Figure 1. The “wave of advance” spread of a globally advantageous mutation.

Arrows indicate how the allele frequencies of a selected allele (red) are expected to change over time, depending on the pattern of selective advantage of the allele (indicated in green above each plot). Vertical arrows represent the magnitude of increase expected due to selection. Horizontal arrows represent how dispersal homogenizes allele frequencies across space. For every selected allele, a representative neutral allele (blue) of similar average frequency is shown for comparison. In each case the allele is supposed to have arisen at location 3 along the x-axis (marked with a vertical dashed line); the spread will continue until the selected allele is at frequency 1 across the whole habitat.

(A) Uniform selective advantage across space. If the novel variant is identically advantageous everywhere, the prediction is that as the variant increases in frequency it will be exceptionally concentrated around its geographic origin relative to a neutral variant of the same age. One effect of this is to create transiently enhanced levels of divergence among populations and clines in allele frequencies that reflect the geographic origin of the allele.

(B, C) Non-uniform advantage across space. In scenario B, the novel allele is introduced to the regions in which it is most advantageous and increase in frequency rapidly in those regions. This can lead to transient correlations between allele frequency and the environmental factor that drives positive selection. In contrast, in scenario C, the novel allele arises in an area distant from where it is most advantageous. It will increase in frequency locally before spreading outwards, and its distribution will carry a strong signature of its geographic origin and be less reflective of spatial variation in selective advantage.

These models assume selection acting on new mutations, which may not be the prevailing model in humans. Selection on pre-existing variation will complicate these simple scenarios.