I guess how our population eventually levels off will probably depend on what causes the level off- something drastic like famine, war, and disease, or something we choose ourselves, like limiting our reproduction.
I'm curious in the deer graph what happened to cause such a sharp decline? I can't quite make out what the two different lines represent, but they also seem to be re-growing at a slower rate than they were before the drop.
Taken from a deer survey exercise from the Department of Conservation and Natural Resources in Pennsylvania:
Populations of deer beyond the carrying capacity of the land causes an unbalanced ecosystem that is skewed in the direction of one species, the deer. Even the deer begin to suffer because of overpopulation and food shortages. This leads to a decline in the general health of the deer population often causing disease and starvation.
That results in a significant decline in the population. In the deer survey on Presque Isle, the population steadily grew from 60 deer to 160 between 1987 and 1990. In 1991, it fell to 110 and 1992 crashed even further to 61.
This also comes from the exercise: "The Penn State University’s Deer Nutrition Research Team in 1992, concluded that the available habitat on Presque Isle State Park cannot support more than 16-20 deer without seriously jeopardizing woody plants, including vegetation to control dune and sand erosion."