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Biodiversity describes the manifestations of life through its many forms at the molecular level and across ecosystems. Biodiversity is the main topic of study for ecologists and evolutionary biologists since it remains a paradox within a number of theoretical paradigms. The fundamental questions are: what are the mechanisms that cause the loss and creation of biodiversity? How are these mechanisms regulated and how is their regulation expected to respond to environmental change?

Since biodiversity is, by definition, a high-dimensional dynamical system, these questions require sophisticated quantitative approaches and a careful balance between the description of biodiversity as an integrated dynamical variable and its study as emerging from the explicit interaction among its components (e.g. genes, species). Similar considerations apply to questions of spatial extent and temporal scales. Novel approaches from mathematics and physics, such as graph theory or statistical mechanics are being used to simplify the formulation of a dynamic theory of biodiversity, but many are in still their infancy and would benefit from greater interactions between ecologists, evolutionary biologists, mathematicians and physicists.

The workshop goal is to present a conceptual framework for the study of biodiversity dynamics, which will be used to identify key mathematical challenges, such as dimensionality, scaling, and nonlinearity. Our hope is to use this framework to formulate the fundamental problems of biodiversity science from a dynamic perspective and across currently disjoint scales and levels of organization, and to advance the mechanistic understanding of observed relationships between biodiversity and ecosystem services.