At the end of this course unit, students will be able to understand and analyse the dynamics of ecological populations and communities using mathematical models. They will be able to determine model equilibria, assess their feasibility and local stability, and interpret the role of species interactions in community dynamics.
Students will also be able to use the generalised Lotka-Volterra model to represent multispecies communities and analyse how environmental factors, including pollution and temperature, can influence the dynamics, diversity and productivity of these communities.
The course aims to understand what determines ecosystem biodiversity and productivity, the role played by species interactions, and how environmental factors influence this diversity.
To address these questions, the course progressively introduces the tools required to analyse models of population and community dynamics. It starts with the dynamics of a single population before introducing species interactions, linear and nonlinear models and, finally, communities containing larger numbers of species.
The theoretical concepts are then applied to the study of environmental change drivers, in particular pollution and temperature.
The course starts by examining population dynamics in the absence of interactions with other species. The concepts of equilibrium, feasibility and stability are introduced using simple models, including the logistic model and a model with an Allee effect.
The course then introduces the dynamics of interacting populations. Linear models are used to introduce vector fields, eigenvalues and eigenvectors and their relationship with stability. These concepts are subsequently generalised to nonlinear models, using different ecological examples.
Particular attention is devoted to the generalised Lotka-Volterra (GLV) model. Its interaction matrix represents the effects of species on one another and can be used to study the ecological structure of the community, its equilibria, their feasibility and their stability.
Finally, the course introduces the effects of environmental factors on community dynamics, with applications focusing in particular on pollution and temperature.
The following topics refer to sections of Otto & Day (2007), A Biologist's Guide to Mathematical Modeling in Ecology and Evolution (Princeton University Press).
Population dynamics without species interactions
a. Models: 5.1
b. Equilibria: 5.2; 5.2.1, 5.2.3
c. Stability: 5.3; 5.3.1; 5.4; 5.4.1
Population dynamics with species interactions
a. Linear models: 7.1, 7.2, 7.3
b. Nonlinear models: 8.1, 8.2 (but use the predator–prey model, p. 307)
c. Many-species Lotka–Volterra; equilibrium as a matrix inverse
d. Models extended with environmental effects
e. Introduction to the central question: effects of environmental drivers on richness and evenness (B), and on total biomass (EF)
Application of ecological models to quantify environmental effects: at the population and community levels. Students will be given one or more problems. They will apply the techniques covered in the theoretical course to solve these problem(s).
Teaching combines theoretical classes, practical exercises and project work.
Theoretical classes aim to provide an understanding of the concepts and mathematical tools required to analyse population and community dynamics. Concepts are progressively developed from simple models before being applied to systems containing multiple species.
The practical exercises focus on applying these concepts to specific problems, including the effects of pollution and temperature. Part of the teaching time is devoted to independent work on these problems.
The work 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.
Slides
Models coded in R
Otto and Day. A Biologist's Guide to Mathematical Modeling in Ecology and Evolution. Princeton, 2007.
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 |