Fig. 6

The CREF eigen graph of the evolution of Canidae fourth and fifth CREF eigen-modules. After the split of the common ancestor from the wolf lineage, the dog lineage experienced a more rapid decrease in the relative distance between the fourth and fifth levels than the wolf lineage. At a specific point, the singular values of two levels became nearly identical and consequently, the two 1-D eigenvectors fused into a 2-D eigen-space. This degenerate point characterizes the onset of saltation. Notably, the red fox is near this degenerate point with a relative distance of only 1.9% between the fourth and fifth levels. In this 2-D eigen-space, any direction was an eigenvector. We refer to this 2-D eigen-space at the degenerate point as a space of CREF-polymorphisms. Then the selection occurred and only the eigen-direction with the highest fitness was eventually selected. After the fixation of the eigen-direction in the dog lineage, the two levels separated again. In comparison to the fourth and fifth motif eigenvectors of the red fox, those of dog, dingo, and dhole were rotated about 70°. Although dingo and dhole evolved in two different continents, they exhibited a strikingly similar rotation in the fourth and fifth CREF modules. The comparison of the relative distance from the degenerate point indicates that both the dog and the dingo are farther away from the degenerate point than the dhole.