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You can't talk about overpopulation without referring to Thomas Malthus and Paul and Ann Ehrlich. Malthus made the observation that populations, given adequate resources, expand exponentially, that is a couple of humans will produce a couple more, giving four, and those two more will each produce two more, giving eight, and so on. Even in Malthus' day of shorter lifespans, this exponential growth was a fact of life. He then observed the growth of resources that we need to survive. Cultivated land was not growing at an exponential rate, we merely added more land as needed. So, Malthus notes that the adding of cultivated land will one day be surpassed by an exponentially growing population, at which point we would have a population crash.

In The Population Bomb, Paul and Ann Ehrlich added another factor to consider. Namely, human populations respond directly to the amount of resources available which are increasingly being made available from outside the region the humans live in. Industrialists in Siberia rely on grain imports from the Sudetenland and so forth. They came up with the concept of an ecological footprint, that is the effect on the planet of all your resource needs. Humans in Africa, even though there be many more and more rapidly growing, have a much smaller footprint, than humans in the industrialized nations. Japanese, due to their recyclable culture and energy conservation measures, tend to have a smaller footprint than Americans, who happen to have the largest footprint of humans the planet over. The conclusion here is that should the Chinese gain a lifestyle comparable to Americans, that the combined footprint will be larger than the planet, and we will experience a population crash, just as happens with deer in wintertime.

It is overconsumption of resources in the U.S., and not overpopulation, that we have to worry about. Simply put, we cannot regulate the population growth in South Africa, China, India, or any other foreign territory for a variety of reasons. We can regulate the size of our footprint. Major efforts are underway to accomplish this, from energy efficient housing to the local production and consumption of food. With a slowing population growth rate, lowering our footprint by eliminating wasteful practices like monoculture farming and over-harvesting the seas of fish and building with recycled materials, this is the best we can do for ourselves.

One more author is worthy of note in this topic, Daniel Quinn author of Ishmael which

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