Federal contract wranglers plan to round up 4,300 wild horses in southwest Wyoming — permanently removing about 70% of them — starting Thursday in an undertaking that culminates years of conflicts among land and wildlife managers, ranchers and horse advocates.

The roundup across 3.4 million acres of “checkerboard” land ownership could last more than a month, said Brad Purdy, a Bureau of Land Management spokesman. The agency will permanently remove — for adoption, training and domestic use — about 3,500 horses. About 800 would be set free again after treating mares in that group...