Models for Total DON

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 ( Table 1). Total growing season precipitation in the current year (PPT _t) also weakly influenced DON, but the effect was Gaussian with a peak at 223 mm. A model in which these two weather terms are combined multiplicatively was stronger than either of the univariate models, but explained only 15% of the variance ( Table 1). None of the other climate variables, deer variables, or prior year's density of larvae (DOL _{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 ( Table 2; Figure 2). In no case was a multiple regression model superior to the chipmunk model ( Table 2).

Table 1

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

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Table 2

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)

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Figure 2

Effects of Population Density of Eastern Chipmunks (T. striatus) on DON

Shows relationship between number of chipmunks per 2.25-ha grid in year t−1 and DON (number per 100 m ²) in year t. This regression model for DON had the most support.

Models for NIP

Among all univariate models, NIP responded only to the density of acorns in year t−2 ( Figure 3), and this relationship explained only 16% of the variance in NIP. Models incorporating the climate variables, deer variables, DOL, mice, chipmunks, and total rodents performed no better than the means model ( Tables 3 and ​and4).4). Because none of the independent variables other than acorns _{t −2} produced an improvement over the means model, there was no justification for testing multiple regression models.

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Figure 3

Effects of Acorn ( Quercus spp.) Density on NIP

Shows effects of acorns per square meter in year t−2 on NIP (percentage of nymphs infected with B. burgdorferi) in year t. This regression model for NIP had the most support.

Table 3

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

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Table 4

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)

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Models for DIN

Similar to the results for DON, the effect of GDD _{t −1} on DIN in year t was positive but very weak in both the magnitude and the strength of evidence for the effect ( Table 5). Total PPT _t also weakly influenced DIN, and again the effect was Gaussian with a peak at 213 mm of rainfall. A model in which these two weather terms are combined multiplicatively was stronger than either of the univariate models, but explained only 11% of the variance ( Table 5). None of the other weather variables, deer variables, nor DOL _{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 ( Table 5). Consequently, we tested linear combinations of these predictor variables in multiple regressions.

Table 5

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

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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 ( Table 6; Figure 4A). The model with multiplicative effects of chipmunks _{t −1} and acorns _{t −2} was nearly as good, with ΔAIC _corr = 1.05, and a slightly higher R ² (0.61) ( Figure 4B).

Table 6

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)

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Figure 4

Effects of Acorn and Rodent Densities on DIN

(A) Effects of the product of acorn density (acorns per square meter) in year t−2 and mouse (P. leucopus) density (number per 2.25-ha grid) in year t−1 on the density of B. burgdorferi-infected nymphs (number per 100 m ²) in year t. This regression model for DIN had the most support.

(B) Effects of the product of acorn density (acorns per square meter) in year t−2 and chipmunk (T. striatus) density (number per 2.25-ha grid) in year t−1 on the density of B. burgdorferi-infected nymphs (number per 100 m ²) in year t. This regression model for DIN had nearly as much support (AIC _corr) as the mouse model (A) and a higher r ² value.

Climate Variables

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 [ 15, 43], but is consistent with the finding that (detrended) incidence of Lyme disease in people is positively correlated with summer temperatures in the prior year [ 44]. Both DON and DIN were influenced, again weakly, by precipitation in the current but not prior year, but intermediate levels of precipitation favored highest nymphal abundances. Again, this result conflicts with the expectation that tick survival increases linearly with ambient moisture [ 18]. Low DON and DIN in years of high precipitation could be caused by either flood-induced mortality or that caused by natural enemies (e.g., fungi) that are facilitated by high moisture [ 45]. As expected, none of the climate variables influenced NIP. NIP is determined by the proportions of larval tick meals taken from the various host species, which vary strongly in their reservoir competence. It seems unlikely that climate variables will influence the choice of hosts by larval ticks or relative abundances of different hosts. It remains possible that climate variables other than the ones we examined influence stage-specific tick survival and abundance and that the weak or absent effects we observed are a result of not including more important variables. Our analytical approach could easily support assessments of other variables for which there is some a priori expectation of an effect.

Deer Variables

The assertion that variable deer abundance is responsible for variable abundance of blacklegged ticks and hence Lyme-disease risk has become almost axiomatic [ 46, 47]. This seems to be based largely on repeated observations that removal of deer by fencing or shooting causes dramatic declines in tick abundance. However, some evidence suggests that the effects of deer on ticks are nonlinear, weak, and variable with tick life stage [ 26– 28]. An effect of deer abundance in year t−2 on nymphs in year t would be expected if (1) the number of autumn blood meals taken by adult ticks is correlated with the abundance of deer, causing (2) density of larval ticks in year t−1 to be correlated with deer in year t−2, and if (3) abundance of nymphs in year t is correlated with that of larvae in year t−1. Here, we found that more than 3-fold variation in our indices of deer abundance did not affect subsequent nymph abundance. This observation supports the assertion that, once deer abundance exceeds a low threshold value, further increases in deer density have little if any effect on nymphal densities [ 48]. We did observe a weak effect of deer on subsequent larval abundance, but larval abundance in any given year had no impact on next year's abundance of nymphs. This clear but surprising result indicates a decoupling of stage-specific abundances and suggests instead that abundance of nymphs depends on larval feeding opportunities the prior year (see below). The lack of demographic forcing from larval to nymphal stage each year also suggests that the effect of larval host abundance in any given year should penetrate only to the next year and not beyond.

Acorn sampling.

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 t−2 was used as an independent variable potentially affecting Lyme-disease risk factors.

Small-mammal sampling.

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 [ 57]. We selected the Jolly-Seber model that incorporates individual heterogeneity in capture probability. Because we were interested in assessing the importance of rodent abundance on nymphal tick abundance the following year, we focused on estimating rodent densities in midsummer, which is the time of peak activity of larval I. scapularis at our sites [ 10]. In order to create a standard metric when actual trapping sessions varied in time, we estimated mouse and chipmunk abundance for each grid and year on August 15 by linear interpolation between rodent abundance estimates for trap sessions immediately before and after August 15. Rodent densities in year t−1 were used as independent variables potentially affecting Lyme-disease risk factors.

Deer abundance estimates.

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 [ 58]. Between seven and 11 hunters per year hunted an average of 40 h each (range, 29–54 h) between mid-October and mid-November. All hunters were IES staff members or volunteers working with the staff wildlife biologist. Each was given exclusive access to one of 34 discrete hunting areas averaging 22 ha (range, 9.3–35.7 ha). Virtually all hunting was from tree stands. Each day, hunters reported the number of hours hunted and the number of deer sighted, and these data were converted to deer observed per hour hunted. As a validation of this method, we asked whether deer observed per hour by bow hunters were correlated with deer counts from annual autumn spotlighting surveys conducted from 1987 to 2000 (details in [ 58]) and found that the two census methods were highly correlated ( r = 0.70, df = 11, p = 0.01; [ 58]).

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 [ 59, 60] have served as an index to trends in browsing rates. These species/genera include red maple (Acer rubrum), sugar maple (A. saccharum), serviceberry (Amelanchier arborea), black birch (Betula lenta), black cherry (Prunus serotina), oaks ( Quercus spp.), hickories ( Carya spp.), and ashes ( Fraxinus spp.). Browsed woody stems detected in spring reflect the distribution of deer foraging activity during the previous autumn and winter. Data were collected along transects of unrestricted width spaced either 200 m or 300 m apart. Starting points were associated with corners of a 100-m grid overlay of the property. A major compass direction was randomly drawn each year for transect direction. As index species were sighted, all buds below 2 m were counted and examined for browsing by deer. At least 100 buds in total were examined for each site. The percentage of available stems browsed was calculated for each site and for each index species. We selected browse survey plots closest to each of the trapping grids (less than 100 m distant) to estimate deer activity specific to each of the plots. Deer browsing intensity in year t−2 was used as an independent variable potentially affecting Lyme-disease risk factors.

Climate variables.

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 [ 61]. To avoid this problem, we selected climate variables that have been reported to influence either changes in the abundance of immature blacklegged ticks or in human Lyme-disease incidence [ 16, 17]. The climate variables selected represent temperature and precipitation conditions in either the current year (year t) or the prior year (year t−1). Values for year t reflect potential impacts of climate on survival of the current year's nymphal stage, whereas those for year t−1 represent possible effects of climate on survival of the prior year's larval stage. Following Jones and Kitron [ 16], for temperature data, we included only those months from the beginning of the growing season through the end of the activity season for the appropriate life stage (July for nymphs, September for larvae; [ 16, 41]). Specifically, we used cumulative growing degree days (GDD) for March 1–June 30 of year t, and cumulative GDD for March 1–September 30 of year t−1. For precipitation, we included only those months from the onset of potential soil moisture limitation (May) to the end of the appropriate activity period [ 16]; i.e., PPT (in mm) for May 1–June 30 of year t; and PPT for May 1–September 30 of year t−1 [ 16]. All climate data came from the IES environmental monitoring station ( http://www.ecostudies.org/emp_purp.html, located less than 1.5 km from our field plots

Tick and Borrelia sampling.

Estimates of the abundance and infection prevalence of nymphal ticks comprised the response variables of interest. In addition, estimates of larval abundance in year t−1 were used as an independent variable. We monitored the abundance of larval and nymphal ticks in each plot and year by dragging 1-m ² white corduroy drag cloths [ 62] along 450 m of transects approximately every 3 wk from April through November. Drag cloths were examined and all ticks counted and removed every 30 m. Frequent sampling in the early 1990s revealed that peak host-seeking activity for larvae occurred in mid- to late August, and for nymphs in mid- to late June, and we timed our annual sampling to coincide with these peaks. For each plot and year, we estimated larval and nymphal abundance as the peak density (ticks per 100 m 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 B. burgdorferi was determined using direct immunofluorescence assay (DIA). Ticks were washed once in 70% ethanol and twice in deionized water and ground in phosphate-buffered saline (PBS). Three 5-ml aliquots of tick suspension were placed in separate wells in a multiwell slide, air-dried, and fixed in cold acetone for 10 min. Fluorescein rabbit anti- B. burgdorferi conjugate was incubated in wells at 37 °C for 45 min, after which slides were washed in PBS, dried, and mounted with a coverslip. Slides were examined systematically to categorize each tick as either infected or uninfected. On average, 378 nymphs (range, 146–660) were examined for infection each year. Our estimates of tick infection based on DIA have been verified by virtually identical infection prevalence estimates (within 1.6 percentage points) for IES ticks based on PCR and reverse-line blotting [ 63, 64].

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.

Competing interests. The authors have declared that no competing interests exist.