I believe it is a well known problem, but I couldn't find the solution.

 

In a vessel at hour 0 there is a 1 million bacteria. Every hour every bacteria produces two new bacteria and dies.

Right after that one half of all bacteria in the vessel is killed by random (i.e. 1 million times one bacteria is chosen uniformly from the vessel and killed). So now we have again 1 million left.

The process is repeated every hour on and on.

 

It intuitively seems to me that after enough repetitions all the bacteria in the vessel will be descendants of just one bacteria from hour 0.

 

Can this be proven?

 

Does it not always work like this: if we take a group of organisms of some species, after some (long enough) time, only the descendants of just one organism (or in sexual reproduction two: mother and father organisms) will remain?

 

For example, all living humans are descendants of just one man (biological Adam), who lived about 300 thousand years ago.

This means that no living human is a descendant (i.e. patrilineal) of another man who lived at the same time as biological Adam and was not his son/father (grand).

 

Does the fact that all humans are descendants of just one man comes from the probability theory and can it be strictly proven, i.e. can the probability be calculated?

Edited April 7, 20169 yr by Leo12345

I have seen this for several historical figures in the past.

Foe example, everyone in Europe is descended from Charlemagne: http://www.itsokaytobesmart.com/post/50523412948/we-are-all-royalty-descended-from-charlemagne

"Not only do all Europeans share Charlemagne as an ancestor, they share everyone alive at the same time as Charlemagne as an ancestor. Everyone who had kids, anyway."

 

Similarly, not only would Jesus have been a descendant of King David as the Bible claims but so would everyone else around at the time.

 

http://www.bbc.co.uk/news/magazine-19331938

 

Every hour every bacteria produces two new bacteria and dies.

 

 

That is not how bacteria reproduce. For all we know both daughter cells are identical. Due to the difference in reproduction we cannot directly translate the clonal model to our ancestry. In fact, the model is pretty much the inverse. Going back each generation, we have two ancestors. And after x generations we will have x^2 ancestors.

In bacteria growth is exponential. I.e. after each generation we will have a doubling. Or if we got back, for two cells we will have one original (clonal) cell.

 

The logic is not that after long enough time only the descendant of one individual will survive. Rather that given sufficient generations we will have sufficient relationship with everyone else that we share same ancestry. I.e. it is not that only Charlemagne's descendants survived, and all others died out, but rather that Chharlemagne's and many of his contemporary's children will have intermixed several generations down. I.e. they are not the descendants of a single person, but generations down they are all interrelated.

"Does the fact that all humans are descendants of just one man comes from the probability theory and can it be strictly proven, i.e. can the probability be calculated?"

All humans alive today -and at any point in the past or future- MUST share a single male and female ancestor. When those ancestors lived changes as time goes on and they are very unlikely to have lived at the same time, or even the same millennium. This is not really the result of "probability" theory. It's basic arithmetic. Humans, like all other sexually reproducing organisms on earth, are the result of reproduction between one male and one female - this results in a pedigree that is binary and bifurcating.

 

It is a mathematical certainty that at any point in time all members of a sexually reproducing species share a single male and a single female ancestor.