Species are experiencing reductions in habitat range due to anthropogenic climate change. The climate sensitive montane mammal Ochotona princeps (American pika) is currently facing a reduction in range at lower elevations, but the demographic mechanisms linking climate to pika losses are unknown. We projected pika territory occupancy (presence or not of a pika) by predicting territory colonization and owner mortality in a large pika population in Montana, USA. We used annual data from the years 2019-2024 to develop Markov models of territory ownership turnover and to project occupancy and stage (juvenile/adult) structure of the population. To suggest turnover mechanisms, we modeled territory colonization and owner mortality as functions of mean summer temperature and mean winter precipitation. We found that higher mean summer temperatures and lower mean winter precipitation predicted less frequent territory colonization and more frequent owner mortality. Projections of occupancy under 2019-2024 climatic conditions suggest long-term stability in this population, perhaps due to the above-average snowfall at this study site, which might offset the negative effects of higher mean summer temperature. By modeling occupancy transition rates as functions of climate, our approach can produce mechanistic projections of occupancy dynamics to better inform conservation management strategies.