For example suppose you have two containers filled with elastically colliding particles. Over an arbitrarily long time you can say that each particle has surely collided with every other particle, however if each container is closed then clearly particles from one container will not have collided with those from the other container over any amount of time
Yes that's why I took the conservative estimate of 7000 years, otherwise with the panmixia hypothesis it only goes back 3000 years or so.
If an allele had made it there, wouldn't it have been selected for?
By the way, the fact that all of us share the exact same set of ancestors from a few thousand years ago isn't new, shocking or controversial, only the exact date is still subject do debate. You may find this link useful: https://en.wikipedia.org/wiki/Identical_ancestors_point
The simulations are nice, and make a theoretical lower bound but a single remote tribe somewhere on earth would push it back tens of thousands of years.
DNA Sequence an Andaman islander and every bushman and Amazonian, then we'll see.
Evolution works in more complicated ways than the toy model of sickle-cell disease/malaria you've been taught in high school. Just having an edge in a particular situation is no guarantee for your alleles being selected. But even then, there could very well have been very little mixing while still everyone shares the same set of ancestors. Even a little mixing is enough.
>The simulations are nice, and make a theoretical lower bound but a single remote tribe somewhere on earth would push it back tens of thousands of years.
The subject is well-refined and the results are old news so I'm going to go on a limp and assume that the researchers who did the simulations know how to do their jobs and accounted for that possibility you described.
>DNA Sequence an Andaman islander and every bushman and Amazonian, then we'll see.
Ignoring the fact that the various peoples in the Amazon have not been isolated at all, or that the Adamans have been settled approximately in the time range of the estimated IAP and have known a few exchanges since, that's not how genealogy works. See, if a single outsider gets into the Adamans or Australia and starts having children with locals, and assuming the line doesn't die out, there's a statistical certainty that eventually every current living person in that territory will be descended from that outsider. Just one is enough. It doesn't matter that their genetic contribution is diluted to the point of being barely detectable. I invite you to read the link about IAP in more detail and do some rudimentary math on why it has to be the case (or more accurately, why the opposite is so statistically improbable as to be pretty much impossible).