In August 1988. the Sixth International Coral Reef Symposium was held in Townsville resulting in an influx of most of the world's coral reef sCientists to the city. We seized this opportunity at the Australian Institute of Marine Science to run a small workshop immediately before the symposium on the outbreaks of the crown-of-thorns starfish. Aeanthaster planei. We invited that small band of mathematicians who had been modelling the phenomenon, (and who may not have normally attended an international meeting so thoroughly dedicated to natural science) to meet with those SCientists who had been been actively working on the phenomenon in the field. John Casti notes in his delightful new book Alternate Realities (Wiley, 1989): 'If the natural role of the experimenter is to generate new observables by which we know the processes of Nature, and the natural role of the mathematician is to generate new formal structures by which we can represent these processes. then the system SCientist finds his niche by serving as a broker between the two. ' I think our book shows the fruits of that brokerage through the wide range of models explored within its pages. the high level of collaboration and interaction across disciplines evident in the individual papers, and in the emerging synthesis that reflects a far deeper understanding of this complex phenomenon than was possible even a few years ago.

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Plenary address.- On modelling.- Global spatial models.- Dispersal and control models of Acanthaster planci populations on the Great Barrier Reef.- Great Barrier Reef hydrodynamics, reef connectivity and Acanthaster population dynamics.- A diffusion-reaction-transport model for large-scale waves in crown-of-thorns starfish outbreaks on the Great Barrier Reef.- Reef syntax: an exploratory data analysis of the Acanthaster phenomenon using strings and grammars.- Stochastic and spatial effects in predator-prey models of Acanthaster-coral interactions.- Local spatial models.- Dispersal of neutrally-buoyant material near John Brewer Reef.- Reef-scale numerical hydrodynamic modelling developed to investigate crown-of-thorns starfish outbreaks.- A numerical scheme for determining trajectories in particle models.- Cellular automata models of crown-of-thorns outbreaks.- Crowns crowding: an individual oriented model of the Acanthaster phenomenon.- Test of a model of regulation of crown-of-thorns starfish by fish predators.- Effects of predation on Acanthaster: age-structured metapopulation models.- Nonspatial models.- Applied Volterra-Hamilton systems of Finsler type: increased species diversity as a non-chemical defense for coral against the crown-of-thorns.- Persistent and transient populations of the crown-of-thorns starfish, Acanthaster planci.- What controls outbreaks?.- Transition matrix models, crown-of-thorns and corals.- The relevance of stochastic effects to the notion of Acanthaster planci as a near-optimal predator.- Nonlinear prediction of crown-of-thorns outbreaks on the Great Barrier Reef.- Rapporteurs' report.- The Acanthaster Phenomenon: A Modelling Approach Rapporteurs' Report.