I've seen it stated occasionally that pre-modern cities were population sinks; that is, their population was sustained by immigration from the surrounding countryside rather than by birth rates within the city. The explanation given is that before modern medicine and sanitation, in the crowded conditions of the city mortality due to disease was horrifically high (to us).
On the surface it seems plausible, but has anyone collected the necessary demographic data to test this? If so, was it universally true, or were there some cities that had the sanitation and public health measures to escape it? It seems implausible that the disease mortality in, say, Tenochtitlan would be as high as contemporary London.
Further (and I doubt there're data to test this, but in case someone's done it, I'll toss this question up), did pre-modern health and sanitation measures, such as aqueducts or garbage services, influence the rate or level of urbanization? That is, did cultures whose cities were safer also have cities that grew faster and sustained larger populations, resulting in higher urbanization?
I'd be especially interested in any papers on this topic that there might be, because my google scholar fu doesn't seem up to the task.
From a Roman perspective, it really is not well known. It is certainly common to say that it was a population sink (from a personal standpoint I would say it probably was) but, as you can guess, the actual data for that tends to come from early modern London. And, indeed, first century Rome was not fifteenth century London. Here is a good paper on this issue.