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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

C2008 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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