(Colour online) Both (a) and (b) show the solution of plotted for g1 = 11.8, g2 = 10, ε1 = ε2 = 0, α1 = α2 = 1, D01 = 1.18 · 10−3 and D02 = 10−3; note that we chose g1/g2 = D01/D02 = 1.18 to facilitate comparison with (see discussion in text). In these units, the habitat is a 1 × 2 rectangle and is initially empty; only the bottom sixty percent of the habitat is shown because the top part remains empty throughout the expansion. The origin of the expansion is a line at the bottom edge of the images, where we impose the boundary conditions that c2(t, x, 0) = 1 and c1(t, x, 0) = 0 except in the width 2−8 region near the center of this boundary, where c2(t, x, 0) = 0 and c1(t, x, 0) = 1. No-flux boundary conditions are imposed along all other edges. is solved on a square grid of 256 × 512 points. (a) The concentration of the first strain is shown in red (dark gray) and of the second strain in green (light gray). The maximal colour intensity corresponds to the concentration of 1, and the lowest to the concentration of 0. This colour scheme is chosen to facilitate the comparison with the experimental data shown in . (b) The same solution as in (a), but only the concentration of the first strain is shown to highlight its establishment as a sector early in the expansion. Brighter regions correspond to higher concentration of the first (red) strain.