Fig. 2.

Ancestral lineages occupy distinct locations in pulled and pushed waves. A illustrates the fixation of a particular genotype. Initially, a unique and heritable color was assigned to every organism to visualize its ancestral lineage. There are no fitness differences in the population, so fixations are caused by genetic drift. B and C show the probability that the fixed genotype was initially present at a specific position in the reference frame comoving with the expansion. The transition from pulled to pushed waves is marked by a shift in the fixation probability from the tip to the interior of the expansion front. This shift indicates that most ancestral lineages are focused at the leading edge in pulled waves, but near the middle of the front in pushed waves. The fixation probabilities were computed analytically, following refs. 35 and 36, as described in SI Appendix, section III. We used $D=0.625$ for both B and C; $r_0=0.01$ and $B=1$ in B, and $r_0=0.0032$ and $B=12.5$ in C.