Unravelling the universal spatial properties of coral reefs

Abstract Coral reefs are under rapid decline due to human pressures such as climate change. Achieving the Kunming-Montreal Global Biodiversity Framework goals, which include restoring 30% of degraded habitats like coral reefs by 2030, requires a comprehensive understanding of their extent and structure, which has been hitherto lacking. We address this limitation based on the unprecedented canonical inventory of coral reefs extracted from the Allen Coral Atlas of shallow-water tropical reefs. We identified a total of 1,579,772 individual reefs globally, extending over a total of 52,423 km 2 of ocean area with mean and median sizes of 3.32 ha and 0.3 ha, respectively. We unravelled three universal laws that are common to all coral reef provinces: the size-frequency distribution, the inter-reef distance distribution and the area-perimeter relation, which follow power laws with an exponent of 1.8, 2.33 and 1.26, respectively. We demonstrate that coral reefs develop universal fractal patterns characterised by a perimeter fractal dimension of D P = 1.3 and a surface fractal dimension of D A = 1.6. Our analysis shows that coral reefs display intricate fractal-like geometries and exhibit universal macroecological patterns, largely independent of their geographical location. The universality of the observed patterns suggests that these features possibly stem from the highly conserved interactions of biological, physical, and chemical processes. Over geological scales, these processes lead to reef landscape patterns common among all provinces, providing new information relevant to reef growth modelling.