## 3 Results
### Negative Binomial Generalized Linear Regression Analysis  
From the regression results, it is clear that the full, alternative, and calibrated models are significantly better than the null model as they have lower AICc and higher pseudo-R\({}^{2}\) values (Table 3). The non-null models produce seemingly contradictory indictors for model fitness. The Nagelkerke's pseudo-R\({}^{2}\) from the full model is higher than the alternative and calibrated models; that is, 0.57 vs. 0.47 and 0.55. The AICc, however, strongly favors the calibrated model, as its value is lower than that of the full model by 14.32. As a general rule, if the AICc of one model is lower than another model by at least 2, we would rather pick the model with the lower AICc. Because the Nagelkerke's pseudo-R\({}^{2}\) does not account for the degree of freedom or the number of explanatory variables, it gives an advantage to models with more predictors. Using the adjusted McFadden pseudo-R\({}^{2}\), which penalizes models including more independent variables, the calibrated model is better than the full and the alternative models. Note that those pseudo-R\({}^{2}\) from the negative binomial modelsshould not be interpreted as the (adjusted) R\({}^{2}\) from regular Gaussian models, although they are useful for comparing competing models, as we see here. Because our dataset is relatively small, we chose the simple leave-one-out cross validation method to further assess the models [62]. Essentially, the method leaves one sample out, re-runs the regression, and compares the predicted value and actual value from that sample. With N equals 80, the cross validation generated 80 predicted values. We used the root mean squared error (RMSE) to evaluate the overall prediction error and normalized it with the range of total number of ticks [63]. The results show that the calibrated model has a minimum prediction error of 5.12 among the four models, which is consistent with AICc in indicating its superiority to the others (Table 3). While the validation supports our selection of the calibrated model [64], the absolute prediction error is still quite large around 5, considering the mean value of the dependent variable is only 7.19. As such, these models, even the best one, have limited prediction power. Overall, the micro-scale  
Figure 5: Total Number of Questing Blacklegged Ticks and Temperature in Each Sampling Site. Blue and red lines are fitted total number of questing ticks using linear and generalized additive models, respectively. Shaded areas are their standard error bounds. The relationship between the number of questing ticks and temperature is nonlinear and varies across parks. The number peaks at approximately 20 \({}^{\circ}\)C. Black-legged ticks still quest under 0 \({}^{\circ}\)C.  
environmental factors can improve the fitness of the model, yet relying on them to predict the quantity of question ticks would be problematic as many critical factors might be still missing, and those included factors have complex interactions that may not be captured by the models. Figure 6: Total Number of Questing Blacklegged Ticks and Relative Humidity in Each Sampling Site. Blue and red lines are fitted total number of questing ticks using linear and generalized additive models, respectively. Shaded areas are their standard error bounds. In the natural environment, the influence of relative humidity on the questing activity of black-legged ticks is complex. Extreme low or high relative humidity seems to negatively affect the number of questing ticks. From the calibrated negative binomial model, the six predictors are all statistically significant at the 0.05 level (Table 4). Their impacts on the quantity of question black-legged ticks are also largely in line with the existing literature. Specifically, the ambient temperature and relative humidity positively contribute to the number of question black-legged ticks. Vegetation also has a positive contribution in general. However, distinct vegetation types show various degrees of impact.