We know, from looking at the amount of genetic variation in the global human population, that it went through a fairly pronounced bottleneck around 70,000 years ago. This has been variously attributed to the founder effect, with only small populations moving out of Africa into Europe & Eurasia, and to the devastating consequences of the eruption of a supervolcano (Toba, in what is now Indonesia). The latter possibility has been the focus of a number of articles (e.g. Ambrose, 1998 - I might post more thoroughly on this another time).
I was idly searching for more information on this when I happened across an article on Anthropology.net that does a good job of presenting contrasting viewpoints on the cause of this bottleneck - and showing how tentative our understanding in this area really is. Well worth a read.
S.H. Ambrose (1998) Late Pleistocene human population bottlenecks, volcanic winter, and differentiation of modern humans. Journal of Human Evolution 34: 623-651