#Robustness, #linear stability analysis

Figure credit: Shai Pilosof

Summary

Ecological networks are constantly subjected to perturbations, from the extinction of a single species to global climate shifts. This class explores the two fundamental ways ecologists define a system’s ability to persist: Structural Stability and Dynamical Stability. We begin by examining structural robustness—the network’s physical integrity in the face of node or link removal—using secondary extinction cascades. We then transition to dynamical stability, focusing on the mathematical conditions that allow a system to return to equilibrium following a state perturbation (e.g., a population crash). We revisit the historic “Diversity-Stability” debate, using Robert May’s landmark application of Random Matrix Theory.

Goals

  1. Introduce the fundamental distinction between structural robustness (network topology) and dynamical stability (population state), specifically focusing on how extinction cascades and state perturbations affect ecosystem persistence.

  2. Provide a mathematical and simulation-based framework for evaluating community stability, utilizing Attack Tolerance Curves (ATCs) and May’s Stability Criterion within Random Matrix Theory.

App to play with robustness

References

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