An assessment of hypoxia-induced coral death via mathematical modeling

Coral populations have been steadily declining for many years due to ocean warming, coastal development, and overfishing. Ocean deoxygenation is worsening this trend, affecting various aspects of coral health and leading to declines in coral fitness, physical size, species diversity, and overall coverage of the reef surface. Coral reefs are believed to be at, or approaching, tipping points, where further declines in ocean oxygen levels could lead to catastrophic disruptions in ecosystem functioning. The specific mechanisms that may be responsible for the coral’s decline are not well understood because of the complexity of relevant ecosystem processes, e.g., as given by interweaving positive and negative feedback. In particular, turf algae that often live in close vicinity of corals are known to respond to water warming positively by increasing primary production and producing more oxygen. Whether that extra oxygen can compensate for the oxygen decrease due to lesser oxygen solubility in warmer water remains unclear. Similarly, the role of accelerated bacterial growth via algal exudates in the overall oxygen balance remains poorly understood. Bacteria tend to concentrate around turf algae, being attracted by the availability of nutrients, and they also consume oxygen, as required for their respiration. In this paper, we have endeavored to address these questions theoretically by developing a novel mathematical model that explicitly includes corals, algae, bacteria, and oxygen, along with the interaction between these agents. The model (consisting of four coupled nonlinear ODEs) has been thoroughly investigated using rigorous mathematical tools and computer simulations. Our analysis has revealed several bifurcations, critical transitions, and long transients, some of them leading to coral extinctions.<p></p>