Learning outcomes

Understand the basic principles of stability analysis of populations and communities;

Apply the basic techniques to quantify the stability of populations and communities;

Use the acquired skills to, as part of a team, solve a problem offered by the teachers during the course.

Soft skills: working in groups, project management; communication in French and English.

Goals

Familiarise the student with the basic principles of stability analysis of populations and communities;
Learn the students to apply techniques to quantify stability;
Let the student apply these techniques as part of a team to solve a problem about ecosystem perturbations.

Content

First, students become familiar with the fundamental principles of stability analysis. They are then presented with a problem that they must solve as a team, with sufficient time to collaborate. To tackle this task, students rely on two types of tools:

  • the use of RStudio to build models and carry out simulations;
  • more formal mathematical approaches to study systems analytically.


Table of contents

1. Introduction and General Concepts

  • Stability of what, against what?

2. Multidimensionality of Stability

3. Dynamical Approach

a. Resistance → Cf. 162

b. Dynamic Stability (Akjouj et al. 2024)

i. Lyapunov stability

ii. Local asymptotic stability

iii. Global stability

iv. Invasion growth rate

v. Uninvadibility

c. Temporal Stability (Loreau & de Mazencourt, 2013)

i. Synchrony

ii. Environmental stochasticity

iii. Demographic stochasticity

4. Dynamic Stability of Large Ecosystems

a. The May result

b. A complex systems perspective (Akjouj et al. 2024)

Exercices

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 methods

  • Ex-cathedra (lectures)
  • Group work (project work)
  • Coding in R


Assessment method

Continuous assessment. Evaluation based on a final group report (40%) and an oral defense of this report (60%)

Sources, references and any support material

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.

Language of instruction

French