Table 1.

Model and simulation parameters used throughout the paper. We note that $N_{\mathrm{bir}}\in \{10,25,50,100,150,200,250\}$ realizations for 2D simulations and N_bir ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} realizations for 1D simulations. As we discuss in the electronic supplementary material, S2, N_sim = 5 × 10³ realizations for most EA ABM solutions of the cell movement model and N_sim = 10³ for all EA ABM results of the cell birth and combined models. We set N_hist = 30 voxels for EA ABM solutions of the cell birth and combined models, and N_hist = N_bin for the cell movement model. (See figure captions for our N_bin values.) The values of $R_{\mathrm{MM}}$ (and $R_{\mathrm{XX}}$, see electronic supplementary material, S1.3) were reported as repulsion strengths (i.e. $R_{\mathrm{MM}}/{\omega }_{\mathrm{MM}}$) in [39].

parameter	value	description and motivation
$R_{\mathrm{MM}}$	0.00124 mm2 day−1	strength of melanophore repulsion potential in equation (2.3); based on [14,39]
AMM	0 mm2 day−1	strength of melanophore adhesion potential in equation (2.3); based on [14,39]
${\omega }_{\mathrm{MM}}$	0.02 mm	melanophore repulsion interaction range in equation (2.3); based on [14,39]
aMM	0.012 mm	melanophore adhesion interaction range in equation (2.3); based on [14,39]
dmax	0.2 mm	maximum cell interaction distance in equation (2.2); based on [14,39]
dloc	0.075 mm	maximum interaction range for cell birth in equation (2.6); based on [14] and chosen slightly larger than measurements of cell–cell distances [78,79]
Nbir	varies	number of positions selected uniformly at random per day for possible cell proliferation (e.g. differentiation from precursors) in equations (2.5) and (2.7)
c−	1 cell	lower bound for the number of cells in a short-range neighbourhood for cell proliferation in equations (2.5) and (2.7)
c+	6 cells	upper bound for the number of cells in a short-range neighbourhood for birth in equations (2.5) and (2.7); based on estimations of data [16,78] in [14]
tfinal	150 or 2000 days	simulation end time (150 days in 2D and 2000 days in 1D)
Δtmove	0.01 or 0.1 days	time step for numerical implementation of equation (2.2) and electronic supplementary material, equation (S3)
Δtbir	1 day	time step for numerical implementation of cell birth in equations (2.5) and (2.7)
ΔtPDE	0.05 days	time step for numerical implementation of equations (2.4), (2.8) and electronic supplementary material, equation (S6)
Δtrecord	1 day	time step for recording data from model simulations
Nsim	varies	number of ABM realizations for computing EA cell densities
$N_{\mathrm{bin}}$	varies	spatial discretization step for solving our continuous models
Nhist	$N_{\mathrm{bin}}$ or 30 voxels	spatial discretization step for binning simulation results for comparison