But it's not uniform. In the span of ~60 years, the average birth rate doesn't matter as much as the distribution and how much the children model their parents.

But it's not uniform. In the span of ~60 years, the average birth rate doesn't matter as much as the distribution and how much the children model their parents. Small example (multiply all numbers by 1M), average birth rate of 1.5 can be a group of 4 people where one had 0 children, one had 1, one had 2, one had 3. If each child has as many children as its parents, next generation, 0 have 0 children, 1 has 1, 2 have 2, 3 have 3, for a new average of 2.33. If you take a higher starting average but a tight spread [2, 2, 2, 2], the next average is only 2. Or if you have [0, 1, 2, 3] but kids model society instead of parents, you get 1.5 again. Of course children didn't model their parents the past couple of generations, but times may be changing.