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Livestock guardian dogs (LGDs) are an effective tool for limiting livestock depredation by wild and feral predators. Unfortunately, LGDs have bitten hikers, joggers, and mountain bikers. Strategies are needed to mitigate LGD-human conflicts, especially in landscapes inhabited by large, aggressive predators where the threat of livestock depredation is greatest. One recommendation is to keep groups of sheep protected by LGDs at least 400 m from high-use recreational sites, but few data exist to support or refute this strategy. We monitored sheep and LGDs with Global Positioning System collars at seven ranches during a 3-yr period to evaluate how far, and under what circumstances, LGDs roamed from their sheep. One band of sheep (i.e., flock) was studied per ranch, with a typical band composed of 600−800 mature ewes with 900−1 200 lambs. Sheep were herded in extensive grazing systems within their traditional summer or fall grazing areas in foothill and mountain landscapes of southwestern and west-central Montana. Three bands of sheep inhabited landscapes with a greater threat of depredation by gray wolves and grizzly bears, and 4 bands of sheep inhabited landscapes where the threat of depredation was mostly from coyotes. The mean and median LGD-sheep distance across all LGDs and time periods was 164 m and 86 m, respectively. LGDs roamed farther from their sheep during nighttime and crepuscular periods than during daytime; farther when the moon was more fully illuminated; farther during fall than summer; and farther in landscapes without gray wolves and grizzly bears. Female LGDs roamed farther than males. Juvenile LGDs did not roam farther than adult LGDs. Overall, our results from extensive domestic sheep grazing systems suggest that keeping range sheep 400 m away from recreation sites and rural residences will likely prevent > 90% of agonistic LGD encounters with humans. © 2020 The Author(s)