To look at some easy things first:
Take a group of fixed size N>>1, 50% male 50% female, group them at random as pairs of (malei
), let each pair have exactly two children at the same time.
A person within this generation has one brother or sister, 2 cousins of first grade, 4 of second grade, ... - this pattern changes significantly near the group size, as it becomes usual that two persons within a generation share multiple independent ancestors.
However, a real population of constant size will always have members which have less than two children, and some with more than 2 childen. In a wild guess, I make up that these two effects cancel.
This gives an expectation value of ~ld(N) generations (+-1, too lazy to calculate) for the common ancestor of two randomly chosen members of this group within the same generation.
However, reality is a bit more complicated. People tend to choose partners which have a similar location, a similar cultural background, ... each with some chances to deviate from the "usual" choice.
In Europe, there are some small villages where the model given above should be a useful approximation. Take one of these with ~500 members, and you get ~9 generations or ~200 years. Another interesting result is that these villages tend to have few but very common last names.
What about a town with 10^5 inhabitants? The same rules gives ~17 generations or ~350 years. Not so much more than the small village, but a town of this size has much more contact with its neighborhood, especially within this time scale (and even more if you live in America (all of it)).
Let's take a county: N=10^8, ld(N)=27 -> ~550 years. Certainly this needs some adjustment towards the higher side, as 550 years are a lot of time for citizens to move into the country or to leave it, which reduces the relationships and therefore increases the time to the last common ancestor. In addition, the assumption of random pairs is now wrong - people prefer to stay at the same place, which also
increases the average time. And they tend to stay within the same cultural region. These effects are even more important as the time-scale reaches into the Middle Ages now.
We have ~2^33 humans on earth. Again using ~20 years per generation, I give a lower bound of ~700 years. Distance on earth will certainly increase this value, but I would expect that a loose connections between regions is actually sufficient to keep this effect small: Imagine one chinese which may have come to Europe at the time of Marco Polo (~1300) and got children in europe. Using the average of 2 children per generation, his descendents are likely to be spread across Europe (and all other regions of the world) now. Something in the region of ~2000 years does not look so implausible, at least if you exclude America.
I did not take the exponential population growth of the recent time into account here. However, I do not expect too large effects from it.
It should be possible to determine upper bounds: Using only mitochondrial DNA, it is possible to track lines of mothers. The deviation in the genome then gives an estimation about the meeting point of the lines of mothers. The same is true for the Y-genome for males and their lines of fathers. However, some Wikipedia searches showed me that there is an article about First-cousin marriages
(sic!), but I did not find interesting numbers. However, the article shows that the assumption of random partners can be very wrong: "but marriages between first and second cousins nevertheless account for over 10% of marriages worldwide. They are particularly common in the Middle East, where in some nations they account for over half of all marriages".Genetic history of Europe
has a lot of stuff, bit it mainly focuses on the pool of genes, not on single individuals which have contributed at some time.
Well... very high, but quite solid upper bounds can be obtained from the big migration waves: Out of Africa ~10^5 years ago (should be enough time for the whole world to have a lot of common ancestor of all), or into America ~1.5*10^4 years ago (only for Native Americans and their descendants of course)
>> If you look at all humans that ever lived, there is no common ancestor at all.
Of course there is. It might be hard to define "human" at the border, but certainly there was a living species which is a common ancestor of all humans. Or do you really think the whole life on earth has two independent lines which both evolved Homo Sapiens independently?