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Grizzly bear population growth and range expansion over the last several decades in the Greater Yellowstone Ecosystem (GYE) has led to increased human-bear conflicts, including livestock depredation on public land grazing allotments. A better understanding of patterns and relationships between grazing allotment management and grizzly bear depredation of livestock is needed for adaptive, sustainable management in the ecosystem. Historic U.S. Forest Service and National Park Service livestock grazing records, grizzly bear habitat attributes, and documented livestock depredations by grizzly bears were collated for 316 public land grazing allotments within the grizzly bear Demographic Monitoring Area (DMA) during 1992-2014. Spatio-temporal relationships between annual livestock depredation counts and grazing allotment characteristics were modeled for each allotment during the study period at two spatial extents, representing daily and annual grizzly bear activity areas. As the Yellowstone grizzly population expanded during the last several decades, more public land grazing allotments were exposed to potential livestock-grizzly bear interactions and results indicated that both livestock stocking and grizzly bear habitat characteristics in and around allotments were related to documented depredations during 1992-2014. Annual numbers of livestock and grizzly bear density on allotments had a large, positive effect on average livestock depredation event counts. Allotment size and summer grazing both were related to higher depredation event counts while the presence of bulls and/or horses was related to lower counts. Allotments with less rugged terrain, lower road density, relatively higher vegetative primary productivity, greater amounts of whitebark pine, and further from forest edge on average were associated with higher average livestock depredation event counts. Managers and livestock producers could use these results to support adaptive management approaches and long-term planning such as increasing herd supervision, especially in areas with quality grizzly bear habitat and high grizzly bear density, or altering grazing management strategies and grazing locations to limit potential livestock depredation events. Results provide insight into historic livestock-grizzly bear conflicts on public lands in a large, complex ecosystem and although challenging, results could support cooperative management strategies to sustain the grizzly bear population and livestock operations in the GYE.