Assessing spatial patterns of disease risk to

biodiversity: implications for the management of the

amphibian pathogen, Batrachochytrium dendrobatidis

Kris A. Murray1*, Richard W. R. Retallick2, Robert Puschendorf3, Lee F. Skerratt4,

Dan Rosauer5,6, Hamish I. McCallum7, Lee Berger4, Rick Speare4 and Jeremy VanDerWal3

1The Ecology Centre, School of Biological Sciences, University of Queensland, Brisbane, Queensland 4072, Australia;2GHD Pty Ltd, 8 ⁄180 Lonsdale Street, Melbourne, Victoria 3000, Australia; 3Centre for Tropical Biodiversity and

Climate Change Research, School of Marine and Tropical Biology, James Cook University, Townsville, Queensland

4811, Australia; 4Amphibian Disease Ecology Group, School of Public Health, Tropical Medicine and Rehabilitation

Sciences, James Cook University, Townsville, Queensland 4811, Australia; 5School of Biological, Earth and

Environmental Sciences, University of New South Wales, Sydney, New South Wales 2052, Australia; 6Centre for

Plant Biodiversity Research, GPO Box 1600, Canberra, Australian Capital Territory 2601, Australia; and 7School of

Environment, Griffith University, Nathan Campus, Queensland 4111, Australia

Summary

1. Emerging infectious diseases can have serious consequences for wildlife populations, ecosystem

structure and biodiversity. Predicting the spatial patterns and potential impacts of diseases in free-

ranging wildlife are therefore important for planning, prioritizing and implementing research and

management actions.

2. We developed spatial models of environmental suitability (ES) for infection with the pathogen

Batrachochytrium dendrobatidis, which causes the most significant disease affecting vertebrate bio-

diversity on record, amphibian chytridiomycosis. We applied relatively newly developed methods

for modelling ES (Maxent) to the first comprehensive, continent-wide data base (comprising

>10000 observations) on the occurrence of infection with this pathogen and employed novel meth-

odologies to deal with common but rarely addressed sources of model uncertainty.

3. We used ES to (i) predict the minimum potential geographic distribution of infection with

B. dendrobatidis in Australia and (ii) test the hypothesis that ES for B. dendrobatidis should help

explain patterns of amphibian decline given its theoretical and empirical link with organism abun-

dance (intensity of infection), a known determinant of disease severity.

4. We show that (i) infection withB. dendrobatidis has probably reached its broad geographic limits

in Australia under current climatic conditions but that smaller areas of invasion potential remain,

(ii) areas of high predicted ES forB. dendrobatidis accurately reflect areas where population declines

due to severe chytridiomycosis have occurred and (iii) that a host-specificmetric of ES forB. dendro-

batidis (ES for Bdspecies) is the strongest predictor of decline in Australian amphibians at a continen-

tal scale yet discovered.

5. Synthesis and applications. Our results provide quantitative information that helps to explain

both the spatial distribution and potential effects (risk) of amphibian infection withB. dendrobatidis

at the population level. Given scarce conservation resources, our results can be used immediately

in Australia and our methods applied elsewhere to prioritize species, regions and actions in the

struggle to limit further biodiversity loss.

Key-words: amphibian declines, bioclimatic modelling, chytrid fungus, chytridiomycosis,

infectious disease, Maxent, species distribution model

*Correspondence author. E-mail: k.murray1@uq.edu.au

Journal of Applied Ecology doi: 10.1111/j.1365-2664.2010.01890.x

� 2010 The Authors. Journal of Applied Ecology � 2010 British Ecological Society

Introduction

Emerging infectious diseases can have serious consequences

for wildlife populations, ecosystem structure and biodiversity

(Crowl et al. 2008). Alarmingly, their incidence appears to be

rising as a result of anthropogenic influences that favour the

growth, dispersal and transmission of pathogens (Daszak,

Cunningham & Hyatt 2000; Jones et al. 2008). Assessing the

extent, effects and dynamics of diseases in host populations are

therefore important for predicting disease emergence and its

consequences, and to plan, prioritize and implement research

andmanagement actions.

Arguably the most serious wildlife disease impacting verte-

brate biodiversity at this time is chytridiomycosis. This disease,

caused by infection with the fungal pathogen Batrachochytri-

um dendrobatidis Longcore, Pessier &Nichols (1999), has been

implicated in many rapid and recent amphibian declines and

extinctions (Stuart et al. 2004; Skerratt et al. 2007; Bielby et al.

2008; Wake & Vredenburg 2008). Batrachochytrium dendro-

batidis (hereafter Bd) appears to have undergone recent global

expansion after the outbreak of a single clonal lineage, the

origin of which remains uncertain (Morehouse et al. 2003;

Rachowicz et al. 2005; but see Goka et al. 2009; James et al.

2009). As an international notifiable disease, reporting of Bd

detection to the World Organisation for Animal Health (OIE)

is now obligatory for member countries (World Organisation

for Animal Health 2008). Bd is currently known from

hundreds of amphibian species and from all continents where

amphibians occur (Speare & Berger 2000; Kusrini et al. 2008;

Olson & Ronnenberg 2008). Given its broad host range, many

more species are likely to be suitable hosts and this number will

rise as search effort and reporting increases.

The potential distribution of Bd is, however, still relatively

poorly understood; the native range has not been delineated

and Bd may still be expanding its range worldwide (Lips et al.

2008; Rohr et al. 2008; James et al. 2009). In Australia, it is

now widely accepted that the invasion and spread of Bd is the

probable cause of many frog declines (Skerratt et al. 2007).

Despite this, little quantitative data on risk of disease have

been available to researchers and managers at broad spatial

scales, hampering efforts to pinpoint areas and species war-

ranting immediatemanagement attention. Tools for predicting

the spread or establishment of Bd and for identifying areas of

high disease risk are therefore critical for policy makers,

researchers and managers charged with detecting this patho-

gen, developing management actions and prioritizing resource

expenditure (Gascon et al. 2007; Skerratt et al. 2008).

Predicting the dispersal and potential range of organisms

is commonly approached by characterizing environmental

suitability (ES) with correlative species distribution models

(SDMs) (Guisan & Thuiller 2005; Kearney & Porter 2009).

‘Presence-only’ SDMs are being used increasingly for their

application to species occurrence data sets for which no reli-

able absence records may be available (e.g. museum ⁄herbar-ium collections, atlases, non-targeted surveys etc.) (Pearce &

Boyce 2006). Rarely used in studies of infectious disease,

presence-only SDMs appear well suited to investigating the

distribution of infection with some pathogens because, anal-

ogous to verifying true absence of rare or endangered species

(Gibson, Barrett & Burbidge 2007), it is a statistical and

sampling challenge to assert ‘freedom from disease’ (Digia-

como & Koepsell 1986; Ziller et al. 2002; Skerratt et al.

2008). This challenge is rarely met for wildlife pathogens

because the cost of sufficient sampling (including diagnostics,

personnel, logistics, etc.) at broad spatial scales is typically

prohibitive. Furthermore, pathogen prevalence may be low

in a host population or may fluctuate temporally, and the

host itself may be difficult to detect, particularly if the patho-

gen has resulted in host declines as has been the case with

Bd (e.g. Lips et al. 2006).

Correlative SDMs will only be appropriate where the

distribution of infection with a pathogen is expected to be

regulated by spatially quantifiable predictors that capture

ES, such as climate or habitat type. For many pathogens,

this may be inappropriate if hosts provide a highly regulated

‘habitat’ in which to grow and no stage of the life cycle is

exposed to external environmental conditions (e.g. for inter-

nal, directly transmitted pathogens of endotherms). In the

case of Bd, however, infections occur on ectothermic

amphibian hosts and there is a direct effect of the environ-

ment (particularly temperature and moisture) on growth and

survival of both free-living and parasitic life stages (Johnson

& Speare 2003; Berger et al. 2004; Piotrowski, Annis &

Longcore 2004; Woodhams et al. 2008). SDMs should thus

be highly suited to characterizing ES for infection with Bd to

provide important insights into its potential distribution,

shed light on the probability of pathogen establishment fol-

lowing invasion into previously naı̈ve areas [as has been

demonstrated for other invasive species (Ficetola, Thuiller &

Miaud 2007), and to help improve detection probability

while reducing cost and effort of surveying for the pathogen

in the future (Guisan et al. 2006)]. In an adaptive manage-

ment context, such models are ideally suited to tailoring

future data collection, which can in turn be used to itera-

tively improve the model (Wintle, Elith & Potts 2005).

We hypothesized that modelling ES for infection with

Bd may also provide useful information about the risk to

amphibian populations posed by chytridiomycosis. Recently,

VanDerWal et al. (2009b) demonstrated that modelling ES

broadly predicts an organism’s abundance. For chytridiomy-

cosis, Bd abundance (infection intensity) on the host is a direct

determinant of disease development, severity and population

effects (Carey et al. 2006; Voyles et al. 2007; Briggs, Knapp &

Vredenburg 2010). Indeed, seasonal and elevational variation

in the prevalence, intensity and virulence of Bd infections has

long implicated climatic suitability as a major factor governing

its effects in the wild (Berger 2001; Berger et al. 2004; Wood-

hams & Alford 2005; Kriger & Hero 2007), and this has been

consistently supported by laboratory infection experiments

(Woodhams, Alford & Marantelli 2003; Berger et al. 2004;

Carey et al. 2006). We would thus expect that our ES results

not only reflect proliferation of Bd on the host at the time scale

used in model training (average annual) but also the risk of

severe chytridiomycosis to populations as a whole, a link we

2 K. A. Murray et al.

� 2010 The Authors. Journal of Applied Ecology � 2010 British Ecological Society, Journal of Applied Ecology

test herein by examining patterns of disease-induced amphib-

ian population declines.

A published SDM already exists for Bd (Ron 2005), in

which a correlative, presence-only SDM (GARP) with rela-

tively few (n = 44) presence records in the New World was

used to predict the global potential range of this pathogen.

While this was of great use at the time of publication, the

model appears to exaggerate suitable area in Australia

(Fig. S1, Supporting Information), is at a spatial scale too

coarse to be useful for regional management or for predicting

population declines, and is likely to suffer from several sources

of uncertainty inherent to correlative SDMs (e.g. extrapolation

beyond the training region, limited sample size, algorithm

nuances, inappropriate pseudo-absence selection; see e.g. Ara-

ujo & Guisan 2006; Pearson et al. 2007; Peterson, Papes &

Eaton 2007; VanDerWal et al. 2009a). These issues together

necessitate the development of independent, regionally specific

predictions for planning future research and management

actions on Bd at finer spatial scales.

To this end, we applied a relatively novel SDM method

(Maxent) (Phillips, Anderson & Schapire 2006) to the most

comprehensive, continent-wide data base available to date on

the occurrence of infection with Bd (Murray et al. 2010) to

model ES for this pathogen. We employed novel methodolo-

gies to deal with common but rarely addressed sources of

SDM uncertainty to provide maximum robustness in our pre-

dictions of ES inAustralia given the available data. The predic-

tions were used to estimate the minimum potential geographic

distribution of infection with Bd in Australia and to test the

hypothesis linking ES to disease risk as indicated by patterns

of disease-induced population declines. We used our results to

identify where chytridiomycosis may pose the greatest risk to

endangered species, allowing prioritization of species, regions

and actions when considering research and management

options given scarce conservation funds (Wilson et al. 2007).

Materials and methods

MODEL DESCRIPTION

The SDMsoftware usedwasMaxent (ver. 3.3.0), for which the under-

lying theory and assumptions have been described in detail elsewhere

(Phillips, Anderson & Schapire 2006; Dudik, Phillips & Schapire

2007). Briefly, Maxent has been shown to generally outperform other

correlative (both presence-only and presence-absence) SDM algo-

rithms (Elith et al. 2006; Peterson, Papes & Eaton 2007; Graham

et al. 2008; Wisz et al. 2008). It requires presence records only (but

uses random background points to sample available environmental

space), accounts for interactions among variables and identifies areas

that fall beyond the range of environmental conditions used during

training when making projections (identified as ‘clamped’ areas). The

output of Maxent corresponds with an index of ES for the organism,

where higher values correspond to a prediction of better conditions

(Phillips, Anderson& Schapire 2006).

We used Bd occurrence records from Murray et al. (2010). Full

details of these data and their collection methods are described in the

Metadata provided therein. Briefly, this newly compiled data set rep-

resents the first comprehensive, continent-wide data base describing

occurrence patterns of Bd on wild amphibian hosts. The data base

comprises 821 sites in Australia at which frogs or tadpoles have been

tested for Bd and includes 10 183 records from >80 contributors

spanning collection dates from 1956 to 2007. Bd was detected on 63

(55%) of the 115 species in the data set (c. 28% of Australia’s 223

species) (Table S1, Supporting Information). Two hundred and

eighty-four Bd-positive sites had sufficient geographic accuracy for

inclusion in the model (Table 1, Fig. S2, Supporting Information).

Few localities in the data base comprise statistically defensible

absence records given the difficulty of asserting freedom from chytrid-

iomycosis. The data base represents records of clinical and aclinical

infection with Bd, which by definition is considered synonymous with

chytridiomycosis (ranging from severe and clinical to benign and

aclinical) by disease authorities (sensu Berger et al. 1998 and as per

the ‘Definitions’ of the OIE’s Aquatic Animal Health Code; see

http://www.oie.int/eng/normes/fcode/en_chapitre_1.1.1.htm) but

distinct from including records of the free-living stage whichmay also

be detected off-host (Kirshtein et al. 2007;Walker et al. 2007).

Bd’s current occurrence pattern in Australia is highly consistent

with the hypothesis that environmental characteristics, such as

climate or habitat type, place direct limits on its distribution. Its

extensive distribution nation-wide (Fig. S2; Murray et al. 2010)

demonstrates that it has had sufficient opportunity to spread great

distances and into new geographic areas from its hypothesized

point(s) of introduction (major ports) (Murray et al. 2010). The large

number of known hosts and the spectrum of potentially susceptible

amphibian hosts nationally (e.g. Litoria spp.) in currently uninfected

regions strongly suggest that Bd is not limited in Australia by the

unavailability of susceptible amphibian host species. Similarly,

its presence in some remote and sparsely populated regions of the

Table 1. Summary of Batrachochytrium dendrobatidis (Bd) data base records. Geo-referenced Bd+ sites are those where the pathogen was

detected and an accurate geographic coordinate was obtained for input to the distribution model. Individuals tested is a minimum estimate;

many site records in the database did not include total number of individuals tested (see Fig. S2 for map and key to State names)

State

Database

records

Individuals

tested

Sites with

records Bd+ sites

Georeferenced

Bd+ sites

ACT 77 77 7 1 1

NSW 494 887 79 39 39

NT 14 14 2 0 0

QLD 6660 8789 359 165 165

SA 42 42 16 8 8

TAS 146 574 122 45 43

VIC 26 32 11 6 6

WA 2647 2446 225 76 22

Australia 10 106 12 861 821 340 284

Spatial patterns of disease risk 3

� 2010 The Authors. Journal of Applied Ecology � 2010 British Ecological Society, Journal of Applied Ecology

country and its absence in some populated regions suggest that it is

not simply dependent on humans for its establishment and persis-

tence, although in some cases human aided spread seems likely (Mor-

gan et al. 2007; Skerratt et al. 2007). In contrast, Adams et al. (2010)

report that Bd occurrence in Oregon and California, USA, does not

correlate with any hypothesized environmental factors, but that Bd

detectability increases with human influence on the landscape. We

thus also evaluated the predictive power of a human-influence

hypothesis for predicting Bd’s current occurrence pattern inAustralia

and compared it with our ES model (Fig. S8, Supporting Informa-

tion).

We used 19 bioclimatic variables (all continuous), one geo-physical

variable (distance to water; continuous) and one vegetation type vari-

able (categorical) at a resolution of c. 250 m (9 arc-seconds) for our

models (Table S2, Supporting Information). We knew a priori that

many of the variables were correlated and potentially meaningful

contributors to the model; to avoid over-sizedmodels (including vari-

ables with no predictive value) or over-fitted models (too many

parameters for the data set) (Parolo, Rossi & Ferrarini 2008), we first

selected the top ranking variables that together contributed c. 90% of

the information to a full model run. We then re-ran a ‘pruned’ model

with the most important variables (Table S2). Model accuracy was

assessed with the area under the curve (AUC) of the receiver operator

characteristic (ROC), which is a singlemeasure of discrimination abil-

ity (presence from random background, where a value of 1 = perfect

prediction, 0Æ5 = prediction no better than random) of the models

(Fielding & Bell 1997). To incorporate uncertainty into our predic-

tions, we used bootstrapping (N = 100) with unique sets of training

and testing data (70 : 30% respectively). Many presence-only SDMs

require background points (or pseudo-absences), the selection of

which can influence the outcome of the models (Phillips et al. 2009;

VanDerWal et al. 2009a). We provide an extended discussion of our

background point selection in Fig. S2 which we used in order to limit

as far as possible the effects of unquantifiable sampling bias andmod-

elling an organismwith considerable invasion potential.

DISEASE RISK

To investigate the hypothesized relationship between ES for Bd and

the risk of chytridiomycosis to susceptible amphibian populations,

we assessed whether our results were consistent with descriptions of

population decline attributed to severe chytridiomycosis (Berger

et al. 1998, 2004). We anticipated that decline sites would be strongly

skewed towards higher values of ES for Bd. Declines attributed to

chytridiomycosis have been best described from uplands in the Aus-

tralian Alps and frommontane rainforest areas in Queensland, where

ill and dead frogs have been rigorously diagnosed as dying from chy-

tridiomycosis at the time of declines (Berger et al. 1998, 2004; Hines,

Mahony & McDonald 1999; McDonald & Alford 1999; Osborne,

Hunter &Hollis 1999) (Fig. S3, Supporting Information).

We next averaged our ES predictions across amphibian occurrence

records for each species in the data set described by Slatyer, Rosauer

& Lemckert (2007 updated 2009, D. Rosauer unpubl. data) to derive

a species-specific metric of ES for Bd that we termed ‘ES for Bdspecies’.

Slatyer et al.’s extensive data set comprises 291 942 occurrence

records for all of Australia’s amphibian species. We removed dupli-

cate records from the same locality (leaving 140 897 records; mean

per species = 640) for calculations. Further details of the metric are

provided in Fig. S4, Supporting Information. Species range size has

previously been identified as the major risk factor for decline and

extinction in Australian amphibians after controlling for other life-

history and ecological factors (Murray & Hose 2005). We thus tested

for an effect of ES for Bdspecies, controlling for the range size effect, in

contributing to whether amphibians have experienced declines or not.

Amphibian trend classifications were sourced from the IUCN (2008).

Range sizes were calculated from extent of occurrence polygons

developed for the Global Amphibian Assessment (GAA) (Stuart

et al. 2004).

Finally, we calculated mean ES values across Australia’s biogeo-

graphic regions to identify those most suitable for infection with the

pathogen (Fig. S5, Supporting Information). We related these results

to amphibian species richness and endemism statistics from the study

of Slatyer, Rosauer & Lemckert (2007) to indicate where infection

with Bd most threatens anuran biodiversity in Australia (Fig. S6,

Supporting Information).

Results

MODEL SELECTION, VAL IDATION AND VARIABLE

CONTRIBUTIONS

After the pruning step, mean test AUC was 0Æ900 (range

0Æ874–0Æ925) and the model contained eight variables. The

jack-knife procedure, which examines the effect of individual

variables, indicated that mean diurnal temperature range and

annual precipitation had the most useful information as single

variables on training data (highest gain scores in isolation) as

well as the highest predictive power (highest AUC in isolation)

(Fig. 1). Response curves characterizing the relationships

between ES and each of the twomost influential predictor vari-

ables are shown in Fig. S7, Supporting Information. In the

comparative analysis incorporating human population density

(HPD), predictive performance of the full model was

unchanged (0Æ903, range = 0Æ852–0Æ936) and HPD had infe-

rior predictive power in isolation (AUC = 0Æ763, ran-

ge = 0Æ716–0Æ811) relative to many of the environmental

predictors. For subsequent analyses, we thus used the model

incorporating environmental variables only (see Fig. S8, Sup-

porting Information for results and further discussion).

PREDICTED DISTRIBUTION

The model suggested that infection with Bd should be largely

restricted to the eastern and southern seaboards of Australia,

with nearly all of inland and northern Australia unsuitable.

Figure 2 represents the average Maxent predictions of ES

(available for download in Appendix S2, Supporting Informa-

tion). Clamping indicated that all of Australia fell within the

environmental limits used to train themodel (data not shown).

DISEASE RISK

Decline sites (mean ESdecline = 0Æ758; 95%CI = 0Æ714–0Æ802,n = 39) were highly skewed towards higher ES values

compared to all sites used for model training and testing

(mean ESall = 0Æ577, 95% CI = 0Æ550–0Æ604, n = 284)

(Fig. 4a,b,d).

Mean ES for Bdspecies varied between population trend cate-

gories (Fig. 3a); three extinct species had the highest value, 42

declining species had an intermediate value and 151 stable

4 K. A. Murray et al.

� 2010 The Authors. Journal of Applied Ecology � 2010 British Ecological Society, Journal of Applied Ecology

species exhibited a comparatively low value. In a logistic model

in which species were grouped by whether they had declined

or not (unknown trend species omitted), ES for Bdspecies was

a highly significant predictor of decline (Ddev = 20Æ932,d.f. = 1, P < 0Æ001), even after controlling for a significant

influence of narrow species range size (Ddev = 22Æ831,d.f. = 1, P < 0Æ001). The best model in terms of AIC con-

tained ES for Bdspecies as a highly significant term (P < 0Æ001),range size as a marginally significant term (P = 0Æ098) and no

interaction term. Table S3, Supporting Information presents a

list of priority species for research and management indicating

where investigation of Bd as a potential threatening process is

critical. Table S4, Supporting Information presents the full list

of Australian species.

Mean ES varied considerably across biogeographic regions

(Fig. 3b); the Wet Tropics (see also Fig. 4a) was predicted to

have the highest mean suitability for Bd, followed by the Cen-

tral Mackay Coast (Fig. 4b), Tasmania’s southern ranges,

northern slopes, north-east (Ben Lomond) and King Island

(Fig. 4e) and the NSW north coast (Fig. 4c). South-east

Queensland (Fig. 4c), the Australian Alps (Fig. 4d), the Swan

Coastal Plain (around Perth) (Fig. 4f) and the Tasmanian

south-east also showed high mean ES values. Many regions

with low mean ES nevertheless showed limited areas of very

high ES as indicated by their maximum values (e.g. Brigalow

Belts, Einasleigh Uplands, NSW south-western slopes)

(Fig. 3b).

Discussion

Infection with B. dendrobatidis occurs across a broad range of

climates in Australia, in areas that are at times very hot, cold,

dry or wet. Those locations range from the hot, humid coastal

lowlands of north-eastern Australia to the highest peaks of the

Australian Alps, where winter snow occurs. Despite its broad

tolerance of conditions, the model suggested that specific envi-

ronmental conditions will restrict infection with Bd to the gen-

erally cooler and wetter areas of Australia (Figs 2 and 4). In

this respect, our model was highly consistent with that of Ron

(2005) (Fig. S1; Fig. 2); however, our results suggested that Bd

should be more restricted, with the majority of central (arid)

Australia being broadly unsuitable for Bd persistence (see also

Fig. S8).

The model indicated that ES increased with annual precip-

itation (with a minimum extreme of c. 500 mm) (Fig. S7).

This is not surprising since desiccation is known to rapidly

kill Bd in vitro (Berger 2001; Johnson et al. 2003) and the

presence of permanent water is known to be an important

feature for sustaining Bd, probably because the transmission

stage for Bd is an aquatic zoospore (Berger et al. 1998). The

model also suggested that mean diurnal temperature range

was an important variable; the response curve indicated that

ES declined rapidly in highly variable temperature regimes,

where the difference in daily maxima and minima is greater

than c. 11 �C. Variation in temperature of itself has not

previously been shown to affect chytridiomycosis (Wood-

hams, Alford & Marantelli 2003). However, high tempera-

tures are known to be lethal to Bd and the effect of

temperature variability may be explained by the observation

that areas with higher temperature variability (e.g. the arid ⁄ -semi-arid interior of the country) also typically exhibit very

high maximum temperatures. This suggestion is supported

by the response of Bd to maximum temperature of the

warmest month, which showed maximum ES in the range of

0 0·2 0·4 0·6 0·8 1 1·2 1·4 1·6

Mean diurnal rangeTemp ann range

Mean temp dry quartAnnual precip

Precip dry quartPrecip warm quart

Precip cold quartVegetation type

Full

Training gain

Only variable Without variable

0·65 0·7 0·75 0·8 0·85 0·9 0·95

Mean diurnal rangeTemp ann range

Mean temp dry quartAnnual precip

Precip dry quartPrecip warm quart

Precip cold quartVegetation type

Full

AUC

Only variable Without variable

(a)

(b)

Fig. 1. Variable contributions to (a) training

gain and (b) AUC of the final ‘pruned’ model

for Batrachochytrium dendrobatidis in Aus-

tralia. ‘Only variable’ indicates the results of

the model when a single variable is run in iso-

lation; ‘without variable’ indicates the effect

of removing a single variable from the full

model (jack-knife). Values are means from

100 replicates. See Table S2 for full variable

names and descriptions.

Spatial patterns of disease risk 5

� 2010 The Authors. Journal of Applied Ecology � 2010 British Ecological Society, Journal of Applied Ecology

maximum temperatures 18–30 �C beyond which there is a

precipitous decrease (data not shown). Our results are thus

highly consistent with those of previous studies indicating

that high temperatures are detrimental to Bd (Kriger & Hero

2007; Muths, Pilliod & Livo 2008; Puschendorf et al. 2009).

DISEASE RISK

Two key results from this study are that (i) our predictions of

ES are strikingly consistent with known associations between

Bd and amphibian population declines in Queensland ⁄New

South Wales (Fig. S3 and Fig. 4a–c) (Hines, Mahony

& McDonald 1999; McDonald & Alford 1999) and in the

Australian Alps (Osborne, Hunter & Hollis 1999; Berger et al.

2004) (Fig. 4d) and (ii) the species-specific metric of ES for Bd

(termed ES for Bdspecies) was a very strong predictor of

amphibian decline at a national level. These findings support

the hypothesis that ES for infection with the pathogen as mod-

elled here is broadly predictive of suitability for, and severity

of, the disease chytridiomycosis via a theoretical and empirical

link with intensity of infection (VanDerWal et al. 2009b). We

thus interpret our ES for Bd results as being a highly useful

source of quantitative information relevant to explaining the

potential effects of infection with B. dendrobatidis (disease

risk).

This association should be interpreted cautiously, however,

as in order for ES for Bdspecies to translate to risk of decline a

number of other conditions relevant to the epidemiology of

chytridiomycosis must be fulfilled, most importantly

transmission. Species with more aquatic life-histories and an

association with permanent water are most susceptible and

at greatest risk of severe disease (Berger et al. 1998, 2004).

Further, species inhabiting different micro-habitats can vary

in their relative risk of infection within a single location

(Woodhams & Alford 2005; Skerratt et al. 2008). As such,

actual disease risk will be a product of the ES for the patho-

gen, the susceptibility of the species and the factors that make

it susceptible to decline (e.g. see Bielby et al. 2008) given the

former.

This is an important consideration as it will be necessary to

stratify host life-history traits for prioritization purposes

(Table S3). Bielby et al. (2008) found that small range size,

altitude and an aquatic life stage are risk factors for rapid

decline in Bd-positive species. However, applying these risk

factors to all species as they do is a considerable extrapolation

because not all species are equally susceptible to infection.

For example, very high-risk values in that study were assigned

to many species with largely terrestrial life-histories, including

many of Australia’s microhylid frogs (e.g. Cophixalus sp).

While some of these also exhibit high ES for Bdspecies values

as described herein, neither index identifies actual risk from

Bd as species in this group appear far less susceptible than

stream-dwelling and permanent water-associated species from

the same region (N = 557 negative results in areas that are

Bd-positive; K. Hauselberger & D. Mendez et al. unpubl.

data; Skerratt et al. 2008). A more sophisticated risk analysis

can be performed when more information is available about

the innate susceptibilities of different amphibian species to

chytridiomycosis and to decline. Integrating host-life history

and ecological traits with the pathogen’s environmental

requirements (as modelled here) to predict infection and

decline is the focus of our current research efforts (Murray

et al. in press).

MANAGEMENT IMPLICATIONS

We have shown that ES for Bdspecies is a strong predictor of

decline at a continental scale. This result was independent of a

previously reported, dominant effect of narrow geographic

range size. Our study provides a species-specific metric, repre-

senting the environmental requirements of the pathogen, with

which to begin to assess this risk and calls for targeted vigilance

Fig. 2.Model predictions of environmental suitability (after

bootstrapping N = 100) for Batrachochytrium dendrobatidis in

Australia.

6 K. A. Murray et al.

� 2010 The Authors. Journal of Applied Ecology � 2010 British Ecological Society, Journal of Applied Ecology

in sampling for this disease and monitoring for its potentially

insidious effects (Murray et al. 2009; Pilliod et al. 2010).

Bd records exist from most regions that were deemed suit-

able by the model, indicating that it has probably reached its

broad geographic limits on this continent. There are, however,

at least two areas that showmarginal suitability for Bd beyond

the known range of the pathogen where testing has failed to

detect it: Cape York (Skerratt et al. 2008) (Fig. 4a) and Tas-

mania’s World Heritage south-west (Pauza & Driessen 2008)

(Fig. 4e). It is possible that Bd has simply not yet dispersed to

these regions, as they are at the extreme limits of the distribu-

tion in northern and southern Australia. However, the results

of this studymay also suggest that establishment or disease risk

could be relatively low in these regions. Our results provide a

testable hypothesis and surveys should continue in these areas

where suitability is predicted to be highest (Fig. 4a,e). Preven-

tion of spread nevertheless remains the best management strat-

egy and these areas should not be regarded as areas in which

Bd could not establish and cause mortalities (Fig. 2). Hygiene

protocols should therefore be enforced for people entering

these areas (Phillott et al. 2010).

Several other marginal to highly suitable regions exist where

no sampling has occurred. These regions represent important

areas for future sampling to establish the actual geographic

limit of Bd in Australia and to establish amphibian population

health. Identification of naive populations at high disease risk

is a particular priority. Examples include uplands in the far

north of Queensland (Cape York; Fig. 4a), upland areas in the

Brigalow Belt (Fig. 4c), a large expanse of the western slopes

of the Great Dividing Range in NSW (Fig. 4c), the south-west

central tablelands ofNSWand the regions surroundingMount

Gambier and theMt Lofty Ranges in SouthAustralia (Fig. 2).

Conversely, our results suggest that several declining species

for which chytridiomycosis is a suspected threatening process

may have relatively low ES for Bdspecies (e.g. Litoria piperata

and Litoria castanea), which provides a way forward when

considering management and research activities. Similarly,

some declining species may be at high risk of disease only in a

subset of populations (e.g. Litoria spenceri, as indicated by

maximum vs. mean ES values – Table S3). We are not assert-

ing that Bd will be absent from these species or populations,

but that other factors may also be involved in their decline, an

example of where our results provide some useful and testable

hypotheses that should be pursued.

Regions of high disease risk in association with high host

endemism should be the highest priority for population moni-

0

0·1

0·2

0·3

0·4

0·5

0·6

0·7

0·8

0·9

1

Extinct (3) Declining (42) Stable (151) Unknown (17)

Env

ironm

enta

l sui

tabi

lity

for

Bd

(95%

CI)

IUCN trend category

0·0

0·1

0·2

0·3

0·4

0·5

0·6

0·7

0·8

0·9

1·0

Env

ironm

enta

l sui

tabi

lity

for

Bd

(±1S

D)

IBRA Ecoregion

MEANMax

(a)

(b)

Fig. 3.Mean environmental suitability forBatrachochytrium dendrobatidis across: (a) species with different IUCN trend classifications, (b) IBRA

ecoregions (averaged across entire region; only regions where the maximumormean value>0Æ2 are shown). See Fig. S5 for map.

Spatial patterns of disease risk 7

� 2010 The Authors. Journal of Applied Ecology � 2010 British Ecological Society, Journal of Applied Ecology

toring and ⁄ormanagement activity. Of the 11 centres of excep-

tional anuran endemism identified by Slatyer, Rosauer &Lem-

ckert (2007), six occur in regions predicted to be highly suitable

for Bd, including the Wet Tropics (Fig. 4a), Central Mackay

Coast (Mackay ⁄Eungella; Fig. 4b), Gladstone (Kroombit

Tops), South-east Queensland (Gympie-Coffs Harbour;

Fig. 4c) and south-west Western Australia (Walpole and Bun-

bury-Augusta; Fig. 4f) (see Fig. S5 for ecoregion names and

Fig. S6 for endemism ⁄ richness). Records of Bd exist from all

of these areas. An additional two areas (Townsville and Cape

York) are predicted to have more restricted regions that are

marginally or highly suitable for Bd (Fig. 4a). Three endemism

hotspots are predicted to be at negligible risk fromBd (Kakadu

and the Arnold River region in the NT and the Mitchell Pla-

teau in WA). Establishing and maintaining a disease-free sta-

tus should be their regional priority.

The methods and results from this study can be used as a

tool for establishing cost-sharing arrangements, prioritizing

future efforts to detect and manage this pathogen (e.g. disease

surveys, preventing further spread to naı̈ve areas), for prioritiz-

ing monitoring programmes for Bd and Australia’s anuran

fauna (e.g. Skerratt et al. 2008) and for identifying priority spe-

cies for potential emergency captive-breeding programmes

(Gascon et al. 2007) (Table S3). We envisage this to be an iter-

ative process, with models such as ours regularly updated and

scrutinized as new systematically collected data accrue (Wintle,

Elith& Potts 2005). Critically, ourmethods can be directly and

rapidly applied to other regions of the world experiencing

amphibian declines; such results will aid in the task of develop-

ing informed management and surveillance decisions for Bd

(Skerratt et al. 2008) and will help to make the most of limited

conservation funds for prioritizing species, regions and actions

for biodiversity conservation outcomes (Wilson et al. 2007).

L IMITATIONS AND FUTURE DIRECTIONS

While our model had high predictive performance and clamp-

ing indicated a well sampled environmental space, relatively lit-

(a) (b)

(d)(c)

(e) (f)

Fig. 4. Selected regions in Australia predicted

to have high average environmental suitabil-

ity for Batrachochytrium dendrobatidis (see

Fig. 2 for key to colours). Stars = ill and

dead frogs positive for Bd in association with

population declines (Qld ⁄Aust. Alps). Grey

lines = IBRA ecoregion boundaries (see

Fig. S5 for map and key).

8 K. A. Murray et al.

� 2010 The Authors. Journal of Applied Ecology � 2010 British Ecological Society, Journal of Applied Ecology

tle sampling has occurred on the western margins of the Great

Dividing Range and in inland Australia, and Queensland and

Western Australia were over represented compared with other

regions. In addition, frogs may take refuge in environments

that are not captured by interpolated bioclimatic or vegetation

mapping data (see also Fig. S8) and we have limited ability to

incorporate microclimatic features into our models given the

enormous diversity of amphibian hosts and their habitats in

this country. Similarly, beyond considerations of HPD

(Fig. S8) we were unable to incorporate models of pathogen

dispersal given very limited knowledge regarding how this

pathogen is spread. We model the realized niche of this inva-

sive species in an invaded range; there is thus the possibility

that Bd’s distribution in Australia has not approached an equi-

librium state, potentially resulting in an underprediction of its

potential range. We consider this an unlikely source of major

bias in our results given Bd’s extensive distribution nation-wide

and the spectrum of potentially susceptible amphibian hosts

(e.g. Litoria spp.) and hypothesized vectors (e.g. humans) in

currently uninfected regions. Nevertheless, our model repre-

sents a baseline, minimum potential distribution rather than a

finite prediction of this organism’s fundamental niche; we

encourage scrutiny and ongoing iteration (e.g. integrated use

of new systematically collected data), particularly to increase

representation of apparently disease-free areas into future

models. Dispersal models should also be a future priority, par-

ticularly in areas that are newly invaded. Finally, genetic differ-

entiation has been noted geographically (Morgan et al. 2007;

James et al. 2009), and strains may undergo local adaptation

(Fisher et al. 2009) and ⁄or show strain specific differences in

adaptive plasticity so distribution in Australia with respect to

available environmental space may not necessarily correspond

exactly to other regions or to the results of other predictive

models. Comparison of these and future studies will thus iden-

tify important areas and avenues for further research and it is

imperative that the predictions of any SDM be independently

compared with other SDM methods and data sources (see

Elith et al. 2006), other methods (e.g. mechanistic models;

K.A.M. unpubl. data) (Morin & Thuiller 2009) and by

comprehensive field surveys during sampling periods thatmax-

imize detection probability (Skerratt et al. 2008).

Acknowledgements

We are indebted to the many authors and contributors named in Murray et al.

(2010) for the production of the Bd occurrence data base. In particular, we

thank K. McDonald, K. Aplin, H. Hines, D. Mendez, A. Felton, P. Kirkpa-

trick, D. Hunter, R. Campbell, M. Pauza, M. Driessen, S. Richards, M. Mah-

ony, A. Freeman, A. Phillott, J-M. Hero, K. Kriger and D. Driscoll. KAM

thanks D. Segan, M. Watts and C. Klein for GIS wisdom and spatial data,

R. Wilson and H. Possingham for lab space, B. Sutherst, M. Zalucki and

D. Kriticos for fruitful discussions and M. Araujo and R. Pearson for running

a timely SDM workshop at the University of Queensland. We also thank

Dr Marc Cadotte, Professor Christl Donnelly and three anonymous reviewers

for excellent comments and discussion on earlier versions of the manuscript.

KAM was supported by an Australian Postgraduate Award, an Australian

Biosecurity CRC professional development award and a Wildlife Preservation

Society of Australia student research award. Part of this work was conducted

when RWRR was supported by the Australian Research Council, the School

of Public Health and Tropical Medicine, James Cook University and a

National Science Foundation Integrated Research Challenges in Environmen-

tal Biology grant awarded to J. Collins at Arizona State University, USA.

RWRR thanks J. Collins andC. Carey.

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Received 31May 2010; accepted 28 September 2010

Handling Editor:Marc Cadotte

Supporting Information

Additional Supporting Information may be found in the online ver-

sion of this article:

Appendix S1. Supporting Information (Tables S1–S4, Figs S1–S8).

Appendix S2.Results of themodel (Bd_in_Australia.asc).

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Spatial patterns of disease risk 11

� 2010 The Authors. Journal of Applied Ecology � 2010 British Ecological Society, Journal of Applied Ecology