A recent story on Slashdot pointed out a paper that looks at human population cycles in terms of environmental availability as a predator-prey relationship. Supposedly it was meant as a commentary on the present economic climate, but it is... uniformly lacking in that department. It's missing a lot of important parameters and assumes constant values for things that fluctuate all the time. (Watch out for section 5.3, where the authors multiply the line representing the Bad Guys by their resource usage in order to make them look more menacing, and note also the incredible introduction, which more or less implicates resource depletion as the key factor in the decline of all civilizations.)

However, what this paper does provide is a rough outline of what might be some very simple (and I mean Easter Island level) rises-and-falls. Anyone who's ever thought about modelling population dynamics for an Iron-age civilization (or earlier) may want to consider taking some inspiration from this. I think it could be neat to define annual population tables for a tribe or village or something.