Today, about 800 bighorns roam the arid backcountry from the U.S.-Mexico border to the San Jacinto Mountains. Peninsular bighorn sheep also live in Baja California, but they are not included in the population classified as endangered by the...

As the five of us hiked around Rising Wolf Mountain, a monolith of ice-chewed rock in the southeast corner of Glacier National Park, we could hear clinking and rattling somewhere in the talus slopes above us—miniature rock slides unleashed by hooves. Kim Keating, a wildlife biologist with the Northern Rocky Mountain Science Center in Bozeman, Montana, was in the lead. He has studied Glacier’s bighorn sheep for two decades, collaring 99 since 2002 and tracking them with GPS recorders and radio telemetry. The tranquilizer dart he carried had enough of the narcotic carfentanil and the sedative xylazine to pacify a 300-pound sheep. Because the dose is lethal to humans, Keating—and only Keating—would handle the dart.

The low-angled autumn sun lit up yellowing larch trees like candles. Stephanie Schmitz—one of three fieldworkers assisting...