Consequences of a refuge for the predator - prey 1 dynamics of a wolf - elk system in Banff National 2 Park , Alberta , Canada

15 Refugia can affect predator-prey dynamics via movements between refuge and non-refuge areas. We examine 16 the influence of a refuge on population dynamics in a large mammal predator-prey system. Wolves (Canis 17 lupus) have recolonized much of their former range in North America, and as a result, ungulate prey have 18 exploited refugia to reduce predation risk with unknown impacts on wolf-prey dynamics. We examined the 19 influence of a refuge on elk (Cervus elaphus) and wolf population dynamics in Banff National Park. Elk 20 occupy the Banff townsite with little predation, whereas elk in the adjoining Bow Valley experience higher 21 wolf predation. The Banff refuge may influence Bow Valley predator-prey dynamics through source-sink 22 movements. To test this hypothesis, we used 26 years of wolf and elk population counts and the Delayed 23 Rejection Adaptive Metropolis Markov chain Monte Carlo method to fit five predator-prey models: 1) with 24 no source-sink movements, 2) with elk density-dependent dispersal from the refuge to the non-refuge, 3) with 25 elk predation risk avoidance movements from the non-refuge to the refuge, 4) with differential movement 26 rates between refuge and non-refuge, and 5) with short-term, source-sink wolf movements. Model 1 provided 27 the best fit of the data, as measured by Akaike Information Criterion (AIC). In the top model, Banff and Bow 28 Valley elk had median growth rates of 0.08 and 0.03 (95% credibility intervals [CIs]: 0.027-0.186 and 0.00129 0.143), respectively, Banff had a median carrying capacity of 630 elk (95% CI: 471.9-2676.9), Bow Valley 30 elk had a median wolf encounter rate of 0.02 (95% CI: 0.013-0.030), and wolves had a median death rate of 31 0.23 (95% CI: 0.146-0.335) and a median conversion efficiency of 0.07 (95% CI: 0.031-0.124). We found 32 little evidence for potential source-sink movements influencing the predator-prey dynamics of this system. 33 This result suggests that the refuge was isolated from the non-refuge. 34