FIG. 2:

Invasion dynamics in pulled waves. (Top): Invasion velocity shows two regimes with dependence on either $\alpha$ or $s$. The horizontal dashed lines are the predicted ‘Fisher velocities’. The curved dashed line is $u=\sqrt{2\alpha v_0}$, as predicted by Eq. (3). For each value of $s_0$ the filled in circle shows the location of the transition point ${\alpha }_c$ between the composite and circular arc morphologies. (Bottom): Depending on $\alpha$, there are three distinct colony morphologies. When $\alpha <0$ the front shape is a V-shaped dent. When $0<\alpha <{\alpha }_c$ the morphology is a composite bulge consisting of a central circular arc transitioning to a constant slope at the bulge edges. When $\alpha >{\alpha }_c$ the front is entirely a circular arc. The red arrow shows the invasion velocity $u$, which is the speed of the mutant-wildtype boundary along the horizontal axis. Parameters used are $v_0=10,D_f=D_h=1$.