Modeling amphibian energetics, habitat suitability, and movements of western toads, Anaxyrus (=Bufo) boreas, across present and future landscapes

Abstract

Effective conservation of amphibian populations requires the prediction of how amphibians use and move through a landscape. Amphibians are closely coupled to their physical environment. Thus an approach that uses the physiological attributes of amphibians, together with knowledge of their natural history, should be helpful. We used Niche Mapper™ to model the known movements and habitat use patterns of a population of Western toads (Anaxyrus (=Bufo) boreas) occupying forested habitats in southeastern Idaho. Niche Mapper uses first principles of environmental biophysics to combine features of topography, climate, land cover, and animal features to model microclimates and animal physiology and behavior across landscapes. Niche Mapper reproduced core body temperatures (Tc) and evaporation rates of live toads with average errors of 1.6 ± 0.4 °C and 0.8 ± 0.2 g/h, respectively. For four different habitat types, it reproduced similar mid-summer daily temperature patterns as those measured in the field and calculated evaporation rates (g/h) with an average error rate of 7.2 ± 5.5%. Sensitivity analyses indicate these errors do not significantly affect estimates of food consumption or activity. Using Niche Mapper we predicted the daily habitats used by free-ranging toads; our accuracy for female toads was greater than for male toads (74.2 ± 6.8% and 53.6 ± 15.8%, respectively), reflecting the stronger patterns of habitat selection among females. Using these changing to construct a cost surface, we also reconstructed movement paths that were consistent with field observations. The effect of climate warming on toads depends on the interaction of temperature and atmospheric moisture. If climate change occurs as predicted, results from Niche Mapper suggests that climate warming will increase the physiological cost of landscapes thereby limiting the activity for toads in different habitats.

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Contents lists available at ScienceDirect
Ecological Modelling
journal homepage: www.elsevier.com/locate/ecolmodel
Modeling amphibian energetics, habitat suitability, and movements of western
toads, Anaxyrus (=Bufo) boreas, across present and future landscapes
Paul E. Bartelta,∗, Robert W. Klaverb, Warren P. Porterc
aDept. of Biology, Waldorf College, Forest City, IA 50436, USA
bU.S. Geological Survey, Earth Resources Observation and Science Center, 47914 252nd Street, Sioux Falls, SD 57198-0001, USA
c207 Zoology Research, 250N. Mills Street, University of Wisconsin-Madison, Madison, WI 53706, USA
a r t i c l ei n f o
Article history:
Received 24 November 2009
Received in revised form 15 July 2010
Accepted 19 July 2010
Available online 24 August 2010
Keywords:
Habitat modeling
Physiological modeling
Cost surfaces
Western toads
Anaxyrus boreas
Bufo boreas
Movement corridors
Climate warming
a b s t r a c t
Effectiveconservationofamphibianpopulationsrequiresthepredictionofhowamphibiansuseandmove
through a landscape. Amphibians are closely coupled to their physical environment. Thus an approach
that uses the physiological attributes of amphibians, together with knowledge of their natural history,
should be helpful. We used Niche MapperTMto model the known movements and habitat use patterns
of a population of Western toads (Anaxyrus (=Bufo) boreas) occupying forested habitats in southeastern
Idaho.NicheMapperusesfirstprinciplesofenvironmentalbiophysicstocombinefeaturesoftopography,
climate, land cover, and animal features to model microclimates and animal physiology and behavior
across landscapes. Niche Mapper reproduced core body temperatures (Tc) and evaporation rates of live
toads with average errors of 1.6±0.4◦C and 0.8±0.2g/h, respectively. For four different habitat types, it
reproducedsimilarmid-summerdailytemperaturepatternsasthosemeasuredinthefieldandcalculated
evaporation rates (g/h) with an average error rate of 7.2±5.5%. Sensitivity analyses indicate these errors
do not significantly affect estimates of food consumption or activity. Using Niche Mapper we predicted
the daily habitats used by free-ranging toads; our accuracy for female toads was greater than for male
toads (74.2±6.8% and 53.6±15.8%, respectively), reflecting the stronger patterns of habitat selection
among females. Using these changing to construct a cost surface, we also reconstructed movement paths
that were consistent with field observations. The effect of climate warming on toads depends on the
interaction of temperature and atmospheric moisture. If climate change occurs as predicted, results from
Niche Mapper suggests that climate warming will increase the physiological cost of landscapes thereby
limiting the activity for toads in different habitats.
© 2010 Elsevier B.V. All rights reserved.
1. Introduction
Amphibians are high-profile elements of the sixth mass extinc-
tion (Wake and Vrendenburg, 2008; Rohr et al., 2008), and loss,
alteration, or fragmentation of both breeding and terrestrial habi-
tat are leading causes of declines (Green, 1997; Stuart et al., 2004;
Lannoo, 2005; Funk et al., 2005; Muths et al., 2006; Harper et al.,
2008). Long-term historical climate change has facilitated genetic
divergence of amphibian species through range alteration or pop-
ulation isolation (e.g., Goebel et al., 2009; Shepard and Burbrin,
2009). In contrast, rapid environmental change could contribute
to amphibian population declines.
Amphibians are wet-skinned ectotherms that are closely cou-
pled to their physical environment; factors that contribute to their
core body temperature include dynamic, complex interactions of
∗Corresponding author. Tel.: +1 641 585 8236; fax: +1 641 585 8194.
E-mail addresses: barteltp@waldorf.edu (P.E. Bartelt), bklaver@usgs.gov
(R.W. Klaver), wpporter@wisc.edu (W.P. Porter).
heat energy fluxes and evaporation (Tracy, 1976). The amount of
energy absorbed by a terrestrial amphibian depends on physical
featuresoftheanimal(e.g.,shape,color,andbehavior)andweather
conditions as modified by habitat structure (Fig. 1). The potential
physiologicalstates(e.g.,coretemperature)experiencedbytheani-
mal then reflect the net energy absorbed, plus the cooling effect of
evaporation. The animal’s actual physiological states will be sub-
sets of the potential states and influenced by factors such as food
availability, predator avoidance, and the animal’s hydration state
(i.e., the more water it is storing, the more evaporation it can tol-
erate). Finally, the actual physiological state of the animal directly
affects its behavior, growth, and other functions. Hence, habitats
selected by an amphibian can have direct physiological and func-
tionalconsequences(Huey,1991),andtherapidclimatechangewe
are experiencing could exacerbate effects of habitat loss (Pilliod
et al., 2002; Semlitsch and Bodie, 2003; Bartelt et al., 2004). We
want to know how climate change might affect the microenviron-
ments of amphibian terrestrial habitats. Predicting the movement
corridors and distribution of amphibians across a landscape and
how habitat changes might affect them is critical for developing
0304-3800/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolmodel.2010.07.009

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Fig. 1. Factors that affect amphibian body temperatures and physiology, and that are modeled by Niche Mapper. Environmental variables interact with intrinsic character-
istics of amphibians to create a mosaic of microsite conditions for them. The microsite chosen by an amphibian will determine its body temperature and hydration state,
and this can affect its physiology, growth, and behavior. Environmental change that alters either habitat structure or weather conditions also can affect amphibian body
temperatures.
effective conservation strategies, especially in light of a changing
environment.
Recent advances in computer technology, the development of
remote sensing to create landscape datasets, and efficient Geo-
graphic Information Systems (GIS) make possible the ability to
modelanimalenergeticsandbehavioracrossentirelandscapes.For
example, Ray et al. (2002) used landscape data layers of estimated
amphibian suitability within a GIS to estimate the ease of amphib-
ianstomovethroughlandscapes.Booneetal.(2006)useddiffusion
models with remotely sensed data to test factors affecting move-
ments of wood frogs (Rana sylvatica) among ponds in Minnesota,
and Kearney et al. (2008) calculated present and future distribu-
tion limits of the cane toad in Australia. We used Niche Mapper, a
process-driven mechanistic model (Porter and Mitchell, 2006), to
modelenergeticsandbehaviorinthecontextofdetailedknowledge
of four highly divergent vegetation types (closed canopy forest,
opencanopyforest,denseshrub,andclearcutforest).Tomodeltoad
energetics and movements and evaluate effects of climate change
on these predictions we used three approaches. First, to test the
accuracy of our approach, we made direct comparisons between
field and laboratory measurements of toads and physical models
(Bartelt and Peterson, 2005) against results calculated by Niche
Mapper using identical environmental data. Second, we applied
the results of Niche Mapper to a landscape where habitat use and
movementandpatternsofWesterntoads(Anaxyrus(=Bufo)boreas)
were previously measured (Bartelt, 2000; Bartelt et al., 2004) and
tested its ability to map these patterns. Third, we ran Niche Map-
peronthislandscapeunderdifferentweatherconditionstotestthe
effects of a warming climate on altering the habitat conditions on
this landscape and its potential effects on toads.

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2. Methods
2.1. The Niche Mapper models
Niche Mapper is a patented collection of three mecha-
nistic models that include a broadly applicable microclimate,
ectotherm and endotherm model of heat and mass transfer and
animal behavior. More details of these models can be found
in Porter et al. (1973), Porter and Mitchell (2006), and at
“http://www.zoology.wisc.edu/faculty/Por/Por.html.”
2.1.1. Microclimate model
The microclimate model translates coarse spatial data, such as
Digital Elevation Models (DEMs), vegetation data, weather station
data and spatially interpolated climate records, into microclimatic
environmental variables relevant to the thermal and hydric ecol-
ogy of organisms. It includes a one-dimensional finite difference
algorithm that simultaneously solves heat and mass balance equa-
tions for the ground surface and specified depths below. It includes
asubroutineforcomputingclearskysolarradiationgivenaspecific
time, latitude, longitude, elevation, slope and aspect (McCullough
and Porter, 1971). The microclimate model requires climate (2m
shadeairtemperature,windspeed,humidityandcloudcover)max-
imumandminimumdataforarbitrarytimeintervals,e.g.,monthly,
weekly or daily, and physical properties of the soil as major input
variables.
2.1.2. Ectotherm model
We modeled hourly core body temperatures (Tc) of toads by
iterative solving for Tcin a steady-state heat (Q) energy balance
equation containing terms representing solar (Qsolar), incoming
(QIRin) and outgoing (QIRout) thermal infrared radiation (IR), gener-
ated metabolic heat (Qgen), respiratory (Qresp) and cutaneous (Qcut)
evaporation, convective (Qconv) and conductive (Qcond) heat trans-
fer:
Qsolar+ QIRin+ Qgen= Qresp+ Qcut+ QIRout+ Qconv+ Qcond
Basicelementsofthemodelhavebeendescribedelsewhere(Porter,
1989; Porter and Gates, 1969; Porter et al., 1973, 1994, Appendix
A; Porter and Mitchell, 2006). A critical aspect of the model in the
contextofawet-skinnedamphibianisheatexchangeviacutaneous
evaporation. Qcut, is determined by the latent heat of vaporiza-
tion, ?, of water together with the rate of mass transfer such that,
Qcut=m·?. The rate of mass transfer is defined as
m = hD· A · (?w,skin− rh · ?w,air)
where m is the rate of mass transfer, hDis the mass transfer coeffi-
cient,Aistheareaoftheskinthatactsasafreewatersurfaceacross
which mass exchange occurs, rh is the local relative humidity, and
?w,skinand ?w,airare the densities of water vapor at saturation at
the temperature of the animal surface and air, respectively. See
Porter and Mitchell (2006) and Tracy (1976) for further details on
the calculation of mass transfer rates.
The distributed metabolic heat generation term, Qgen, in Eq.
(1) was taken from Lillywhite et al. (1973) data for A. boreas,
regressed to yield O2 in ml/(g/h)=0.00861×Tc−0.06128; and
converted to J/s assuming a protein diet (4.5kcal/L O2). Qgen
defines skin temperature, Tsfor current environmental conditions,
a (spherical) geometry and a given iterative guess of Tc, since
Qgen=6kV(Tc−Ts)/R2(Porter et al., 1994; p. 156, Eq. (2)), where V
andRareanimalvolumeandradiusandkistheeffectivefleshther-
mal conductivity (0.5W/mC). Qgen also determines the requisite
mass that must be absorbed from the gut, mabsin Eq. (3).
Mass (molar) balance (g/d)
(1)
(2)
min= mabs+ mout
(3)
Fig. 2. Location of Stamp Meadows study area in southeastern Idaho, USA.
defines molar balances for the respiratory and digestive system,
where minis the rate of mass entering the imaginary surface across
the entrance to the system, moutis the rate of mass exiting through
the imaginary surface across the exit of the system and mabsis
the mass crossing the internal surface of the system (the gut wall
or the respiratory surface (lungs and skin)) (Fig. 2 in Porter et al.,
2006). The metabolic processes of the body require that a specified
mass of daily fuel and oxygen be available. Thus mass that must
be absorbed daily, mabs, from the gut can be calculated from Qgen
requirements. Daily food intake required to maintain body weight
is computed using the digestive efficiency of a particular diet com-
position. The daily mass balance of the gut can be determined from
basic principles of environmental biophysics, since calculating the
required intake and the absorbed mass allows by difference the
mass out of the animal’s gut. Similarly, a molar balance on the res-
piratory system allows calculation of the mass of oxygen that must
flow through the respiratory system on a daily basis to meet the
demands of metabolism. Niche Mapper used an assumed oxygen
extractionefficiencyof12%foramphibians.Thiswasbasedonwork
byWithersandHillman(1983)thatreportsanextractionefficiency
for two species of forced exercised anurans as 18%. Kalliokoski et
al. (2001) report oxygen extraction efficiency for exercising human
muscle at 49% compared to resting efficiency of 29%. This suggests
that resting oxygen consumption is approximately 59% of active
efficiencies or for an 18% active anuran efficiency, a resting anu-
ran efficiency of 11%. An additional 1% was added for cutaneous
functions.
2.2. Testing the models
We tested the models at multiple scales. At the finest scale, we
tested the ability of Niche Mapper to predict Tcand rates of evap-
orative water loss (EWL) of individual animals under controlled
laboratory conditions. We then tested its ability to reproduce daily
patterns of operative temperature, Te(Bakken, 1989; Porter et al.,
1973) and rates of EWL among four different habitats measured by
physical models (Bartelt and Peterson, 2005). At the largest scale,
we applied Niche Mapper to an 8km2landscape to test its ability
to predict known movements and habitat use patterns of West-
ern toads in a forested area in southeastern Idaho, on the southern
slopes of the Centennial Mountains (Fig. 2; Bartelt et al., 2004).

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2.3. Predicting Tcand rates of EWL
BarteltandPeterson(2005)usedawindtunnelundercontrolled
laboratory conditions to compare rates of heating and cooling and
rates of EWL of physical models to those of live toads. We entered
weather values for these conditions into Niche Mapper to calculate
expected Tcand EWL rates under the same controlled conditions
and compared these results against the actual Tcand EWL rates.
2.4. Comparing patterns of Teand EWL among habitats
Before applying Niche Mapper to a landscape, we modified
the shade calculations to correct for solar zenith angle effects on
vegetation specific shade patterns and effects of different foliage
densities on daily variations of relative humidity.
2.4.1. Modifying Niche Mapper
To improve the ability of the microclimate model to predict
variations in temperature and humidity in different habitats across
the landscape we collected additional environmental information,
includingmeasuresofsolarabsorptivityandthepercentofthesur-
face that is wet for different habitat types in nearby Yellowstone
National Park (D. Anderson, USDA Forest Service, unpubl. data).
We also used a sling psychrometer and sets of physical models in
Yellowstone National Park to measure daily differences in vapor
densities (≤20cm above ground) among vegetation cover types
during summer and used these data to adjust the vapor density
inputs at 2m height for corresponding habitats into the microcli-
mate model.
Wecollecteddataonpercentshadeofdifferentvegetationtypes
at different solar altitudes in the Big Horn Crags of the Frank
ChurchWildernesswithfourseparateMicroWeatherStationsfrom
OnsetComputerCorp(Pocasett,MA).Thecanopycovervalueswere
calculated with a GAP Light Analyzer (Simon Frazier University,
REM Department, 1999) using image data collected with a fish-eye
lens (Nikon Fisheye Converter FC-E8, 35mm focal length equiva-
lent, 183◦angle) and camera (Nikon, 4500 Coolpix). The equation
describing these results we used was:
% shade reduction from vertical sun values
= 0.0973122 − 0.9297X + 0.0286672X2− 0.00021071X3
+334.216Y − 835.91Y2+ 1072.99Y3− 468.996Y4
where X is the zenith angle (◦) and Y is the % cover/100. The regres-
sion includes data over the range of 0.7–70.2% cover with an R2of
0.797.
2.4.2. Comparing Niche Mapper to field data
To test the ability of Niche Mapper to predict Teand rates of
EWL in particular habitats, we used field data collected on 25 July,
1995withreplicatesofphysicalmodelsplacedwithinfourdifferent
forested habitats (Bartelt, 2000). These habitats included mature
forest (canopy cover=67%), thinned forest (canopy cover=25%),
shrub (tree canopy cover=5% and shrub canopy cover=80%), and
clearcut (canopy cover=2%). By placing these stationary physical
models in exposed and shaded microsites, we were able to bound
the extremes of conditions available to free-ranging toads among
these habitats. Using data from an on-site weather station, we ran
Niche Mapper to calculate hourly values of operative temperature
and EWL for these habitats.
2.5. Using Niche Mapper to map the landscape for toad suitability
WeappliedNicheMappertoan8km2studysiteinsoutheastern
Idaho (Stamp Meadows) to test its ability to accurately map daily
habitats for Western toads and estimate movement patterns. We
compared these results to known patterns of toad movements and
habitat use (Bartelt et al., 2004). Although Western toads are con-
sidered habitat generalists (Muths and Nanjappa, 2005), field data
show that microenvironmental variation among habitats affect
their activity and habitat selection (Bartelt, 2000; Bartelt et al.,
2004).
2.5.1. Study area
Stamp Meadows is located on the Targhee National Forest in
southeastern Idaho. It is a grassy meadow surrounded by a mosaic
of coniferous habitats (Pinus, Picea, and Abies spp.) that have been
modified by logging. In spring of normal to wet years, water
collects to form a large (10–15ha) pond, bordered by willows
(Salix spp.), aspen (Populus tremuloides), and lodgepole pine (Pinus
contorta). Toads bred in this filled pond from late May through
mid-June.
2.5.2. Input data
We compiled all geospatial information as raster data at 30-
m cell size. We used a Digital Elevation Model (DEM; Gesch
et al., 2002) to acquire topographic data (elevation, slope, and
aspect) and DayMet weather model (Thornton et al., 1997;
http://www.daymet.org) to acquire maximum and minimum tem-
peratures and vapor densities. Because the weather data were
compiled at 1-km resolution, we resampled the data to 30-m cell
size and adiabatically adjusted temperature (−5.5◦C/km) for each
cell according to changes in elevation relative to the elevation for
the 1km cell. Habitat data (cover types and percent canopy cover)
were acquired from previous field measurements (Bartelt et al.,
2004). Because these field measurements were collected for each
of two years (1993 and 1995), we ran Niche Mapper twice, once for
each year.
2.5.3. Derived variables for the suitability index
In addition to the standard output variables computed by Niche
Mapper(e.g.,dailyevaporation,maximumcorebodytemperature),
we derived additional data related to the biology of Western toads.
Lillywhite et al. (1973) found that 27.3◦C was an optimal Tcfor a
number of physiological functions; hence, we counted the num-
ber of hours that Tc≥27◦C (Tc27). We counted the number of
hours that air temperature (Ta)<8◦C (Tc8), because toads gener-
ally moved least during cool night-time air temperatures (Ta≤8◦C
in Bartelt et al., 2004; Ta<5◦C in Sullivan et al., 2008). We also
counted the number of hours that Tcranged between 15 and 27◦C
(Tc20) to estimate the daytime hours available for toads to forage,
etc. Basking toads shuttled between sunlight and the moist sub-
strate of shade, apparently balancing their thermal and moisture
needs. In drying habitats, hydroregulation can be costly to toads
because lower body water content constrains their activity. The
maximum water that toads would voluntarily lose before seeking
shadewasabout7.5g(∼14%ofbodyweight;Bartelt,2000).Inmore
humid habitats, this was not a problem; but in drier conditions
toads showed reduced basking and/or foraging times and cooler
Tcs. Cooler body temperatures can reduce growth rates (Lillywhite
et al., 1973), sprint speeds (Tracy et al., 1993), and have cumula-
tive physiological consequences (Huey, 1991). To estimate the cost
of hydroregulation to toads (i.e., potential hours of basking and
solar heating constrained by evaporation), we divided the calcu-
lated evaporation by 7.5 and reduced the values of Tc27 by this
proportion.
Finally, we wanted to create a single, composite and unitless
measure that would capture the totality of a habitat’s suitability
for toads (similar to an approach used by Karr, 1981). We created a
unitless overall “suitability index” through a linear combination of
the derived variables described above. Toads were most active and

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Table 1
The set of seven a priori models used to predict the daily habitats used by Western
toads in the Stamp Meadows area, southeastern Idaho. For each of 13 toads, 80% of
the field data were used to build logistic regression models and 20% reserve data to
validate the best models.
Model #Predictor variables
1
2
3
4
5
6
7
Suitability
Evaporation
Tc27
Evaporation+Tc27
Evaporation+suitability
Evaporation+Tc27+Tc20+suitability
(Evaporation×Tc27)+Tc20+suitability
made long-distance movements during the months of June, July,
andAugust;hence,this“suitabilityindex”useddatacalculatedonly
for these months:
?
Suitability = Tc20 +
Tc27 −
?daytime evap
7.5
??
− Tc8 (4)
2.6. Predicting habitat use and movements
At the Stamp Meadows site, toads selected daily retreat sites
in habitats where they could hydroregulate and thermoregulate
during daytime activities, such as foraging, basking (Bartelt, 2000),
and making shorter (≤50m) movements. We used Niche Map-
per to test the hypothesis that toads selected sites that were less
costly. To map the distribution of these sites (a measure of habi-
tat selection), we used a Geographic Information System (GIS) and
logistic regression models with data layers for each of several stan-
dard and derived Niche Mapper output variables. For each toad, we
used the coordinates of its retreat sites, coordinates from an equal
number of randomly selected sites, and sampled the data layer for
each of the variables. We used Niche Mapper results from 1993
or 1995, depending which year the toad was studied. Eighty per-
cent of the data were used to build the logit models, reserving the
remaining 20% for validation. For each toad, we tested an a pri-
ori set of models (Table 1) and selected the best model with an
information–theoretic approach (Burnham and Anderson, 2002),
then validated its accuracy.For each toad, we tested an a priori set
of models (Table 1) and selected
By restricting their long-distance (>100m) dispersal move-
ments primarily at night, these toads avoided the higher
hydroregulatory costs of drier daytime conditions. By connecting
the sequential coordinates of daily retreat sites, Bartelt et al. (2004)
estimated the seasonal paths followed by toads. They found that
female toads traveled longer distances from their breeding pond
and selected daily habitats with warmer and more humid condi-
tions. We used Niche Mapper and cost-surface analysis to calculate
cumulative costs and replicate patterns of movement. Cost-surface
(orfrictionsurface)functionsarefundamentaloperationsoftheGIS
toolbox (Berry and Tomlin, 1982; Berry, 1987; Douglas, 1994). We
used the GIS (ArcMap v. 9.2) function “COSTPATH” to calculate two
sets of ideal least-cost paths for each of six toads that traveled the
longest distances; one set was created using the “overall suitability
index” and the second with calculated amounts of daily EWL. We
compared the cost of paths used by toads to those of straight lines
connecting the beginning and ending points of travel (the shortest
Euclidian distance), and some randomly generated paths for each
toad. Cost-surface analysis uses two input maps: a map of habitat
patches that function as sources and a map of the cost of mov-
ing among patches. The output mapped locations with the least
accumulated cost (i.e., the summated cost of sequential cells) for a
toad to reach it from the source habitat patches. The locations may
be interpreted as a species-specific connectivity measure that is
weightedbytheinterveningmatrix.WeusedNicheMapperresults
for 1993 for toads #25 and 31, and 1995 results for toads #4, 72,
73, and 78.
2.7. Testing scenarios of environmental change
We used Niche Mapper to estimate how a warming climate
might affect conditions of the habitats used by toads in Stamp
Meadows. We based this test on long-term (1937–2008) average
weather conditions collected at the Island Park weather station
(∼10km from Stamp Meadows and similar elevation), because
thesedatashowthatmonthlysummertemperaturesfor1993were
cooler than average (0.5–7.1◦C for maximum temperatures and
0.2–2.9◦C for minimum temperatures); because precipitation for
the summer of 1993 was greater by only 0.5cm, we used 1993 val-
ues for moisture. A number of climate scenarios predict a range of
warmer temperatures, from a minimum of about 2◦C to a maxi-
mum of 6◦C (IPCC, 2007) and increased precipitation. Therefore,
we tested three different warming scenarios (Table 2) with Niche
Mapper.
3. Results
3.1. Predicting Tcand rates of EWL
Niche Mapper reproduced toad Tc with an average error of
1.6±0.4◦Coverthetemperaturerangeof8–29◦C(Fig.3A).Itrepro-
ducedratesofEWLwithanaverageerrorof0.8±0.2g/hoveratotal
EWL range of 0.2–6.7g/h (Fig. 3B).
3.2. Comparing patterns of Teand EWL among habitats
In some habitats, daily variations of Te recorded by physical
models included the effect of shading and sun flecks as they moved
across the ground (Fig. 4). While Niche Mapper did not capture
these short-term temporal variations, its general predictions of
toad Tcshowed similar maxima and minima as Tefor the differ-
ent habitats and a similar number of hours that Tcand Teoccurs
within certain temperature ranges (Table 3). The average error was
1.4±0.2h.Thiswasexpectedgiventhatthetimestepintheanimal
calculations was hourly and rounding error could account for most
of these differences.
Under similar weather conditions, Niche Mapper calculated
greater amounts of EWL for habitats with less cover (Fig. 5A).
The average error in predicting amounts of EWL was 2.4±1.7g/d
(7.2±5.5% of that measured by the physical models; Fig. 5A). Aver-
age daily Ta increased from May to July and then decreased to
Table 2
Three different scenarios of climate change for the Stamp Meadows area tested with Niche Mapper. Each scenario is described by a change in maximum temperature (Tmax),
minimum temperature (Tmin), and relative humidity (RH; estimated from predicted changes in precipitation). These values were added to long-term (1937–2008) average
temperatures.
Scenario #
?Tmax(◦C)
?Tmin(◦C)
?RH
JuneJulyAugJuneJulyAugJuneJulyAug
1
2
3
+2
+4
+6
+2
+4
+5
+1
+3
+5
+0.5
+2
+4
+0.5
+2
+4
0
×1.05
×1.1
×1.15
×1.05
×1.1
×1.15
×1.05
×1.1
×1.15
+1
+6

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Table 3
Number of hours within selected temperature ranges.
Habitat <8◦C8–15◦C15–27◦C >27◦C
Physical models (Te)
Closed Canopy
Open canopy
Shrub
Clearcut
7
9
9
10
7
4
5
6
5
5
3
1
3
6
6 10
Niche Mapper (Tc)
Closed Canopy
Open canopy
Shrub
Clearcut
6115
3
3
2
2
5
6
7
10
10
7
6
5
8
Difference
Closed Canopy
Open canopy
Shrub
Clearcut
1
−11
2
3
1
−1
−2
−1
−1
1
−1
−3
0
3
−1
September, and average daily RH varied inversely (Fig. 5B). As pre-
dicted by Niche Mapper, monthly rates of EWL generally increased
from May to July, then decreased to September. However, the
amount of change varied among the habitats, with less variation
occurring in habitats with greater amounts of shade and foliage
density.
3.3. Using Niche Mapper to reclassify a landscape
Results from Niche Mapper generated a patchy landscape
where,forexample,toadscouldmaintainaTcof≥27◦Cfordifferent
hours in a day (Fig. 6A), or the amount of water toads would lose
Fig.3. Comparisonofactualtoadbodytemperaturesandratesofevaporativewater
loss to those calculated by Niche Mapper. Bartelt and Peterson (2005) compared the
behaviorofphysicalmodelstolivetoadsunder10separatetrialsofcontrolledcondi-
tions. We entered these same experimental conditions into Niche Mapper to test its
abilitytoreproducetheTcandEWLratesoflivetoads.(A)Bodytemperatures.Except
for two points, Niche Mapper temperatures were within 1.5◦C of actual tempera-
tures. The two points of larger differences may have resulted from measurement
error. (B) Evaporative water loss (EWL). Niche Mapper tended to underestimate
higher rates of EWL.
through evaporation during the day (Fig. 6B). The patterns of these
maps reflect the patterns of vegetation and cover on this landscape
(Fig. S1).
3.3.1. Predicting habitat use and movement paths
In predicting daily habitats, models that used a combination of
warmerbodytemperaturesand“suitability”,constrainedbyevapo-
ration, scored highest (Table 4). Maps of daily habitats produced by
these models (Fig. S2) were consistent with differences observed
in patterns of habitat selection between male and female toads
(Bartelt et al., 2004). That is, the models had weak or no predictive
power for males and better predictive power for females, reflecting
strongerpatternsofhabitatselectionamongfemales.Limitingtests
of validation to toads with at least six observations in the reserve
data, predictive accuracy for seven males averaged 53.6±15.8%,
and that for six females averaged 74.2±6.8%.
DailyamountsofEWLprovidedthebestresultsforcost-analysis
and produced idealized least-cost paths that best replicated paths
used by toads (Fig. 7). In all cases, accumulated costs for least-
cost paths were substantially less than costs for either used or
Fig. 4. (A) Daily variation of operative temperature (Te) in the Stamp Meadows area
(southeastern Idaho) recorded by physical models on 25 July 1995. (B) Variation in
core body temperature (Tc) of Western toads as predicted by Niche Mapper using
weather conditions recorded for the same area on the same day.

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Fig. 5. (A) Total amounts of water lost for 25 July 1995 as recorded by physical
models and predicted by Niche Mapper for the Stamp Meadows area (southeast-
ern Idaho). (B) Monthly variation of EWL predicted by Niche Mapper, compared to
variation in Taand RH.
straight-line paths (Fig. 8). With one exception, the accumulated
cost difference between used and straight-line paths diminished
as the total distance traveled decreased.
3.3.2. Testing scenarios of environmental change
Ignoring the need for hydroregulation, toads could theoretically
maintain a warmer body temperature (Tc≥27◦C) under the sce-
nario of a warmer climate (Fig. 9A). Evaporation rates, however,
also increased over a large percentage of the landscape (Fig. 9B);
thereby, constraining the number of hours a toad could maintain a
warm body temperature by its need for hydroregulation. The effect
of all three warming scenarios was similar: compared to average
conditions, a smaller proportion of the landscape would provide
toads the ability to maintain a warm body temperature without
dehydrating (Fig. 10). Furthermore, this proportion decreased with
increased warming.
4. Discussion
4.1. Predicting Tcand EWL
Niche Mapper was able to predict Tcof live toads under con-
trolled conditions with an average error of 1.6±0.4◦C. Among the
total 10 trials, it overestimated Tc in trials #4 and 9 by 4.2 and
3.3◦C, respectively; a difference up to 10 times greater than the
error for other trials. Excluding these two data points reduced the
average error to 1.1±0.2◦C. Niche Mapper underestimated rates
of EWL in four trials with peaks of evaporation rates. The overall
error was 0.92g/h; excluding these four trials reduced the error to
0.44±0.1g/h.
Cause for these large errors is uncertain. It could have resulted
frompotentialmeasurementerrorreportedinBarteltandPeterson
(2005), or Niche Mapper may simply be under-calculating higher
rates of EWL. The trials where Tcwas overestimated were also two
of the four where evaporation was underestimated. This pattern
of error would be consistent with the physiology of amphibians
where, within steady-state conditions, reduced rates of evap-
oration would translate into higher Tc (Tracy, 1976; Campbell
and Norman, 1998). If so, this discrepancy can be adjusted: toad
EWL=(Niche Mapper×1.3925)+0.0541; R2=0.932, F1,9=124.6,
p<0.001.
The practical effect of these errors would be to incorrectly
estimate animal metabolism and activity, because physiological
performance in amphibians is markedly temperature dependent
(Carey, 1978). However, because their physiological performance
lacks broad plateaus of thermal independence (Carey, 1978) and
change in metabolic rate diminishes at warmer temperatures
(Lillywhite et al., 1973; Carey, 1978) when toads are more active,
the amount of error will change with Tc and may be relatively
small. For example, using calculations of hourly CO2consumption
(mol/h) and wet food requirements (g/d) from Niche Mapper (fit-
ted to linear regression models), at temperatures of Tc≥20◦C the
Table 4
Summary of ability of logit models to predict daily habitat use by Western toads in the Stamp Meadows area, southeastern Idaho. Only toads with reserve data sets of ≥6
were used for this analysis.
Toad #
n
Best model AICw
ROCPrediction accuracy (%)
Male toads
5
50
61
63
65
67
71
Average=53.6±15.8%
Female toads
4
22
31
46
72
78
Average=74.2±6.8%
6
6
6
8
8
7
6
7
4
6
6
6
0.310
0.898
0.854
0.208
0.754
0.305
0.530
0.708
0.878
0.844
0.647
0.694
0.593
0.781
50
100
100
0
50
120
8
75
124
4
6
7
6
6
0.537
0.594
0.501
0.648
0.953
0.646
0.715
0.728
0.750
0.853
0.901
0.814
70
67
50
100
75
83
6
8
6
8
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Fig. 6. (A) The Stamp Meadows area (southeastern Idaho) reclassified to map areas where a toad could maintain a warm body temperature (Tc>27◦C) for different lengths
of time. (B) The Stamp Meadows area (southeastern Idaho) reclassified to map rates of evaporative water loss (EWL), reflecting relative costs to a toad.
averageerrorrateof±1.6◦CwouldaffectratesofCO2productionby
±8% (F1,85=1,027,616, p<0.001, R2=0.95). This is within the range
of temperature-induced changes in metabolic rates experimen-
tally measured by Lillywhite et al. (1973) and Carey (1978) for A.
boreas.Dailywetfoodrequirementsincreasedby2.1%for1◦Cerror
of Tcestimation (F1,8189=23,859, p<0.001, R2=0.74). In addition,
physiological and ecological performance does not scale directly
(Huey and Swenson, 1979). For example, improving physiologi-
cal performance by 20% may not result in an equal improvement
of ecological performance (e.g., activity time). Therefore, for the
purposes and scale of this modeling, we consider the amount of
error evident in Tcestimates by Niche Mapper to be inconsequen-
tial.
OurapproachalsoplacesanemphasisonthecostofEWLamong
toad habitats (i.e., greater rates of EWL diminishes the ability of
toads to maintain a warm Tc). The tendency of Niche Mapper
to underestimate EWL (especially at higher rates of EWL) could
be important in overestimating a toad’s amount of activity time
(Bartelt, 2000). Quantifying and correcting this EWL error greatly
reduced the error produced in later landscape-scale tests.
4.2. Patterns of Tcand EWL
There were some distinct differences in the predictions of Niche
Mapper compared to the actual field data. For example, maximum
Tepredicted by Niche Mapper exceeded that of the field data and

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Fig. 7. (A) Using rates of EWL and cost-analysis to predict the movement of toad
#31 across the Stamp Meadows landscape. (B) Using rates of EWL and cost-analysis
to predict the movement path of toad #78 across the Stamp Meadows landscape.
Fig. 8. Differences in relative costs of paths across the Stamp Meadows landscape.
Because total distances traveled by toads were different, the costs of paths for each
toad were standardized by the cost for its least-cost path to allow comparisons.
Except for toad #78, as the total distance traveled by a toad decreased, so did the
differences in cost between the three paths. From location to location, the care
employedbytoadstoselectlowercosttravelpathsmaybesmall,butthisdifference
becomes more important over longer distances.
briefly entered the range of the critical thermal maximum for A.
boreas(Brattstrom,1968).Whythemid-dayTefortheshrubhabitat
dipped briefly is unclear to us.
Computer models cannot capture the totality of natural vari-
ation. Comparing the Tedata recorded in the field among various
habitatsforadaytothatcalculatedbyNicheMapperusingweather
data collected on the same day, Niche Mapper did not replicate the
exact shading pattern of different habitats. For example, it did not
replicate the periodic sun flecks as they moved across the physical
models, briefly warming them. With the broader goal of model-
ing conditions across a landscape, however, capturing such minute
details as periodic sun flecks may be less important than character-
izing daily conditions available to amphibians in different habitats.
Comparing the number of hours Tewas within different tempera-
ture ranges, Niche Mapper was within 1h of the actual field data in
69% (11 out of 16) of the measurements. Because of our modifica-
tion of correcting for shade change due to angle for this particular
study site, the calculated estimates of EWL were very close to the
measured field data.
4.3. Reclassifying the landscape
4.3.1. Habitat use
Comparing our results to those of Bartelt et al. (2004), we con-
sider Niche Mapper to be a robust approach for modeling the
distribution of suitable toad daily habitats across this landscape,
because our modeling results closely reflect the actual patterns
observed in these toads. For example, clear habitat selection pat-
terns were discernable for female toads, but not male toads,
because male toads remained within the vicinity of the breeding
pond and this probably released them from the need to carefully
conservetheirbodywater.InBarteltetal.(2004)andthisstudy,the
predictive models for females were stronger than those for males.
4.3.2. Movements
Using cost-analysis to predict the dispersal movements of these
toads may have only limited value, because they moved primar-
ily at night when temperatures were cooler and relative humidity
was higher (Bartelt et al., 2004; Sullivan et al., 2008). Connecting
sequential locations with straight lines very likely excludes much
detail in their movement paths. In addition, the pattern evident
in Fig. 8 (diminishing differences between used and straight-line
paths as the total difference decreased) suggests that the cost of
the path used by toads is more a function of distance traveled,
ratherthananydiscerningbehaviorofthetoads.Ontheotherhand,
these differences also may suggest that while the toads did select
sites with lesser costs, the differences, while real, were small and
accumulated over longer distances. Regardless, given that a 60g,
free-ranging toad does not have the same total landscape perspec-
tive as does a computer, the spatial distribution of the idealized,
least-cost paths compared to the paths used by toads suggests that
thisapproachholdsvalue.Forexample,althoughthepathfollowed
by toad #78 (Fig. 7B) did not closely follow the least-cost path, it
does follow a least-cost corridor. Exceptions (i.e., near the west end
of the path) occurred on rainy days when daytime activity costs
were reduced.
4.3.3. Global climate change: an application
Like any other taxon, amphibians do not tolerate habitat mod-
ification/change well. Habitat loss and fragmentation is credited
for being a principle (if not the most important) factor contribut-
ing to amphibian population declines (Green, 1997; Noss et al.,
1997), and Gallant et al. (2007) suggests that continued trends of
human population growth and resource use will continue the loss
of habitat.

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Fig. 9. The estimated effect of global warming on the Stamp Meadows landscape for toads, expressed as a percentage of the total landscape. (A) Niche Mapper predicts an
increase in the percentage of the landscape where toads could achieve and maintain a warm body temperature (Tc>27). (B) The rate of evaporation also will increase over a
larger proportion of the landscape.
While the loss of habitat is an extreme change, what might be
theeffectofsubtlechanges(suchasclimatewarming)inseemingly
intact habitats on amphibians? The answer, of course, depends on
the extent of change, but results from this study suggest that the
Stamp Meadows landscape would become less friendly to toads
by making it more difficult for them to balance their thermal
and hydrological needs. Although a greater proportion of Stamp
Meadows would support warmer body temperatures under cli-
matewarming(Fig.9A),agreaterproportionalsowouldexperience
Fig. 10. The estimated effect of global warming on the Stamp Meadows landscape
for toads. These results suggest that, because of increased rates of evaporation, less
of the landscape would facilitate a toad’s ability to maintain a warm body tempera-
ture (Tc>27). Such an effect could reduce the connectivity of the landscape for toad
movements, and/or reduce the amount of a toad’s daytime activity (e.g., foraging
and basking).
greater amounts of EWL (Fig. 9B). When combined, a toad would
be more constrained in maintaining warmer body temperatures
and suitable hydration levels (Fig. 10); this would translate into
reduced activity hours that could impact growth and reproductive
potential for both individuals and populations. Constraining the
amountoftimethattoadscouldmaintainwarmbodytemperatures
would reduce their amounts of time for activities such as bask-
ing and foraging, which could also reduce physiological function
including growth rates or the ability to produce eggs. For example,
juvenile toads allowed access 5h/d grew (snout-vent-length; SVL)
four times faster over eight weeks than those allowed access to
heat for only 1h (Lillywhite et al., 1973). Similarly, P.S. Corn (pers.
commun., 2007) measured growth (SVL) of brown morph leopard
frog(Ranapipiens)metamorphsinColoradoasafunctionofdegree-
days. He estimated that a 20% change in degree-days would result
in a 25% change in growth. Our study suggests a reduction by up
to 40% for the amount of time that toads could effectively maintain
a body temperature ≥27◦C (in effect, reducing its degree-days).
Using the measurements of Lillywhite et al. (1973) and Corn, this
could translate into a reduction in growth of up to 50%. While we
don’t know if adult toads would experience this much reduction, it
seems clear their growth rates could be negatively affected under
global warming.
The vulnerability of amphibians to certain diseases may also be
exacerbatedbyclimatechange.Awarmingclimatemightaffectthe
spread and incidence of Batrachochytrium dendrobatidis, a major
and deadly pathogen of amphibians (Voyles et al., 2009). Our mod-
eling approach may help address this relationship (e.g., Pilliod et
al., 2010).

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Increasing the physiological cost of a landscape could also
affect amphibian populations by affecting dispersal patterns and
metapopulationstructure.Becausefrogsandtoadsmaytravelkilo-
meters overland to reach other ponds, foraging areas, hibernacula,
etc. (e.g., Pilliod et al., 2002; Muths, 2003), habitat fragmentation
could be an important factor in amphibian population declines
(Laan and Verboom, 1990; Funk et al., 2005). Before climate warm-
ing affects plants directly and alters the physical structure of
habitats, results from this study suggest that microenvironmen-
tal conditions could be altered sufficiently to increase the cost of
movements or diurnal activities such as foraging. Habitats may not
bephysicallyfragmented,butfromanamphibianperspective,they
could be “thermally fragmented.”
A different set of results could be produced under a differ-
ent set of assumptions. Because the long-term Island Park data
showedaverysmalldifferenceinrainfallcomparedto,1993condi-
tions, we assumed negligible differences in atmospheric moisture
for the climate scenario tests. If rainfall increases proportion-
ally to increases in temperature, then the resulting warming and
more humid microenvironmental conditions of habitats might
reduce the physiological cost of amphibian terrestrial habitats.
On the other hand, in areas where rainfall and moisture is
predicted to decrease (e.g., large portions of western and south-
western U.S.), the physiological cost of landscapes could greatly
increase.
5. Conclusions
A careful comparison of laboratory and field experimental data
against Niche Mapper shows that robust estimates of body tem-
perature, water loss rates, and likely movement and habitat use
patterns of A. boreas on the landscape can be obtained knowing
only measurable landscape and animal properties. We are working
with other populations in other areas (central Idaho, Yellowstone
National Park, northern Midwest) to begin assessing the applica-
bility of these results to this and other species (Rana luteiventris, R.
pipiens, Anaxyrus americanus).
The effect of a warming climate on these wet-skinned
ectotherms depends also on changes in atmospheric moisture pat-
terns. Under the assumptions of this study, relatively constant
atmospheric moisture could accentuate drying conditions and fur-
ther stress amphibians. A warmer climate with greater amounts of
atmospheric moisture could benefit these wet-skinned ectotherms
by reducing physiological costs. The resulting warmer Tcs might
also reduce the incidence of chytridiomycosis (Woodhams et al.,
2003; Rohr et al., 2008), although a connection between warmer
Tcs and chytridiomycosis is uncertain (Pilliod et al., 2010). A. boreas
can adapt to habitat change (e.g., fire; Hossack and Corn, 2007),
provided water sources (Hossack and Corn, 2008) or adequate
protective cover (Bartelt et al., 2004) are available. Our mechanis-
tic modeling suggests that projections of consequences of climate
change for toads and their climate constrained distribution limits
in the future can be assessed reliably within the confidence limits
of global climate simulations that drive these mechanistic mod-
els. Analogous calculations for Tuataras on coastal islands of New
Zealand (Mitchell et al., 2008), Hawaiian honeycreepers on Maui
(Porter et al., 2006), the endangered Japanese Serow deer on Hon-
shu (Natori and Porter, 2007), cane toad and the mosquito, Aedes
aegyptiinAustralia(Kearneyetal.,2008,2009)usingthesamesoft-
ware package suggest that this approach is robust for simulations
of animals’ energetics, behavior and distribution limits in the geo-
logical past, current climatic conditions and future climate events.
As these calculations have also shown, different critical variables
apply to different species depending on their properties, the prop-
erties of the landscapes that harbor them and the questions being
asked.
Acknowledgements
C.R. Peterson, A.L. Gallant, and D.S. Pilliod participated in the
early development of the ideas presented in this paper. D.S. Pilliod
also provided field assistance. S. Searcy assisted with analysis of
the relationship between solar zenith and shade patterns. P.S. Corn
and D.S. Pilliod reviewed an earlier draft of this manuscript. The
initial work presented here was completed at the USGS EROS Data
Center where PEB held a National Research Council Research Asso-
ciateship Award. Any mention of trade, product, or firm names is
for descriptive purposes only, and does not imply endorsement by
the US Government.
Appendix A. Supplementary data
Supplementary data associated with this article can be found, in
the online version, at doi:10.1016/j.ecolmodel.2010.07.009.
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