IMPERIAL SAND DUNES, CALIFORNIA Registrations of all-terrain vehicles in Riverside County, a few hours from the dunes, have gone up fourfold in recent years.

DURANGO, Colo. — In the San Juan National Forest here, an iron rod gate is the last barrier to the Weminuche Wilderness, a mountain redoubt above 10,000 feet where wheels are not allowed.

But the gate has been knocked down repeatedly, shot at and generally disregarded. Miles beyond it, a two-track trail has been punched into the wilderness by errant all-terrain-vehicle riders who have insisted on going their own way, on-trail or off.