Joe Chang’s Proof

Joe Chang proved that the number of generations back to the most recent common ancestor in a randomly mating population is very closely approximated by the base two logarithm of the size of the population.  So, for a population of a million people, it takes 20 generations to reach the MCRA — or about 500 years — because 2 to the 20th power is about a million.  For a randomly mating population of a billion people, it takes 30 generations — 750 years — because 2 to the 30th power is a billion.