Ok, this is just admitting that I have been rather stupid in my ways of thinking until recently. Just sharing this so you don’t do the mistakes that I have been making.
For a little while I was working on a coalescent model for admixture where I was thinking in terms of tracing lineages back in an admixed population until those lineages moved into source populations where they could then coalesce with lineages there.
In my mind, the scenario looked like this
It is a good model. Easy to model and easy to reason about. It is just very likely to be wrong.
If you have three populations, where one is admixed between two of them, how likely is it that the admixed population directly obtained genes from those two? Not bloody likely is what it is.
Much more likely is a scenario like this
The “source” populations are not directly the source populations; they are merely related to the source populations. And they are not necessarily equally related to them.
If you trace back the lineages from population C to the admixture time, you won’t be able to coalesce with lineages from A or B at that time. You can coalesce further back in time, when the admixed populations merge with population A and B — and that can happen a lot further back in time and at very different time points for A and B.
It isn’t that much harder to model it. You need to model that lineages from population C at some point gets separated into two different populations that now cannot coalesce, then have to wait a bit further before they can coalesce with lineages from A or B, but it isn’t that hard to model.
I just didn’t think about that, and now I feel really stupid.
Realising the full complexity of what you have to work with makes it all a lot more interesting, though.