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.
A central debate when studying ecological communities concerns the relative importance of selective processes relative to stochastic ones. This has significance for understanding the dynamic behaviour of these systems, for assessing features such as fragility and resilience, and ultimately, for determining how to correctly approach them. At the core of dealing with this challenge is the need...
The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive abundances. However, this key assumption has not been tested. We provide analytical results complemented by simulations which show that equilibrium...
An ecological community is called structurally unstable if it is feasible (a positive equilibrium exists) but feasibility is sensitive to changes in parameters, external pressures, or species composition. Absent such sensitivities, a feasible community is called structurally stable.
Mathematically one can show that, due to amplification of perturbations through indirect interactions,...
There exists a growing body of empirical evidence that suggests biodiversity regulation – the emergence of dynamic equilibrium diversity – may be a common or even general feature of ecosystems. However a mechanistic understanding of what tends to constrain diversity in nature remains elusive. Here we introduce a metacommunity assembly model in which regional diversity converges on dynamic...
In his theoretical work of the 70’s, Robert May introduced a Random Matrix Theory (RMT) approach for studying the stability of large complex biological systems. Unlike the established paradigm, May demonstrated that complexity leads to instability in generic models of biological networks having random interaction matrices A. Similar random matrix models have since been applied in many...