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Adequate connectivity between discontinuous habitat patches is crucial for the persistence of metapopulations across space and time. Loss of landscape connectivity is often a direct result of fragmentation caused by human activities but also can be caused indirectly through anthropogenic climate change. Peary caribou (Rangifer tarandus pearyi) are widely dispersed across the islands of the Canadian Arctic Archipelago and rely on sea ice to move seasonally between island habitats throughout their range. Seasonal connectivity provided by sea ice is necessary to maintain genetic diversity and to facilitate dispersal and recolonization of areas from which caribou have been extirpated. We used least-cost path analysis and circuit theory to model connectivity across Peary caribou range, and future climate projections to investigate how this connectivity might be affected by a warming climate. Further, we used measures of current flow centrality to estimate the role of High Arctic islands in maintaining connectivity between Peary caribou populations and to identify and prioritize those islands and linkages most important for conservation. Our results suggest that the Bathurst Island complex plays a critical role in facilitating connectivity between Peary caribou populations. Large islands, including Banks, Victoria, and Ellesmere have limited roles in connecting Peary caribou. Without rigorous greenhouse gas emission reductions our projections indicate that by 2100 all connectivity between the more southern Peary caribou populations will be lost for important spring and early-winter movement periods. Continued connectivity across the Canadian Arctic Archipelago, and possibly Peary caribou persistence, ultimately hinges on global commitments to limit climate change. Our research highlights priority areas where, in addition to emission reductions, conservation efforts to maintain connectivity would be most effective.