What is a good estimate of the Earth's ecological optimum?

Question

An area's ecological optimum is the density of population which can be supported by that area's natural resources. If we take the entire planet to be the area, what would its ecological optimum be? In other words, how many human inhabitants would it take for the Earth to reach its absolute limit of sustainability?

Answer 1

12 no more, no less.  It all about balance, grasshopper.