Linking continuous and discrete models of cell birth and migration

Self-organization of individuals within large collectives occurs throughout biology, with examples including locust swarming and cell formation of embryonic tissues. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of biological intuition. Discrete models provide straightforward interpretations by tracking each individual yet can be computationally expensive. Alternatively, continuous models supply a large-scale perspective by representing the \"effective\" dynamics of infinite agents, but their results are often difficult to translate into experimentally relevant insights. We address this challenge by quantitatively linking spatio-temporal dynamics of discrete and continuous models in settings with biologically realistic, time-varying cell numbers. Motivated by zebrafish-skin pattern formation, we create a continuous framework describing the movement and proliferation of a single cell populat..., Individual-based data were produced by simulating the ABM listed in the paper, using Matlab (version 2022a). The PDEs were simulated using either Matlab programmes (for the cell birth-only model) or using custom codes in Julia (version 1.7.3). Codes used to simulate the models may be found at the following Github repository: https://github.com/wdmartinson/Self-Organization-One-Species ., , # Data from: Linking continuous and discrete models of cell birth and migration

[https://doi.org/10.5061/dryad.s4mw6m9cb](https://doi.org/10.5061/dryad.s4mw6m9cb)

This dataset contains the ABM and PDE results for the mathematical models discussed in the article \"Linking continuous and discrete models of cell birth and migration\" by W. D. Martinson, A. Volkening, M. Schmidtchen, C. Venkataraman, and J. A. Carrillo.

## Description of the data and file structure

The data file contains three folders: \"Birth\" refers to results obtained using mathematical models incorporating only cell birth, \"Migration\" to those obtained from models incorporating migration alone, and \"Combined (Birth and Migration)\" to results obtained from models in which both mechanisms occur simultaneously. Each of these folders contains subfolders detailing whether they contain results from the discrete agent-based model (ABM Results) or continuous model (IDE Results or PDE results). Results are grouped by the initia...