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I observed recently that some people born the same year in not too distant areas (say, in the same country whose size is not too big, like France) share similar phenotypical features, for example they look like each other though they are not of the same family. If confirmed, this would suggest that some alleles are more common within a given period, and hence that the global evolution of the human genetic pool could be statistically determined. One can go one step further and see the considered genetic pool in a given range as a quantum-like system governed by some kind of Schrodinger's equation. I think here of a theoretical framework like Laurent Nottale's scale relativity that could explain these similarities. Have such questions been considered so far?

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Welcome to Biology.SE Sylvain!

I observed recently that some people born the same year in not too distant areas (say, in the same country whose size is not too big, like France) share similar phenotypical features, for example they look like each other though they are not of the same family.

You are likely doing a confirmation or some kind of extended Barnum effect.

You will need to provide a rigorous study for this claim and not just a vague feeling you're having.

If confirmed, [..]

This piece of sentence suggests that you agree with my previous comments. We expect the OP to provide reference for a claim on which the question lies. One cannot ask "Why do elephants have such a huge genome?" without providing an evidence that they do have a huge genome.

[..] this would suggest that some alleles are more common within a given period,

If there is such effect it is much more likely caused by shared environment than by shared genetic. Have a look at this post to understand the underlying sources of phenotypic variance.

and hence that the global evolution of the human genetic pool could be statistically determined.

Sure, it can but this is not a consequence of the above supposed observation nor by the above hypothesis for the supposed observation.

Of course, specific processes could cause some cyclic process in evolution. A population overshooting carrying capacity could go under an oscillatory behaviour around this carrying capacity. As population size affects genetic diversity, such cyclical behaviour can have some impact. However, this is quite negligible. Also, there might be fluctuating selection (typically fluctuating on a seasonal basis) but this tends to be rather negligible for species of long lived individuals. I am sure you can think of some complex mechanism in structured populations would could yield to some oscillatory behaviour as well.

One can go one step further and see the considered genetic pool in a given range as a quantum-like system governed by some kind of Schrodinger's equation. I think here of a theoretical framework like Laurent Nottale's scale relativity that could explain these similarities.

I don't understand that part. I know pretty much nothing in quantum physics (have basic understanding in general relativity but not in Nottale's attempt to merge relativity and quantum physics). You might need to expand your thoughts I guess if you want biologists to understand where you're heading. However based on the above, I suspect, there is no reason to think this cross-talk would matter in any way.

Have such questions been considered so far?

I doubt so, because I don't think any of it makes much sense (no offense).

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