Biodiversity describes the manifestations of life through its many forms at the molecular level and across ecosystems. Biodiversity has always been the main topic of study for ecologists and evolutionary biologists since it remains a paradox within a number of theoretical paradigms. More recently, it has also become a key property for conservation biologists given the growing body of evidence for the relationship between biodiversity and ecosystem services. Conservation biologists are more specifically concerned that accelerating environmental changes will reduce overall biodiversity because of slow adaptation to the environment. These concerns bring us back to fundamental questions: 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. For example, we need to achieve a 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). We also need to integrate the critical role played by spatial extent temporal scales in the local loss and adaptation of species to their environment. 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. Most of these efforts are in their infancy and would benefit from greater interactions between ecologists, evolutionary biologists, mathematicians and physicists.

The proposed workshop will 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 goal will be twofold: we will first organize sessions to generalize the use of mathematical methods across specific biological questions. We will then use this methodological integration to provide a quantitative framework for the study of biodiversity as a dynamic and non-equilibrium system. At the end of the workshop, our hope is to use this framework formulate the fundamental problems of biodiversity science from a dynamic perspective and across currently disjoint scales and levels of organization. Our hope is to advance the mechanistic understanding of observed relationships between biodiversity and ecosystem services.

Invited speakers and participants (confirmed):
Priyanga Amarasekare (UC Los Angeles), Peter Chesson (Arizona), Rampal Étienne (Groningen, Netherlands), Marie-Josée Fortin (Toronto), Tad Fukami (Stanford), Gregor Fussmann (McGill), Dominique Gravel (U Quebec, Rimouski), Jessica Green (Oregon), Simon Levin (Princeton), Mark Lewis (Alberta), Michel Loreau (CNRS, France), Kevin McCann (Guelph), Brian McGill (Maine), James O'Dwyer (Santa Fee Institute), Robin Snyder (Case Western), Mark Velland (Sherborooke), Colleen Webb (Colorado State, Forth Collins)