Taxonomic and regional uncertainty in species-area
relationships and the identification of
Franc ¸ois Guilhaumon*†, Olivier Gimenez‡, Kevin J. Gaston§, and David Mouillot*
*Laboratoire Ecosyste `mes Lagunaires, Unite ´ Mixte de Recherche 5119, Centre National de la Recherche Scientifique-IFREMER-UM2, Universite ´ Montpellier 2,
cc 093, Place Euge `ne Bataillon, 34095 Montpellier Cedex 5, France;‡Centre d’Ecologie Fonctionnelle et Evolutive, Unite ´ Mixte de Recherche 5175, Centre
National de la Recherche Scientifique, 1919 Route de Mende, F-34293 Montpellier Cedex 5, France; and§Biodiversity and Macroecology Group, Department
of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, United Kingdom
Edited by Michael P. H. Stumpf, Imperial College London, London, United Kingdom, and accepted by the Editorial Board August 22, 2008
(received for review April 14, 2008)
Species-area relationships (SARs) are fundamental to the study of
key and high-profile issues in conservation biology and are par-
ticularly widely used in establishing the broad patterns of biodi-
versity that underpin approaches to determining priority areas for
biological conservation. Classically, the SAR has been argued in
general to conform to a power-law relationship, and this form has
been widely assumed in most applications in the field of conser-
vation biology. Here, using nonlinear regressions within an infor-
mation theoretical model selection framework, we included un-
certaintyregarding both model
estimation in SAR modeling and conducted a global-scale analysis
of the form of SARs for vascular plants and major vertebrate
groups across 792 terrestrial ecoregions representing almost 97%
of Earth’s inhabited land. The results revealed a high level of
power-law model is clearly the most appropriate in only a minority
of cases. Incorporating this uncertainty into a hotspots analysis
using multimodel SARs led to the identification of a dramatically
different set of global richness hotspots than when the power-law
that assume a power-law model may be at severe odds with real
ecological patterns, raising significant concerns for conservation
priority-setting schemes and biogeographical studies.
conservation biology ? ecoregions ? model selection ? vascular plants ?
present understanding of many key and high-profile issues in
conservation biology. They have, for example, variously been
as a consequence of such pressures as deforestation and climate
change (1–4) and to predict species extinction rates in blocks of
remnant habitat, including protected areas, as a consequence of
their isolation (5). More fundamentally, the SAR is an essential
tool used to estimate broad patterns and to identify hotspots of
species richness when regions differ in area (6–13).
In the main, applications of SARs have assumed that these
relationships take the classical form of a log-linearizable power
function, S ? cAz, where S is species richness, A is area, and c and
z are constants (14). Depending on the objectives and opportu-
nities, the parameters of this function (notably the exponent, or
rate, z) are derived from theory (15–18), from particular datasets
or from broad collations of datasets (19–22). However, although
the power function has been applied extremely widely, in prac-
tice there is much variation in the basic form of SARs (23, 24).
Attention has focused foremost on how this form changes with
spatial scale (25–27) or assemblage properties (28). Other kinds
of systematic variation may also exist, but analyses have princi-
pally only rather narrowly addressed these by comparing the
pecies-area relationships (SARs), the change in species
numbers with increasing area, are fundamental to the
parameter values estimated from fitting a power function rela-
tionship (e.g., space, refs. 21, 29, 30; environment, ref. 31; and
anthropogenic threats, ref. 22).
Given that a single generic form for SARs is widely assumed
to pertain, of particular concern for conservation biology would
be if the underlying form actually differed markedly between
major taxonomic groups and/or biomes (global-scale biogeo-
graphic regions distinguished by unique collections of ecosys-
tems and species assemblages; ref. 32). Whether such variation
was systematic, it could have significant implications particularly
for the fundamental understanding of the distribution of biodi-
versity that underlies much of the prioritization of lands for
conservation investment and action (33). For example, studies
have variously sought to incorporate the effects of variation in
area on species richness at large spatial scales (often ecoregions)
of different higher taxa (13, 34), patterns of protected area
coverage (35), the impacts of urbanization on biodiversity (36),
and the allocation of conservation resources (37, 38).
In this article, we conduct an analysis of global-scale SARs
with two aims. First, we investigate the uncertainty about the
best-fitting SAR model by quantifying the relative probabilities
those probabilities vary systematically for the same higher taxon
in different biomes and for different higher taxa in the same
biome. Second, we conduct a global identification of hotspots of
richness, incorporating the uncertainty about the best-fit SAR
model, and compare these results with those obtained when it is
assumed that the power model is the best-fitting SAR model. We
use data on the species richness of vascular plants and verte-
brates across the world’s terrestrial ecoregions (13, 39) [support-
ing information (SI) Text and Table S1]. Ecoregions are large
units of land containing geographically distinct species assem-
blages and experiencing geographically distinct environmental
conditions and have proven valuable for addressing a range of
issues in conservation prioritization (13, 40, 41).
Taxonomic and Regional Uncertainty in Species-Area Relationships.
The relative fit of eight different potential forms for SARs
(Table S2) was evaluated for each combination of higher taxon
Author contributions: F.G., O.G., K.J.G., and D.M. designed research; F.G., O.G., K.J.G., and
D.M. performed research; F.G., O.G., K.J.G., and D.M. analyzed data; and F.G., O.G., K.J.G.,
and D.M. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission. M.P.H.S. is a guest editor invited by the Editorial
†To whom correspondence should be addressed. E-mail: francois.guilhaumon@univ-
This article contains supporting information online at www.pnas.org/cgi/content/full/
© 2008 by The National Academy of Sciences of the USA
October 7, 2008 ?
vol. 105 ?
no. 40 www.pnas.org?cgi?doi?10.1073?pnas.0803610105
and biome. These forms encompassed convex, sigmoid, asymp-
totic, and nonasymptotic models, with the fit being evaluated
using nonlinear regressions in the so-called model selection
framework (42). This emerging approach in the context of SARs
(43) aims to evaluate, for a given dataset, the strength of
evidence for alternative explanatory models (44). Furthermore,
by averaging across statistically valid models, this framework
allows the construction of robust inferences incorporating un-
certainty regarding both model selection and parameter estima-
tion (multimodel SARs; see Materials and Methods for details).
Surprisingly, given the apparent generality of the SAR, the
analysis revealed substantial variation in the strength of the
effect of area on species richness. Although the R2for multi-
model SARs had an overall mean of 0.30, values for different
combinations of higher taxa and biomes ranged from 0.02 for
amphibians in Tropical Dry Forests to 0.69 for total vertebrates
in Tropical Grasslands (Table S3). Furthermore, for several
datasets (21 of 78), the SAR cannot be adequately described by
any of the candidate models (Fig. 1, Table S4). This latter
tendency was not limited to those datasets with narrower ranges
of variation in species richness or area but is more obvious for
biomes than for higher taxa. For example, SARs were statisti-
cally validated across temperate forest ecoregions only for
mammals and vascular plants.
The best-fitting model varied markedly across biomes for all
higher taxa and across higher taxa for each biome (Fig. 1, Table
S4). It was the asymptotic negative exponential (convex) and the
Monod (convex) models in 18 and 13 cases, respectively, the
nonasymptotic power and exponential models in 10 cases each,
and the logistic and Lomolino models in five and one case,
respectively. The rational function and the cumulative Weibull
models never provided the best fit. However, with the exception
of four datasets (amphibians and mammals in Tropical and
Subtropical Moist Broadleaf Forests, vascular plants in Temper-
ate Conifer Forests, and reptiles in Deserts), there was a
substantial degree of uncertainty about the best-fitting SAR
model (Fig. 1, Table S4). For most of the datasets, no single
model was clearly superior.
Furthermore, for almost all higher taxa, model probabilities
differed markedly across biomes (Fig. 1, Table S4). Although for
almost all biomes, model probabilities also differed markedly
across higher taxa (Fig. 1, Table S4), summing these probabilities
across the different models revealed some coarse tendencies.
Indeed, for Boreal Forests, except for amphibians, the sum of the
probabilities of nonasymptotic models that best describe the
SAR was always ?0.5. In contrast, for the Tundra and Medi-
terranean Forests, the SAR was likely to be asymptotic for most
higher taxa (Fig. 1, Table S4).
Hotspot Detection. Using multimodel SARs could result in a
rather different set of species richness hotspots being recognized
than was the case when it was assumed that the power model was
the best-fitting SAR model (Fig. 2). For example, using the
of ecoregions as hotspots, between 30% (birds) and 78% (am-
phibians) of the hotspots identified by the two approaches were
the same. Inevitably, the similarity in the composition of the
hotspots increased as the cut-off was increased, but it remained
quite variable even when this cut-off was rather high (Fig. 2).
The differences in the hotspots recognized were especially
marked when focusing on particular combinations of higher taxa
and biomes. In one of many possible examples, for birds in
Tropical Grasslands, the five richest ecoregions (approximately
the richest 10%) were, with one exception, entirely different
when determined using multimodel SARs and when using a
power model (Fig. 3, Table 1).
Although it has long been apparent that the assumption of a
43), the practice has remained widespread. In part, this has been
because of the understandable demand to address important,
and often urgent, conservation issues in circumstances for which
information on the actual form of SARs is wanting and difficult
to obtain. The results of the analyses reported here highlight
several key issues that result from such an approach.
sented for each biome for amphibians (Amp.), reptiles (Rep.), birds (Avi.),
mammals (Mam.), total vertebrates (Tot.), and vascular plants (Vas.). The
height of each fraction of the colored band is proportional to the probability
(Akaike weight) that each model [see color legend, exponential (expo.),
negative exponential (neg. expo.), rational function (rational func.)] is the
best in explaining the dataset. A lack of colored band means that none of the
eight SAR models was statistically valid for the corresponding dataset.
SAR model selection patterns. Patterns of model selection are pre-
Guilhaumon et al.
October 7, 2008 ?
vol. 105 ?
no. 40 ?
First, the assumption that SARs follow a single generic form
overlooks the fact that the effect of area on species richness can
differ dramatically among datasets. At one extreme, the majority
of variation in richness can be explained by area, and individual
models can provide excellent fits; and, at the other extreme, no
single model may adequately describe the relationship between
species richness and area (19, 43). Although such lacks of fit have
been reported (43), our study highlights that this circumstance
may not always be a rare one, pertaining in 27% of the cases (Fig.
1, Table S4, combinations of higher taxon and biome) that we
studied, despite our using a particularly wide range of possible
models (embracing most forms that have been discussed in the
Second, where one or more of the models tested did fit
datasets, that which fit best was extremely variable (Fig. 1, Table
S4); a power model was the best fit in only 10 of 57 cases.
Although it has been suggested that the most appropriate model
may depend on scale and the nature of the organisms or of the
environment (19, 22, 23, 43, 45), no simple tendencies in these
regards seem to emerge from our analyses. Indeed, all of the
different shapes of SARs represented by the set of models used
(convex, sigmoid, asymptotic, and nonasymptotic) were selected
at least once for the different datasets. This suggests that none
of a wide range of potential SAR models can a priori be ignored,
and that a universal model does not emerge. The applied
implications of this observation could be further complicated if,
as some have suggested, the form of SARs can be influenced by
human activities, although thus far this influence has principally
been explored in terms of power models (22, 46).
Third, where more than one of the models tested fitted a
dataset, there was often substantial uncertainty as to which of
the importance of considering multiple models when making
inferences about SARs. It also draws attention to the need to
remember there is commonly substantial spatial variation in
species richness not attributable to variation in area, even when,
as here, comparisons are constrained to the same biome. This
said, summing the probabilities across the different types of
models allowed us to infer coarse tendencies about the shape of
SARs. Globally, intrabiome SARs are more likely to be convex
more likely to be asymptotic than nonasymptotic (mean summed
probabilities: 0.68 vs. 0.32 ? 0.26); this does not imply that
species richness generally tends actually to saturate when areas
are large (Fig. 1, ref. 47, and Table S4). This suggests the
possibility that there may be some general patterns in the
circumstances under which different kinds of models tend to
prevail. Extensive metaanalyses of large numbers of datasets
(with a wide range of average area sizes), and building on the
approaches developed here, could be used to explore this issue
to obtain more definitive conclusions.
Finally, given the above, assuming that a power model is the
most appropriate description of SARs can make a substantial
difference to the outcome of analyses and the conservation
recommendations that may follow (6, 12). Certainly, a rather
alternative models are considered (Figs. 2 and 3). Moreover,
there will tend to be systematic biases in these hotspots. For
example, in the case of birds in Tropical grasslands (Fig. 3, Table
1), those hotspots recognized using a linearized power model
tend to be smaller than when using multimodel SARs (summed
areas of hotspots using power model is 198,292 km2and incor-
porating uncertainty is 2,600,618 km2, Table 1). We anticipate
that such variation in outcomes will be very common, and that
the conclusions of a number of studies of the distribution of
species richness and its consequences for conservation prioriti-
zation will need to be revisited to ascertain their sensitivity to
assumptions about the underlying form of SARs.
In conclusion, we recommend that, particularly in the context
of studies whose outcomes may be of significance for conserva-
tion decision making, (i) in empirical analyses involving SARs,
the relative fit of different models is examined, and uncertainty
and those identified when using multimodel SARs. The percentage similarity among the two methods was determined as the number of ecoregions identified
as hotspots by both, divided by the total number of ecoregions in a group. For example, the highest 2.5% of ranks in a dataset consisting of 200 ecoregions
mean percentage similarity averaged across biomes for each higher taxon, gray polygon is the associated standard error of the mean, and dashed horizontal
line indicates the percentage similarity at the 2.5% cut-off.
Relationship between the criterion used to define hotspots (% of ecoregions) and the similarity between hotspots identified assuming a power SAR
www.pnas.org?cgi?doi?10.1073?pnas.0803610105Guilhaumon et al.
in this fit is accounted for; and (ii) in more theoretical studies
involving SARs, the consequences of assuming different under-
lying forms of these relationships are examined. Failing to do so
may well lead to conclusions at odds with real patterns of spatial
variation in species richness, as exemplified in the identification
of hotspots of richness among areas of differing size.
Materials and Methods
Data. Analyses were based on the numbers of species of vascular plants,
amphibians, reptiles, birds, and mammals in each terrestrial ecoregion of the
world as delimited by Olson et al. (32). Data were obtained on vertebrates by
overlaying range maps of extant species compiled from numerous scientific
works, field guides, or directly from experts (32), and on vascular plants from
published and unpublished richness data and from a variety of additional
information (39). Following Lamoreux et al. (13), we excluded Mangrove
ecoregions and large uninhabited parts of Greenland and Antarctica because
of lack of data reliability or availability. The resulting database contains 78
datasets (combinations across 13 biomes and 6 taxonomic groups) and covers
792 ecoregions that represent 96.3% of Earth’s inhabited land, making our
analysis a good descriptor of global distribution patterns (Table S1).
bootstrap confidence interval used to rank ecoregions (see Materials and Methods) and the brown solid curve is a log linear fit on the arithmetic scale (B). (B
and C) Log-linear power analysis. On all subplots the color of an ecoregion (A, B: points; C, D: regions) represents a rank (see color chart) according to the
corresponding analysis. On subplots A and B, the size of a point is inversely proportional to its rank according to the corresponding analysis. On all subplots, the
five richest ecoregions (corresponding to an ?10% cutoff of higher rank hotspot criterion) are presented (A and D: Roman numerals, B and C: Arabic numerals).
Ecoregions are Itigi–Sumbu thicket (1), Northwestern Hawaii scrub (2), Serengeti volcanic grasslands (3), Mandara Plateau mosaic (4), Victoria Basin forest-
savanna mosaic (5, II), Northern Acacia-Commiphora bushlands and thickets (I), Southern Acacia-Commiphora bushlands and thickets (III), Central Zambezian
Miombo woodlands (IV), and Northern Congolian forest-savanna mosaic (V).
Ecoregions of Tropical grasslands, birds SAR, and richness hotspots maps. SAR for the birds of Tropical grasslands (A and B) and maps of ecoregion ranks
Table 1. Five leading bird richness hotspot ecoregions of Tropical grasslands
Rank Ecoregion namesArea, km2
richnessRankEcoregion namesArea, km2
1 Itigi-Sumbu thicket7,809.2365I Northern Acacia-Commiphora bushlands
Victoria Basin forest-savanna mosaic
Southern Acacia-Commiphora bushlands
Central Zambezian Miombo woodlands
Northern Congolian forest-savanna
Northwestern Hawaii scrub
Serengeti volcanic grasslands
Mandara Plateau mosaic
Victoria Basin forest-savanna
Totals 198,291.81,815Totals 2,600,6183,278
Guilhaumon et al.
October 7, 2008 ?
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no. 40 ?
Statistical Analyses. All statistical analyses conducted in this study were im-
plemented within the R statistical programming environment (R 2.7, ref. 48).
Toward Consensual Inference. We discriminated the different SAR models in
the so-called model selection framework (42, 49), which is now widely used
across biological fields (44, 50–52). Through the use of information theoretic
criteria such as the Akaike Information Criterion (AIC, ref. 42), it provides a
rigorous way in which to evaluate and compare the relative support of
nonnested differently parameterized models of a given dataset. In this study,
of each SAR model given the data and the set of models. Akaike weights
are directly interpreted in terms of probabilities of a given model being the
best of a defined set of alternative models in explaining the data (42, 50).
relying on only the best model is inadequate, and multimodel inference is
for differently parameterized models, we use model averaging and consider
the weighted average of model predictions with respect to model weights.
One of the most important challenges in information theoretic analyses is
the construction of a consistent set of models (42, 52). Here, we propose a set
(Table S2), including four convex models (power, exponential, negative ex-
Lomolino, and cumulative Weibull). This includes convex, sigmoid, asymp-
totic, and nonasymptotic functions, thus encompassing the various shapes
attributed to SARs in the literature. The linearized forms (via logarithmic
transformations) of the power and exponential models were not included in
the set because of nonequivalence in the study of the variation in a variable
and in its transformation (23, 53) and bias of back-transformed results ob-
tained on a logarithmic scale (54). Furthermore, the nonlinear form of the
power equation leads to a more realistic detection of biodiversity hotspots
than does the log-linearized power equation (54).
AIC and other model selection criteria that estimate Kullback–Leibler in-
formation (see SI Materials and Methods) are used widely in the ecological
literature, but other criteria such as the Bayesian Information Criterion (BIC)
not derived in similar contexts [AIC is based on the Kullback–Leibler informa-
tion theory, whereas BIC was derived in a Bayesian context (42, 50)] and have
different properties: AIC aims to select the best model approximating reality
the true model that generates the data independently of sample size and
given that this true model is one of the candidate models. Although AIC and
BIC do not share the same conceptual bases and penalize differently for the
dimension of the models (BIC tends to select models with fewer parameters
than AIC), the results of our analyses were robust to the criterion used for
model selection and averaging. Using the BIC, the model ranks were globally
maintained across the datasets, and the substantial uncertainty revealed by
the AIC analysis persists (Fig. S1).
residual sum of squares (RSS) using the unconstrained Nelder–Mead optimi-
zation algorithm (55). Assuming normality of the observations, this approach
produces optimal maximum likelihood estimates of model parameters (56).
Regressions were evaluated by statistical examination of normality and ho-
moscedasticity of residuals: a model was excluded from final averaging if the
moment correlation coefficient with areas was significant at the 5% level. To
avoid numerical problems, such as local minima, and speed up the conver-
gence process, we paid particular attention to the starting values that were
used to run the optimization algorithm. We obtained initial values for those
parameters that were directly interpretable (e.g., an asymptote) by taking
corresponding values in the datasets (e.g., the observed maximum of species
richness in the case of an asymptote) and calculated initial values for the
remaining parameters using the standard procedures of Ratkowsky (57, 58).
coefficient of determination (R2) is not advocated (53, 57), these indices were
useful indicators of the proportion of variation in intrabiome species richness
explained by area.
Confidence Intervals and Ecoregion Ranking. By synthesizing and extending
recent advances and solving major concerns about the methodology of
hotspot detection (6–9, 11, 12, 54), ecoregions were ranked with respect to
their positions in the confidence interval of the model-averaged SAR (Fig.
3, SI Materials and Methods). To fully incorporate uncertainty in this
process, confidence intervals were calculated by using a nonparametric
bootstrapping procedure (59, 60). As advocated for regression (59, 61), we
ref. 60), and we applied the model selection and averaging procedure to
each of these resamples. In so doing, we generated robust confidence
intervals explicitly incorporating uncertainty regarding both model selec-
tion and parameter estimation.
Comparison of Hotspot Detection Methods. To investigate the effect of ac-
we assessed the similarity between the ranking obtained from our approach
and that obtained from usual methods (e.g., ref. 13). Classical methods rank
regions according to their residuals in a log-linear power regression: the
higher the residual, the higher the region in the ranking. The percentage
similarity was defined as the number of ecoregions identified as hotspots by
the two methods, divided by the total number of ecoregions in a set of
hotspots (6). For all higher taxa studied and for a varying proportion of
ecoregions identified as hotspots, the percentage similarity between the two
methods was averaged across the fitted biomes.
anonymous reviewers for helpful comments and/or discussions. K.J.G. holds a
Royal Society-Wolfson Research Merit Award.
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