## 2 Materials and Methods
In addition to the temperature and relative humidity measured during fieldwork, we obtained LiDAR and NAIP (National Agriculture Imagery Program) images of 1 m resolution from the _Discover GIS Data NY_ and _USGS Earth Explorer_ websites (Figure 2). Applying geospatial methods, we derived other environmental variables, including elevation, solar radiation, normalized difference vegetation index (NDVI), and ecotone length. All these variables were confined and/or averaged within the bound of each sampling site. Specifically, we used the LiDAR data to derive elevation and solar radiation. Prior research suggests that elevation is correlated with tick activity and abundance [42; 53]. Solar radiation is the amount of solar energy received at the ground level and is largely determined by seasonality, vegetation, and terrain factors such as slope and aspect. Solar radiation directly impacts temperature, humidity, vegetation, and therefore, the question activities of black-legged ticks. Using geoprocessing tools in ArcGIS, both the elevation and solar radiation were calculated from the LiDAR data, the coordinates of the sampling sites, and the dates when the sampling was conducted. With the NAIP aerial imagery, we applied supervised maximum likelihood image classification to derive land cover and vegetation types and calculated NDVI, as well as ecotone boundary length. NDVI primarily measures the greenness and the density of vegetation and is a well-known predictor for tick abundance [54; 55]. Ecotone is the transitional area at the boundary between two different plant communities. Therefore, we extracted the total length of ecotone boundaries in each sampling site to represent the degree of diversity and fragmentation of vegetation. This essentially measures the length of the edges between different vegetation land cover types (Figure 3). To carry this out, we converted the classified vegetation images to vector polygons to avoid overestimation. Within each 5 m by 5 m sampling site, the total length of the edges between polygons of different vegetation types was then calculated. Figure 3: Ecotone Inside Sampling Site. An ecotone is the boundary between different vegetation land-cover types. The length of ecotone is one indicator of the diversity, fragmentation, and heterogeneity of the land-cover types. With data in hand, we applied descriptive analysis and regression to investigate the variation in the numbers of question ticks against environmental variables. Since tick expeditions were scheduled across different state parks and seasons, they could have significant spatiotemporal variations, for which we illustrated the trends in both linear and nonlinear fashions. To formally establish the quantitative relationships between the number of questions ticks and micro-scale environmental factors, we built multiple generalized linear regression models based on the negative binomial distribution. Negative binomial regression is particularly applicable to over-dispersed count data, which is the case for the question ticks in our study [56]. Unlike Poisson distribution (\(var(Y)=\mu\)), the variance of a variable following a negative binomial distribution is greater than its mean and controlled by an extra parameter (\(var(Y)=\mu+\mu^{2}/k\)). We also used the corrected Akaike information criterion (AICc) to calibrate and choose a model with the highest fitness [57; 58; 59]. More specifically, we constructed four negative binomial regression models to test the explanatory power of the environmental variables on the quantity of question black-legged ticks. We started from a _\"full\"_ model containing all variables. Using the corrected Akaike information criteria (AICc) as guidance, we also developed a _\"calibrated\"_ model that had the lowest AICc and, therefore, the best fitness. This was carried out by dropping the insignificant variables and variables that were highly correlated. For example, NDVI was correlated with specific land-cover types such as mixed hardwoods and dwarf shrubs.