Say Hello to Your Cousin

During the sheltering-in-place phase of the Covid-19 crisis, I've been reaching out to relatives across the country. We all have the same concerns of protecting family members who may be at risk or helping others who are struggling during the crisis. In the conversations, I discovered that I have a number of cousins working on family genealogy projects. It is interesting as one learns about their extended family trees. 

If two people at random meet, what are the chances the two are cousins? Very rare if you limit the term cousin to mean the two subjects have a common grandparent or great-grandparent. If we only go back two generations, our two subjects each have four grandparents and they are not related (as first cousins) if they have no common grandparent. We can continue this exercise, comparing great-grandparents, great-great-grandparents and so on. With each generation we go back, there is a doubling of potential ancestors of whom our two subjects may have in common. Eventually, every random pair of people will have one or more common ancestors thus making them cousins (although very distant). 

How many generations do we have to go back to guarantee this matching will occur? Making an assumption of one generation for every 25 years, and going back about 28 generations, brings us to the 14th century. Two raised to the power of 28 is 268 million. If our two subjects each have 268 million super-great-grandparents, that would require there be no overlap in any of the 526 million ancestors for the two subjects not to be related. The reason I took this exercise back 700 years, is the world's population at that time was only 300-400 million people which means the two people must be distant cousins.

Some have taken this topic much further using mitochondrial DNA analysis to estimate that determine all humans have a single common female ancestor, termed Mitochondrial Eve. 

(Image: screenshot from https://worldpopulationhistory.org/map/1302/mercator/1/0/25/)

Update (1/19/2021) - Numberphile has a video that explores the math of ancestors with similar results: Numberphile Ancestors.

Update (10/8/2022) - If you have blue eyes and meet someone else with blue eyes, you can also greet that person as your cousin. See this article reporting that everyone with blue eyes is a descendant of a single human from about 6000 - 10000 years ago.