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Many natural and social phenomena involve individual agents 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 specific example of skin pattern formation in zebrafish. Wild-type zebrafish are named for their dark and light stripes, but mutant zebrafish 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? The longterm motivation for my work is to help shed light on this question and better link genes, cell behavior, and visible animal characteristics. Toward this goal, 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 and discuss how methods from topological data analysis can be used to quantitatively describe cell-based patterns and compare in vivo and in silico images. |