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The event that is likely to occur as the population of the mountain lions increases is that competition for territory and other resources acts to slow the growth rate of the population.

The population of any species of organisms cannot keep increasing infinitely because resources are limited in reality.

As the population of mountain lions in the alpine forest increases, intra-species competition increases as well. This competition could be for food, mates, space or any other limited resources.

Unless the resources available to a population increase to match up with population increase, the population growth will slow down and eventually levels off around the environments carrying capacity.

By carrying capacity, it means the maximum number of individuals of a species that an environment can support based on the resources it has.

More on carrying capacity can be found here: