Movement state

We fit hidden Markov models to grizzly bear and wolf GPS step lengths and turn angles so that we could incorporate movement behaviour into SSFs and to create biologically realistic simulations of animal movement. We used functions from the moveHMM package version 1.7 to fit hidden Markov models [21]. For each species and season, we fit two-state movement models to reflect slow (feed and rest behaviour) and fast (travelling and hunting) movements, following previous studies of GPS movement [12]. We note that interpretation of movement behaviours for slow and fast states can differ between wolves and grizzly bears. Wolves are obligate predators that feed for hours to days at predation sites and thus are likely foraging, resting, or denning in slow states, and hunting/traveling in fast states. Grizzly bears are omnivores and can thus forage on berries, roots, and herbaceous plants either in concentrated habitat patches (slow movements) or while travelling (fast states). Regardless, we associate resting behaviour with slow states for both species. We fit movement models with the gamma distribution for step length and the circular von Mises distribution for turn angles [29]. We included time of day (cosine of hour) as a covariate to allow for diurnal variation in the frequency of slow and fast states. We also included proximity to town and trail-road density calculated using a 500 m radius (km/km²) as we expected carnivores to transition to fast states when near areas with high human activity. We evaluated five exponential and linear decay functions for proximity to town with asymptotes between 500 m and 5 km (Additional file 2, Table S1). For each GPS location, we predicted the probability of being in a fast state (p_Fast), which we then incorporated into the SSF below (Fig. 1). We used parameters from the resulting movement models to simulate movement states, step lengths, and turn angles in path simulations below.