First, I identified, using qp3Pop a set of population with significantly negative f3(Sardinian, Karitiana, Target) statistics:
This is actually a very helpful figure, as it shows how the f3 signal of admixture becomes weaker for more drifted populations (e.g., Finns) even if they have more of the investigated admixture than others (e.g., French).
It also shows that most West Eurasian populations appear admixed between Sardinians and Karitiana, whereas most East Eurasian ones (see spreadsheet) do not appear to be so, at least on the basis of the f3 test.
I next used qpF4Ratio to estimate the extent of this admixture. This depends on the following topology (Fig. 4 of Patterson et al. 2012):
I used: A=Papuan, B=Karitiana, C=Sardinian, and O=San, with X= any of the different investigated populations.
Note that this topology does not really hold for all X target populations whose admixture we are investigating. In particular, some populations have African admixture, hence O=San is not really an outgroup for them.
In the following, you can see the admixture proportion estimates using the F4 ratio test:
It should be obvious now how admixture estimates using the f4 ratio method depend on an appropriate outgroup. The f3-statistics indicate that all the above-listed populations are admixed between a Sardinian-like and a Karitiana-like population. But, the estimate of admixture based on the f4 ratio becomes negative, because f4(Papuan, San; X, Sardinian) is negative in populations where X has African admixture.
So, the Karitiana-like admixture of populations such as Spanish_D (est. 1.2%) is lower than their actual such admixture, because Spanish_D includes African admixture. For the Portuguese_D (est. -3.3%) where African admixture is even more significant, the effect is even stronger, and a nonsensical negative admixture score appears.
The converse took place when the f4 ratio method was applied by Moorjani et al. (2011). In that case, negative f4 scores with CEU as a parental population were taken as evidence of African admixture. But, since CEU has Amerindian-like admixture, the estimates of African admixture in that paper were higher than the actual values.
It will be interesting to derive corrected African admixture estimates after taking into account that CEU have Amerindian-like admixture, and, covnersely, corrected Karitiana-like admixture estimates after taking into account African admixture in some populations.
In any case, the data used for the above plots can be found in the spreadsheet, together with the list of all considered populations.