The third dimension is actually the same dimension we have seen many times when doing the PCA plot for the European panel in this project giving the characteristic "V" shape where South Europeans cluster at the root while Finns, Saamis cluster on one branch while Eastern Europeans branch on the other. This dimension is the Saami-Finnish branch variation vs South Europe. This variations peaks on one side among Saamis and Finns and as we can see from the gradient map it also exists consistently among the Siberians but not among the East-Asians. On the other side it peaks among Sardinians, Basque and Italians and the East-Asians cluster here with the South-Europeans. I am very unsure about the interpretation here but as both Siberians and East-Asians is not at the extreme on either side of the variation I tend to believe it may represent a gene flow from Europe towards Siberia and East-Asia. Maybe the northern spread represent a geneflow of Saami/Finnish like hunter gatherers eastward into Siberia and the lower part a geneflow from Europe towards East-Asia through todays India.
Dimension 4 is the equivalent to the other branch of the "V" in Europe. On one extreme we found the Lithuanians, Mordovians and other Eastern European populations (actually here there is a Chukchi individual that a very little higher value than the top Lithuanian). The other extreme is Basque, Western Europeans, Saamis, Scandinavians and also the East-Asians. Also here I am unsure about the interpretation but it appear to show consistency as in dimension 3 but this time with a different spread. It may be a geneflow spread from Eastern Europe eastward through Siberia.
Dimension 5 appear to be a dimension that peaks among East-Asians on one side and Siberians on the other with the Europeans between. As we can see there is tendency to Siberian like influence in western part of Europe.
The PCA coordinates for all individuals and all dimensions can be downloaded here.