Appendix S2: Analysis of sensitivity of utilization distributions to sampling interval and
cell spacing, and schematic of philopatry calculation
While the continuous-time correlated random walk (CTCRW) model described by Johnson et al.
(2008a; 2008b) is continuous in both time and space, to develop utilization distributions from
these models in practice requires discrete sampling in both dimensions. To ensure that these
discrete representations accurately represented the continuous process, we assessed the
sensitivity of our analysis to variation in the time between predicted animal locations and the size
of the grid over which we estimated the utilization distribution. We chose the overlap in
consecutive year's ranges as the metric over which we would assess sensitivity. We first chose
100 animal locations from two separate years that were broadly overlapping in space. We fit the
CTCRW model (Johnson et al. 2008a) to both datasets and estimated locations at every 2.5
seconds, 5 seconds, 10 seconds, 30 seconds, 1 minute, 2 minutes, 3 minutes, 5 minutes, and 10
minutes. We then predicted the probability of being at any point on a grid of points spaced 5
meters apart, calculated the overlap between the two years of data and examined the difference in
the overlap value across time scales (Fig. 1). Using only 100 locations the computer time
required to create the utilization distributions was substantial at the finer time scales (several
hours at 2.5 seconds between locations). Thus, we attempted to balance computer time with
accuracy of the representation of the utilization distribution and selected the 1 minute time scale
to use in further assessment of the sensitivity of the utilization distributions to the size of the grid
over which they were calculated (Fig. 1).
To assess the sensitivity of the utilization distributions to the size of the grid over which
they were calculated, we next estimated the utilization distributions over grids with varying
distances between points (0.05, 0.1, 0.5, 1, 2, 3, 4, 5, 10, 20 and 30 meters). This analysis
showed that at a grid size of 5 m or less there was less than a 5% difference between the overlap
values (Table 1).
To further assess the sensitivity of the utilization distributions to the size of the grid we
estimated utilization distributions for two full winter seasons for a single deer. We fit the
CTCRW model as above and estimated locations every minute. We then attempted to estimate
the utilization distribution over the same grid sizes as above. At grid sizes of less than 1 m the
computation time became prohibitive (greater than 1 day). Thus we assessed the sensitivity of
the overlap in utilization distributions to a reduced set of grid sizes (Table 2).
The results of the above analyses allowed us to make a decision concerning the trade-off
between computation time and accuracy of the approximation of the continuous process. We
decided that predicting locations every minute and estimating the utilization distribution over a 5
m grid was the optimal set of conditions. We note that these conditions still required substantial
computational time. To fit all models and estimate all utilization distributions required over 1
month of processing time on the Colorado State University ISTeC Cray High Performance
Computing System, a supercomputer housed at Colorado State University.
Table S2.1. Grid cell size, resulting overlap value and the percent difference between the
calculated overlap value and that calculated on the grid with the smallest cell size for utilization
distributions calculated for 100 locations from consecutive years of mule deer data in the
Piceance Basin Northwest Colorado.
Cell size
Overlap value
Percent difference from smallest grid
0.05
0.194
0
0.1
0.194
<0.001
0.5
0.194
0.002
1
0.195
0.006
2
0.196
0.01
3
0.198
0.021
4
0.2
0.031
5
0.202
0.043
10
0.213
0.09
20
0.269
0.281
30
0.311
0.378
Table S2.2. Grid cell size, resulting overlap value and percent difference between the calculated
overlap value and that calculated on the grid with the smallest cell size for utilization
distributions calculated for two complete winter seasons from consecutive years of mule deer
data in the Piceance Basin Northwest Colorado.
Cell size
Overlap value
Percent difference from smallest grid
1
0.373
0
2
0.378
0.014
5
0.384
0.028
10
0.384
0.028
20
0.387
0.036
30
0.367
-0.017
Figure S2.1. Results of analysis assessing sensitivity of overlap in utilization distributions to the
time between predicted animal locations assessed using the continuous time correlated random
walk model.
Figure S2.2. Schematic detailing calculation of overlap between utilization distributions used in
analyses of mule deer range overlap.
References
Johnson DS, London JM, Lea MA, Durban JW (2008a) Continuous-time correlated random walk
model for animal telemetry data. Ecology 89:1208-1215. doi: Doi 10.1890/07-1032.1
Johnson DS, Thomas DL, Hoef JMV, Christ A (2008b) A general framework for the analysis of
animal resource selection from telemetry data. Biometrics 64:968-976. doi: DOI
10.1111/j.1541-0420.2007.00943.x