Figure 2: The PDE for cell migration does not accurately describe the EA ABM result when its scaling param-
eter αMM is set to unity. (a) To compute our EA ABM result, we solve Eqn. (2) using an initial condition of
400 melanophores placed uniformly at random in a 1 mm × 1 mm square; group cell positions in a 240 × 240
histogram; and average such data over 10000 ABM realisations. (b) We compute the corresponding PDE solution
by simulating Eqn. (4) with αMM = 1 from a uniform density of 400 cells/mm2 in the same square region. The
ABM and PDE solutions use the same potential (given by Eqn. (3) with parameters in Table 1). We overlay an
example ABM realisation for comparison; the results demonstrate that the support of the PDE is larger than that
of the ABM by about 200 to 250 μm. Because melanophore–melanophore distances have been measured to be
roughly 50 μm in vivo [84] and stripes are only about 7–12 cells wide [14], this is a large difference. (c) The
distribution of nearest-neighbor distances across 100 ABM realisations demonstrates that cell–cell separation
ranges from roughly 60 to 100 μm. Based on visual inspection of the graphs, nearest-neighbor distances appear
inversely proportional to the EA cell density. In (a)–(c), we show results at t = 150 days.
eter αMM is set to unity. (a) To compute our EA ABM result, we solve Eqn. (2) using an initial condition of
400 melanophores placed uniformly at random in a 1 mm × 1 mm square; group cell positions in a 240 × 240
histogram; and average such data over 10000 ABM realisations. (b) We compute the corresponding PDE solution
by simulating Eqn. (4) with αMM = 1 from a uniform density of 400 cells/mm2 in the same square region. The
ABM and PDE solutions use the same potential (given by Eqn. (3) with parameters in Table 1). We overlay an
example ABM realisation for comparison; the results demonstrate that the support of the PDE is larger than that
of the ABM by about 200 to 250 μm. Because melanophore–melanophore distances have been measured to be
roughly 50 μm in vivo [84] and stripes are only about 7–12 cells wide [14], this is a large difference. (c) The
distribution of nearest-neighbor distances across 100 ABM realisations demonstrates that cell–cell separation
ranges from roughly 60 to 100 μm. Based on visual inspection of the graphs, nearest-neighbor distances appear
inversely proportional to the EA cell density. In (a)–(c), we show results at t = 150 days.