Dienekes notes the latest estimate of the population size of modern humans ca. 130,000 years ago, which would be just prior to the Out of Africa event, citing and quoting from Per Sjödin, Agnès E Sjöstrand, Mattias Jakobsson and Michael G B Blum, "Resequencing data provide no evidence for a human bottleneck in Africa during the penultimate glacial period" Mol Biol Evol (2012)doi: 10.1093/molbev/mss061.
Using the estimates of autosomal mutation rates derived from actual direct measurement in mother-father-child trios, which I believe to be more accurate than the mutation rate inferred from human-chimpanzee divergence, the effective population size was about 12,000 (95% confidence interval 9,000-15,000), implying a "census" population of about 90,000-150,000 modern humans who are ancestral to people who remain in the gene pool today in Sub-Saharan Africa.
The researchers note that:
Assuming that the range of humans extends over all the 24 millions km2 of Sub-Saharan Africa, the density of humans at that time would have been extremely low between 0.5 and 1.4 individual per 100 km2, which is even lower than the lowest recorded hunter gatherer density of 2 individuals per 100 km2 reported for the !Kung (Kelly 1995) and the density of 3 individuals per 100 km2 estimated for Middle Paleolithic people (Hassan 1981). However, this discrepancy disappears if humans were restricted to an area some 3-6 times smaller than the entire Sub-Saharan Africa.
However, as the modern population densities of Sub-Saharan Africa make clear, an assumption of a uniform population density in Middle Paleolithic Africa makes no sense. Some habitats are better for modern humans hunter-gatherers than others, and the !Kung continue to survive as a hunter-gatherer and herder society precisely because they live someplace with among the worst conditions for modern humans that it is possible to survive upon. In contrast, Middle Paleolithic modern human hunter-gatherers would have lived in the optimal environments for their life style in which they evolved in the first place.
A better estimate of Middle Paleolithic population densities would be to assume that the 120,000 modern humans of 130,000 years ago were distributed in a way roughly proportional to modern population densities (which still have to reflect ecological habitability due to a lack of economic development), with areas that would not have a floor population density of at least the 2 per 100 km2 population density of the !Kung being effectively uninhabitable by sustainable modern human populations in that area, and the population densities of modern humans in prime territory like the African Rift Valley being much greater - approaching peak population densities seen in hunter-gatherer socities based on fishing in places like the Pacific Northwest during the Pre-Columbian era. A population density of 10 per 100km2 with a much smaller percentage of Sub-Saharan Africa within the modern human range at that point (perhaps just 5% to 10% of the total area) seems like a more plausible assumption.