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Contributed Paper
A Matrix-Calibrated Species-Area Model for
Predicting Biodiversity Losses Due to Land-Use
Change
LIAN PIN KOH∗AND JABOURY GHAZOUL
Institute of Terrestrial Ecosystems, ETH Z¨
urich, CHN G 74.2, Universit¨
atstrasse 16, 8092 Z¨
urich, Switzerland
Abstract: Application of island biogeography theory to prediction of species extinctions resulting from
habitat loss is based on the assumption that the transformed landscape matrix is completely inhospitable
to the taxa considered, despite evidence demonstrating the nontrivial influence of matrix on populations
within habitat remnants. The island biogeography paradigm therefore needs refining to account for specific
responses of taxa to the area of habitat “islands” and to the quality of the surrounding matrix. We incor-
porated matrix effects into island theory by partitioning the slope (zvalue) of species–area relationships
into two components: γ, a constant, and σ, a measure of taxon-specific responses to each component of
a heterogeneous matrix. We used our matrix-calibrated model to predict extinction and endangerment of
bird species resulting from land-use change in 20 biodiversity hotspots and compared these predictions with
observed numbers of extinct and threatened bird species. We repeated this analysis with the conventional
species–area model and the countryside species–area model, considering alternative zvalues of 0.35 (island)
or 0.22 (continental). We evaluated the relative strength of support for each of the five candidate models
with Akaike’s information criterion (AIC). The matrix-calibrated model had the highest AIC weight ( wi=
89.21%), which means the weight of evidence in support of this model was the optimal model given the set
of candidate models and the data. In addition to being a valuable heuristic tool for assessing extinction risk,
our matrix-calibrated model also allows quantitative assessment of biodiversity benefits (and trade-offs) of
land-management options in human-dominated landscapes. Given that processes of secondary regeneration
have become more widespread across tropical regions and are predicted to increase, our matrix-calibrated
model will be increasingly appropriate for practical conservation in tropical landscapes.
Keywords: agriculture, biodiversity crisis, countryside biogeography, equilibrium theory, forest regeneration,
power model, reconciliation ecology, secondary succession
Un Modelo Especies-´
Area Calibrado para la Matriz para Predecir las P´
erdidas de Biodiversidad Debido a Cambios
en el Uso de Suelo
Resumen. La aplicaci´
on de la teor´
ıa de biogeograf´
ıa de islas a la predicci´
on de extinciones de especies
como resultado de la p´
erdida de h´
abitat se basa en el supuesto de que la matriz de paisaje transformado es
inh´
ospito para los taxa considerados, no obstante la evidencia que demuestra la influencia no trivial de la
matriz sobre las poblaciones en los remanentes de h´
abitat. Por lo tanto, el paradigma de la biogeograf´
ıa de
islas requiere refinaci´
on para explicar las respuestas espec´
ıficas de los taxa al ´
area de las “islas” de h´
abitat y
a la calidad de la matriz circundante. Incorporamos los efectos de la matriz en la teor´
ıa de islas dividiendo la
pendiente (valor z) de las relaciones especies-´
area en dos componentes: γ, una constante, y σ, una medida de
las respuestas espec´
ıficas del tax´
on a cada componente de una matriz heterog´
enea. Utilizamos nuestro modelo
∗email lian.koh@env.ethz.ch
Paper submitted May 22, 2009; revised manuscript accepted October 27, 2009.
994
Conservation Biology, Volume 24, No. 4, 994–1001
C
2010 Society for Conservation Biology
DOI: 10.1111/j.1523-1739.2010.01464.x
Koh & Ghazoul 995
calibrado para la matriz para predecir la extinci´
on y estatus de riesgo de especies de aves como resultado del
cambio en el uso de suelo en 20 sitios de importancia para la biodiversidad y comparamos estas predicciones
con el n´
umero observado de especies de aves extintas y amenazadas. Repetimos este an´
alisis con el modelo
especies-´
area convencional y el modelo especies-´
area rural, considerando valores alternativos de z de 0.35
(isla) o 0.22 (continental). Evaluamos la solidez relativa del soporte de cada uno de los cinco modelos con el
criterio de informaci´
on Akaike (AIC). El modelo calibrado para la matriz tuvo el mayor AIC ( wi=89.21%),
lo que significa que el peso de la evidencia que soporta este modelo fue el modelo ´
optimo dado el conjunto
de modelos candidatos y los datos. Adem´
as de ser una herramienta heur´
ıstica valiosa para evaluar el riesgo
de extinci´
on, nuestro modelo calibrado para la matriz tambi´
en permite una evaluaci´
on cuantitativa de los
beneficios para la biodiversidad de las opciones de manejo de suelo en paisajes dominados por la actividad
humana. Debido que los procesos de regeneraci´
on secundaria se han extendido en las regiones tropicales y
que se espera que incrementen, nuestro modelo calibrado para la matriz cada vez ser´
am
´
as apropiado para
la conservaci´
on en paisajes tropicales.
Palabras Clave: agricultura, biogeograf´
ıa rural, crisis de biodiversidad, ecolog´
ıa de reconciliaci´
on, modelo de
poder, regeneraci´
on de bosques, sucesi´
on secundaria, teor´
ıa del equilibrio
Introduction
Globally, habitat loss, fragmentation, and degradation
continue to threaten the long-term persistence of ter-
restrial ecosystems and biodiversity (Sodhi et al. 2004;
Bradshaw et al. 2009), undermine ecosystem services and
human well-being (Diaz et al. 2006; Dobson et al. 2006),
and exacerbate dangerous climate change (Houghton
2005; Gullison et al. 2007). The most direct and visi-
ble consequence of habitat perturbation arguably is the
extinction of populations and species. Thus, current re-
search is focused on understanding the patterns and pro-
cesses of species extinction to predict future biodiver-
sity scenarios and guide conservation actions (Brook et
al. 2008). Island biogeography theory (MacArthur & Wil-
son 1967) and metapopulation dynamics (Hanski 1998)
are key theoretical frameworks underpinning most eco-
logical and conservation studies on species extinction
(Ricketts 2001). In particular, the power model (Arrhe-
nius 1920)—one of several alternative models used to de-
scribe species–area relationships (Tjørve 2003; Dengler
2009)—has been applied widely to predict biodiversity
losses resulting from deforestation in terrestrial systems
(e.g., Brooks et al. 1997; Brooks et al. 2002; Brook et al.
2003). The power model is expressed as
S=c·Az,(1)
where Sand Aare the number of species and area of
habitat, respectively; cis a constant that depends on the
taxon and region; and z, another constant, indicates the
rate of change in the number of species per unit area
(Rosenzweig 1995). When a habitat shrinks from an orig-
inal size (Aorg) to a current size (Anew ), one can derive
from Eq. 1 the expected number of species (Snew)asa
proportion of the original number of species (Sorg):
Snew
Sorg
=Anew
Aorg z
.(2)
Some researchers question the relevance of applying is-
land theory to real-world situations, particularly for un-
derstanding the effects of deforestation and habitat frag-
mentation (e.g., Simberloff & Abele 1976; Gilbert 1980;
Laurance 2008). Confounding factors that could limit ap-
plicability of island theory include nonrandom habitat
conversion, edge effects, community-level changes, inter-
species interactions, and differential responses of species
to the matrix (Laurance 2008). Matrix effects, notably,
have received increasing research attention. Empirical
studies demonstrate that land-use change typically results
in a matrix that comprises a mosaic of habitat types with
variable degrees of suitability and permeability for differ-
ent taxa (e.g., Ricketts 2001; Revilla et al. 2004; Umetsu
et al. 2008).
Although most researchers acknowledge the impor-
tance of the matrix (Ricketts 2001), the species–area
approach of assessing extinction risk is still based on
a binary landscape of either habitat (e.g., an old-growth
forest remnant) or nonhabitat (e.g., farmland). Recently
two conceptually similar methods have been proposed to
reconcile the island biogeography paradigm with the het-
erogeneous nature of the landscape matrix. They are both
based on building and combining species–area models for
subgroups of taxa that presumably respond differently
to different landscape components (Tjørve 2002; Pereira
& Daily 2006). These methods advance understanding
of how taxa might respond to the matrix. But they still
rely on an arbitrary definition of the slope (zvalue) of
species–area relationships, and slope has a strong influ-
ence on extinction predictions (Rosenzweig 1995; Lau-
rance 2008). Of course, the fact that a model is sensitive
to zvalues does not lessen the utility of the model for pre-
dicting species’ extinctions as long as the model’s zvalue
is appropriately calibrated for every system considered.
We propose an alternative approach to incorporate ma-
trix effects into island theory by calibrating the zvalue
of the power model (Eq. 1) on the basis of taxon-specific
responses to each component of a heterogeneous
Conservation Biology
Volume 24, No. 4, 2010
996 Matrix-Calibrated Species-Area Model
landscape. The rationale behind our approach is as fol-
lows: between two alternative landscape matrices that
differ in terms of suitability and permeability to a taxon,
the more hospitable matrix (e.g., diverse agroforestry)
alleviates extinction pressure from habitat loss and low-
ers the slope of species–area relationships more than the
more hostile matrix (e.g., intensive monoculture planta-
tions). This hypothesis is supported by two recent em-
pirical observations. Cook et al. (2002) experimentally
investigated the effects of patch size and isolation on
plant species richness in 106 habitat patches ranging in
size from 32 m2to 5000 m2. They reported that patch
size and isolation significantly affected species richness
of only those species that could not survive in the ma-
trix; species that thrived in the matrix were unaffected by
these island effects. In a meta-analysis, Watling and Don-
nelly (2006) investigated whether zvalues consistently
differed across matrix types and taxa in 148 studies sam-
pled from the primary literature. They concluded that for
all taxonomic groups considered (i.e., invertebrates, am-
phibians, reptiles, birds, nonvolant mammals, and bats),
zvalues were significantly lower in the least hostile ma-
trix, agriculture, compared with the other matrix types
of desert, urban area, and water.
Matrix-Calibrated Model
We propose that the zvalue of the power model (and
more generally, the slope of species–area relationships)
can be partitioned into two components: γ, a constant,
and σ, a measure of the sensitivity of the taxon to the
transformed habitat (quantified as the proportional de-
crease in the number of species [0 <σ<1]):
z=γ·σ.(3)
Substituting Eq. 3 into Eq. 2 yields
Snew
Sorg
=Anew
Aorg γ·σ
.(4)
Equation 4 implies that the expected level of species
extinction and endangerment depends on the extent of
habitat loss and on the sensitivity of the taxon to the ma-
trix (Fig. 1). In an extreme scenario, where rising sea lev-
els drive the formation of land-bridge islands, the ocean
becomes the matrix, which presumably represents a com-
pletely inhospitable habitat for the taxon (σ=1). In this
case, Eq. 4 reduces to the classical island biogeography
model (Eq. 2):
Snew
Sorg
=Anew
Aorg γ
.
From this scenario (ocean as matrix), one can infer that
γis equivalent to the observed zvalue of the taxon in
true island archipelagos. In an alternative scenario, where
Figure 1. The matrix-calibrated model ( Eq. 6),
illustrating the functional relationships between
species extinction risk ( 1 −Snew
Sorg ), extent of habitat loss
(1−Anew
Aorg ), and sensitivity of taxon to the matrix (σ)
(Sorg,original number of species; Snew, expected
number of species;A
org,original habitat size;A
new,
current habitat size; γ=1 for this illustrative
purpose).
land-use change results in no (or negligible) change in
habitat quality for the taxon (σ=0) (e.g., when part of an
intact forest is managed for the harvesting of nontimber
forest products), Eq. 4 reduces to
Snew
Sorg
=Anew
Aorg 0
=1,
which implies that even though Anew <Aorg, this form
of land-use change results in no expected change in the
number of species (i.e., no change in extinction risk).
Nevertheless, if the managed forest declines in habitat
quality over time, for example, owing to the encroach-
ment of agriculture or other development pressures,
taxon sensitivity (σ) to this habitat would increase, lead-
ing to biodiversity losses.
In most real-world situations, land-use change results
in a mosaic of several habitat types of varying quality
for the taxon. To account for this, one can incorporate
an area-weighted average of the taxon’s response to each
component of this heterogeneous transformed landscape
into the exponent described by Eq. 3 which becomes:
z=γ·n
ipiσi,(5)
where pis the proportional area of the ith habitat type
relative to the total converted land area (matrix), and n
represents the total number of habitat types. Substituting
Eq. 5 into Eq. 2 yields our calibrated species–area model
Conservation Biology
Volume 24, No. 4, 2010
Koh & Ghazoul 997
Table 1. Observed and predicted percentage of extinct and threatened endemic bird species in 20 biodiversity hotspots.
a
Predicted bird extinction and endangerment (% total known endemic species)c
Biodiversity matrix–
hotspot Observedbconventionalcontinental–zconventionalisland–zcountrysidecontinental –zcountrysideisland–zcalibrated
Atlantic Forest 38.5 42.5 (+) 58.5 (+) 14.4 (−) 21.6 (−) 36.9 (−)
Caribbean
Islands
29.0 39.7 (+) 55.3 (+) 11.6 (−) 17.6 (−) 30.7 (+)
Cerrado 58.8 28.6 (−) 41.5 (−) 12.0 (−) 18.3 (−) 25.3 (−)
Coastal Forests of
Eastern Africa
18.2 39.7 (+) 55.3 (+) 10.4 (−) 15.8 (−) 28.5 (+)
Eastern
Afromontane
33.0 39.1 (+) 54.6 (+) 10.7 (−) 16.3 (−) 28.7 (−)
East Melanesian
Islands
22.1 23.3 (+) 34.4 (+) 10.9 (−) 16.6 (−) 21.1 (−)
Guinean Forests
of West Africa
41.3 34.1 (−) 48.5 (+) 10.7 (−) 16.3 (−) 26.1 (−)
Horn of Africa 37.5 48.3 (+) 65.0 (+) 8.0 (−) 12.3 (−) 27.3 (−)
Indo-Burma 28.1 48.3 (+) 65.0 (+) 12.8 (−) 19.3 (−) 38.4 (+)
Madagascar &
Indian Ocean
Islands
31.5 39.7 (+) 55.3 (+) 7.3 (−) 11.3 (−) 21.6 (−)
Madrean
Pine-Oak
Woodlands
31.8 29.8 (−) 43.1 (+) 6.5 (−) 10.0 (−) 16.1 (−)
Mesoamerica 15.4 29.8 (+) 43.1 (+) 8.2 (−) 12.6 (−) 19.7 (+)
New Caledonia 30.4 25.0 (−) 36.8 (+) 9.4 (−) 14.5 (−) 19.9 (−)
Philippines 30.1 44.3 (+) 60.6 (+) 16.0 (−) 23.9 (−) 40.2 (+)
Polynesia-
Micronesia
56.4 28.9 (−) 41.9 (−) 16.5 (−) 24.5 (−) 30.3 (−)
Sundaland 30.3 44.8 (+) 61.2 (+) 11.9 (−) 18.1 (−) 34.5 (+)
Tropical Andes 19.0 26.3 (+) 38.4 (+) 6.1 (−) 9.4 (−) 14.1 (−)
Tumbes-Choc´
o-
Magdalena
19.1 26.9 (+) 39.3 (+) 8.0 (−) 12.2 (−) 18.1 (−)
Wallacea 18.7 34.1 (+) 48.5 (+) 13.4 (−) 20.2 (+) 30.1 (+)
Western Ghats
and Sri Lanka
28.6 27.6 (−) 40.2 (+) 9.4 (−) 14.5 (−) 21.0 (−)
aExtinct and threatened species are those classified as vulnerable, endangered, critically endangered, or extinct ( IUCN 2008).
bObserved percentage of extinct and threatened species in each biodiversity hotspot is based on latest estimates by IUCN (2008) and Conservation
International (2008).
cPredictions of species extinction and endangerment are based on the conventional species–area model assuming a zvalue of ei-
ther 0.22 (conventionalcontinental–z)or0.35(conventional
island–z), the countryside species–area model assuming a zvalueofeither0.22
(countrysidecontinental–z) or 0.35 (countrysideisland–z), or the matrix-calibrated model. For the countryside and matrix-calibrated species–area
models, we performed Monte Carlo simulations (10,000 runs) to account for variability in taxon sensitivity to each transformed land-use type
and calculated a mean predicted value and its associated variance (not presented here) for each biodiversity hotspot (+, overestimate; −,
underestimate).
(hereafter, matrix-calibrated model) expressed as
Snew
Sorg
=Anew
Aorg γ·n
ipiσi
.(6)
We tested our model on 20 biodiversity hotspots in
the tropics (Table 1), which represent geographic re-
gions that each contain at least 0.5% of the world’s flora
and have already lost over 70% of their original habitat
(Myers et al. 2000). The focus of research attention on
biodiversity hotspots over the past decade has produced a
considerable amount of biodiversity and biophysical data
(Conservation International 2008). Thus, these hotspots
are ideal test sites for our matrix-calibrated model. We
used our model to predict species extinction and endan-
germent resulting from land-use change in each hotspot.
We then compared these predictions with observed num-
bers of extinct and threatened species (i.e., classified as
“vulnerable,” “endangered,” “critically endangered,” or
“extinct”; IUCN [International Union for Conservation of
Nature] 2008). We included extant species threatened
with extinction to account for extinction debts (lag ef-
fects) that might take decades or centuries to unfold
(Tilman et al. 1994; Brooks et al. 1999). (Henceforth,
extinction refers to both extinction and endangerment,
and extinct species include both extinct and threatened
species.)
We repeated our analysis with the conventional
species–area model (Eq. 2; henceforth, referred to as
conventional model) and the countryside species–area
Conservation Biology
Volume 24, No. 4, 2010
998 Matrix-Calibrated Species-Area Model
model proposed by Pereira and Daily (2006) (henceforth,
referred to as countryside model), which is expressed as
Snew
Sorg
=n
ihiAi
Aorg z
,
where his the affinity of a species to the ith habitat type
(proportion of habitat that can be used by a taxon; for
this study we let h=1–σ). Finally, we assessed which
set of model predictions (conventional, countryside, or
matrix calibrated) most accurately reflects the observed
number of extinct species in these hotspots.
Methods
As with previous studies (e.g., Pimm & Askins 1995;
Brooks et al. 2002), we restricted our analysis to species
endemic to each hotspot (i.e., not occurring elsewhere;
Conservation International 2008). We focused only on
birds because they are well studied in terms of their sen-
sitivity to different forms of land-use change in the tropics
(e.g., Sodhi et al. 2009) and data on their conservation sta-
tus are most reliable, updated, and readily available from
Conservation International (2008) and IUCN (2008). A
species qualifies for listing as vulnerable, endangered, or
critically endangered on the IUCN Red List if it meets
any of a range of quantitative criteria, including habitat
loss (i.e., decrease in area of occupancy; IUCN 2001). To
address the issue of circularity that might arise from the
use of the IUCN Red List to verify extinction predictions
made based on habitat loss, we excluded all species red
listed by the IUCN solely on the basis of criteria A1c, A2c,
and B2a-c. These criteria are based entirely on species’
habitat decline. Out of a total of 2664 species of endemic
birds occurring in the 20 biodiversity hotspots consid-
ered, only two species were thus excluded: Restinga
Antwren (Formicivora littoralis) and Black-capped Pe-
trel (Pterodroma hasitata).
We calculated area for the following land-use classes
occurring in each biodiversity hotspot on the basis of
land-cover data from Conservation International (2008)
and the European Space Agency (ESA) (2008): original
vegetation extent, vegetation remaining, disturbed for-
est, agricultural land, and urban area (see Supporting In-
formation). In addition, on the basis of data compiled
by Watling and Donnelly (2006), we calculated mean
slope of species–area relationships of birds on land-bridge
archipelagos and used this value, z=0.35 (SE 0.06, n=
6), as the γvalue in the matrix-calibrated model and as the
zvalue in the conventional and countryside models. Con-
tinental habitat islands typically have lower species–area
slopes than true island archipelagos (Rosenzweig 1995).
Therefore, we also calculated a continental species–area
slope for birds (z=0.22 [SE 0.02], n=17; Watling &
Donnelly 2006).
To determine the sensitivity (i.e., the σvalue in Eq.
6) of birds to each transformed land-use type, we used
data compiled by Sodhi et al. (2009) to calculate mean
percent decrease in bird species richness when a pris-
tine habitat is converted to either a disturbed forest (σ
=0.25 [SE 0.03], n=42) or agricultural land (σ=0.68
[SE 0.05], n=17; Supporting Information). We assumed
urban areas are completely inhospitable to birds (σ=
1). We performed a Monte Carlo simulation to account
for variability in taxon sensitivity to the land-use types of
disturbed forest and agricultural land. In 10,000 runs, we
generated a random σvalue derived from the mean and
standard deviation of the calculated σvalue and by assum-
ing a normal distribution. We entered the randomized σ
value to the matrix-calibrated model to calculate the mean
number (and 95% confidence interval) of species extinc-
tion resulting from land-use change in each biodiversity
hotspot.
Finally, we used the conventional and countryside
models to estimate species extinction in each hotspot,
considering alternative slopes of 0.35 (island zvalue) or
0.22 (continental zvalue). We evaluated relative strength
of support for each of the following five candidate models
with the Akaike’s information criterion (AIC; Burnham &
Anderson 1998): conventional model with continental z
value (conventionalcontinental−z), conventional model with
island zvalue (conventionalisland−z), countryside model
with continental zvalue (countrysidecontinental−z), coun-
tryside model with island zvalue (countrysideisland−z),
and the matrix-calibrated model.
Results
Across all biodiversity hotspots considered, the ob-
served percentage of extinct bird species ranged
from 15.4% in Mesoamerica to 58.8% in the Cerrado
(Table 1). Of the five models considered, the matrix-
calibrated model had the highest AIC weight (wi=
89.21%), which reflects the weight of evidence in sup-
port of this model being the optimal model given
the set of candidate models and the data considered
(Table 2). The matrix-calibrated model was 13.5 times
more strongly supported by the data than the next-
best model, conventionalcontinental−z(wi=6.61%). Both
countryside models—countrysideisland−z(wi=3.89%)
and countrysidecontinental−z(wi=0.28%)—performed
more poorly than either the matrix-calibrated or
conventionalcontinental−zmodels. The conventionalisland−z
model performed the worst (wi=0.01%).
The matrix-calibrated model produced prediction er-
rors that were more evenly distributed (seven overes-
timates and 13 underestimates) than in the other four
models (Table 1; Fig. 2). The conventionalcontinental−z
model overestimated species extinction for 14 out of
Conservation Biology
Volume 24, No. 4, 2010
Koh & Ghazoul 999
Table 2. Candidate models for predicting extinct or threatened
endemic bird species in 20 biodiversity hotspots.∗
Evidence
Candidate model ε2AIC wi(%) ratio
Matrix calibrated 4592.749.289.21 1
Conventionalcontinental−z8363.554.46.61 13.5
Countrysideisland−z9447.255.53.89 22.9
Countrysidecontinental−z17,384.560.80.28 324.1
Conventionalisland−z34,320.666.70.01 6215.7
∗See Table 1 for explanation of candidate models (ε2,sumofdif-
ferences between predicted and observed values of extinction risk
in 20 biodiversity hotspots; AIC, Akaike’s information criterion; wi,
Akaike weight, defined as the weight of evidence in support of a can-
didate model; evidence ratio, ratio of Akaike weights between the
optimal model and each candidate model). The AIC is calculated as,
AIC =nlog(ε2
n)+2K, where n=20 biodiversity hotspots and K
(number of parameters) is 1 ( Burnham & Anderson 1998).
the 20 hotspots (the most extreme values being Tropi-
cal Andes, Wallacea, and the Philippines) and underes-
timated extinction for six hotspots, including the Cer-
rado and Polynesia-Micronesia (Table 1; Fig. 2). The
conventionalisland−zmodel overestimated species extinc-
tion for 18 hotspots, whereas both countryside models
produced extinction predictions that were mostly under-
estimates (Table 1).
Discussion
Biodiversity hotspots largely encompass developing na-
tions that typically have limited conservation exper-
tise and resources (Sodhi et al. 2004; Bradshaw et al.
2009). Given these challenges, heuristic tools are par-
ticularly useful for conservation scientists and decision
makers to accurately and rapidly assess the consequences
of land-use decisions for biodiversity. To this end the
species–area approach has been adopted widely by ecol-
ogists because the underlying island theory is elegant
and intuitive. Nevertheless, this approach is limited by its
simplicity; specifically it does not account for quality of
the matrix. Our approach of calibrating the species–area
model retains the heuristic property of the conventional
model, but also includes a more realistic calibration that is
based on extent and habitat quality of transformed land
uses as perceived by the taxon. Our matrix-calibrated
model performed considerably better than the conven-
tional and countryside models in predicting biodiversity
losses. In addition, although we removed species listed
primarily on the basis of habitat area to avoid circu-
larity, a similar analysis with the entire data set gener-
ated nearly identical conclusions, which implies that our
matrix-calibrated method can be applied broadly in con-
servation practice.
These conclusions must be considered in view of the
following caveats. First, we did not exclude species on
the IUCN Red List (classified as extinct or threatened) for
reasons other than habitat loss (e.g., overexploitation), as
some studies have done (e.g., Brooks et al. 2002). Instead,
we assumed that the red-listing of a species is always
ultimately attributable to land-use change. This assump-
tion is supported by considerable evidence that overex-
ploitation in tropical forests is facilitated by increased
accessibility that accompanies forest clearance (Nepstad
et al. 2001; Laurance et al. 2002). Second, given that
the conventional approach consistently overestimated
extinction, it could be construed as being more precau-
tionary than the matrix-calibrated method because there
is less likelihood of underestimating biodiversity losses.
Erring on the side of caution may be desirable from a strict
conservationist perspective, but our matrix-calibrated
estimation of extinction, being more realistic, would pro-
vide more objective guidance to conservation policy.
Figure 2. Comparisons of
observed and predicted numbers
of extinct and threatened
endemic bird species in 20
biodiversity hotspots. Predicted
values are based on either the
conventional species–area model
( Eq. 2), assuming a continental z
value of 0.22 or the
matrix-calibrated species–area
model ( Eq. 6). For the
matrix-calibrated model, we
plotted the mean of predicted
values with error bars
representing 95% confidence
intervals. Dashed line reflects
perfect match in predicted and
observed values.
Conservation Biology
Volume 24, No. 4, 2010
1000 Matrix-Calibrated Species-Area Model
Figure 3. Plot of spatial scale and
error of predictions from the
matrix-calibrated model for 20
biodiversity hotspots. The spatial
scale of analysis ranged from
18,972 km2(New Caledonia
hotspot) to 2,373,057 km2
(Indo-Burma hotspot). Model
prediction errors were calculated
as the square of the difference
between predicted and observed
number of threatened or extinct
endemic bird species.
Third, our analysis is necessarily crude because we have
treated birds as a single homogeneous group, whereas
birds may differ in their response to the matrix by tax-
onomic or functional subgroups. Although current in-
formation does not permit more detailed analysis, our
method provides the means to undertake such analyses as
the information becomes available. Fourth, we assumed
the σvalues we used—which were extracted from a trop-
ical Asian data set (Sodhi et al. 2009)—are applicable to
other tropical regions. To the best of our knowledge, a
pan-tropical data set of σvalues has not been compiled,
but extracting them from the literature would have re-
quired effort beyond that available for this analysis. Fi-
nally, although we cannot be certain our model predic-
tions will remain robust at spatial scales beyond what
we considered, there was no discernible effect of spa-
tial scale on model prediction errors, at least within the
range of spatial scales we considered (i.e., from 18,972
km2[New Caledonia hotspot] to 2,373,057 km2[Indo-
Burma hotspot]; Fig. 3).
In addition to being a valuable tool for assessing ex-
tinction risk, our calibrated species–area model also has
important implications for land management in human-
dominated landscapes. First, for a given amount of un-
avoidable deforestation in a landscape undergoing devel-
opment, our model suggests that extinction risk could be
minimized by improving the habitat quality of the matrix
for the taxon of interest (i.e., by lowering the σvalue in
Eq. 6). More importantly, the model enables a quantitative
assessment of the biodiversity benefits (and trade-offs) of
such mitigation measures. Second, for a landscape that
has experienced historical land-use change, biodiversity
could be enhanced by improving the habitat quality of
the matrix (i.e., Snew
Sorg can be >1whenσ<0). In the
context of tropical forests, this could be achieved by al-
lowing farmland to regenerate to secondary forests or by
facilitating the succession of young secondary forests to
old-growth forests. For example, the natural regeneration
of abandoned pasture and coffee plantations in Puerto
Rico produced secondary forests with similar structure
and species diversity compared with the island’s mature
forests (Zimmerman et al. 2007). Such processes of re-
generation are widespread across tropical regions (Chaz-
don 2008) and are predicted to increase over coming
decades (Wright & Muller-Landau 2006), which indicates
our calibrated model will be increasingly appropriate for
practical conservation in future tropical landscapes.
Acknowledgments
We thank W.R. Turner, J.I. Watling, N.S. Sodhi, T.M. Lee,
C.J.A. Bradshaw, and B.W. Brook for helpful discussions.
We thank T. Donovan and two anonymous reviewers for
useful suggestions. This study was inspired by a ques-
tion posed by D.S. Wilcove, to which the answer is, con-
verting 1 acre of Borneo’s primary forest to oil palm is
roughly as bad for biodiversity as selectively logging 2.5
acres of the forest. L.P.K. was supported by an ETH (Eid-
gen¨
ossische Technische Hochschule) Fellowship and the
Swiss National Science Foundation.
Supporting Information
Data used in the analysis (Appendices S1 and S2) are
available as part of the on-line article. The authors are
responsible for the content and functionality of these
materials. Queries (other than absence of the material)
should be directed to the corresponding author.
Conservation Biology
Volume 24, No. 4, 2010
Koh & Ghazoul 1001
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Conservation Biology
Volume 24, No. 4, 2010
