From Networks to Traveling Waves and Back: Persistent Pattern Generation Across Collective Phases in C. elegans
Thousands of C. elegans placed adjacent to a food patch self-organize sequentially into a visible branching network off-food and then a coherent traveling consumption wave -- a multi-phase collective phenomenon we term wurmuration. Dynamical networks and traveling waves have previously only been described separately in this organism. Using a minimal agent-based model, we show that a single generative program produces both collective phases and their topological continuity. Four components (elongated body geometry, roaming-dwelling switching, preferred local worm density navigation, and food chemotaxis) are necessary and sufficient; what changes between phases is only the food environment they act on. We show that network-like organization persists cryptically (visible only through temporal integration) across the qualitatively distinct wave phase, indicating that the two phases differ in environmental context rather than in underlying behavioral rules. Finally, tuning the preferred density component alone recapitulates N2 vs. DA609 differences in wave dynamics; N2 additionally shows greater per-trial variability in cryptic network topology than DA609, in line with less consistent collective engagement in this lower-sociality strain. Our findings suggest that complex multi-phase collective phenomena can be unified by a shared generative program, shifting the description of spatial organization from the emergent patterns to their underlying components.