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The mathematical analysis of an outbreaking species, the crown-of-thorns starfish found on Indo-Pacific coral reefs was the central topic that brought together mathematicians, ecologists and oceanographers in an attempt to create a new paradigm for understanding this complex phenomenon. A wide variety of mathematical approaches was offered in the workshop, from traditional qualitative stability analysis to work on Finsler spaces, grammars and adaptive systems. Together they point to a new understanding of the dynamics of the outbreaks and of the stability of the coral reef ecosystems in which they occur.