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Taxonomic and regional uncertainty in species-area

relationships and the identification of

richness hotspots

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-

certaintyregardingbothmodel

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

uncertaintyinmodelselectionacrossbiomesandtaxa,andthatthe

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

SARwasassumed.Ourfindingssuggestthattheresultsofanalyses

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.

selectionandparameter

conservation biology ? ecoregions ? model selection ? vascular plants ?

vertebrates

S

present understanding of many key and high-profile issues in

conservation biology. They have, for example, variously been

usedtopredictregionalspeciesextinctionratesafterhabitatloss,

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)

whenconsideringtheconcordanceofspatialvariationinrichness

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

thatdifferentmodelsbestdescribeSARsanddeterminewhether

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).

Results

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

Board.

†To whom correspondence should be addressed. E-mail: francois.guilhaumon@univ-

montp2.fr.

This article contains supporting information online at www.pnas.org/cgi/content/full/

0803610105/DCSupplemental.

© 2008 by The National Academy of Sciences of the USA

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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

frequent(butarbitrary)cut-offofdistinguishingtherichest2.5%

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).

Discussion

Although it has long been apparent that the assumption of a

singlegenericformforSARswaspotentiallyproblematic(19,23,

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.

Fig. 1.

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.

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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

literature).

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

theseprovidedthebestfit(Fig.1,TableS4).Againthishighlights

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

thansigmoid(meansummedprobabilities:0.7vs.0.3?0.18)and

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

differentsetofhotspotswouldbeidentifiedthanisthecasewhen

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

Fig. 2.

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

comprisesfiveecoregions.Ifthreeecoregionsoccurinthetwogroups,thenthepercentagesimilarityamongthetwomethodsis60%.Darkplainlinerepresents

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

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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).

Fig. 3.

accordingtobirdspeciesrichnessinTropicalgrasslands(CandD).(AandD)Nonlinearmultimodelanalysis;dashedlinesarethefittedmodelpredictions(brown:

power,red:exponential,light-blue:Lomolino,dark-blue:Weibull),andthegreensolidcurveistheresultofmodelaveraging,grayshadingisthenonparametric

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

Bird

species

richnessRankEcoregion names Area, km2

Bird

species

richness

1 Itigi-Sumbu thicket7,809.2 365I Northern Acacia-Commiphora bushlands

and thickets

Victoria Basin forest-savanna mosaic

Southern Acacia-Commiphora bushlands

and thickets

Central Zambezian Miombo woodlands

Northern Congolian forest-savanna

mosaic

324,481.6 697

2

3

Northwestern Hawaii scrub

Serengeti volcanic grasslands

14.7 47

437

II

III

165,041.8

226,769.7

636

60917,947.6

4

5

Mandara Plateau mosaic

Victoria Basin forest-savanna

mosaic

7,478.5

165,041.8

330

636

IV

V

1,179,319.1

705,005.8

712

624

Totals198,291.81,815Totals2,600,6183,278

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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,

weuseAkaikeweightsderivedfromtheAICtoevaluatetherelativelikelihood

of each SAR model given the data and the set of models. Akaike weights

(normalizedbyconstructionacrossthesetofcandidatemodelstosumtoone)

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).

Inthemodelselectionframework,modelselectionuncertaintyariseswhen

thedataathandsupportseveralmodelswithasimilarstrength.Insuchacase,

relying on only the best model is inadequate, and multimodel inference is

recommendedasawaytoconstructarobustfinalinference(42).Asadvocated

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-

ponential,andMonod)andfoursigmoidalmodels(rationalfunction,logistic,

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)

arealsocommonlyusedtocarryoutmodelselection(42,50).AICandBICwere

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

giventhesamplesizeandthesetofmodels,whereasBICwasdevisedtoselect

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).

FittingtheModels.Nonlinearregressionmodelswerefittedbyminimizingthe

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

LillieforsextensionoftheKolmogorovnormalitytestorthePearson’sproduct

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).

Althoughtheselectionofnonlinearregressionmodelsthroughtheuseofthe

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

generatedbootstrapresamplesfromthemodifiedresiduals(inthesenseof

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-

countingforuncertaintyinrichnesscomparisonamongplacesofvaryingarea,

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.

ACKNOWLEDGMENTS.WethankS.Buckland,K.L.Evans,L.Marini,andthree

anonymous reviewers for helpful comments and/or discussions. K.J.G. holds a

Royal Society-Wolfson Research Merit Award.

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