Some visit the Big Bend for a day or a week – and have their fill. But an intrepid few find they're suited to this harsh terrain, and make it their home.

Native to northern Africa, aoudad – or Barbary sheep – were introduced to Texas the 1950s. In the desert-mountains of the Trans-Pecos, they've found a land in which they can flourish. Watching aoudad storm up a rocky slope in the Guadalupe, Davis or Chisos mountains, it's hard not to admire these hardy newcomers.

But as their populations swell, aoudad appear to be edging out native species – mule deer, pronghorn, bighorn sheep. And that raises tough questions for landowners and wildlife managers.

Introduced on ranches and s...