Appendix 1. Time-intervals and associated radii of Pareto kernels used to define available habitat for the SSFs and PathSFs. We fit a Pareto distribution to the empirical distribution of displacement distances at each time-period and defined the maximum radii of the Pareto distribution by either using the 97.5 quantile of the distribution, or the maximum observed displacement distance, whichever was smaller.

Time-
interval (minutes) / Radius of Pareto kernel (meters)
5 / 532
20 / 1351
40 / 2117
60 / 2618
80 / 3027
100 / 3278
120 / 3505
140 / 3834
160 / 4185
180 / 4296
200 / 4717
220 / 5064
240 / 5275
260 / 5486
280 / 5579
300 / 5802
320 / 6327
340 / 6555
360 / 7390

Appendix 2. Flow chart depicting the statistical analysis procedure for our step data. The same procedure was followed for our path data. For further information please refer to the methods section of the main paper.

Appendix 3. AIC values for the single scale and multi-scale multiple regression SSFs and PathSFs. Note, AIC values between the SSFs and PathSFs cannot be compared due to different sample sizes.


Appendix 4. Regression coefficients for the simple paired logistic regression SSF models across the 19 scales of analysis for the true steps and the 60-min pseudo steps.

Appendix 5. Quantiles of (a) SSF and (b) PathSF resistance surfaces predicted in the paired and unpaired frameworks at select scales.

a)

Quanitle
Resistance Value
SSF Paired
Scale / SSF Unpaired
Scale
532m / 2618m / 4296m / 7390m / Multi-scale / 532m / 2618m / 4296m / 7390m / Multi-scale
1% / 1.64 / 1.12 / 1.05 / 1.01 / 1.01 / 1.07 / 1.04 / 1.04 / 1.06 / 1.06
5% / 1.79 / 1.23 / 1.13 / 1.05 / 1.06 / 1.16 / 1.06 / 1.1 / 1.12 / 1.09
10% / 1.88 / 1.34 / 1.21 / 1.11 / 1.13 / 1.21 / 1.15 / 1.2 / 1.26 / 1.22
25% / 1.99 / 1.65 / 1.51 / 1.35 / 1.38 / 1.31 / 1.35 / 1.6 / 1.8 / 1.78
50% / 2 / 2.14 / 2.11 / 1.98 / 1.95 / 1.33 / 2.35 / 2.58 / 2.74 / 3.19
75% / 2.02 / 2.58 / 2.88 / 3.24 / 3.18 / 2 / 3.25 / 5.4 / 22.79 / 21.98
90% / 2.11 / 3.39 / 5.14 / 13.66 / 12.95 / 2.32 / 10.91 / 43.03 / 864 / 855
95% / 2.24 / 4.15 / 7.63 / 32.19 / 30.33 / 2.32 / 10.91 / 43.03 / 864 / 855
99% / 2.61 / 6.5 / 15.41 / 134 / 125 / 2.32 / 10.91 / 43.03 / 864 / 855
100% / 7.3 / 36.68 / 168 / 3897 / 3923 / 2.32 / 10.91 / 43.03 / 864 / 855

b)

Quanitle
Resistance Value
PathSF Paired
Scale / PathSF Unpaired
Scale
532m / 2618m / 4296m / 7390m / Multi-scale / 532m / 2618m / 4296m / 7390m / Multi-scale
1% / 1.03 / 1 / 1 / 1 / 1 / 1 / 1 / 1 / 1 / 1
5% / 1.19 / 1 / 1 / 1 / 1 / 1 / 1 / 1 / 1 / 1
10% / 1.41 / 1 / 1 / 1 / 1 / 1 / 1 / 1.01 / 1.03 / 1.13
25% / 1.9 / 2.15 / 1.05 / 1.05 / 1.07 / 1.03 / 1.44 / 2 / 2 / 2.32
50% / 2 / 2.64 / 2.58 / 2.37 / 3.12 / 2 / 4.6 / 4.6 / 4.6 / 3011
75% / 2.2 / 10.6 / 31.97 / 29.09 / 33.91 / 4.6 / 7470 / 5.8xe4 / 7.8xe5 / 3.0xe4
90% / 3.08 / 123 / 113 / 1034 / 606 / 6.59 / 4.1xe7 / 1.6xe9 / 3.1xe10 / 3.0xe7
95% / 5.34 / 632 / 1.1xe4 / 9849 / 3570 / 6.59 / 4.1xe7 / 1.6xe9 / 3.1xe10 / 3.0xe7
99% / 42.17 / 1.3xe4 / 5.9xe5 / 5.1xe5 / 9.3xe4 / 6.59 / 4.1xe7 / 1.6xe9 / 3.1xe10 / 3.0xe7
100% / 2.8xe4 / 1.1xe10 / 2.6xe12 / 3.3xe11 / 1.4xe11 / 6.59 / 4.1xe7 / 1.6xe9 / 3.1xe10 / 3.0xe7

Appendix 6. Resistance surfaces obtained from the PathSF models. The first column contains the resistance surfaces predicted in the unpaired framework, the second column contains resistance surfaces predicted in the paired framework, and the last column contains resistance surfaces predicted with pseudo paths in the paired framework. The first row contains the resistance surfaces from the smallest scale model, the middle row, the mid-scale model, and the last row the multi-scale model., and the last row the multi-scale model.

Appendix 7. PathSFCircuitScape current density surfaces (log10 transformed) and road pixels with the highest current densities.The vertical line represents Interstate-15, the black dots represent the top 20 pixels along I-15 with the highest current. The first column contains current maps resulting from predicting resistance in the unpaired framework, the second column contains maps predicted in the paired framework, and the last column contains maps predicted with the 60-min pseudo paths in the paired framework. The first row contains the current maps from the smallest scale model, the middle row, the mid-scale model, and the last row the multi-scale model.