First, he writes:
In his post Dienekes takes the phylogeny I used for running the F4 ratio estimation program and shows that it won’t work for f3 statistics.
No kidding.No kidding indeed. Either genetiker believes in his phylogeny or he doesn't. The fact that the F4 ratio estimation program requires a phylogeny with that structure is meaningless: as I have shown, that phylogeny is wrong because it makes a prediction that is falsified by the data. Garbage in-garbage out, so the estimates obtained by genetiker with the wrong phylogeny are of course... wrong.
Second, he presents an even more elaborate phylogeny, where "V is Veddoids, C is Caucasoids, M is Mediterraneans, N is Nordics, G is Mongoloids, S is Sardinians, E is Europeans, and A is Amerindians."
This phylogeny is of course also wrong, for at least two reasons:
- It ignores post-admixture drift in Europeans, i.e., the drift that has accumulated after E was formed by M+N. This drift is always traversed in the same direction from E to S and to A, so it contributes a constant positive term in the value of F3(E; S,A)
- It proposes instantaneous formation of S, E, and A, e.g., the "Nordic" component in Europeans is symmetrically related to the "Nordic" component in Sardinians and Amerindians. genetiker clearly does not believe this, since he argues in his site (i) for I-M26 bearing "White Gods" coming to the Americas via the Canary islands, (ii) that mtDNA haplogroup X in the Americas is Caucasoid and so is (iii) Y-haplogroup C, which although "originally Veddoid" was carried by "Caucasoids" into the Americas. Now there's zero evidence that any of this has anything to do with Caucasoids, let alone Nordics in the Americas, but in any case it would be nice if genetiker harmonized his convoluted model of "Nordic" migrations with his phylogeny. In other words, his mental model of what happened isn't only inconsistent with the data, it's also inconsistent with itself.
Finally, genetiker attempts to work out the mathematical details of his model, arriving at the conclusion that:
There are four paths from Europeans to Sardinians and four paths from Europeans to Amerindians, so there are sixteen path combinations.This is of course wrong, because these paths are not independent; one actually needs to sum over 8 (=2^3) different trees for the different combinations of α, β and γ in the model; genetiker is therefore using wrong math applied to a wrong model. I believe his confusion stems from conflating admixture edges with drift edges.
It is not clear what he has aimed to accomplish with this "model", but let's analyze it properly:
- If α,β or 1-α,1-β then because of the instantaneous derivation of S,E from M and N respectively there is no drift in the degenerated length-0 "path" E-to-S, and hence F3(E; S,A) = 0. So, we only have to consider the cases α, 1-β and 1-α, β:
- If 1-γ then if α,1-β we have drift overlap MC, or if β,1-α we have drift overlap CN
- If γ then then if α,1-β we have drift overlap MC+CN, or if β,1-α we have drift overlap 0
So, in total we have a positive F3(E; S, A) statistic again, since we are summing over positive or zero drifts. If we also added the post-admixture drift in E, that statistic would be even higher -although this is not really necessary to falsify genetiker's model.
In any case, I still applaud genetiker for engaging with the data, and I'm happy to contribute to his continuing education!