genetiker, a new genome blogger questions the existence of Amerindian-like admixture in Europe. I am generally well-disposed to anyone who tries their hand at analysis of genetic data. On the other hand, if one accuses me of writing a series of posts "chock-full of stupidity", then there's a good chance I might respond. This should also be useful for anyone wishing to understand the evidence for this admixture.
genetiker proposes that the "Amerindian-like" admixture in North Europeans is misunderstood and can be in fact explained by the existence of "North European-like" admixture in Amerindians. In support of this, he presents the results of an F4 Ratio estimation analysis which suggests that there is "Nordic admixture of the Amerindian populations in the 10 to 20 percent range."
F4 Ratio estimation produces admixture estimates but does not prove the existence of such admixture. The admixture estimates are as good as the relationship proposed for a particular set of populations. If the relationship is nonsensical, so will be the admixture estimates.
According to genetiker, the following relationship holds, with A=Sardinian, B=Orcadian, C=Dai, and O=Yoruba, with X=Amerindians.
F3(European; Sardinian, Amerindian)
which is signifantly negative for North Europeans. Now, consider the value of this statistic for genetiker's phylogeny.
F3(B = North European; A = Sardinian, X = Amerindian)
In the above figure I color-coded the path from B=North European to A=Sardinian (red) and from B=North European to X=Karitiana (green, if it goes via the supposed "North European" admixture, or blue, if it goes via the "Amerindian" admixture). The value of the F3 statistic is then the weighted sum of the overlap of the red/green and red/blue paths:
F3(B; A, X) = αBZ+(1-α)(BZ+ZW)
where BZ and ZW are drifts along the paths indicated in the figure. This statistic is then always positive, since the common segments in the graph are traversed in the same direction.
genetiker's model is thus falsified by the data: it predicts a positive f3(North European; Sardinian, Amerindian) statistic, but we in fact observe negative ones.