A Population Paradox

I had two ‘ancestors’ in the last generation, my mother and my father. I had four in the generation before that. Going back generation by generation, I can estimate the number of my ancestors at any particular time by calculating 2ⁿ, where n is an estimate of the number of past generations. Jesus Christ was born 2000 years ago; say, 80 generations. 2 to power 80 is approximately 1 followed by 24 zeros, or one million, billion, billion. Current scientific estimates of the human population at the beginning of the first millennium centre at about 300 million. My calculations seem to be overestimating by a factor of 3.3 million, billion and that’s only my ancestors; what about yours and everyone else’s? What’s gone wrong?

 

It is apparent that the 2ⁿ assumption overestimates the number of ancestors at generation n in two ways. Firstly, males can impregnate more than one female; the number of biological fathers will therefore be overestimated. Secondly, groups of siblings among the ancestors will have the same parents. Do these sources of over-estimation account for a 3.3 million, billion error factor? And, remember, we are only considering my ancestors and ignoring those of the 6 billion others currently in the world? Can someone please explain?

 

 

John Jacob Lyons