Title: Agent-based modeling and topological data analysis of fish patterns
Abstract: Many natural and social phenomena involve individuals coming together to create group dynamics, whether the agents are drivers in a traffic jam, cells in a tissue, or locusts in a swarm. Here I will focus on the example of skin pattern formation in zebrafish. Zebrafish are named for their dark and light stripes, but mutant fish feature variable skin patterns, including spots and labyrinth curves. All of these patterns form as the fish grow due to the interactions of tens of thousands of pigment cells in the skin. This leads to the question: how do cell interactions change to create mutant patterns? To help address this question, I develop agent-based models to describe cell behavior in growing 2D domains. However, my models are stochastic and have many parameters, and comparing simulated patterns and fish images is often a qualitative process. In this talk, I will overview our models, discuss how methods from topological data analysis can be used to quantitatively describe cell-based patterns, and share ongoing research connecting different modeling approaches.