However, our most recent common ancestor is not that first single-celled organism, nor is it the first Homo sapiens, or even the first Cro-Magnon.
The majority of the people who read this blog probably share a common ancestor who lived no more than 640 years ago.
You and I, whoever you are, have each two parents. Each of our parents have (or had) two parents, who themselves had two parents. And so on.
If we keep going back in time, and assume that you and I do not share a common ancestor, there will be a point where the theoretical world population would have to be impossibly large.
Assuming a new generation coming up every 20 years, and going backwards in time, we get a theoretical population chart like the one below. The theoretical population grows in an exponential, or geometric, fashion.
As we move back in time the bars go up in size. Beyond a certain point their sizes go up so fast that you have to segment the chart. Otherwise the bars on the left side of the chart disappear in comparison to the ones on the right side (as several did on the chart above). Below is the section of the chart going back to the year 1371.
The year 1371 is a mere 640 years ago. And what is the theoretical population in that year if we assume that you and I have no common ancestors? The answer is: more than 8.5 billion people. We know that is not true.
Admittedly this is a somewhat simplistic view of this phenomenon, used here primarily to make a point. For example, it is possible that a population of humans became isolated 15 thousand years ago, remained isolated to the present day, and that one of their descendants just happened to be around reading this blog today.
Perhaps the most widely cited article discussing this idea is this one by Joseph T. Chang, published in the journal Advances in Applied Probability. For a more accessible introduction to the idea, see this article by Joe Kissell.
Estimates vary based on the portion of the population considered. There are also assumptions that have to be made based on migration and mating patterns, as well as the time for each generation to emerge and the stability of that number over time.
Still, most people alive today share a common ancestor who lived a lot more recently than they think. In most cases that common ancestor probably lived less than 640 years ago.
And who was that common ancestor? That person was probably a man who, due to a high perceived social status, had many consorts, who gave birth to many children. Someone like Genghis Khan.