Figure 2.

The profile of a B island as a function of time as it follows the random motion of an A agent. The cross-section of the island is taken through the current location of the A agent. (Inset) The time evolution of the height of the B concentration at the point at which A currently is located (solid blue line). The B colony is seen to grow, although the average growth rate over the entire space is negative (n_A is extremely low because there is only one in the whole simulation space, thus λn_A − μ ≈ −μ). The dashed red line shows the exponential growth with coefficient ɛ₀ − 2dD_Aκ, where κ = Log_e(λ/D_B) is the slope of the island (this slope is exhibited in the main graph and can be derived from a simple approximate calculation). ɛ₀ is λ − μ − 2dD_B derived similarly.