Table 2 Best models for prediction of density of nymphs (DON), nymphal infection prevalence (NIP), and density of infected nymphs (DIN)

1

DON_t+1

\({ = 1} . 2 8\times {\text{rodent density }} - 8. 7 5\times I_{\text{year = 2014}} + 1 1. 7 7\times I_{\text{treatment = control}}\)

LM

–

↑***

2

NIP_t+1 B. afzelii

\(= - 3.25 + 0. 0 2\times {\text{rodent density}}\)

GLM, binomial

–

↑***

3

DIN_t+1 B. afzelii

\(= 5.33 + 0. 7 5\times {\text{rodent density}}\)

LM

–

↑***

4

NIP_t+1 N. mikurensis

\(= - 2.85 + 0. 0 3\times {\text{rodent density}}\)

GLM, binomial

–

↑***

5

DIN_t+1 N. mikurensis

\(= 6. 8 4+ 1.52 \times {\text{rodent density }}\)

LM

–

↑***

6

NIP_t+1 B. miyamotoi

\(= - 3.33 + 0. 0 3\times {\text{rodent density }} \times I_{\text{year = 2014}}\)

GLM, binomial

2013

↓

2014

↑**

7

DIN_t+1 B. miyamotoi

\(= 4.88 + 0. 3 4\times {\text{rodent density}}\)

LM

–

↑*

8

NIP_t+1 B. microti

\(= - 2. 9 3- 0.02 \times {\text{rodent density}}\)

GLM, binomial

–

↓***

9

DIN_t+1 B. microti

\(= 2.64 - 0.04 \times \left( {\text{rodent density}} \right){}_{{}}^{2} + 1.62 \times {\text{rodent density}}\)

LM

–

↑↓*

10

NIP_t+1 B. garinii

\(= - 4.28 - 0. 0 4\times {\text{rodent density }} + 0. 8 3\times I_{\text{year = 2014}}\)

GLM, binomial

–

↓***

11

DIN_t+1 B. garinii

\(= 3.00 \left( {null} \right)\)

LM

–

→

12

NIP_t+1 R. helvetica

\(= - 3.52 + 0.03 \times {\text{rodent density}} \times I_{\text{year = 2014}}\)

GLM, binomial

2013

→

2014

↑***

13

DIN_t+1 R. helvetica

\(= 3.21 + 0. 7 0\times {\text{rodent density}}\)

LM

–

↑*

14

NIP_t+1 S. ixodetis

\(= - 1.04 - 0. 0 1\times {\text{rodent density}}\)

GLM, binomial

–

↓***

15

DIN_t+1 S. ixodetis

\(= 24.94 - 0.12 \times \left( {\text{rodent density}} \right){}_{{}}^{2} + 5.88 \times {\text{rodent density}}\)

LM

–

↑↓***