Unlike climatic data, past demographics are difficult to reconstruct from the archaeological record. In many periods there were no formal burials, so human remains do not survive, and in other periods where we have cemetery data, we cannot be certain that the buried populations reflect living populations. For instance, in the Roman period babies were not buried in cemeteries but rather stored in the eaves of houses or placed in enclosure ditches. Because of the difficulties of reconstructing ancient population levels, most data within the public remit suggest population began to increase around the Roman period.

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http://en.wikipedia.org/wiki/File:Population_curve.svg

There is, however, one period that is beginning to show clear changes in human fertility (and therefore most probably population increase) – that is, the Neolithic, when people first began to abandon a hunter-gatherer lifestyle and instead adopt farming.

Bocquet Appel et al. have demonstrated, on a global scale, that the transition from a hunter-gather to farming lifestyle was accompanied by major demographic change, characterized by an abrupt increase in immature skeletons, indicating a notable increase in birth rates. On the basis of this evidence it would appear that farming brought about the first major population explosion. Details of this research can be downloaded for free here

For many researchers, such as archaeologist Wickham-Jones (2010) and anthropologist Ingold (2000) the transition from hunter-gather to farmer marks the start of the problems faced by the world today. Certainly, by comparison to low-density mobile communities, the increased population of sedentary communities would have been more at risk to the effects of environmental change – something that is becoming clear today.