Figure 3.

Our modular pipeline for matching the solutions of continuous and discrete models and identifying how cell movement and birth interact in both settings. We first isolate the discrete-model terms from [14] corresponding to movement (left column) and birth (right column) and simplify them to consider only one cell type. We then produce multiple realizations of our ABMs, sorting the cell locations into a grid of N_hist × N_hist voxels to yield the EA discrete-model results. We simulate our continuous model for cell movement (respectively, cell birth) and compare it on the same spatial mesh, with values of ${\alpha }_{\mathrm{MM}}$ (respectively, c⁺ and γ) obtained from a least-squares optimization approach; see electronic supplementary material, S2, for details. Finally, we combine the fitted movement and birth models to produce our full continuous model. While an extension of this pipeline to fit all three parameters simultaneously is straightforward, fitting separately allows us to better understand the effects of cell movement and birth in discrete and continuous frameworks.