[iskander]

I'm still not completely getting it. Let's say in some year there are a billion people alive and the average life expectancy is 50 years. How are these two pieces of information sufficient to determine how many children were born in that year?

[amalcon]

You also need the previous year's population. With population and life expectancy, you can approximate the per capita death rate, and then it's a straightforward linear equation.

[a-priori]

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.

[iskander]

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.