. To generate a null distribution of movement paths,
We used a biased random walk model (e.g., Bartoń et al., 2009) to simulate movement paths beginning at the point an animal first came within 15 km of the road and continued until the number of steps matched the actual number of steps an animal took after coming within 15 km of the road (i.e., until 15 Dec). To simulate steps, we obtained an empirical distribution of step lengths from each individual from the beginning of the migration period until it first came within 15 km of the road. From these same steps we determined the directional persistence of steps by
calculating the mean resultant length. We then sampled the direction of each simulated step from a wrapped normal distribution with the concentration parameter set from the mean resultant length and the mean direction set to the location that the individual actually crossed the road
using the ‘rwrpnorm’ function in the ‘CircStat’ package for R (R Development Core Team, 2013). Themean direction changed at each simulated step. Once a simulated path crossed the road, we changed the mean direction to the location of that individual on 15 Dec. For individuals
that came within 15 km of the road but did not cross it, we set the mean direction to the point on the road the individual came closest to.We simulated 100 paths for each individual, based on each individual's empirical distributions of step lengths and turn angles.