Fig. 5.

Genetic diversity is lost at different rates in pulled, semipushed, and fully pushed waves. (A) The average heterozygosity, $H$, is a measure of diversity equal to the probability to sample two distinct genotypes in the population. For both pulled and pushed expansions, the decay of genetic diversity is exponential in time: $H\sim e^{-\mathrm{\Lambda }t}$, so we used $\mathrm{\Lambda }$ to measure the strength of genetic drift. (B) Genetic drift decreases with $N$. For pulled waves, $\mathrm{\Lambda }\sim {\ln }^{-3}N$ (33), while, for fully pushed waves, we predict that $\mathrm{\Lambda }\sim N^{-1}$; see Eq. 5. To quantify the dependence of $\mathrm{\Lambda }$ on $N$, we fit $\mathrm{\Lambda }\sim N^{{\alpha }_{\mathrm{H}}}$. The dashed red line shows that even though ${\alpha }_{\mathrm{H}}$ should equal $0$ for pulled waves, the limited range of $N$ results in a different value of ${\alpha }_{\mathrm{H}}\approx -0.33$. (C) The dependence of the scaling exponent on cooperativity identifies the same three classes of waves as in Fig. 4C; the transitions between the classes occur at the same values of $B$.