A Stochastic Method for Predicting Recovery of Coral Reefs

An immense amount of biodiversity is imperiled by the rapid decline of coral reefs exemplified by the Great Barrier Reef (GBR), the world’s largest coral reef ecosystem. The risk assessment of coral reefs to project its future trajectory often relies on the past physiological dynamics of the reefs. In this paper, we take the degradation of the GBR as a case study to provide an analytical framework for coral reef assessment which could significantly benefit other coral reef systems in the same predicament. We look at the mean percentage of hard coral cover of GBR and analytically capture its behavior as a stochastic process with memory through its mean square deviation (MSD). This procedure allows us to obtain an explicit form for the probability density function (PDF) describing the percent coral cover of the GBR. From the PDF, we derive an exact expression for the first passage time density sensitive to a given threshold for coral cover loss. We further assess the predictive capability of the first passage time density by calculating the percent error in forecasting changes in coral cover. The results indicate that the model can both project percent coral loss and predict potential recovery of coral reefs. This framework is applied to multiple other reef systems, including two sites in Moorea (French Polynesia), St. John (U.S. Virgin Islands), and the Florida Reef. The analytical procedure developed here provides a generalizable tool for assessing the long-term sustainability of coral reef systems also affected by climate change and anthropogenic pressures.