Fortunately, there’s an entire field called mathematical biology that we can steal equations from. Unfortunately, it’s not a field I know. But that’s never stopped me before! In words, here’s what we’re trying to describe. I’ll define cultural capital here as a culturally transmitted toolset (both memes like the Levallois technique, and mores like ritual burial of the dead) for solving common problems to better exploit the environment. Neanderthals create cultural capital, sociopaths sell cultural capital, and MOPs consume cultural capital (in the sense of destroying it by increasing information entropy). I’ll split sociopaths into two groups: simple psychopaths, who merely prey on MOPs (either literally eating them, raping them, or siphoning their resources), and sociopaths proper who prey on geeks by siphoning cultural capital to MOPs in exchange for resources/dominance/prestige/etc.
(Please recall my theory is that denisovans were originally a race of man-eating giants/trolls, i.e. psychopaths, whereas melonheads were a mix of denisovans with neanderthals, i.e. sociopaths.)
Psychopaths prey on homo sapiens (aka neurotypicals, Clueless) in the natural state of homo sapiens, which is Africa. The population distributions will follow the predator-prey equations:
This model meets the assumptions, but it ignores interbreeding between psychopaths and neurotypicals. Neither psychopaths nor unmixed homo sapiens change their environment much on a 40,000-year timescale (our window of interest), because they are too busy competing within their own populations, so we can assume cultural capital remains constant.