Stochastic Modelling of Coral-Algal Symbiosis on the Great Barrier Reef

Abstract

The Great Barrier Reef is the largest coral reef system on earth, but is threatened by the phenomenon of coral bleaching. We create a stochastic fluid flow model for coral bleaching, with the aim of better understanding its underlying mechanisms. Analysing this model involves the inversion of Laplace-Stieltjes transforms, a process ripe with difficulties. A recently developed method for Laplace transform inversion, called the Concentrated Matrix Exponential method, is very effective in overcoming these difficulties. Proceeding our analysis, we explore the concept of Parisian ruin to improve the biological realism of the model, which inspires a novel modelling framework for the problem. This framework includes an explicit energy process for the coral, and takes into account the traits of different algal species. We find that under our model, corals can benefit from hosting the two most prevalent algal species on the Great Barrier Reef, as opposed to only one species.