Phase diagram and representative patterns of the competing population. (A) Phase diagram. The grey shaded region corresponds to the case when both CDI+ or - extinctions are possible when the population is well mixed, identical to the grey region in Figure 1A. The green, blue and navy lines are the phase boundaries between spatial coexistence (beak regions) and extinction (outside of beak regions) when the rate of population diffusion is 0.0001, 0.001, and 0.01 respectively. (B-G) The most likely localized patterns of the competing population with different growth advantages and inhibitions. 104 random initial conditions are used here as we move across the phase diagram with a growth advantage of 3.5, a diffusion constant of 10-3, and an inhibition varying from 1.7 to 2.3. (B) For an inhibition of 1.7, patterns may be present depending on initial conditions, but the most likely state is the extinction of species v. (C-D) For an inhibition of 1.8 and 1.9, the most likely pattern changes to a single stripe configuration. (E-F) For an inhibition of 2.0 and 2.1, the most likely pattern changes to a double stripe configuration. (G) For an inhibition of 2.3, only the extinction states are observed, with the most likely state being the extinction of u.