You might research the "exponential growth" issue. Ecological speaking deer are K strategists and will typically grow up to a land carrying capacity and then fluctuate in stasis within the land carrying capacity.

R strategists experience exponential growth. Exponential growth is followed drastic population reduction as the growth raped the land capacity of every resource available to the organism. Very few organisms (especially of higher order) are r strategists and experienience exponential growth patterns.