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Recognition that polar bears are shared by hunters in Canada and Alaska prompted development of the "Polar Bear Management Agreement for the Southern Beaufort Sea." Under this Agreement, the harvest of polar bears from the southern Beaufort Sea (SBS) is shared between Inupiat hunters of Alaska and Inuvialuit hunters of Canada. Quotas for each jurisdiction are to be reviewed annually in light of the best available scientific information. Ideal implementation of the Agreement has been hampered by the inability to quantify geographic overlap among bears from adjacent populations. We applied new analytical procedures to a more extensive radiotelemetry data set than has previously been available to quantify that overlap and thereby improve the efficacy of the Agreement. We constructed a grid over the eastern Chukchi Sea and Beaufort Sea and used two-dimensional kernel smoothing to assign probabilities to the distributions of all instrumented bears. A cluster analysis of radio relocation data identified three relatively discrete groups or "populations" of polar bears: the SBS, Chukchi Sea (CS), and northern Beaufort Sea (NBS) populations. With kernel smoothing, we calculated relative probabilities of occurrence for individual members of each population in each cell of our grid. We estimated the uncertainty in probabilities by bootstrapping. Availability of polar bears from each population varied geographically. Near Barrow, Alaska, 50% of harvested bears are from the CS population and 50% from the SBS population. Nearly 99% of the bears taken by Kaktovik hunters are from the SBS. At Tuktoyaktuk, Northwest Territories, Canada, 50% are from the SBS and 50% from the NBS population. We displayed the occurrence of bears from each population as probabilities for each cell in our grid and as maps with contour lines delineating changes in relative probability. This new analytical approach will greatly improve the accuracy of allocating harvest quotas among hunting communities and jurisdictions while assuring that harvests remain within the bounds of sustainable yield. [ABSTRACT FROM AUTHOR]