The View from Above - Are Reefs Fractal Because of Neutral-Random Construction?

Satellite remote sensing has shown numerous aspects of coral reef seascapes to be fractal. That is they display characteristics of scale-invariance and complexity. This property is pervasive and recognized in the geometries of both framework and lagoonal bedforms in reefal settings across the Pacific. To date, the interpretation of this curious scaling has been hampered by a lack of understanding as to why the morphometrics of reefs should be fractal. We investigate this property using high-resolution terrain models of the shallow Puerto Rico insular shelf built using bathymetric LiDAR soundings. We find that a computer-simulation model constructed using simple random processes is adequate to describe the intricacies of actual coral reef terrain. This model, based on fractional-Brownian motion (fBm), produces surfaces that are visually and statistically indistinguishable from natural seabeds, at spatial scales of 0.001 – 25 km ² . The conformity between model and nature prompts us to question whether the processes used in the simulation can provide insight into the construction of real-world reef platforms. Through this comparison we are able to identify simple natural processes that mimic the construction of the modelled terrains. We demonstrate that random settlement of coral colonies, followed by focused development of topographic highs, is sufficient to explain the production of fBm-like reef terrain. Importantly, this negates the requirement for secondary factors such as complex lateral interactions between habitat types, and/or the overprinting of landscape-altering processes such as sedimentation and erosion, to produce a fractal reef surface. By comparison, for terrestrial systems, such secondary processes have been identified as a necessary precursor for the creation of fractal landscape. The findings of this study add weight to the hypothesis that the fractal property of reef terrain is the product of many simple random processes interacting at a variety of scales.