ENVIRONMENT : Mountain Lions Thrive in West, Find Civilization : The large predators have attacked livestock, pets and occasionally humans.

While many animal species are struggling to survive, the mountain lion is thriving in the Western states and occasionally coming face-to-face with humans--with terrifying and sometimes tragic results.

Wildlife officials have documented dozens of incidents in which lions ate family dogs, challenged hunters on trails and prowled around--if not through-- such cities as Boulder, Colo., and this mini-metropolis of 35,000 people. In California, the normally rockbound and elusive cats were spotted on a Fresno golf course, in a Central Valley garlic field and on the outskirts of Sacramento.

In Montana, a young boy in one of the most crowded picnic areas of Glacier National Park survived a mauling by playing dead, as he had been taught, and gamely said from his hospital bed: “Children should listen to their parents.”

A 5-year-old in nearby Evaro was not so lucky in September, 1989--he was slain by a “kitten” that was later treed by hounds and killed by a hired hunter. It was one of the few times a mountain lion has killed a human.

“There’s no question that we have more mountain lions than ever before,” says John Firebaugh, a state wildlife manager for western Montana. (Cougars, panthers and mountain lions are synonymous; jaguars, the lions of Central and South America, are a different breed.)

“They’re in good shape and widely distributed,” said Terry Mansfield of the California Fish and Wildlife Department. He estimates that the population doubles every five years in California and that more than 5,000 now roam the state.

Why the big cats are thriving is a subject of endless conjecture among those who dart, measure, collar and track them. The mountain lion’s secretive, generally nocturnal habits have helped. So has an abundant food supply: Mountain lion populations have risen with careful human management of deer and elk. A shift in people’s attitudes also is credited--or blamed-- for the mountain lion boom.

During the 1960s, states began changing the mountain lion’s status from bounty-hunted varmint to sport-hunted game animal. Lions that develop a taste for livestock generally can still be shot by ranchers, with approval by state game wardens or federal officials.

But only Texas allows unregulated shooting. At the other extreme, California last year passed an initiative that forbids sport hunting of mountain lions.

Ranchers see that as a dangerous trend. “You’ve got to have predation control or people will take it into their own hands, whether it’s the wolf, the coyote or the mountain lion,” says Bob Acord, deputy administrator for animal damage control at the U.S. Department of Agriculture. “Most of the people in California and some of the Eastern states think the mountain lion is an endangered animal. It just isn’t true.”

Only two Eastern subspecies are classified as endangered: The Florida panther has retreated to the Everglades, and the eastern cougar has not been seen in decades. But Acord is talking about the kind of mountain lion that Utah sheep rancher Lorin Muench contends with.

“One winter, we had a pack that would kill 20 or 30 sheep a night,” says Muench, who ranches by the remote Deep Creek Mountain Range on the Nevada border.

“They were after the excitement, attacking, swatting, leaving them and then coming back to drag them up the canyon. We lost about 200 head in four days.” At about $100 a sheep, he said, that gets expensive.

A 150-pound mountain lion prowls as far as 200 square miles and eats 20 or 30 pounds of meat at a sitting. Males will occasionally fight to the death. Females take as long as two years to train their kittens to hunt properly--which may be why lions and people occasionally tangle.

The child in Evaro was killed by a 60-pound kitten, perhaps brought up too close to the city and certainly confused about its target, said the Missoula tracker who shot it.

“The ones that know better would obviously rather not mess with humans,” says Bob Wiesner, who uses his hounds to help the state with nuisance animals. “That one was a kitten and probably got separated from the mother, so it didn’t know what it was attacking.”