Coincidentally enough, despite the fact that my own field of study is 20th century America, i’ve been reading about Rome recently while doing research for a professor.
Based on the works i’ve been looking at, many of which are economic histories and labor studies, the summary provided by Whack-a-Mole, above, seems to fall well within the accepted limits. One of the more recent studies, Metropolis and Hinterland: The City of Rome and the Italian Economy, 200 BC - AD 200, by Morley, summarizes earlier findings and attempts to arrive at a conclusion.
He points out that the figures of Beloch and Brunt have tended to dominate the field, giving a total population for Italy of about 6 million, with about 2 million of these people (or about one third) being slaves in the late first century BC and early first century AD. In contrast, Tenney Frank offers considerably greater figures, putting the free population at up to 10 million, with another 4 million slaves.
Morley notes that deciding between Beloch and Brunt’s figures, on one hand, and Frank’s on the other, cannot be done “on philological grounds alone.” Instead, he attempts to look at the figures “with respect to economic and demographic considerations.” From an economic viewpoint (agricultural production, population sustainability, etc.) he concludes that Beloch and Brunt’s Italy was “slightly underpopulated,” but that Frank’s was “far too crowded.” From a demographic viewpoint, taking into account rates of natural increase, the burden of wars, migration patterns, etc., he comes to a similar conclusion, but seems to lean more towards the lower end of the scale.
Population figures for this period are notoriously difficult to determine, even with the relatively comprehensive nature of the Roman census. And it’s worth noting that these figures i’ve been giving are for the late Republic and early Empire only, and do not necessarily carry over to the later Empire and the decline of Rome.