At the end of this course unit, students will be able to define and distinguish different concepts of ecological stability and understand how they can be quantified.
They will be able to analyse the stability of ecological systems using mathematical approaches, in particular through the study of local stability and the properties of the Jacobian matrix. Students will also be able to explain and analyse relationships between biodiversity and stability at different levels of ecological organisation.
The course aims to provide a conceptual and quantitative understanding of ecological stability. It shows that stability can be defined and measured in different ways and examines the relationships among these different dimensions.
The course then provides the mathematical foundations required to study the stability of dynamic ecological systems. Particular attention is paid to local stability, the linearisation of dynamical systems and the use of the Jacobian matrix.
Finally, the course examines relationships between biodiversity and stability, and the mechanisms that may explain these relationships.
The course addresses different ways of defining and measuring the stability of ecological systems. It distinguishes different dimensions of stability and examines the relationships among them.
An important part of the course is devoted to the mathematical analysis of stability. Dynamical systems are studied around their equilibria using linearisation and the Jacobian matrix, providing a basis for introducing and analysing local stability.
The course then addresses relationships between diversity and stability, including how the properties and dynamics of different populations contribute to stability at higher levels of ecological organisation.
Concepts and definitions of ecological stability
Quantifying stability
Dynamical systems and equilibria
Local stability
Linearisation and the Jacobian matrix
Stability analysis of ecological systems
Diversity and stability
Mechanisms linking diversity and stability
Application of several techniques to quantify stability. The students will be given one or more problems on the broad topic of stability in populations/communities. They will apply the techniques seen in the theoretical course to solve this/these problem(s).
Sessions "project work": during these sessions the students will work on their projects
Teaching combines theoretical classes and exercises. Stability concepts are progressively introduced and formalised using graphical and mathematical approaches.
Exercises allow students to apply the concepts and methods introduced in the course to ecological systems and develop their understanding of the relationship between the mathematical formulation of a dynamical system and its stability.
Part of the work carried out during the course culminates in a presentation, followed by an individual oral defence.
Assessment consists of two components:
Presentation: 60%
Individual oral defence: 40%
The presentation assesses students’ ability to apply the concepts and methods covered in the course and to clearly communicate their analysis.
The oral defence is individual and assesses each student’s personal understanding of the concepts and methods covered in the course and used in the presented work.
The final grade is the weighted average of the two components.
Presentation slides
Models coded in R
Otto and Day. A Biologist's Guide to Mathematical Modeling in Ecology and Evolution. Princeton, 2007
Various scientific papers
All these materials can be found on WebCampus.
| Training | Study programme | Block | Credits | Mandatory |
|---|---|---|---|---|
| Master in Biology of Organisms and Ecology | Finalité approfondie | 1 | 2 | No |
| Master in Biology of Organisms and Ecology | Finalité didactique | 1 | 2 | No |
| Master in Biology of Organisms and Ecology | Finalité approfondie | 2 | 2 | No |
| Master in Biology of Organisms and Ecology | Finalité didactique | 2 | 2 | No |