A function I’d love to see plotted — how many of my ancestors were alive at time t?
As the curve goes back in time, it would at first grow larger, but then shrink again at the genetic bottlenecks. (The entire human species has less genetic diversity than a chimpanzee troop.)
And it would be fun to see this plotted for two or more people along with a plot of the intersection count, the number of their common ancestors alive at time t. As the curves go back in time, they would all tend to converge with the intersection count, because in genetic bottlenecks we share the same small set of ancestors.
Another interesting graph would be the number of people alive at time t who have living descendants. I’d guess that even years with large populations were more “bottlenecky” than generally supposed, and that few people contributed long-term to the human genetic pool. For example, J.S.Bach, who died in 1750, had 10 children who survived to adulthood, yet has no known living descendants.