  Self-organized pattern behavior is ubiquitous throughout nature, from fish
schooling to collective cell dynamics during organism development.
Qualitatively these patterns display impressive consistency, yet variability
inevitably exists within pattern-forming systems on both microscopic and
macroscopic scales. Quantifying variability and measuring pattern features can
inform the underlying agent interactions and allow for predictive analyses.
Nevertheless, current methods for analyzing patterns that arise from collective
behavior only capture macroscopic features, or rely on either manual inspection
or smoothing algorithms that lose the underlying agent-based nature of the
data. Here we introduce methods based on topological data analysis and
interpretable machine learning for quantifying both agent-level features and
global pattern attributes on a large scale. Because the zebrafish is a model
organism for skin pattern formation, we focus specifically on analyzing its
skin patterns as a means of illustrating our approach. Using a recent
agent-based model, we simulate thousands of wild-type and mutant zebrafish
patterns and apply our methodology to better understand pattern variability in
zebrafish. Our methodology is able to quantify the differential impact of
stochasticity in cell interactions on wild-type and mutant patterns, and we use
our methods to predict stripe and spot statistics as a function of varying
cellular communication. Our work provides a new approach to automatically
quantifying biological patterns and analyzing agent-based dynamics so that we
can now answer critical questions in pattern formation at a much larger scale.
