Unnatural? Not sure I understand the use of the term here. They were here for several hundred thousand years so there were only natural forces at work. There must have been some kind of balance if they thrived for that long. At the very least food availability would have limited their numbers in some way. It isn't dissimilar to the situation with bears.

Just guessing, but I would think there would have been a lot of cougars eating a lot of calves. That would also have some restraining impact on the population.