Phylograph · Roadmap project 2 · after the Storyboarding notebook, p. 10
Genealogical Diamond
You have two parents, four grandparents, eight great-grandparents. Keep doubling and, a few dozen generations back, you would need more ancestors than there were people. The lines have to fold back into each other. Follow them far enough and they fold into ancestors you share with everyone alive.
your ancestorsancestor of everyone alive nowno descendants alive nowyour partner’s ancestorsancestors you share
Click anyone in the top row (the present) to make them “you.”
The dashed line is the naive count of ancestor slots, 2ᵍ. The red line is how many distinct people actually fill those slots. The gap between them is pedigree collapse: the same ancestors appearing in many places in your family tree.
The diamond
Seen from you, your ancestry widens generation by generation until it fills most of the population, then stops widening. The storyboard drew it as small trees for you and your spouse opening into a large-scale convergence. A maximum network diameter would be reached at a finite time in history, after which your ancestors would converge on a common human ancestor.
Two thresholds
Going back, the first threshold is the most recent common ancestor: the first person who is an ancestor of everyone alive now. The second is the identical ancestors point, where everyone in a generation is either an ancestor of all of us or of none of us. For one well-mixed population of N people, Chang (1999) showed these fall near log₂N and 1.77·log₂N generations back.
A correction to the notebook
The storyboard put the convergence at 100,000–200,000 years ago. That is the range for mitochondrial Eve and Y-chromosomal Adam, who are ancestors along a single line of inheritance each. Counting every line, the genealogical common ancestor of everyone alive is far more recent. Rohde, Olson & Chang (2004), modelling real geography and migration, estimated it at only a few thousand years ago, with the identical ancestors point perhaps 5,000–15,000 years back.
What the model leaves out
Generations here don't overlap, each person has two parents chosen at random within the mixing rules, and the population is small enough to see. Real populations are billions strong and very unevenly mixed, which is why the real dates are thousands of years rather than the centuries a perfectly mixed world would give.