EcoHealth 2, 1–11, 2005
DOI: 10.1007/s10393-005-3877-5
2005 EcoHealth Journal Consortium
Sharon K. Collinge,
1,2
Jack F. Cully, Jr.,
5
Andrew P. Martin
1
Whitney C. Johnson,
Kenneth L. Gage,
6
1
Chris Ray,
1
Michael Y. Kosoy,
6
Randy Matchett,
3
Jenella E. Loye,
7
John Grensten, and
4
1
Department of Ecology and Evolutionary Biology, 334 UCB, University of Colorado, Boulder, CO 80309-0334
2
Environmental Studies Program, 334 UCB, University of Colorado, Boulder, CO 80309-0334
3
Charles M. Russell National Wildlife Refuge, U.S. Fish and Wildlife Service, P.O. Box 110, Lewistown, MT 59457
4
Malta Field Office, Bureau of Land Management, HC 65 Box 5000, Malta, MT 59538
5
Kansas Cooperative Fish and Wildlife Research Unit, United States Geological Survey, 204 Leasure Hall, Kansas State University, Manhattan,
KS 66506-3501
6
Bacterial Zoonoses Branch, Division of Vector-Borne Infectious Diseases, Centers for Disease Control and Prevention, Fort Collins, CO 80522
7
Department of Entomology, University of California, Davis, CA 95616
Abstract: Climate may affect the dynamics of infectious diseases by shifting pathogen, vector, or host species abundance, population dynamics, or community interactions. Black-tailed prairie dogs ( Cynomys ludovicianus ) are highly susceptible to plague, yet little is known about factors that influence the dynamics of plague epizootics in prairie dogs. We investigated temporal patterns of plague occurrence in black-tailed prairie dogs to assess the generality of links between climate and plague occurrence found in previous analyses of human plague cases. We examined long-term data on climate and plague occurrence in prairie dog colonies within two study areas. Multiple regression analyses revealed that plague occurrence in prairie dogs was not associated with climatic variables in our Colorado study area. In contrast, plague occurrence was strongly associated with climatic variables in our Montana study area. The models with most support included a positive association with precipitation in April–July of the previous year, in addition to a positive association with the number of
‘‘warm’’ days and a negative association with the number of ‘‘hot’’ days in the same year as reported plague events. We conclude that the timing and magnitude of precipitation and temperature may affect plague occurrence in some geographic areas. The best climatic predictors of plague occurrence in prairie dogs within our Montana study area are quite similar to the best climatic predictors of human plague cases in the southwestern United States. This correspondence across regions and species suggests support for a (temperature-modulated) trophic-cascade model for plague, including climatic effects on rodent abundance, flea abundance, and pathogen transmission, at least in regions that experience strong climatic signals.
Key words: climate, disease, grassland, plague, prairie dogs, trophic cascade
Published online:
Correspondence to: Sharon K. Collinge, Department of Ecology and Evolutionary
Biology, Environmental Studies Program, 334 UCB, University of Colorado, Boulder,
CO 80309-0334, e-mail: sharon.collinge@colorado.edu
I
NTRODUCTION
Climate may affect the dynamics of infectious diseases by shifting pathogen, vector, or host species abundance, population dynamics, or community interactions (Harvell

2 Sharon K. Collinge et al.
et al., 2002; Yates et al., 2002). For example, human cases of plague and hantavirus in the western United States and visceral leishmaniasis in Brazil have been linked to periodic climatic cycles, such as the El Nin˜o Southern Oscillation
(ENSO) (Parmenter et al., 1999; Hjelle and Glass, 2001;
Enscore et al., 2002; Franke et al., 2002; Yates et al., 2002;
Stapp et al., 2004). If there is a close association between climate and disease occurrence, then the distribution and prevalence of both human and wildlife diseases may shift in response to global climate changes that affect the abundance, distribution, or seasonal activity patterns of vectors or pathogens (Benning et al., 2002; Harvell et al., 2002). It is crucial, therefore, to further understand factors that affect disease occurrence to better predict the temporal dynamics of epidemics, particularly for wildlife species of conservation concern whose populations may be severely reduced by infectious diseases.
Disease can significantly elevate mortality for blacktailed prairie dogs ( Cynomys ludovicianus ), a species of conservation concern in western North America (Miller et al., 1990, 1994; Gober, 2000). In particular, prairie dogs are highly susceptible to plague, yet little is known about factors that influence spatial and temporal occurrence of plague epizootics in prairie dogs. Sylvatic plague, caused by the bacterium Yersinia pestis , was introduced to North
America from Asia, circa 1900, and is now present throughout most of the western US (Barnes, 1982; Gage et al., 1995; Antolin et al., 2002). The plague pathogen spreads through contact between flea vectors and many mammalian host species (Barnes, 1982; Perry and Featherston, 1997; Gage et al., 1995). Because prairie dog populations suffer high mortality from plague, they are not likely to be effective reservoir hosts for the disease. Consistent observations of plague prevalence in small mammals such as deer mice ( Peromyscus maniculatus ) that appear moderately resistant to the disease suggest that these animals may serve as reservoir hosts in which plague persists in the enzootic portion of the plague cycle (Barnes, 1982;
Gage et al., 1995). When plague enters prairie dog colonies, it causes nearly 100 % mortality in black-tailed ( C. ludovicianus ) and Gunnison Õ s ( C. gunnisoni ) prairie dogs
(Cully, 1997), and high but more variable mortality in white-tailed ( C. leucurus ) (Anderson and Williams, 1997) and Utah ( C. parvidens ) prairie dogs [Biggins, personal communication].
Because grassland rodents may serve as reservoir hosts for the plague bacterium, disease outbreaks in prairie dogs may be strongly correlated with population and commu-
Figure 1.
Hypothesis for plague prevalence in the American southwest, based on arguments and results found in Parmenter et al. (1999) and Enscore et al. (2002). This temperature-modulated trophic-cascade hypothesis includes lagged trophic effects (solid arrows) and more immediate climatic effects (broken arrows) on the potential for local plague prevalence.
nity dynamics of these animals. Previous studies have proposed links between climate, primary productivity, rodent abundance, and human cases of plague and hantavirus in the southwestern US (Parmenter et al., 1999; Enscore et al., 2002; Yates et al., 2002). In particular, temporal variation in rainfall in the arid southwest may produce predictable variation in rodent abundance, which appears to be correlated with human cases of plague and hantavirus. These findings suggest that certain aspects of climate could be used by public health agencies as useful predictors of disease outbreaks in humans.
Based on associations between climate and disease occurrence, several authors (Parmenter et al., 1999; Enscore et al., 2002; Yates et al., 2002) proposed a trophic-cascade hypothesis to explain the number of human plague and hantavirus cases in the southwestern US (Fig. 1). They hypothesized that high precipitation increases plant productivity, which in turn increases rodent and flea populations 1 or 2 years later. Furthermore, they suggest that higher rodent populations lead to higher contact rates between hosts and vectors, higher probability of contact with humans and, given a suitable temperature regime (warm but not too hot), higher probability of successful pathogen transmission to humans. Here, we term this a ‘‘temperature-modulated trophic-cascade hypothesis’’ for plague.
Brown and Ernest (2002) challenged the trophic-cascade aspect of this hypothesis because their long-term rodent data from southeastern Arizona show that rodent population dynamics are complex, nonlinear, and not well pre-

Trophic-cascade Model of Plague 3 dicted by climatic variables. Given the equivocal evidence in support of the trophic-cascade model for plague outbreaks, further investigations are warranted.
Plague outbreaks in prairie dogs may be associated with climatic variation and rodent fluctuations in a similar manner as outbreaks in humans. Many rodents that serve as reservoir hosts also interact directly or indirectly with prairie dogs by occupying the same grassland habitat and often by using prairie dog burrows as shelter (Koford, 1958;
Agnew et al., 1986; Kotliar et al., 1999; Johnson, 2002).
Hence, prairie dogs may be even more likely to interact with infective rodents and vectors than are humans. If the association between climate and plague in humans is mediated by rodent population fluctuations, then an association between climate and plague occurrence in prairie dogs should be evident, and may be even stronger than that between climate and human plague cases.
Our objective was to determine whether climatic models similar to those developed to explain human plague cases could explain temporal patterns of plague occurrence in black-tailed prairie dogs. We developed a set of candidate models, using the results of Parmenter et al. (1999) and Enscore et al. (2002) to guide our hypotheses regarding associations between precipitation, temperature, and plague occurrence in prairie dogs. We examined plague outbreaks over the past 10–20 years in two study areas within the geographic range of black-tailed prairie dogs, and related these outbreaks to climatic variables for each study area over the same time period. Finally, we used an information criterion (Burnham and Anderson, 2002) to identify which models were best supported by the data, and to evaluate whether plague in prairie dogs can be explained by climatic models similar to those developed for humans.
M
ETHODS
We selected two study areas within the range of the blacktailed prairie dog, one in Colorado and one in Montana, based on the availability of long-term data on plague occurrence. Complete plague datasets were available for the periods 1980–2002 and 1990–2002 at our Colorado and
Montana study areas, respectively. We used these same two study areas in a related analysis of plague occurrence in relation to landscape structure (Collinge et al., in press).
The Colorado study area is located in Boulder County, in the midst of an urban corridor that runs along the Front
Range, east of the Rocky Mountains. The human population in Colorado has increased at a rate three times the national average since 1990 (U.S. Bureau of the Census,
2000), and the Colorado Front Range is one of the most rapidly urbanizing regions in the USA (Riebsame, 1997).
The City and County of Boulder own or manage properties comprising approximately 12,000 ha of grassland habitats that are protected from development. There are approximately 1200 ha of active prairie dog colonies that lie within these properties. The mean and median colony sizes in this study area are 4.6 ha and 0.8 ha (Johnson, 2002). Prairie dog colonies in Boulder County are typically located in shortand mixed-grass prairies, all historically grazed by cattle.
Short-grass prairies near Boulder are dominated by western wheatgrass ( Agropyron smithii ), blue grama ( Bouteloua gracilis ), buffalo grass ( Buchloe dactyloides ), pasture sagebrush ( Artemisia frigida ), and woolly plantain ( Plantago patagonica ), and mixed-grass prairies are dominated by blue grama ( Bouteloua gracilis ), side-oats grama ( Bouteloua curtipendula ), blazing star ( Liatris punctata ), prairie sage
( Artemisia ludoviciana ), and aster ( Aster falcatus ) (Bennett,
1997; Collinge, 2000).
The Montana study area is located in rural southern
Phillips County, spanning part of the Charles M. Russell
(CMR) National Wildlife Refuge and a patchwork of Bureau of Land Management (BLM) parcels intermixed with private property. The CMR and BLM lands comprise approximately 400,000 ha and support larger prairie dog colonies than those in our Colorado study area. The mean and median colony sizes on the CMR are 15.8 ha and 2.8
ha, respectively. This area is characterized by short- and mixed-grass prairies and sagebrush shrublands. Shrubdominated areas include two common shrubs, big sagebrush ( Artemesia tridentata ) and greasewood ( Sarcobatus vermiculatus ), and grassland areas are dominated by western wheatgrass ( Agropyron smithii ), blue grama ( Bouteloua gracilis ), needle-and-thread ( Stipa comata ), and green needlegrass ( Stipa viridula ) (Reading and Matchett, 1997).
Cattle ranching and recreation are the dominant land uses in this area.
Time-lagged precipitation is the putative driver in the trophic-cascade model for plague (Parmenter et al., 1999;
Enscore et al., 2002). We acquired total monthly precipitation values for each study area from the ‘‘Annual Climatological Summary’’ prepared by the National Oceanic

4 Sharon K. Collinge et al.
and Atmospheric Administration for the National Climatic
Data Center (http://www.ncdc.noaa.gov/oa/ncdc.html).
For our Colorado study, we used data from the Boulder weather station. Because our Montana study area was much larger, we averaged the total monthly precipitation values from four weather stations located within southern Phillips
County (Content 3SSE, Malta 35S, Valentine, and Winifred). To allow for lagged effects of precipitation (see
‘‘Model Development,’’ below), we used data from 1979–
2001 for our Colorado analysis and 1989–2001 for our
Montana analysis. We replaced any missing monthly values during these periods with the long-term average for that month and site (1949–2003 for Colorado, 1971–2000 for
Montana). Long-term average monthly precipitation values were highly correlated with monthly precipitation during the study period (Pearson correlation coefficients=0.99 and
0.98 for Colorado and Montana study areas, respectively).
There were 23 missing values out of 276 station-months
(8.3
% ) for the Colorado study area, and 39 missing values out of 624 station-months (6.3
% ) for the Montana study area. In both study areas, missing precipitation values occurred most frequently during winter (November to
March).
Maximum daily temperatures (MDT) may modulate the potential for pathogen transmission and plague epizootics under the trophic-cascade model. Based on a review of the literature, Enscore et al. (2002) identified a range of
MDT (26.7–37.8
C, or 80–100 F) likely to encompass optimal conditions for flea-mediated transmission of plague bacteria between hosts. Their modeling results suggest increased transmission to humans when maximum daily temperatures range 29.4–35 C (85–95 F). Because the optimal temperature envelope identified by their models lay well within the range of MDT considered, we considered a similar range of MDT in our models (see ‘‘Model
Development’’).
For each study area and year, we acquired daily temperature data (using the ‘‘Surface Summary of the Day’’ from each weather station named above) and counted the total number of days in which MDT ‡ 26.7, 29.4, 32.2, 35, and 37.8
C (80, 85, 90, 95, and 100 F). For the Montana study area, we averaged temperature data from the two weather stations closest to the study area (Content 3SSE and Malta 35S). As with the precipitation data, we used the long-term daily temperature average to replace missing values for each station. There were 24 missing values out of
8391 days used (0.29
% ) for the Colorado study area and 20 missing values out of 9486 days used (0.21
% ) for the
Montana study area. In both study areas, missing values occurred most frequently during winter (November to
March).
The two study areas differ substantially in key climatic characteristics. For example, the timing of precipitation varied among years much more in the Colorado study area than in the Montana study area over the period 1990–2002
(Fig. 2). In the Montana study area, the annual peak in monthly precipitation generally occurred in June (Fig. 2a), whereas in the Colorado study area, this peak could occur in any month from March to November (Fig. 2b). The average annual precipitation for the Colorado study area
(1949–2003) was 48.5 cm, and for the Montana study area
(1971–2000) was 34.2 cm. For both study areas, monthly maximum temperature was relatively consistent among years (Fig. 2c, d). The annual peak in temperature occurred at similar times (July) and was of similar magnitude (26–
32 C) for both study areas, but the monthly maximum temperatures during the winter months were much lower in the Montana study area than in the Colorado study area
(Fig. 2c, d). For example, the average January maximum temperature was 7.5
C for the Colorado study area and
) 2 C for the Montana study area. Overall, the Colorado study area was wetter all year, warmer in winter, and exhibited much more variability in the timing of precipitation over the study period.
We acquired data on plague occurrence in prairie dogs for
Boulder County, Colorado, for the years 1980–2002 from the Centers for Disease Control (CDC), Boulder County
Health Department records, and Boulder County wildlife managers. Data from the CDC are the geographic locations
( x , y coordinates) of prairie dogs or prairie dog fleas (primarily Oropsylla hirsuta ) in which plague was detected.
These data result from routine CDC investigations of prairie dog ‘‘die-offs’’ (Cully and Williams, 2001) in which colonies are rapidly and conspicuously decimated. These data underestimate the actual number of prairie dog colonies affected by plague in a given year because the CDC investigates only a sample of colonies involved in each spatio-temporal cluster of colony die-offs. Therefore, we supplemented these data with die-offs reported by Boulder
County health officials and local wildlife managers. Because of the close proximity of prairie dog colonies to urban areas, Boulder County health officials and wildlife managers closely monitor local prairie dog colonies. Colonies on

Trophic-cascade Model of Plague 5
Figure 2.
Monthly precipitation and temperature data for two study areas used in the analyses described. Monthly precipitation (cm, rain and snow equivalents) for ( a ) Southern Phillips County, Montana and ( b ) Boulder County, Colorado from 1990–2002; monthly maximum temperature ( C) for ( c ) Southern Phillips County,
Montana and ( d ) Boulder County, Colorado from 1990–2002. See panel a for legend.
Boulder City Open Space properties have been regularly monitored and incorporated into grassland management plans since 1976 [M. Gershman, personal communication]
(City of Boulder Open Space and Mountain Parks, 1996).
In 1981, the Boulder County Health Department began regular flea collections from prairie dog burrows for plague surveillance [CDC, unpublished data]. In 1986, wildlife managers in Boulder reported many colony die-offs. The
CDC confirmed that plague was present in each colony where wildlife managers had reported prairie dog die-offs by screening for plague bacteria in the fleas collected by
Boulder County Health Department officials. These data, combined with the widespread observation that plague epizootics represent the only known natural cause of rapid colony die-offs (Gage et al., 1995; Hoogland, 1995; Cully,
1997; Cully and Williams, 2001), give us confidence that die-offs observed by wildlife managers represent epizootics of plague. Using a combination of reports from County health officials and wildlife managers, we constructed a database containing the number of colony die-offs observed in prairie dog colonies throughout Boulder County from 1980–2002.
For southern Phillips County, Montana, observational data on plague occurrence on CMR and BLM lands have been collected since 1979 as part of a prairie dog population-monitoring program associated with reintroduction of the black-footed ferret ( Mustela nigripes ) .
We collated plague data for the years 1992–2002. No colony die-offs were observed in Phillips County from 1979–1991
[Matchett, unpublished data].
We used the approach and results of Enscore et al. (2002) to guide the selection of our candidate models. Enscore et al. (2002) defined plague-year t as beginning in mid-June of calendar-year t , and modeled the number of human plague cases in plague-year t as a function of: temperatures

6 Sharon K. Collinge et al.
Figure 3.
Temporal structure of climatic models developed to explain human plague cases in Arizona (Enscore et al., 2002) and prairie dog colony die-offs in Montana (see the Methods section), including lagged relationships between plague response (black bars) and precipitation (striped bars), and more immediate relationships between plague response and temperature (stippled bars). The temporal relationship between variables is shown by month, over a span of 2½ years. Note that precipitation and plague response may be separated by about 2 years in the human model, and 1½ years in the prairie dog model. Differences in model structure are due, in part, to differences in local patterns of precipitation and differences in the temporal resolution of the response variables (weekly dating of human plague cases vs. annual dating of prairie dog colony die-offs).
in calendar-year t ; spring precipitation in calendar-years t , t
)
1 , etc.; and monsoon precipitation in calendar-years t
)
1 , t
)
2 , etc. (Fig. 3). Because our data on prairie dog die-offs were reported by calendar year, we defined plague-year t as calendar-year t , and modeled the number of colony die-offs as a function of temperatures in calendar-year t and precipitation in calendar-year t
)
1 (cf. Fig. 3).
Ideally, we might define a ‘‘plague year’’ such that there are appropriate temporal lags between the predictor variables (precipitation and temperature) and the response variable (plague-induced die-offs). Our model enforces a temporal lag between the plague response (measured in plague-year t ) and the precipitation predictor (measured in plague-year t
)
1 ). We define a plague year as a calendar year based on data from our Colorado study area, where die-off reports peak in the middle of the calendar year (mean dieoff report date = July 16, median = July 9, range = March
5–November 24, n = 40 dated reports). Because these urban prairie dog colonies are effectively under year-round surveillance, the fact that die-off reports tend to peak mid-year suggests that the plague year within this study area is congruent with the calendar year. We must assume the same seasonal pattern of die-offs in our Montana study area, where colonies are not under constant surveillance. In contrast, our model allows temporal overlap between the plague response and the temperature predictor, both measured in plague-year t . This apparent overlap is in keeping with the hypothesized effect of temperature on plague transmission: hot days may reduce the ability of fleas to transmit plague bacteria, so hot days in the midst of an epizootic may reduce the number of colony die-offs within that plague year.
Our models differed from those of Enscore et al.
(2002) in the number and timing of precipitation variables.
Although monthly precipitation generally peaks twice annually in the American southwest (Enscore et al., 2002), it peaks only once annually in our Montana study area and is quite variable in our Colorado study area (Fig. 2). We characterized precipitation in year t
)
1 as
X
S t 1
¼ P t 1 ; M
;
M
ð 1 Þ where P t
)
1 ,M is the total precipitation in month M of year t ) 1 , and the ‘‘running’’ sum S t ) 1 is taken over 2 or more consecutive months. For Montana, we considered all such running sums between April and August, allowing for 10
(nonnested) models based on precipitation alone. For
Colorado, we considered all such running sums between
March and November, allowing for 36 models based on precipitation alone. Due to the large number of potential predictors based on precipitation in t
)
1 , we did not consider longer time lags within our initial set of candidate models. However, after identifying a set of well-supported models based on a 1-year precipitation lag, we compared support for these models with support for similar models extended to include a 2-year precipitation lag. This exercise increased the number of models considered by just three, because only three models based on precipitation were well supported by the data (see ‘‘Results’’).
Enscore et al. (2002) considered five predictors related to temperature in year t : each predictor, D t
T
, represented the number of days in which the maximum temperature rose above T, where T = 26.7, 29.4, 32.2, 35, or 37.8
C (80, 85,

Trophic-cascade Model of Plague 7
90, 95, and 100 F).
D t
37.8
did not appear among their best plague models, and because few days reached 37.8
C within our study areas, we considered only the four predictors
D t
26.7
)
35
. To account for reduced vector efficiency above a temperature threshold, or enhanced vector efficiency between thresholds, we considered models based on one or two temperature thresholds, allowing for 10 models based on temperature alone.
Our initial set of candidate models included at most one precipitation variable and up to two temperature thresholds. Given 10 models based on temperature alone and 10 (Montana) or 36 (Colorado) models based on precipitation alone, plus models including no effects of temperature and/or precipitation, we constructed 121 models for our Montana data and 407 models for our Colorado data. Testing such a large number of models is not advisable, and may lead to the selection of a model with spuriously good fit (Burnham and Anderson, 2002). We proceeded on the basis of two arguments. First, we lacked any biological rationale for further reducing the set of candidate models.
We had already reduced the set considerably by reducing the number of temperature thresholds and time lags relative to those considered by Enscore et al. (2002). Second, we did not seek a single ‘‘best’’ model. Rather, we sought evidence that a group of similar models, all consistent with the temperature-modulated trophic-cascade hypothesis, were well supported by the data. In order for a model to be consistent with this hypothesis, it would have to include: 1) a positive association between a period of peak precipitation and plague response (with less support for models that include only periods of off-peak precipitation); and/or 2) a positive association between plague response and a temperature envelope similar to that suggested by Enscore et al.
(2002), including a positive effect of ‘‘warm’’ days and/or a negative effect of ‘‘hot’’ days (where ‘‘warm’’ and ‘‘hot’’ are similar to the values modeled by those authors).
We considered two model structures. First, we modeled the annual number of colony die-offs ( ‡ 0) as a Poisson-distributed random variable with mean k , ln ð k t
Þ ¼ b
0
þ b
1
S t 1
þ
X b
T
D t
T
;
T
ð 2 Þ where all b x are fitted parameters, S t
)
1 and D
T t are the precipitation and temperature variables defined above, and the sum represents at most two temperature thresholds.
This model assumes that the variance in the response variable equals its mean ( k ). When the variance exceeds the mean (as in our datasets), a variance inflation factor / can be estimated as the Pearson Chi-Squared statistic divided by the residual degrees of freedom for the ‘‘global’’ model.
Because our candidate models were not nested, we estimated / using several parameter-rich models of the form ln ð k t
Þ ¼ b
0
þ
X b
M
P t 1 ; M
M
þ
X b
T
D t
T
;
T
ð 3 Þ where the sums are taken over several of the (consecutive) precipitation months and temperature thresholds considered for each study area. Using estimates for / based on these ‘‘global’’ models, we adjusted the log-likelihood obtained for each candidate model (Eq. 2), and used an information criterion based on quasi-likelihood (QAIC c
) to determine the relative support for each candidate model
(Burnham and Anderson, 2002).
It can be argued that plague-induced die-offs should be modeled as a threshold response. Therefore, we also used logistic regression to model the annual number of colony die-offs as a binomially distributed random variable with mean p , logit ð p t Þ ¼ b
0
þ b
1
S t 1
þ
X b
T
D t
T
;
T
ð 4 Þ where the right-hand-side of this model is as described in
(Eq. 2). We coded years of low plague prevalence (few colony die-offs) as response = 0; otherwise, response = 1.
We used an information criterion (AIC c
) to determine the relative support for each candidate model (Burnham and
Anderson, 2002).
R
ESULTS
We found evidence in support of the temperature-modulated trophic-cascade hypothesis for plague occurrence in our Montana study area. Three of the four models with highest support included positive associations between prairie dog colony die-offs and ‘‘peak’’ (April –July) precipitation in the previous year (Table 1). Similar models that included a longer (2-year) lag in the precipitation variable were not supported by these data. The number of die-offs in this study area was also positively related to the number of ‘‘warm’’ (>26.7
C) days and negatively related to the number of ‘‘hot’’ (>29.4
C) days (Table 1). Each of these four ‘‘best’’ models fits our Montana data well, as does the weighted average of these four models (Fig. 4).

8 Sharon K. Collinge et al.
Table 1.
Models of Plague Occurrence in Prairie Dog Colonies a
AICc Model a) Montana
0.020 + 0.492
S t ) 1, Apr-Jul
) 0.163
D
35 t
) 0.211 + 0.567
S t ) 1, Apr-Jul
26.7
1.988 + 0.128
D t
) 0.191
)
D t
0.087
29.4
D
32.2
t
0.684 + 0.516
S t ) 1, Apr-Jul
) 0.057
D t
29.4
b) Colorado
) 145.3
) 21.515
S t ) 1, May-Jun
+ 7.076
D
29.4
t
) 7.988
D t
32.2
)
)
)
)
161.67
161.33
161.11
159.06
15.43
D
0
0
AICc
0.34
0.56
2.61
Akaike weight
0.287
0.242
0.217
0.078
0.434
Rescaled weight
0.348
0.294
0.263
0.095
1.0
R 2 a
All models with D AICc < 5 are shown.
St ) 1, X-Y represents the total amount of precipitation during months X–Y of the previous year, and D
X t represents the number of days warmer than the threshold temperature X ( C) during the current year (see Fig. 3 for temporal relations between explanatory variables). Coefficients of determination (R
2
) were rescaled for Poisson or logistic regression.
a) Poisson regression models for colony die-offs in southern Phillips County, Montana. Akaike weights were rescaled to this set of best models (see Rescaled weight) to produce the weighted-average model in Figure 4.
b) Logistic regression model for colony die-offs in Boulder County, Colorado. For this regression, plague years were coded as response = 1 for years with ‡
2 colony die-offs (open circles and squares in Fig. 4b). Other coding methods yielded similar results for this model-selection analysis. The fit of this model is probably spurious: it is the only model that fits the Colorado data ( D AICc > 5 and R
2
< 0.10 for all other models), and it includes a negative relationship between lagged precipitation and colony die-offs (see the Results section for further discussion).
0.87
0.81
0.87
0.78
0.92
In contrast, we did not find evidence supporting the trophic-cascade hypothesis for plague occurrence in our
Colorado study area. Of the 407 Poisson regression models considered, only one fit the data, and that model included a negative association between plague occurrence in the current year and precipitation in the previous year. We have no a priori reason to expect a negative relationship between precipitation and plague. If the fit of this model were not spurious, then similar models (based on similar periods of precipitation) should also fit the data. This was not the case.
Using logistic regression did not suggest alternative climatic models, and did not improve model fit (Table 1).
D
ISCUSSION
We found that the best models of our data on plague in
Montana prairie dogs are strikingly similar to the best models of Enscore et al .
(2002) for human plague cases in
Arizona and New Mexico. Both studies suggest time-lagged, positive effects of precipitation on the number of plague cases, combined with an optimal temperature range for plague outbreaks. These similarities imply consistent climatic effects on plague prevalence across disparate landscapes and host–vector communities.
On the other hand, we were not able to model our data on plague in Colorado prairie dogs using similar data on precipitation and temperature. These disparate results may be due to differences between study areas in landscape structure, climate, or characteristics of the data. We may lack sufficient data to detect temporal patterns of plague prevalence in Colorado. There have been only two major and four very minor epizootics of plague recorded in Boulder County over the past 20 years. After each major epizootic, colonies must recover (numerically) before another epizootic can be detected. In our Montana study area, a large fraction of colonies do not succumb to plague in each epizootic, leaving many colonies available to suffer plague in each year, regardless of recent epizootics. In our Colorado study area, a much smaller fraction of colonies escaped each major epizootic, leaving few colonies available to experience a detectable die-off. The timing of precipitation in our Colorado study area is also highly erratic when compared to the timing of precipitation in other modeled regions (see Fig. 2 and Enscore et al., 2002). This variability may interrupt the potential for a trophic cascade that could boost plague prevalence.
Differences in the landscape structure of our Montana and Colorado study areas may also influence the potential for plague response to local climate. For example, if anthropogenic or riparian features can act as barriers to plague transmission (Collinge et al., in press), then plague epizootics may often be hampered in our urban Colorado study area.

Trophic-cascade Model of Plague 9
Figure 4.
Prairie dog colony die-offs.
a : Observed and modeled dieoffs in southern Phillips County, Montana. The model represents a weighted average of the four models in Table 1 (weighted by rescaled
Akaike weights). Consistent with the (temperature-modulated) trophic-cascade model for plague proposed by Enscore et al.
(2002), this model includes positive effects of April–July precipitation during the year prior to plague-induced die-offs, positive effects of days > 26.7
C during the plague year, and negative effects of days >
29.4
C during the plague year. The coefficient of determination for this model (R
2
= 0.91) was rescaled for Poisson regression.
b :
Observed die-offs in Boulder County, Colorado. For the purposes of logistic regression, we considered three coding methods for the plague response variable: response = 1 for years with ‡ 1 colony dieoff (all open symbols); response = 1 for years with ‡ 2 colony die-offs
(open circles and squares); response = 1 for years with > 2 colony die-offs (open squares only). Regardless of our coding method, only one model fit these data (Table 1), and its fit was likely spurious (see the Results section).
A comparison of results between our study and that of
Enscore et al. (2002) suggests that the optimal temperature regime for plague transmission may differ with latitude.
Temperature was significantly associated with plague occurrences in our Montana study area. The best model included a negative association of plague with the number of days above 35 C (95 F), and all models with strong support (Table 1) included a negative threshold effect of high summer temperatures. In this respect, our models are consistent with Enscore et al.
Õ s (2002) best models for human plague cases in Arizona. These authors related the strong effect of temperature on plague occurrence in humans to flea mortality and vector competence. They suggested that when summer temperatures exceed 35 C, fleas are less likely to survive and to effectively transmit plague between hosts. They also found that the number of human plague cases was positively related to the number of days in which the maximum temperature rose above a lower threshold, suggesting an optimal temperature envelope for plague transmission of approximately 29.4–35 C (85–
95 F). Among our best models (Table 1), we found evidence for an optimal temperature envelope of 26.7–35 C
(80–95 F). It is interesting to note that the optimal temperature for plague transmission may be somewhat lower in northern than in southwestern climates.
In their interpretation of the link between precipitation and human plague and hantavirus cases, several authors
(Parmenter et al., 1999; Enscore et al., 2002; Yates, 2002), proposed that high precipitation initiates a trophic cascade that ultimately causes rodent population increases and enhanced disease transmission. In their southwestern US study areas, local climate is predictably linked with the broader scale ENSO climate pattern. Years with high numbers of human plague and hantavirus cases lag 1 to 2 years behind years with significant ENSO precipitation anomalies. In contrast, long-term climate records reveal that there is not a significant precipitation anomaly during the generally mild ENSO conditions recorded in northeastern Colorado, which includes our study area (http:// www.cdc.noaa.gov/people/klaus.wolter/SWcasts/).
Also, because climate is highly unpredictable in our Colorado study area, rodent populations may not closely track climatic variables.
Stapp et al. (2004) recently examined patterns of prairie dog die-offs in relation to El Nin˜o Southern Oscillation (ENSO) events at the Pawnee National Grassland in northern Colorado. Their study sites are located from 100–
150 km northeast of our Boulder study area. They reported some correlation between ENSO years and prairie dog colony die-offs, although they noted no correlation between January–March precipitation and ENSO events for their study area. The results of our study may differ for two reasons. First, their study sites are further east than our

10 Sharon K. Collinge et al.
Boulder study area, which means they experience slight but perhaps biologically meaningful differences in the timing and abundance of precipitation. Second, Stapp et al. (2004) did not observe a correlation between January–March precipitation and their colony die-offs. Moreover, they noted that several colony die-offs occurred in non-ENSO years, and that most colonies survived one of the ENSO events, suggesting that factors other than climate may drive plague outbreaks in prairie dogs. Based on these results, we conclude that the timing and magnitude of precipitation and temperature may be associated with plague occurrence in some regions, but are not consistently strong predictors of plague occurrence in black-tailed prairie dogs.
The general success of these climatic models for plague prevalence suggests that it would be fruitful to investigate the proximate mechanisms suggested by these predictors.
Some attention has already been given to investigating the trophic-cascade hypothesis. Brown and Ernest (2002) reported a lack of evidence for this hypothesis, given a lack of correlation between small rodent densities and time-lagged precipitation. It should be noted, however, that their longterm studies of rodent population dynamics have occurred in areas where plague is not regularly found. In contrast, in plague-endemic areas, if rodent hosts experience significant plague-related mortality, then attempts to relate precipitation and host density would be complicated by plague prevalence. For example, rodent density may increase after each period of higher precipitation, only to decrease whenever temperatures favor plague transmission. Under this scenario, if precipitation in 1 year were uncorrelated with temperatures in the next, then rodent density in 1 year would be uncorrelated with precipitation in the previous year. Due to the potentially complex interaction between climate, plague prevalence, and the densities of hosts and vectors, it would be useful to investigate whether the density of small rodent populations is related to both lagged precipitation and non-lagged temperature regimes. Rodent density might be explained by these combined predictors in areas that are regularly exposed to plague.
It is likely that multiple factors influence the spatial and temporal distribution of diseases for which rodents serve as reservoir hosts. For example, Langlois et al. (2001) assessed prevalence of Sin Nombre virus in deer mice at 101 sites across Canada in relation to both climatic and landscape variables. They concluded that landscape structure had stronger effects on virus incidence than other variables that are often correlated with Sin Nombre virus, such as climate and season. We similarly found that plague occurrence was strongly associated with landscape structure in both the Colorado and Montana study areas (Collinge et al., in press), but found that climate also was closely associated with plague occurrence in the Montana study area. This suggests that for the Montana study area, we may be able to predict years in which plague outbreaks will likely occur based on climatic variables. Further, our combined results suggest that we may be able to predict which prairie dog colonies are likely to be affected by plague, based on their landscape context.
Black-tailed prairie dogs are subject to several stressors across their geographic range, which spans 10 western states. Plague in prairie dogs previously has been considered highly unpredictable in space and time, a fact that challenges our ability to effectively prevent further population declines. Our models relating climate and plague occurrence in our Montana study area suggest that it would be fruitful to further investigate associations between climate and plague occurrence in prairie dogs across their geographic range. If such analyses reveal strong relationships between climate and plague occurrence, then we may be able to make predictions about the temporal patterns of plague occurrence in a given geographic area. In areas where climate is more variable, other factors may better predict plague occurrence in prairie dogs. In these situations, factors such as landscape structure may be more useful predictors of plague occurrence. Ultimately, it will be beneficial to elucidate combinations of factors that allow us to predict both spatial and temporal patterns of disease occurrence in this imperiled species.
A
CKNOWLEDGMENTS
We gratefully acknowledge the City of Boulder Open
Space Department, and Boulder County Parks and Open
Space Department, particularly Mark Gershman, Cary
Richardson, Bryan Pritchett, Lynn Riedel, Mark Brennan,
Ann Wickman, and Jeanne Scholl for providing data on plague occurrence and information on prairie dog colonies in Boulder County. Brian Holmes helped assemble plague occurrence and prairie dog colony data in Phillips
County, Montana. Sue Rodriguez-Pastor helped gather plague data from Boulder land management agencies. This

Trophic-cascade Model of Plague 11 research was supported by a grant (R-82909101-0) from the National Center for Environmental Research (NCER)
STAR program of the US-EPA, and a grant from the NSF/
NIH joint program in Ecology of Infectious Diseases
(DEB-0224328).
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