Many people believe that our human population will be reduced by the scarcity of oil and other resources that our society has come to depend on. That this reduction will actually correspond much like it had exploded when the rate of resources consumed, soared. Put another way, as our resources deplete, so will the population in comparison to it. Or yet another way, our population will decline at the same rate of depletion. Many contend that following the population trend that has increased in the last 100 years will decrease in much the same matter and time, in the next 100 years. Much like those "bell graphs" or "Hubbert's curve", everyone is used to seeing on sites such as LATOC, Die-off, The Oil Drum, etc.. Most show how the human population has followed the rate at which oil has been consumed and now many contend we're at the peak or around there somewhere.
It would be an assumption on our part to project anything in the future. We're simply not there yet! Facts can be only found in the past. It would be a pretense on our part to project that the population dynamics would follow a similiar pattern on the back side of the curve as opposed to the front side. Perhaps, we're on some kind of plateau as of now, and our energy demand is barely being met to support the present population. Once demand surpasses energy production, would it be reasonable to start to see decline in population? No. The momentum of the population expansion will "carry over" or "overshoot", the actual resource base that can sustain it. Overshoot occurs when a population exceeds the long term carrying capacity of its environment. The consequence of overshoot is called a "crash" or die-off". There are some who contend that overshoot, likely started in the late 1970's and some estimates are suggesting that we're over 25% past carrying capacity now. To my knowledge, world population continues to grow, however at a slower rate than the recent past.
My point here, is that no one knows for sure how our population will descend, but a some point it will, once resources cannot support the existing population in this environment. Since no one can accurately predict how consumption of energy and other resources will play out in the future, it's impossible to predict how populations around the world will react, with any certainly.