^{1}

^{*}

^{1}

^{1}

^{1}

^{1}

^{2}

RSO conceived and designed the experiments. KO and RJW performed the experiments. RSO, CDC, and FK analyzed the data. CDC contributed reagents/materials/analysis tools. RSO and CDC wrote the paper.

The authors have declared that no competing interests exist.

Risk of human exposure to vector-borne zoonotic pathogens is a function of the abundance and infection prevalence of vectors. We assessed the determinants of Lyme-disease risk (density and

A long-term study of tick dynamics simultaneously assesses the impact of multiple ecological variables on Lyme disease risk and strongly implicates a role for rodent hosts and their food resources.

Many emerging and re-emerging infectious diseases of humans are zoonoses transmitted by vectors. Examples include West Nile virus, ehrlichiosis, anaplasmosis, tick-borne encephalitis and Lyme disease. In each case, the vector—usually a mosquito or tick—acquires the pathogen from a vertebrate host during a blood meal taken early in the life cycle and becomes capable of transmitting it to humans during a later blood meal. Risk of human exposure to the disease increases with increasing abundance and infection prevalence of the vectors [

Lyme disease is the most frequently reported vector-borne disease in the US [

Owing to its tiny size, potentially high abundance, and summer feeding, the nymphal stage is most likely to transmit

Prior studies of the factors influencing DIN and DON have focused largely on variation in climate and in the abundance and distribution of white-tailed deer

Because adult

Less attention has been paid to the potential effects of variation in abundance of hosts for larval ticks in influencing variation in DIN, DON, and NIP. This is perhaps a consequence of the lack of specialization by larvae on any particular host species. However, larval

The food resources for tick hosts might also be important to Lyme-disease risk. Oak trees (

No prior study has assessed simultaneously the effects of variation in temperature, precipitation, deer, mice, chipmunks, and acorns, on variation in entomological risk of exposure to Lyme disease (

Shows the four life stages, egg, larva, nymph, adult, and the times during the life cycle that both abiotic (GDD, PPT), and biotic (acorns and various hosts) factors might exert influence. Year

The principal entomological Lyme-disease risk factor, DIN, varied by an order of magnitude among years, ranging from 1.07 infected nymphs × 100 m^{−2} in 1997 (averaged across all six plots) to 10.00 × 100 m^{−2} in 1996. This variation was due primarily to variation in DON, which varied 6-fold among years (3.59 to 21.07 × 100 m^{−2}). In contrast, NIP varied less than 2-fold among years, from 0.24 in 2005 to 0.45 in 1999.

Effect of growing degree days in the previous year (GDD
_{t}
_{−1}) on DON in the current year was positive but very weak in both the magnitude (estimated slope of the regression) and the strength of evidence for the effect (_{t}
_{t}
_{−1}) had any effect on DON; i.e., Akaike's information criterion corrected for small sample size (AIC_{corr}) values were much higher than those of the means model. Abundance of acorns
_{t}
_{−2}, mice
_{t}
_{−1}, chipmunks
_{t}
_{−1}, and rodents
_{t}
_{−1} (sum of mice and chipmunks) all independently influenced DON, and in all cases linear models were superior to exponential or power functions. The best univariate model for DON was a simple linear model of chipmunks
_{t}
_{−1}, which explained 40% of the variance (

Model Comparison Statistics for Independent Variables Potentially Influencing the DON Based on the Full Dataset (58 Plot Years)

Model Comparison Statistics for Independent Variables Potentially Influencing the DON Based on the Subset of Plot Years for Which All Independent Variables Were Estimated (42 Plot Years)

Shows relationship between number of chipmunks per 2.25-ha grid in year
^{2}) in year

Among all univariate models, NIP responded only to the density of acorns in year
_{t}
_{−2} produced an improvement over the means model, there was no justification for testing multiple regression models.

Shows effects of acorns per square meter in year

Model Comparison Statistics for Independent Variables Potentially Influencing NIP Based on the Full Dataset (58 Plot Years)

Model Comparison Statistics for Independent Variables Potentially Influencing NIP Based on the Subset of Plot-Years for Which All Independent Variables Were Estimated (42 Plot Years)

Similar to the results for DON, the effect of GDD
_{t}
_{−1} on DIN in year
_{t}
_{t}
_{−1} had any effect on DIN, with AIC_{corr} values higher than those of the means model. Abundance of acorns
_{t}
_{−2}, mice
_{t}
_{−1}, chipmunks
_{t}
_{−1}, and rodents
_{t}
_{−1} all independently influenced DIN. For acorns
_{t}
_{−2}, mice
_{t}
_{−1}, and rodents
_{t}
_{−1}, the best models were nonlinear, but the difference in AIC_{corr} (ΔAIC_{corr}) between the best model and corresponding linear model was always less than 1 (i.e., they had equivalent levels of support in the data), and the shapes of all nonlinear models were very close to linear (

Model Comparison Statistics for Independent Variables Potentially Influencing the DIN Based on the Full Dataset (58 Plot Years)

A model combining mice
_{t}
_{−1} and acorns
_{t}
_{−2} multiplicatively was the best model of all multiple regressions combining predictor variables that were supported by univariate analyses, and it explained 57% of the variance in DIN (_{t}
_{−1} and acorns
_{t}
_{−2} was nearly as good, with ΔAIC_{corr} = 1.05, and a slightly higher
^{2} (0.61) (

Model Comparison Statistics for Independent Variables Potentially Influencing the DIN Based on the Subset of Plot Years for Which All Independent Variables Were Estimated (42 Plot Years)

(A) Effects of the product of acorn density (acorns per square meter) in year
^{2}) in year

(B) Effects of the product of acorn density (acorns per square meter) in year
^{2}) in year
_{corr}) as the mouse model (A) and a higher
^{2} value.

Densities of both mice and chipmunks responded strongly to the prior year's acorn abundance, and in both cases the relationship was best described by saturating power functions (

Shows effects of acorn density (acorns per square meter) in year

Shows time series of acorn density (acorns per square meter), chipmunk density (number per 2.25-ha grid), and DON (number per 100 m^{2}) on the two longest-established study plots, Henry Farm (A) and Teahouse (B). Note that, typically, chipmunk density tracks acorn density with a 1-y lag, and DON tracks chipmunk density also with a 1-y lag.

Given their relatively long generation times and low reproductive potential, it is unrealistic to expect deer population abundance to track annual variation in acorn production. However, the potential exists for deer to be attracted from nonoak to oak habitats by the presence of abundant acorns [_{t}
_{−2} and DOL
_{t}
_{−1}, with this model being only a slight improvement over the means model (ΔAIC_{corr} = 0.39;
^{2} = 0.04). In addition, no relationship existed between acorns_{
t−2
} and DOL
_{t}
_{−1}; all models, whether linear or nonlinear, were worse than the means model.

Climate, deer, and acorns each have been proposed as primary determinants of temporal variation in risk of human exposure to Lyme disease, as measured by abundance and

Of the four climate variables, two influenced DON and DIN, but they did so in unanticipated ways. Both DON and DIN increased linearly, albeit weakly, with increases in the prior year's temperature (GDD
_{t}
_{−1}). This result conflicts with the expectation that heat-caused mortality is an important regulator of tick abundance [

The assertion that variable deer abundance is responsible for variable abundance of blacklegged ticks and hence Lyme-disease risk has become almost axiomatic [

Previous research [_{t}
_{−2} boosted larvae
_{t}
_{−1} by enhancing deer
_{t}
_{−2}, and the other in which acorns_{
t−2
} boosted rodents
_{t}
_{−1}, which in turn elevated nymphs
_{t}
_{t}
_{−1}, PPT
_{t}
_{t}
_{−2}, mice
_{t}
_{−1}, and total rodents
_{t}
_{−1} all had support, the best model had chipmunks in the previous year as the sole predictor of DON. A stronger role for chipmunks than for mice was somewhat surprising given the lower population densities of chipmunks (

In contrast to previous results based on a shorter time series [_{t}
_{−1} nor chipmunks
_{t}
_{−1} influenced NIP. Instead, we found that the univariate model of acorns_{
t−2
} was the only one supported by the data. Empirically based models [

Because DIN is the product of DON and NIP, one might expect that the best explanatory model would be more complex than those for its component parts. Indeed, we found that the model of multiplicative effects of mice
_{t}
_{−1} (the second best predictor of DON) and acorns_{
t−2
} (the best predictor of NIP) had the most support. The model with multiplicative effects of chipmunks
_{t}
_{−1} (the best predictor of DON) and acorns_{
t−2
} was almost as strongly supported.

Tick abundance and Lyme-disease risk can be high in habitats with few or no oaks [

Previous studies of the determinants of variable Lyme-disease risk or incidence have tended to focus on one or a small number of potential independent variables, and statistically significant effects of both climate [

Field studies were conducted on the property of the Institute of Ecosystem Studies (IES) in Dutchess County, southeastern New York (lat 41^{°}50′N, long 73^{°}45′W), in the center of the northeastern US endemic zone for Lyme disease. Dutchess County has had among the highest incidence rates of Lyme disease in the US during the past 10 y [

Acorn abundance was monitored on each of the six plots by placing circular baskets under the canopies of mature oaks distributed throughout the plot. The original two plots had twenty 0.5-m^{2} baskets, and the remaining four had twenty-five 1.0-m^{2} baskets. Seed baskets were supported by monofilament line attached to nylon stakes and were resistant to seed predators. Intact, mature acorns were counted monthly during autumn of each year, and the total number of acorns from all baskets within a plot was divided by the total basket area to derive an estimate of annual acorn production on each plot. Full-season acorn data were collected from 1993 through 2004 on the original two plots and from 1999 through 2004 on the remaining four plots. Acorn density in year

Each year from 1991 (the two original plots) or from 1995 (remaining plots) through 2005 we have monitored abundance of small mammals at IES using capture–mark–recapture techniques. On each plot we established an 11 × 11 point grid of Sherman live traps, with 15 m between trap stations and two traps per station, for a total of 242 traps per grid. Trapping was conducted for 2–3 consecutive days every 3–4 wk, generally from May to November of each year. Traps were baited with crimped oats (with sunflower seeds and cotton batting added during cold weather), set at 1600 hours and checked between 0800 hours and about 1200 hours the following morning. This schedule allowed us to capture both diurnal (chipmunks) and nocturnal (mice) small mammals. These two species comprised more than 90% of captures. Small mammals were marked with individually numbered metal ear tags and released after handling at the point of capture. Data on age, sex, body mass, ectoparasite burden, and trap station were recorded on each capture. Protocols for animal handling were approved annually by an Institutional Animal Care and Use Committee.

We estimated population densities of white-footed mice and eastern chipmunks by inputting data from all trap sessions in a year into the Jolly-Seber open population model in program POPAN5 [

Deer abundance was estimated at two levels, one at the scale of the IES property and the other at the scale of individual plots. For estimating property-wide deer abundance annually, we used population estimates from the IES limited-access bow-hunting program, which has run continuously from 1987 to the present [

To estimate deer distribution on a smaller scale, we used deer browse surveys conducted each spring (1983–2004) at a number of sites (range, 38–50) distributed throughout the IES property. Commonly browsed tree species or genera [

An almost infinite number of climate variables (temperature, precipitation, minimum, maximum, variance, mean, specific to months or seasons, etc.) potentially could influence tick survival and densities of nymphs. Consequently, the probability of uncovering spurious relationships between climate and tick abundance is quite high if many explanatory variables are included without clear a priori justification [

Estimates of the abundance and infection prevalence of nymphal ticks comprised the response variables of interest. In addition, estimates of larval abundance in year
^{2} white corduroy drag cloths [^{2}). Peak densities were highly correlated with cumulative seasonal densities (correlation coefficients typically greater than 0.80; R. Ostfeld, unpublished data) on each plot.

Infection of individual ticks with

Our goal was to evaluate the strength of evidence for effects of a series of plausible independent variables on temporal variation in entomological risk of human exposure to Lyme disease (_{corr}. We created both linear and nonlinear (exponential, power function, Gaussian) models, as appropriate. We first compared evidence for each of the 11 independent variables separately by comparing the AIC_{corr} of their regression models to the AIC_{corr} value of an intercept-only (i.e., mean) model. The 11 independent variables included two temperature variables, two precipitation variables, two indices of deer abundance, abundance of larval ticks, acorn abundance, and three measures of small mammal abundance. We checked for colinearity among the independent variables using correlation coefficients. Because there were missing values for some variables in some years and plots, the univariate models were compared against mean models estimated with the same subset of (nonmissing) observations. We then tested series of increasingly complex models by combining sets of independent variables for which there was evidence (as measured by AIC) of univariate effects. Our choices for the forms of the multiple regression models were guided by the dictates of parsimony: while our dataset represents an enormous sampling effort over a 13-y period, the actual sample sizes (a given plot in a given year) were still relatively small, ranging from 42 to 58 observations for the various models.

We used simulated annealing (a global optimization algorithm) to find the maximum likelihood estimates for the parameters of each model. The observations were assumed to be normally distributed with a homogeneous variance. Examination of the residuals indicates that this assumption was appropriate for all three of the response variables. The specific annealing algorithm we used (based on Goffe et al. [

We thank the many field assistants for all their hard work in gathering data for this study over the years. Jesse Brunner provided helpful comments on a draft. This is a contribution to the program of the IES.

_{corr}

Akaike's information criterion

density of infected nymphs

density of larvae

_{ t−1 })

prior year's density of larvae

density of nymphs

growing degree days

_{ t−1 }

growing degree days in the previous year

Institute of Ecosystem Studies

nymphal infection prevalence

total precipitation

_{ t }

total growing season precipitation in the current year