Corals and starfish waves on the great barrier reef: Analytical trophodynamics and 2-patch aggregation methods

In this paper, singular perturbation theory is applied to the Antonelli/Kazarinoff limit cycle model of the Crown-of-Thorns starfish (COTS) predation of corals on the Great Barrier Reef. At the microscale of individual reefs, the previously published 2-patch dynamics based on aggregation of individual behaviour is extended to include social interactions, spatial diffusion, and advection currents. As a consequence, the parameters which characterize the well-known wave solutions (i.e., the Reichelt starfish waves) are reinterpreted in terms of individual behaviour parameters. Likewise, the analytical trophodynamics of coral community production (without starfish), involving geometric invariants of second-order ODEs is defined at the microscale by direct manipulation of the reefal structure. The aggregation method leads to new insights into Liapunov stability of production of the coral community as a whole.