That isn't over population. Six billion people on Earth is just six billion people on Earth. At what point do you start saying it is overpopulation? At the point the Earth's resources can't naturally replenish to sustain the population size. In return, you have starvation etc..
Are we at the point that the Earth's resources can't naturally replenish to sustain the population size? Yes and no. The problem is inefficiency. Inefficiency works as a multiplier effect, which it is artificially created. Not only is it artificially created, but it is preventable.
Lets see, how can I illustrate what I'm saying? Look at globalization with a microscope. All the countries unified as one entity, isolated on a rock in space. Now, take this thought and apply it to one country. Look at the country as a unification of states as one entity, isolated from the rest of the world. Lets say that one country is all that is on the world. Can that country self sustain itself? Yes it can, but it isn't. The effects of negligence etc. would be comparable to what happens on a global scale of what you call over population. The country can't self sustain itself because of inefficiency. On a greater scale, there is not one country in the world that can self sustain itself because none are self sufficient. Does overpopulation cause this? No.
If overpopulation were genuinely real, then the Earth will purge us to normalize. It seems many think that is already happening because of starvation in Africa etc.. But like I said before, that is artificially created.
You see, overpopulation is an illusion and inefficiency is a control mechanism.
Just a different perspective.