Abstract
Regularly patterned reef ridges develop in the lagoons of at least one-third of Earth's coral reefs. The interactions between corals and their environment, occurring at scales from millimeters to meters, can lead to self-organized spatial patterns spanning hundreds of meters to kilometers. To understand the mechanism behind pattern formation, we first characterize these spatial patterns using satellite imagery from 63 sites across the Atlantic, Pacific, and Indian Oceans. Next, we develop a generalized Turing morphogenesis model. Corroborated by observed spatial patterns, results from our numerical model suggest that patterned ridges develop through a four-phase trajectory, dictated by changes in the lagoon's hydrodynamic regime. Initially, after an atoll lagoon forms, the first colonizing reefs establish as isolated pinnacles. These pinnacles then evolve into low-relief ridges and eventually form semi-enclosed inter-ridge ponds. In the terminal phase, a dense interconnected, branching, and rejoining ("anastomosing") pattern of reef ridges develop into a network, fully enclosing the ponds. Once enclosed, wind- and tide-induced currents are significantly reduced. Since corals rely on flow for feeding and shedding metabolites, ridge development stalls, and the pattern stabilizes. By combining empirical observations from around the world with a theoretical model, our study reveals the mechanism of reef pattern formation. Such a mechanistic understanding enables the use of emergent reef patterns to identify reef stress at the coral colony scale.