4 ancestral populations emerge at this level of resolution, which I have named: European, Asian, African, Amerindian. The names aren't important, and you can replace them with whatever you prefer.
The interesting thing about this K=4 analysis is that European populations show evidence of Amerindian admixture, consistent with the pattern inferred using f-statistics, where European populations show admixture between Sardinians and a Karitiana-like population.
This pattern may have emerged at previous ADMIXTURE analyses at this level of resolution, but thanks to the f3 evidence presented in previous posts, it is now clear that it is no quirk of ADMIXTURE, but indicative of a real (albeit still rather mysterious) pattern of gene flow that differentially affected European populations.
For example, the Irish_D population has 7.6% of the Amerindian component, and so do HGDP Orcadians. HGDP Sardinians have only 1.7% of it, which appears to be the minimum in Europe, with French_Basque having more at 4.6%.
Another interesting observation is that West Eurasian populations that show an excess of East Eurasian-like admixture appear to be doing so for two separate reasons. For example, HGDP Russians have 11.7% of Amerindian component, but also 4.5% of "Asian", and 1000 Genomes Finns have 3.3% Asian and 12% Amerindian. Behar et al. (2010) Turks, on the other hand, have 9.9% Asian and 2.2% Amerindian. All these populations are East Eurasian-shifted relative to Sardinians, a pattern which can also be observed by looking at the K=3 analysis, but for apparently different reasons.
The pattern for Near Eastern populations is also interesting. For example, Yunusbayev et al. (2011) Armenians have 0% of the Amerindian component, and 5.7% of the Asian, and all three HGDP Arab populations (Druze, Palestinian, Bedouin) also have 0% of the Amerindian component, with variable levels of the Asian.
It would appear that whatever process contributed Amerindian-like admixture in Europeans, minimally affected Near Eastern populations, with Sardinians being demonstrably related to Neolithic Europeans (thanks to ancient DNA evidence), tilting towards the Near Eastern pattern. On the other hand, Near Eastern populations show evidence of Asian admixture, which probably involves unresolved East Asian/ASI ancestry, and will be resolved at higher K. Sardinians appear to be at the end of three clines: (i) Amerindian-like cline of Europe-Siberia-Americas, (ii) East Asian-like cline of Europe-Central Asia/Siberia-East Asia, (iii) ASI-like cline of Europe-Near East-South Asia. These are separate, but not independent phenomena.
To confirm that the signal picked up by ADMIXTURE tracks the signal picked up by ADMIXTOOLS formal tests, I calculated the following D-statistic:
D(Sardinian, European, Karitiana, San)
where European is any population with a sample size of at least 10, and which belonged at 99% in the European+Amerindian components:
And, here is a scatterplot:
What of the actual estimates of admixture produced by ADMIXTURE? Using the F4 ratio test, I recently showed that African admixture in Sardinians confounds estimates of Amerindian-like admixture in northern Europeans and vice versa (Amerindian-like admixture in northern Europeans confounds African admixture in Sardinians).
In that experiment, I "scrubbed" Sardinians to remove segments of African ancestry, and showed that estimates of Amerindian-like admixture in the CEU population diminished from 13.9% to 8.8%. The latter seems reasonably close to the 7.1% inferred by ADMIXTURE.
On balance, I would say that ADMIXTURE at K=4 provides a good proxy for the effect described in Patterson et al. (2012). Its results are more difficult to interpret, because its underlying model does not take into account evolutionary relationships between populations. On the other hand, it has the advantage of being able to handle multiple ancestral populations, and has consistently proven able to generate useful data that correlate well with those from other techniques of population genetics.