Uncovering the drivers of coral reef shapes using a mathematical model

• A new study led by IFISC scientists presents a simple yet powerful mathematical model that explains the large-scale structure of coral reefs using fundamental ecological and physical principles.
• The research uncovers how excitable dynamics can generate the spatial patterns seen in real coral reefs, providing a new perspective on how these vital ecosystems develop and persist.

How do centuries-old coral reefs acquire their breathtaking shapes and resilience? In a new paper published in Physical Review Research, a team from the Institute for Cross-Disciplinary Physics and Complex Systems (IFISC, CSIC-UIB) introduces a mathematical framework that captures the essence of coral reef formation at the macro scale. The model integrates key biological and physical processes, such as coral growth, resource competition, and aragonite (a crystalline phase of calcium carbonate that corals use to build their exoskeletons) accumulation, into a set of equations that reproduce the emergence of complex reef structures. 

In their study, IFISC researchers Miguel Álvarez-Alegría, Pablo Moreno-Spiegelberg, Manuel A. Matías, and Damià Gomila demonstrate that coral reefs can be described as excitable media, a type of system where small disturbances can trigger large, self-propagating waves. In other words, reefs can spontaneously generate traveling pulses and waves of growth (much like the electrical waves in heart tissue or the spread of vegetation in arid environments), leading to self-organized spatial structures. Remarkably, these patterns arise without relying on classical mechanisms like Turing instabilities, which have been the prevailing explanation for biological pattern formation. 

“Our model shows that the interplay between coral growth, competition, and aragonite accumulation naturally leads to excitable behavior”, explains Miguel Álvarez-Alegría, lead author of the study. “This excitable dynamics gives rise to traveling waves and pulses that shape the reef, closely matching the diversity of forms observed in nature”. 

The researchers conducted a detailed analysis of the model’s bifurcations (critical points where the system’s behavior changes dramatically) by varying two ecologically significant parameters: coral mortality and aragonite erosion rates. This approach allowed them to map out the different dynamical regimes that coral reefs can experience, from stable growth to wave propagation and pattern formation. 

Beyond its theoretical elegance, the model has practical implications for understanding the resilience and vulnerability of coral reefs in a changing climate. By linking macro-scale reef structures to underlying ecological feedbacks, the research offers a quantitative tool to predict how reefs might respond to threats such as ocean acidification, warming, and human disturbances. 

“Coral reefs are facing unprecedented challenges globally”, notes Álvarez-Alegría. “Our model provides a new lens to study how these ecosystems form and persist, and could inform conservation strategies aimed at preserving their unique biodiversity and ecological functions”, concludes. 

This work represents an advance in the mathematical modeling of complex ecosystems. By bridging ecological theory, nonlinear physics, and real-world observations, the study offers a new framework for understanding how large-scale reef patterns emerge. Gaining insight into these underlying dynamics is a key step toward developing more effective, data-informed strategies for coral reef conservation and management in the face of global environmental change. 

This study was featured in Physics 18, s46 (2025), Internal Feedback Shapes Coral Reefs.

Miguel Álvarez-Alegría, Pablo Moreno-Spiegelberg, Manuel A. Matías, i Damià Gomila, Excitable dynamics and coral reef formation: A simple model of macro-scale structure development, Phys. Rev. Research 7, 023196 (2025). https://doi.org/10.1103/PhysRevResearch.7.023196

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