What about infant mortality? If a million babies are born in the year 234BC, and die before 233BC rolls around, they won't be counted in the population for either year.
That's what I'm wondering about. The infant mortality rates in pre-industrial times were astoundingly high, but I don't see anything that tries to explicitly account for them. I guess they get rolled in with life expectancy (bringing the mean way down), but it would be nice to see an explicit formula for births_t.