At the scale of large populations of organisms, they tend to show very similar behavior, regardless of the species of the population.
Basically, it's "energy in, population up." As a species, humans do have the distinction of being able to have extrasomatic energy inputs, not just food.
Russell Hopfenberg and David Pimentel (Duke and Cornell, respectively), in
their paper "Human Population Numbers as a Function of Food Supply," made a strong case that increases in the amount of food available actually drives up the population. With our oil-based agriculture, it's no surprise that the population growth curve has closely tracked the energy growth curve.
The so-called Green Revolution thought it was answering the question "how do we add enough food to feed this growing population?" Apparently, it's the same logic as asking "how do we add enough fuel to feed this growing fire?" Answer: it's growing because you're feeding it.
I think this also raises an unexpected point in discussions about potential "high-tech" energy sources. If we did create some breakthrough that provided cheap and abundant energy long-term (fusion, for example), it may turn out that we should be careful what we wish for: all that limitless energy continuing to pump up a population that will eventually push other, even more profound, limits in this finite world.
Given the issues of scale, I don't believe there is significant potential for bringing down the population numbers "from the inside," so to speak. Just as traffic behaves according to its own logic, regardless of the wishes of many individual drivers, so, too, population can be expected to follow its own rules -- among them, "energy in, numbers up" -- regardless of the efforts of many individual humans.
This gets us into that taboo territory. The implications here are that any significant reductions in population will most likely come from external forces -- reduction in energy/food, plague, disasters, etc. While Momma Nature may be serenely indifferent to that, it makes us individual humans a little edgy.