## Schematic of the three invasion regions considered.

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Invasion regions are displayed in red, whereas a background of resident cells is displayed in green. When considering invasion of red cells into an empty domain, the uniform concentration of the green cells is *c*_{G} = 0. When considering invasion of red cells into a non-empty domain, the uniform concentration of the green cells is taken to be *c*_{G} = 0.6, unless otherwise stated. The domain has dimensions *L*_{x} × *L*_{y} = 200 × 20. In a) the red cells enter the lattice from a 2D band in the middle region of the lattice defined by coordinates *x* ∈ [90, 109] and *y* ∈ [1, 20]. In b) the red cells enter the lattice from the horizontal midline of the lattice defined by coordinates *x* ∈ [90, 109] and *y* = 10. In c) the red cells enter the lattice from upper horizontal boundary of the lattice defined by coordinates *x* ∈ [90, 109] and *y* = 20. Homogenous vertical and reflecting horizontal boundary conditions are implemented in all simulations of the agent–based model. In all simulations, invasion of red cells occurs at a rate of 4 attempts per time-step.