.5 206 17.70 (0.92) 0.062 (0.007) 12.45 0.60
Note: Models for all dependent variables are of the form Y=a∗(1 −exp(−b
×X)) where Yis the dependent variable (total tree height (m)), Xis the
predictor variable (dbh (cm)) and aand bare constants in the equation. SE
is the asymptotic standard error of the parameter estimate, MSE is the mean
square of the error, and R2is the coefficient of determination. All models were
highly significant (P<0.001).

Estimating Biomass in Hawaiian Woody Plants 315
the curve developed from the harvested trees (i.e., we determined if
the curve for individual sites fell within the 95% CIs of the harvested
tree curve across the entire data range).
Total biomass estimates for individual plants derived from the
allometric model developed here for M. polymorpha were compared
to existing generalized equations for tropical trees (Brown 1997,
Chave et al. 2005) by plotting the models on a common axis, and
by estimating biomass in each model across a range of dbhs and
calculating percent difference. In all model comparisons we used
a common range of dbhs (5–35 cm) that encompassed the entire
range of the harvested M. polymorpha trees (0.3–33 cm). This is well
within the range of dbhs used to construct the generalized allometric
models—the Brown (1997) and Chave et al. (2005) models were
constructed from trees ranging in dbh from 4–148 and 5–156 cm,
respectively.
The Brown (1997) and Chave et al. (2005) models were devel-
oped separately for moist and wet climatic zones, defined as 1500–
3500 mm and >3500 mm MAP, respectively. The Brown (1997)
models require only dbh (cm) to predict total aboveground biomass
(kg dry weight). However, the Chave et al. (2005) models require
species-specific information on wood specific gravity and provide
a set of equations for each climatic zone that requires either dbh
alone or both dbh and total tree height to predict total aboveground
biomass. We used a wood specific gravity of 0.69 g/cm3for M. poly-
morpha (R.F. Hughes, pers. comm.) when estimating aboveground
biomass with the Chave et al. (2005) generalized models.
The generalized allometric models used to predict total above-
ground biomass (kg dry weight) in individual trees were:
Brown Moist : exp( −2.134 +2.530 ×ln(D)) (1)
BrownWet:21.297 −6.953 ×D+0.740 ×D2(2)
Chave Moist : ρ×exp(−1.499 +2.148 ×ln(D)+0.207
×(ln(D))2−0.0281 ×(ln( D))3)(3)
Chave Wet : ρ×exp(−1.239 +1.980 ×ln( D)+0.207
×(ln(D))2−0.0281 ×(ln( D))3)(4)
Chave Moist : 0.0509 ×ρD2H(5)
Chave Wet : 0.0776 ×(ρD2H)0.94 (6)
where Dis diameter at breast height (cm), His total tree height (m),
and ρis wood specific gravity (g/cm3).
Dodonaea viscosa
ALLOMETRY.—Dodonaea viscosa is a pantropical
species that typically occurs as a shrub in Hawaii, but can also be a
small tree (Stemmermann & Ihsle 1993, Wagner et al. 1999). Much
like M. polymorpha, this species occupies, and often dominates,
a wide variety of sites ranging from pastures, coastal dunes, low
elevation and subalpine shrublands, dry, mesic and wet forests, to
open and recently disturbed areas, from sea level to 2350 m elevation
in both early and late seral stages (Wagner et al. 1999).
Twenty individuals of D. viscosa ranging from 4.8 to 29.1 mm
basal diameter were harvested from Hawaii Volcanoes National
Park at elevations of 440–500 m to develop allometric models for
predicting foliage, wood, and total aboveground biomass from basal
diameter. Harvest sites were in open shrubland/grassland where D.
viscosa is a dominant component of the landscape. We measured
basal diameter (mm; measured at ground level) and total height
(cm) for each individual, cut the shrubs at ground level, transported
entire plants to the laboratory, dried all material to a constant weight
in a forced air oven, separated biomass into foliage and wood, and
weighed all dried samples to the nearest 0.01 g.
We compared total aboveground biomass estimates for indi-
vidual plants from the allometric model developed here for D.
viscosa, with an existing species-specific equation presented by Aplet
et al. (1998) across the entire range of harvested basal diameters
(5–29 mm) by plotting both models on a common axis. The Aplet
et al. (1998) model requires both basal diameter and shrub height
to predict total aboveground biomass, and was developed from an
unknown number of individuals of unknown sizes harvested from
unknown locations on the leeward side of the island of Hawaii (R.F.
Hughes, pers. comm.). Thus, it is possible that our model com-
parison is somewhat arbitrary because it may extend the use of the
Aplet et al. (1998) equation to individuals outside of its intended
size range. In light of this, we emphasize the comparative nature
of this exercise and aim to demonstrate differences and similarities
between the two models that will allow future researchers to make
informed decisions about appropriate model selection.
STATISTICAL ANALYSES.—Nonlinear regression techniques were used
to develop allometric models to predict individual plant foliage,
wood, and total aboveground biomass from dbh (cm) for M. poly-
morpha and basal diameter (mm) for D. viscosa in SPSS 10.0 for
Windows (SPSS Inc., Chicago, IL, U.S.A.) using untransformed
data and a power function of the form:
Y=aXb(7)
where Y=the dependent variable (e.g., aboveground foliage
biomass; kg dry weight for M. polymorpha and g dry weight for
D. viscosa), X=the independent variable (dbh [cm] for M. poly-
morpha and basal diameter [mm] for D. viscosa), and aand bare,
respectively, the scaling coefficient (or allometric constant) and scal-
ing exponent derived from the regression fit to the empirical data.
We also explored the use of log transformed linear models for
estimating biomass. While many authors note that the nonlinear
power function in equation (7) is the most common mathematical
model used in biomass studies (e.g., Ter-Mikaelian & Korzukhin
1997, Zianis & Mencuccini 2004, Pilli et al. 2006), it has become
conventional practice to linearize data by means of logarithmic
transformation (Niklas 2006). However, Niklas (2006) argues that
log transforming data does not necessarily provide a better fit of data
to a regression model compared to nonlinear techniques, and that fi-
nal model choice should be based on analyses of residuals. In all cases
we used nonlinear models because: (1) all of the relationships we
examined were nonlinear; (2) linear regression techniques using log
transformed data introduce a systematic bias that must be corrected
when back-transforming values (Sprugel 1983, Duan 1983); and

316 Litton and Kauffman
(3) for our data nonlinear models always resulted in better model
fit than log transformed linear models based on the goodness-of-fit
parameters outlined below, including analysis of residuals.
For the M. polymorpha dbh versus tree height curves, nonlinear
regression techniques were also used with untransformed data and
an exponential rise to a maximum function
Y=a(1 −exp(−bX)) (8)
where Y=the dependent variable (tree height (m)), X=the in-
dependent variable (dbh [cm]), and aand bare, respectively, the
scaling coefficient and scaling exponent derived from the regression
fit to the empirical data. A variety of models are purported to pro-
vide superior fit for constructing dbh-height curves (e.g.,Huang
et al. 1992, Fang & Bailey 1998), including the exponential model
used here (Meyer 1940). Feng and Bailey (1998) compared 33 dbh-
height models for 8352 tropical island trees and found the exponen-
tial model in equation (8) to be the best solution. Many dbh-height
models are merely slight variations of equation (8) that add one or
more parameters to the regression equation. We ultimately chose
equation (8) for its simplicity and ease of use and because for our
data it provided at least as good a fit as other commonly used mod-
els such as the Chapman-Richards and Weibull-type functions (see
Huang et al. 1992).
Goodness of fit for all regression equations was determined
by examining P-values, the mean square of the error (MSE), the
coefficient of determination (R2), the coefficient of variation (CV),
and by plotting the residuals (observed minus predicted values)
against dbh. R2was calculated as 1 minus the sum of squares of the
residuals (SSR) divided by the total sum of squares of deviations
from the overall mean (Corrected SST). The best-fit models were
selected as having the highest R2;thelowestP-value, MSE, and CV;
and the least amount of bias for under or over prediction of biomass
across the entire range of sizes.
RESULTS
Metrosideros polymorpha
ALLOMETRY.—Diameter at breast
height was an effective predictor of all categories of aboveground
live biomass in M. polymorpha (Fig. 1A–C), with R2values rang-
ing from 0.94 to 0.96 (P<0.01 for all models; Table 1). Larger
diameter trees exhibited greater error variance than smaller trees
(Fig. 1D–F), and such heteroscedasticity is common for biomass
data (Parresol 1993). However, plots of the residuals demonstrated
that there was no large or systematic bias toward over- or underesti-
mation of biomass at any dbh within the range used to develop the
models.
Size structure models (dbh vs. tree height) for the harvest
trees and four sites along the precipitation gradient were all highly
significant (P<0.01), with R2values of 0.84–0.92 (Table 2).
Maximum tree heights occurred at dbhs of ∼30–40 cm, regardless
of site. The acoefficient in each model specifies the maximum tree
height for a given site (Table 2), and maximum heights were very
similar for the harvest trees and the two high precipitation sites but
FIGURE 1. Allometric models for predicting (A) leaf, (B) wood, and (C) total
aboveground tree biomass (kg) from dbh (cm) in individuals of Metrosideros
polymorpha, and biomass residuals (D–F; observed minus predicted values).
Equation parameters are given in Table 1.
were 29 and 57 percent lower at the 1730 and 1630 mm MAP
sites, respectively. The dbh versus height curves revealed that there
was little difference between size structures of the harvest trees and
trees from the two highest precipitation sites, while size structures
for the two lowest precipitation sites varied somewhat (Fig. 2). Size
structure curves for all sites except the lowest precipitation area fell
well within the 95% CIs for the model derived from the harvested
trees.
FIGURE 2. Diameter versus tree height relationships for M. polymorpha trees
that were harvested to develop the allometric models for predicting biomass
(Harvest, bold solid line), and M. polymorpha trees from four sites across a
precipitation gradient in Hawaii Volcanoes National Park. The solid gray lines
are the 95% CIs for the dbh versus height curve based on the harvested trees.
Regression parameters are given in Table 2.

Estimating Biomass in Hawaiian Woody Plants 317
We found large differences in aboveground biomass estimates
for individual trees when comparing the results of the allometric
model developed in this study with generalized tropical tree models
across a range of 5–35 cm dbh (Fig. 3A–C). All generalized models
greatly underestimated biomass at smaller dbhs (<15 cm) and
tended to greatly overestimate biomass at larger dbhs (>25 cm),
with better agreement at intermediate dbhs (Table S1). No single
generalized model performed well across the entire range of dbhs.
The Brown (1997) model for wet climates displayed the least bias
at dbhs >25 cm (4–12%), but greatly underestimated biomass
FIGURE 3. Comparison of allometric model fit for M. polymorpha total above-
ground biomass in individual trees between that developed here (Harvest, bold
line) and existing generalized equations for moist (Moist, dotted line) and wet
(Wet, dashed line) tropical forests. Existing equations are from: (A) Brown
(1997); (B) Chave et al. (2005) with dbh alone as the predictor variable; and (C)
Chave et al. (2005) with both dbh and total tree height as predictor variables.
FIGURE 4. Allometric models for predicting (A) leaf, (B) wood, and (C) total
aboveground shrub biomass (g) from basal diameter (mm) in individuals of
Dodonaea viscosa, and biomass residuals (D–F; observed minus predicted values).
Equation parameters are given in Table 1.
at dbhs <20 cm (23–71%). No generalized model was a good
fit to small diameter individuals. The Chave et al. (2005) model
for wet climates based on both dbh and tree height displayed the
least amount of bias across the entire data range for estimating
aboveground biomass in M. polymorpha.
Dodonaea viscosa
ALLOMETRY.—Basal diameter alone was an ef-
fective predictor variable for estimating aboveground biomass in D.
viscosa (Fig. 4A–C). Models were highly significant for all biomass
categories (P<0.01), with R2values of 0.78–0.95 (Table 1). Model
fit was better for wood and total biomass than foliage biomass. How-
ever, all models showed minimal bias across the entire range of basal
diameters (Fig. 4D–F).
The allometric model developed in this study for predicting
total aboveground biomass in D. viscosa individuals differed from
an existing model (Aplet et al. 1998) by an average of 43 percent
across the entire data range (5–29 mm basal diameter). The Aplet
et al. (1998) model consistently underestimated biomass, and un-
derestimates were particularly large (up to 80%) at basal diameters
<18 mm (Fig. 5).
DISCUSSION
Metrosideros polymorpha
ALLOMETRY.—The allometric models
presented here predict biomass accurately in M. polymorpha individ-
uals across the range of dbhs used to develop the equations (0–33
cm; Fig. 1). Extrapolating beyond the data range used in model con-
struction (i.e.,>33 cm dbh) may cause bias in estimating biomass
for larger trees, which is problematic because the largest trees at a

318 Litton and Kauffman
FIGURE 5. Comparison of allometric model fit for Dodonaea viscosa total
aboveground biomass in individual shrubs between that developed here with
basal diameter as the sole predictor variable (Harvest, bold line) and an existing
allometric equation from Aplet et al. (1998), which uses both basal diameter and
total shrub height (Aplet, dotted line).
given site can account for most of the biomass in the continental
tropics (Brown & Lugo 1984). However, M. polymorpha-dominated
forests in Hawaii do not contain many individuals >33 cm dbh
as is often the case in the continental tropics. In the same relatively
pristine forests in Hawaii Volcanoes National Park where we quan-
tified size structures, prior work demonstrated that M. polymorpha
comprises 94 percent of the trees in these forests, and <8percent
of M. polymorpha have dbhs exceeding 33 cm and <1.5 percent
have dbhs in excess of 50 cm (Ainsworth 2007).
The size structure analysis indicates that care should be taken in
applying these models to estimate biomass across the entire climatic
gradient in which this species is found (Fig. 3). In particular, the
models we developed are likely to be less accurate in predicting
biomass at the driest sites because of differences in size structure.
The allometric models developed here appear to be adequate for
predicting biomass in sites receiving >1700 mm MAP, as size
structure curves for all sites above this MAP fell well within the 95%
CIs for the curve derived from the harvested trees. However, total
yearly precipitation may not be useful at all sites for determining the
applicability of the models, due to interactions between substrate
age (i.e., soil development) and precipitation in determining plant
available water. We suggest that the most reliable way to determine
if the models are appropriate at a given site is to sample a random
set of trees to construct a size structure curve, and then compare the
curve to that presented here for the harvested trees (Table 2).
Prior studies have demonstrated that a single allometric model
based solely on dbh can accurately predict biomass in Eucalyptus
pilularis across sites that vary in MAP and temperature by 55 and
35 percent, respectively, as well as tree size, wood density, and
size structure (Montagu et al. 2005). This is particularly useful for
estimating biomass and carbon sequestration across large spatial
scales using forest inventory data. Thus, even though we found
differences in size structure as a result of precipitation, the allometric
models we developed here may be applicable at drier sites depending
on the desired accuracy or information needed. However, the degree
of departure would be verifiable only by harvesting individuals from
drier areas and comparing predicted versus actual biomass estimates.
The allometric models we present for predicting aboveground
biomass in foliage and wood for M. polymorpha rely on dbh alone,
while earlier models required estimates of both basal diameter and
total tree height (Aplet & Vitousek 1994, Raich et al. 1997). The
practicality of measuring only dbh makes the equations presented
here more attractive and more likely to be used by both land man-
agers and researchers. In addition, dbh measurements are typically
more accurate, with measurement error for dbh at 3 percent while
that for tree height is of the order of 10–15 percent (Montagu
et al. 2005). Moreover, measuring tree height is a labor intensive
and costly endeavor in closed canopy evergreen tropical forests where
tree heights cannot be easily seen from within the sampled stand.
Finally, most private, state, and federal forest inventories typically
measure dbh for individual plots and trees, but do not commonly
measuretreeheight.
The models presented here were based on harvested trees, pre-
cluding the need for estimates of specific wood gravity. Generalized
equations for tropical trees have recently been improved by incor-
porating wood density information as a model parameter (Chave
et al. 2005). These equations did not fit the M. polymorpha data well
(Fig. 4), and earlier work has also shown that generalized allometric
equations do not accurately predict biomass in Hawaiian dry forests
(Litton et al. 2006). Our estimate of M. polymorpha wood density
(0.69) is a mean value derived from multiple samples taken at one
site (R.F. Hughes, pers. comm.), and wood density can vary across
sites for a given species, as well as within a given site (Montagu
et al. 2005). Better estimates of wood specific gravity for a par-
ticular site should, theoretically, improve the ability of generalized
models to accurately predict aboveground biomass. However, wood
specific gravity is a constant parameter in the equation for a given
species at a given site. Therefore, unless wood density for each tree
is measured, the pattern we observed (i.e., generalized equations do
not compare well with our species-specific model) would hold true
even if more accurate wood density data were available (i.e.,theline
would shift to the left or the right, but the shape of the line in Fig.
4C would not change).
Dodonaea viscosa
ALLOMETRY.—Basal diameter accurately pre-
dicted aboveground biomass in the shrub D. viscosa. In contrast,
height was not as good a predictor of biomass, either alone or in
combination with basal diameter (R2<0.75; data not shown). As
before, simple measurements of diameter are not only easier to take
in the field but are also more likely to exist in historical data.
Little information is available on the species-specific equations
for D. viscosa presented in Aplet et al. (1998). In particular, it
is unknown how many individuals were sampled, what the size
distribution was for harvested individuals, or even where individuals
were harvested. Despite this, their model has a very similar shape to
that developed here. However, it underestimates biomass across the
entire data range, and this may well be a result of differences in site
characteristics and, therefore, growth form between the two areas
where plants were harvested.

Estimating Biomass in Hawaiian Woody Plants 319
In conclusion, the species-specific allometric models we present
for quantifying aboveground biomass in two of the most widespread
woody plants in Hawaiian forests and shrublands should signifi-
cantly improve capacity to accurately estimate biomass, fuel loads,
and carbon sequestration in Hawaiian terrestrial ecosystems. In par-
ticular, the use of dbh as a sole predictor variable for M. polymorpha
and basal diameter for D. viscosa will facilitate the use of inventory
data to examine temporal and spatial variability in ecosystem struc-
ture and function. In addition, our models can be used to predict
aboveground biomass in foliage and wood separately. The utility
of estimating biomass by component is readily apparent for stud-
ies of carbon sequestration and fire dynamics, as foliage and wood
have different residence times and fuel characteristics. However, care
should be taken in applying the allometric models developed in this
study to other sites within the archipelago without knowledge of
size structures. We recommend that dbh versus tree height curves be
constructed for the area of interest and compared to that presented
in this study to determine how appropriate the allometric models
are for a given site.
ACKNOWLEDGMENTS
Support for this study was provided by the Joint Fire Sciences
Program (Project No. 03–3-3–15) and the USDA Forest Service,
Pacific Southwest Research Station. We would like to thank R. Loh
of Hawaii Volcanoes National Park for facilitating the work. A.
Ainsworth, M. Tetteh, C. Cole, C. Dupuis, J. Shackeroff, D. Riley,
and J. Carbon provided valuable field assistance. J. Raich kindly
shared the original data used to develop the allometric models for
M. polymorpha.
SUPPLEMENTARY MATERIAL
The following supplementary material for this article is available
online at: www.blackwell-synergy.com/loi/btp
Table S1. Percent difference in Metrosideros polymorpha predicted to-
tal aboveground biomass for individual trees between that estimated
with the allometric model developed here versus that estimated with
generalized models for tropical trees.
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