Abstract

Mathematical models of collective movement come in many different forms, including macroscopic PDE approaches and on- or off-lattice microscopic models. Especially in the case of spatial dynamics and pattern formation, it can be difficult to compare models and data, or even the output of different types of models. The presence of variability in stochastic simulations and in vivo data adds further difficulty, since we may need to view many patterns before drawing conclusions. This makes it difficult to determine the impact of computational implementation and other modeling choices on predictions. To help address this challenge, we adapt methods from topological data analysis to robustly relate different models of the same biological system. As an illustrative case study, I will focus on the specific example of zebrafish-skin pattern formation, and I will show how to quantify patterns that arise from agent-based and cellular automaton models in this setting. Applying persistent homology to patterns involves choices, and I will also highlight the role of hyper-parameters in our process.