I'll answer from an Aegean perspective, as that's my area of expertise. Some of the broader issues and methodological concerns will apply across the whole Eastern Mediterranean, but I don't want to suggest that the picture for one area is the picture for the whole - indeed, that's a common mistake among interpretations of this period.

In this earlier (warning: long) answer, I looked at the Late Bronze Age (LBA) 'Collapse' and what it actually meant in the Aegean and wider context. I think it's important to have a look at that to get a sense of what actually happened - that what we're talking about is a period of social, political and economic change, brought on by technological changes that made traditional forms of organisation obsolete. There's no reason to talk (at least in the Aegean) about mass violence, devastation or the sort of conceits that 'Collapse' usually brings to mind and would lend themselves to the loss of a huge number of people.

It's also important to note that population estimates from pre-modern societies are incredibly approximate and fraught with difficulty. There must be a detailed answer on the subject knocking around here somewhere - if someone could point me towards it, I'd be very grateful; otherwise I might put one together. It's a hugely important methodological issue that you absolutely have to be aware of if you're going to make judgements about the scale of ancient societies, and some idea of scale comes into nearly all of the interesting questions about them. It's therefore not uncommon for big interpretations of the past to be completely undermined when new evidence totally changes the population figures that underpin them.

To go through a complicated issue quickly, the main method of estimating population is from surface survey - sending out teams of (usually) undergraduates to walk transects across an area, picking up any pottery they find and noting its location. Whatever pottery can be is then dated, and the results plotted to find the density of pottery discards in a certain period as a proxy for the density of habitation. It's difficult to aggregate these results because project-specific considerations affect the results - how large an area you choose to cover, how widely you space people, the experience (or not) of the fieldwalkers, and how much expertise exists to correctly identify pottery of different periods. In particular, the study of LH IIIC pottery - immediately postdating the 'collapse', and therefore necessary to judge any change in population over it - has developed massively in the last 20 years, but there haven't really been any intensive, large-scale survey projects on the Greek mainland to make use of that knowledge. In general terms, this sort of landscape survey has been identified as something Greek archaeology - particularly for the Bronze Age - badly needs since the 1980s, and that's still true despite a number of important and successful regional surveys, mostly in that decade.

Part 1: Where Did People Live?

Robin Osborne discusses this problem at the start of his important 1996 work *Greece in the Making.*^(1) If we date the 'collapse' crudely to the end of the pottery period known as LH IIIB (that is, about 1190 BC, though the chronology here is complicated), then from about 220 sites known in 1996 with remains from LH IIIB we are down to about 100 in the following LH IIIC. However, Osborne notes that, though many areas show less dense evidence of inhabitation, none are abandoned, and that two major themes are movement of people (particularly towards the eastern coasts of Greece and Attica) and the increasing use of local artefact styles rather than standard forms popular in preceding periods. Both of these make it likely that archaeologists will pick up less evidence of habitation - because people moved away from the sites we know about, and left traces that are less easy to pin on an exact time period - even if numbers stayed similar.

The defining picture isn't so much that people died so much as they moved and their ways of life changed. Sigrid Deger-Jalkotzy gives a good, short survey of the 'winners and losers' in her 2008 chapter of the Cambridge Companion to the Aegean Bronze Age - which I'd very much recommend as the best introduction to all things Aegean prehistory. In Achaea, Crete and some Cycladic islands, people often moved inland and uphill, dispersing away from previous centres, and the same seems to have been true in Messenia (more on which later) and perhaps Laconia. In many other Cycladic islands, though, in the Argolid and possible on Rhodes, the opposite happened, and people tended to move away from small sites and nucleate together. Some regions seem to have gained quite a lot of people, particularly those placed to take advantage of new networks of trade - eastern Attica, Euboea and Kephallenia are the classic examples, and we might now be able to add some of the Aegean islands to that list.^(2) The trends in movement are highly local, and her attempts to explain them all through reactions to the dangers of a more violent world are a little unconvincing - under her model, people moved away from larger settlements into hilltop villages of Achaea because it was safer, and also moved out of the hilltop villages of the Argolid into larger settlements because that was safer.

It's important not to look at the situation backwards - in the LBA, we have large (for the time) settlements developing around palatial centres, but we need to remember that the palaces aren't coincidental to that - a large part of the reason that people live in these settlements is because the palace is there. We know from the Linear B records that the palaces could offer work and rations for a large number of people and were the major route to status for aristocrats, as well as possibly exercising a degree of coercive control to keep people in the area around them. The defining feature of the 'Collapse' in the Aegean is that these palaces cease to function - take them away, and a lot of the reason why you'd want to live in (say) Pylos or Mycenae disappears.