We recently modeled the distribution of suitable habitat for I. scapularis in Minnesota at a subcounty scale (30 × 30 m) using the machine learning ecological niche model Maxent, which was fit using tick occurrence records previously collected by the Minnesota Department of Health.⁷ Suitable areas in that study were best described by seven variables: land cover (especially cool temperate forests), maximum temperature during the warmest month, the amount of precipitation during the wettest quarter, the annual temperature range, the mean diurnal temperature range, elevation, and the amount of precipitation during the coldest quarter of the year. To estimate the density of host-seeking nymphs within a suitable habitat for the tick and to refine estimates of the suitable habitat based on a larger sample size, in this study, we directed tick sampling efforts to areas considered suitable for tick survival based on our previous model.⁷

To be considered for inclusion as a sampling site for the present study, a site had to be 1) classified as suitable habitat for I. scapularis by the Maxent model,⁷ 2) publicly owned, 3) larger than 500 × 500 m, 4) accessible from maintained public access roads, and 5) have suitable vegetation, for example, contiguous forest with at least 50% closed canopy, as assessed by reviewing recent aerial imagery (GoogleEarth v 7.1.8.3036). These criteria were intended to ensure a reasonable expectation of finding ticks if they are present, and adequate area that was accessible to sample. To extrapolate model findings across Minnesota while minimizing instances where we were making predictions about areas with environmental characteristics that were not included in our build set, in addition to the five inclusion criteria already described, we selected sites with climatic and environmental variables characteristic of the rest of the state (Table 1) and also sought vast geographic coverage of the state. To accomplish the latter, we specified that all potential sampling sites had to be separated by at least 10 km. To accomplish the former, we sampled sites by using a scheme based on the concept of conditional Latin hypercube sampling (cLHS).

The cLHS method works by maximally stratifying the distribution of each variable into as many strata as sampling sites desired. The method allows for efficient sampling of existing data and has been shown to be the most effective way to replicate the distribution of variables, proving superior to random sampling, principal components, and equal spatial strata sampling schemes.^22,23 Using cLHS, or similar approaches, results in a sample set that covers the full range of conditions encountered among the design variables. This minimizes the potential for extrapolation to a set of predictors not used to fit the model. Conditional Latin hypercube sampling has been used extensively to guide sampling site selection for soil and vegetation modeling.^24–28

To identify the range of each variable across suitable habitats in Minnesota (Table 1), we resampled each of the seven variables used in our original suitability model⁷ to a resolution of 90 × 90 m to create a manageable number of data points. These variables represent several key predictors of the density of host-seeking Ixodes spp. nymphs from other areas and include measures of forest type or coverage, temperature, precipitation, and elevation.^19,29–40 Moreover, these seven variables are not strongly correlated with each other, but are strongly correlated with several other potential predictive variables, as described previously.⁷ The value of each of these seven variables was extracted to each 90 × 90 m pixel falling within the distribution of Maxent-predicted suitable habitat meeting the aforementioned selection criteria using the Extract Multiple Values to Points tool in ArcGIS (ArcMap 10.2; ESRI, Redlands, CA).

The site selection algorithm used in this study is not strict cLHS as we sample from the marginal distributions of the covariates and incorporate a proximity constraint. These modifications yield sample sites that span the domains of the covariates, individually, and provide more complete geographic coverage. We divided the distribution of each of the seven variables into five classes or bins based on quantiles, except land cover, which was binned according to the proportion of each land cover type predicted by the Maxent model; for example, 67.1% of binned values were cool temperate forests and 15.7% lowland and montane boreal forest,⁷ using the cut2 package in R (R v 3.2.1; R Foundation for Statistical Computing, Vienna, Austria). We then randomly chose two points (potential sampling locations) without replacement from each bin. To minimize geographic clustering of sampling sites, we limited the proximity of selected points to 10 km from the nearest selected point by placing a 10-km buffer around a selected point and removing all other points falling within the buffer. The order of selection was based on the importance of each variable in the Maxent model as listed previously. Because of the potential for some selected sites to be inaccessible as a result of unforeseen circumstances such as flooding or closed roads, we chose a second set of sampling sites, here referred to as backup sites. Backup sites were chosen from the points that remained after the first dataset was chosen and points within the 10-km buffer had been removed from the dataset. Eighty primary and 80 secondary sampling sites were chosen, yielding a total of 160 candidate sampling sites. Each of the 80 primary sites was visited in April 2015, before sampling to ensure habitat suitability, that is, wooded and brushy mesic areas with at least 50% canopy coverage. If the primary site was found to be unsuitable or inaccessible, the secondary site was assessed for suitability.

Random site selection using the modified cLHS resulted in a distribution of 80 points located in 41 counties. We ultimately sought to predict the distribution and density across the state; however, potential sampling sites identified by the cLHS were extremely limited in the north, with only a single sampling site chosen in far northeastern Minnesota. To increase the spatial extent of sampled sites, we chose to include an additional sampling site at Voyageurs National Park. The site sampled at Voyageurs National Park met all of the aforementioned inclusion criteria. Ultimately, 81 sites located in 42 counties were chosen for sampling (Figure 1). All initial site selection was performed in R (R v 3.2.1).

Eighty-one sites were sampled on two occasions, each separated by a range of 6–22 days, from May 31 to June 30, 2015. This sampling period was timed to coincide with the predicted peak of I. scapularis nymphal questing activity and just before the reported onset of illness for most Lyme disease cases in Minnesota.^41–43 The density of host-seeking I. scapularis nymphs (DON) was estimated by drag sampling 750 m² of forest floor with a 1-m² tick drag made of rubber-bonded cotton sheet (JoAnn Fabric no. 1491315) with a rope attached to a 48″ dowel inside the top edge. Weighted “fingers” were sewn to the bottom half of the drag to ensure sampling occurred near the forest floor and leaf litter layer. To minimize the likelihood of ticks falling off the drag before being collected, samplers stopped every 15 m, removed all ticks from the drag and themselves, and placed them in prelabeled vials containing 70% ethanol. All ticks were sent to the Centers for Disease Control and Prevention, Fort Collins, CO, identified to species^44–46 and life stage, and tested for pathogens.

The variables in the Maxent model informing site selection were based on average monthly climate data for 1960–1990.^7,47 We sought to produce a risk model which included current climate conditions that may have affected nymphal tick collections in 2015 and, therefore, chose to use 35-year climate averages (1980–2014) from version 2 of the 1-km spatial resolution Daymet dataset^48,49 to derive the BIOCLIM variables used to select sampling sites. This likely had minimal effect on the model as common variables among the two datasets were highly correlated (Pearson’s r ≥ 0.80; data not shown). In addition to the 19 BIOCLIM variables, we also considered eight other climate variables, including quarterly and annual measures of vapor pressure, growing degree days, soil water depletion, and annual precipitation accumulation (Table 2).

In addition to the eight climate candidate variables, we included measures of vegetation, elevation, and distance to streams which have been shown to be associated with tick abundance.^19,50,51 All sites chosen for sampling were located in closed canopy deciduous forest; thus, to simplify vegetation into categories, we chose two general measures of land cover surrounding each study site. The percentage of cool temperate forest and the percentage of agricultural land within a 5.25-km² square buffer were calculated for each sampling location as well as the percentage of each land cover type within each 5.25 km² pixel across the state. Because white-tailed deer serve as the primary host for adult ticks and are likely a considerable dispersal mechanism for ticks to inhabit new areas, the buffer area of 5.25 km² was chosen to represent the home range of a male white-tailed deer (Odocoileus virginianus Zimmerman) in Minnesota (Minnesota Department of Natural Resources; www.dnr.state.mn.us/index.html). We calculated the distance to a stream or river corridor (http://www.arcgis.com, last visited July 2015) for each site and for each pixel in the state using the Near tool in ArcMap (v10.3; ESRI), which calculates the distance from each study site or centroid of each pixel to the nearest river or stream. For example, if a stream or river runs through a pixel, then the pixel value is zero. We extracted values for the variables for each of the 81 sampling sites using the aforementioned Extract Multiple Values to Points tool. We identified correlations among the 31 variables, that is, Pearson’s correlation coefficient ≥ 0.75 (Table 2), and ultimately included eight variables, four of which were also represented in the habitat suitability model.⁷ All ecological data were preprocessed using ArcMap (v10.3; ESRI). Preprocessing included projecting all layers to Albers Equal Area North American Datum 1983, resampling all layers to a resolution of 30 × 30 m, and extracting the values of variables for each sampling site.

We considered both the nature of our site selection and our data structure when choosing a modeling framework. All sites selected for tick sampling were located within the predicted distribution of suitability (see Johnson et al.⁷) and visually confirmed to have wooded and brushy mesic areas with at least 50% canopy coverage in April 2015. We observed zero ticks at 17 of 81 sites (21%), more than would be expected under a Poisson distribution. For sites where only a single nymph was collected per 750 m² sampled, DON was equal to 0.13 nymphs/100 m²; therefore, we defined the lowest risk category as < 0.13 nymphs/100 m² (Figure 2). To represent the highest potential risk of encountering nymphal I. scapularis in a given area, we identified the single sampling visit that yielded the highest number of nymphs and used this number of ticks to create a predictive model of the peak number of ticks likely encountered per 750 m². Overdispersion, relative to a Poisson distribution, in the data (variance > mean) was tested for and identified using the AER package in R (R v 3.2.1; [dispersiontest: P = 0.001]).

To account for excess zeros and overdispersion in the data, a zero-inflated negative binomial (ZINB) model was fit to the peak number of nymphs observed. As a mixture model, the ZINB model incorporates two sources of zeros: structural zeros, which represent sites where ticks are truly absent, and random zeros, which represents low-density sites where, on a given day, the observed count was zero when sampling occurred. The ZINB comprises a discrete, nonnegative distribution describing tick counts (Equation S1) and a binary distribution describing the source of true zeros or absences in the dataset (Equation S2). The two portions of the model are then combined to estimate the number of ticks expected at each site based on the aforementioned ecological variables (Equation S3). To ensure the ZINB model represented the best fit to the data, we used Vuong statistic⁵² to determine if the ZINB distribution fit the data better than a negative binomial distribution.

To select variables to include in the final model, we first fit a full model containing all possible variables represented in both portions of the ZINB model (Table 2) using package pscl in R (R v 3.2.1). We then fit a reduced model including variables contributing significantly to model fit as identified by backward stepwise regression. We tested for spatial autocorrelation of observed DON/100 m² and among model residuals given by the best fit reduced ZINB model using Moran’s I (Spatial Analyst, ArcMap v 10.3; ESRI). Model performance (fit) was assessed by examining the scaled Pearson’s residuals and using 5-fold cross-validation (CV); CV was performed 10 times and the mean absolute prediction error was computed. Examination of the distribution of residuals allowed us to further evaluate the model and identify outliers in the predicted number of ticks among the 81 sites. We used the parameter estimates given by the ZINB model and Raster Calculator (ArcMap v10.3; ESRI) to predict the number of nymphs (Equation S3) and evaluated statewide model fit using the delta method to estimate variance (Equation S4). Based on the predicted number of nymphs per site (750 m²), we calculated and produced a continuous risk map of the DON/100 m² by dividing the number of nymphs predicted by 7.5. To present a more realistic distribution, we masked out areas deemed uninhabitable by ticks, for example, pixels defined as open water, swamp, agriculture fields, and high-intensity developed areas.

Voyageurs National Park was not selected using the cLHS framework but was included to extend the northern extent of sampling sites in central Minnesota. To verify that the inclusion of this point did not influence the predicted DON, we reran the ZINB model without that site and then compared parameter estimates and slope between models with or without the site included. Predictive maps were compared between those developed with versus without Voyageurs National Park using Raster Calculator (ArcMap v 10.3; ESRI).

We assessed the agreement between DON, as estimated by the ZINB model with Lyme disease incidence from 2000 to 2015 (http://www.cdc.gov/lyme/stats/), and categorical county-level tick-borne disease risk based on the average incidence of reported I. scapularis–borne disease cases, including Lyme disease, anaplasmosis, and babesiosis from 2007 through 2015. Risk categories were defined as cases of I. scapularis–borne disease per 100,000 population: low risk: < 10 cases, moderate risk: 10–24.9 cases, and high risk: ≥ 25 cases, to effectively create a risk map of the state that generally incorporated the potential exposure risk to I. scapularis based on the natural biomes of Minnesota (http://www.health.state.mn.us/divs/idepc/diseases/lyme/highrisk.html). Within these categories, 32 counties are classified by the Minnesota Department of Health as high risk, 22 counties are classified as moderate risk, and the remaining 33 counties are classified as low risk (Figure 1). In addition to epidemiological outcomes, model-predicted DON was compared with previously described county-level status of I. scapularis populations, that is, no records, reported, and established.³

For each county, we calculated the percent area classified in each of three categories: 1) predicted risk (≥ 0.13 nymphs/100 m²), 2) predicted low risk (< 0.13 nymphs/100 m²), and 3) unsuitable habitat (masked out), using the Tabulate Area Spatial Analyst tool (ArcMarp v 10.3; ESRI). Differences in percent area predicted as risk and county-level tick-borne disease risk and county-level tick establishment were analyzed using the nonparametric Kruskal–Wallis rank sums test with the Dunn method for correction of multiple comparisons using the PMCMR package in R. The association of percent area predicted as risk with county-level Lyme disease incidence was assessed using linear regression and controlled for county population size. All statistical tests were carried out at a significance level of α = 0.05 performed in R (R v 3.2.1).

Sampling sites were located in 42 of 87 Minnesota counties. Most sampling sites (70%; 57/81) were located in counties classified as high risk for I. scapularis–borne disease, 20% (16/81) of sites were located in counties classified as moderate risk, and the remaining 10% (8/81) were located in counties classified as low risk (Figure 1). Using the definitions of established (≥ 6 ticks, or two life stages) and reported (presence of at least one tick) populations described by Dennis et al.,⁵³ established populations of I. scapularis were identified at 80% of the sites sampled. Nine sampling sites were located in counties where previous records of I. scapularis were lacking.³ From these nine sites, we documented new records of established populations in two counties, Benton and Sibley, and new records of reported populations in two counties, Rice and Nicollet (Figure 1).

Among the 81 sites sampled between May 31 and June 30, 2015, a total of 1,386 I. scapularis nymphs were collected from 64 of the 81 (79%) sites sampled; 35% of all I. scapularis collected were nymphs. The number of nymphs collected per site ranged from 0 to 77 on a single visit, with a median of five nymphs (0.66 nymphs per 100/m²). The largest number of nymphs collected during a single sampling session per site was used to calculate the DON for each site; DON ranged from zero to as high as 10.3 nymphs/100 m². The highest DON was observed near the Minneapolis-St. Paul metropolitan area, and the geographic distribution of other high-density sites trended in a northwest direction away from the metropolitan area (Figure 2). Incidental captures included 831 adult I. scapularis from 66 sites, at least 1,721 I. scapularis larvae from 53 sites, 1,236 Dermacentor variabilis adults and two nymphs from 71 and two sites, respectively, and four Haemaphysalis leporispalustris nymphs from three sites. One male Ixodes marxi was collected from Otter Tail County and a single Ixodes texanus nymph was collected in Wright County, which is a new record of this species in Minnesota (L. Beati, Personal Communication; National Tick Collection, Georgia Southern University).

The zero-inflated (predicted absence) portion of our ZINB model showed a strong positive association with tick absence as the proportion of agricultural land increased (Table 3). More intuitively, the probability of tick presence increased as the proportion of agricultural land decreased (Figures 2 and 3). Because of the distribution of agricultural land in Minnesota, large portions of western and southern Minnesota were classified as unsuitable (Figures 2 and 3). The ZINB correctly predicted the presence of I. scapularis nymphs with high accuracy (79%). Most of the sites where the model predicted suitability but ticks were not collected were in areas where the model predicted low abundance of host-seeking nymphs (Figure 2).

Five variables contributed significantly to the negative binomial (number of nymphs) portion of the ZINB model (Table 3). Higher amounts of agricultural land in the surrounding area had the strongest negative impact on the predicted number of nymphs. Mean diurnal temperature range and elevation also had a negative association with increasing numbers of nymphs (although their influence was less than the percentage of agricultural land), whereas annual temperature range and the amount of summer precipitation were positively associated with increasing numbers of nymphs (Table 3). Mean diurnal temperature range was highly correlated with annual and summer vapor pressure, and precipitation during the wettest quarter was highly positively correlated with annual mean temperature, annual and summer precipitation, and spring and fall vapor pressure (Table 2). Annual temperature range was significantly correlated (Pearson’s r > 0.75) with measures of extremes in temperature and precipitation, including minimum temperature of the coldest quarter, mean temperature and precipitation during summer and winter months, and annual precipitation (Table 2).

Examination of Pearson’s χ² residuals produced by the ZINB model showed that all absolute values were less than three and only four sites had absolute values greater than two, fewer than would be expected by chance. Pearson’s scaled residuals > |2| represent sites where the predicted number of ticks is higher or lower than would be expected, which may lead to increased uncertainty of these predictions. Positive residuals greater than two indicate that the model is underestimating the number of nymphs at these four sites (Figure 2). Despite sites with large residuals being located near each other, no spatial autocorrelation was observed among the ZINB scaled residuals (Moran’s I: z-score = −1.01, P = 0.31) nor was spatial autocorrelation noted in observed DON (Moran’s I: z-score = 0.82, P = 0.41). That is, sites located in close proximity to one another were not significantly more likely to have similar DON. Five-fold CV of the model consistently predicted DON within 1.3 nymphs/100 m² and the mean standard deviation across the state was 0.93 nymphs/100 m² (Figure 2). As would be expected for a negative binomial distribution, the variance estimated using the delta method shows the highest variance in the metropolitan area and in Lake of the Woods and Koochiching counties in northern Minnesota, where the predicted number of nymphs was high.

Statewide predicted DON ranged from 0 to 19.6 nymphs/100 m², with the highest densities predicted in Hennepin, Anoka, Ramsey, and Dakota counties (within the Minneapolis-St. Paul metropolitan area) and in northern Minnesota in St. Louis, Koochiching, Lake of the Woods, and Roseau counties (Figure 2). Overall, 31% of the state was predicted to support peak host-seeking nymphal densities of at least 0.13 nymphs/100 m² (Figure 2). The inclusion of Voyageurs National Park had minimal effects on the ZINB model (Table 3). The predicted distributions were examined by subtracting the distribution of the model containing Voyageurs National Park from the distribution produced after removing Voyageurs National Park. All estimates of DON were slightly higher when Voyageurs National Park was removed. However, > 99% of pixels in the state differed by less than 1 nymph/100 m². Among the remaining pixels comprising < 1% of the state, the maximum difference at any given location in the predicted nymphal density between the model with and without Voyageurs National Park was 1.6 nymphs/100 m².

The percent area predicted to have ≥ 0.13 nymphs/100 m² in each county was significantly higher in “high” I. scapularis–borne disease incidence counties (median area predicted as risk per county = 43%) than “moderate” incidence counties (median area predicted as risk per county = 11%) and “low” incidence counties (median area predicted as risk per county < 0.5%) (Kruskal–Wallis rank sums test, P < 0.02; Figure 4). In addition, the percent area predicted as risk in each county was significantly higher for counties with established populations of I. scapularis (median area predicted as risk per county = 39%) than counties with reported populations (median area predicted as risk per county = 5%) or no records of I. scapularis (median area predicted as risk per county = 1%) (Kruskal–Wallis rank sums test, P < 0.001; Figure 4). There was no significant association between the percent area predicted as risk in each county and the cumulative number of Lyme disease cases reported per county from 2000 to 2015 when county population was accounted for (linear regression, P = 0.11).