Sines of expansion

Cavalli-Sforza and colleagues used Principal Component Analysis (PCA) to summarize general spatial patterns of human allele frequencies across continents into maps. They interpreted peaks in these PCA maps to indicate sources of colonization, e.g. Neolithic expansions etc. However, a new paper by Novembre and Stephens (Novembre and Stephens 2008) questions this interpretation. They show that many forms of spatial covariance of allele frequencies between nearby populations can generate characteristic peaks in PCA maps. For example, simple isolation by distance or stepping stone models also give rise to peaks in the PCA maps, despite having homogeneous migration. These peaks arise because PCA analysis of data with covariance that decreases with spatial distance lead to PCA components that are sines and cosines.

The paper has some really pretty examples, I particularly enjoy the fact that these patterns also appear in Greenish warblers (a famous example of a ring species, i.e. isolation by distance). These results do not to say that human populations did not expand out of particular regions, just that PCA maps are not the best tool to judge this. The authors also note that this does not invalidate the use of PCA to correct for structure in association studies, and in fact might aid in their interpretation in epidemiological models.

Reference
Interpreting principal component analyses of spatial population genetic variation
John Novembre, Matthew Stephens. Nature Genetics
Published online: 20 April 2008 doi:10.1038/ng.139