Session

Feasibility and stability properties of complex ecological networks: New perspectives

12 Jul 2018, 10:30
New Law School/--104 (University of Sydney)

New Law School/--104

University of Sydney

100

Conveners

Feasibility and stability properties of complex ecological networks: New perspectives: Part A

  • Lewi Stone (Discipline of Mathematical Sciences, School of Science, RMIT University, Melbourne, Australia. / Biomathematics Unit, Department of Zoology, Faculty of Life Sciences, Tel-Aviv University, P.O. Box 39040, Tel-Aviv 69978, Israel)

Feasibility and stability properties of complex ecological networks: New perspectives: Part B

  • Lewi Stone (Discipline of Mathematical Sciences, School of Science, RMIT University, Melbourne, Australia. / Biomathematics Unit, Department of Zoology, Faculty of Life Sciences, Tel-Aviv University, P.O. Box 39040, Tel-Aviv 69978, Israel)

Description

With the enormous research activity now invested in studying the Science of Networks, new theoretical approaches have recently emerged. This minisymposium will explore how some of these new network approaches are being used to investigate ecological systems.
In the 70’s Robert May used Random Matrix theory to gain basic insights into how the complexity of a system impacts ecological stability. Following May’s inspiring approach, Alan Roberts (1974) soon after extended this work using Lotka-Volterra type models. In recent years there have been major advances in the study of Random Matrix theory that have widened some of these early results. Some of our speakers will examine these more recent achievements, and explain the mathematics behind them. In particular, new techniques for estimating the probability of feasibility, of structural stability (robust feasibility) and of dynamical stability of large ecological networks will be presented. These results make it possible to assess, e.g., whether, or not, feasibility is more constraining a persistence criterion than stability. A recent characterization of areas in parameter space where both feasibility and stability hold will be introduced. These methods provide avenues for assessing the structural and dynamical stability of observed, complex ecological networks.
Other speakers will use modelling approaches to examine conservation issues, such as the role of rare species in ecological networks and their impact on the dynamics and stability of ecosystems.

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