Theoretical Ecology

Bifurcations in dynamical systems

29 September - 3 October 2025

Hotel De Bosrand, Ede (NL)

Scope

This first instance of a PhD course on Theoretical Ecology will focus on qualitative changes in dynamics of biological systems that occur when conditions change. Examples of such qualitative changes are when a system changes from being in a constant and stable equilibrium state to exhibiting fluctuations, that is, cyclic dynamics. As another example, even in popular media we may nowadays encounter the term ‘tipping point.’ For example, in the fifth report of the IPCC (the Intergovernmental Panel on Climate Change) a tipping point is defined as an irreversible change in the climate system. These qualitative changes in dynamics occur in many different systems and at many different levels of organization. They are generic phenomena in mathematical models when the value of a particular model parameter changes. These qualitative transitions in dynamics are called bifurcations. The course aims at giving students an understanding about possible phenomena in dynamic models and transitions between different dynamical outcomes, as well as practical training how to apply the theory themselves. The basics are going to be taught while focusing on simple ordinary differential equation (ODE) models. We will then add to it and also discuss the connections to more complex models, such as individual-based models, spatial models or physiologically structured models.

Set-up

The course will start on Monday morning and end on Friday at lunch time. The course is composed of:

1. Introduction lectures
The course starts off on Monday morning with an introductory lecture on the theory and relevance of bifurcation models is explained. Background information will be given in lectures by the course organisers, followed by hands-on application in the computer labs.

2. Computer labs
The computer labs in the afternoons will provide the opportunity of practical training how to apply the theory. Students should bring a laptop with a recent version of R (version 4.0 or higher) and Rstudio installed (the exact version is not so important, just that it is recent). Preferably, students should install the required R package already before the start of the course by issuing the command: install.packages("deBif") in Rstudio. This will also immediately make clear that the laptop is properly set up for the course.

3. Evening sessions
Evening hours will be filled with presentations about applications in different case studies.

4. Poster carousel
After dinner of the first day of the course there will be a poster carousel during which participants present themselves, their research and interest in the course. The carousel will consist of approx. 5 sessions. Per session approx. 5 participants present their poster (5-10 minutes), followed by 5-10 minutes discussion. Between sessions there is a 5-minute break to switch. For the next session. The schedule of the carousel can be found further on in this hand-out. Posters will be displayed on the walls of the course venue throughout the course.

5. Key-note/guest lecture
As guest lecturer, Prof. Max Rietkerk (Utrecht University) will give 2 lectures about his work on spatial interactions in ecosystems, which represent prominent examples of the power of bifurcation theory for understanding the dynamics of real ecosystems.

Lecture notes about bifurcations in biological dynamics: https://staff.fnwi.uva.nl/a.m.deroos/projects/BifurcationTheory/.

Programme (preliminary)

Monday 29 September
Morning:  Intro ODE & isoclines
Afternoon:  computer practicum to learn the program
Evening:     Poster carousel; Why would you use theoretical biology, what questions in your PhD would you like to answer with a model (some reading beforehand required)?

Tuesday 30 September
Morning:  Intro to bifurcation theory
Afternoon:  computer practicum
Evening:  Guest by lecture Max Rietkerk: Bifurcations in spatial systems

Wednesday 1 October
Morning:  Guest lecture by André de Roos: Size-structured populations
Afternoon:  excursion
Evening:     Facultative hour mathematical background bifurcation theory (Eigenvalues etc)

Thursday 2 October
Morning:  Bifurcation theory
Afternoon:  computer practicum
Evening:     Reflection/Discussion on how to use theory

Friday 3 October
Topic:  Guest lecture and computer practicum by Martijn Egas: Adaptive dynamics
Afternoon: Course wrap-up

Confirmed Speakers

• Prof. dr. Max Rietkerk (Department of Spatial Ecology and Global Change, Utrecht University)
• Prof. dr. André de Roos (Theoretical and Computational Ecology, Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam)
• Prof. dr. Martijn Egas ( Evolution and behaviour, University of Groningen)
• Dr. Hanna ten Brink (Theoretical and Computational Ecology, Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam)
• Dr. Jasper Croll (Swedish University of Agricultural Sciences/ University of Amsterdam)

Course organisers

• Hanna ten Brink (Theoretical and Computational Ecology, Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam)
• Jasper Croll ( Swedish University of Agricultural Sciences) 
• Sanja Selakovic (PE&RC) 

General information

Fees ¹

¹ The course fee includes accommodation, all meals, course materials, coffee/tea, and water. It does not include beverages in the bar.
² The Early-Bird Fee applies to anyone who REGISTERS ON OR BEFORE 4 AUGUST 2025

Note:

• The Early-Bird policy is such that the moment of REGISTRATION (and not payment) is leading for determining the fee that applies to you.
• Please make sure that your payment is arranged within two weeks after your registration. Arrange your payment immediately if you register two weeks or less before the start of the course. 
• It is the participant's responsibility that the payment is correct and in time.

Cancellation Conditions

IMPORTANT: ALWAYS read the Cancellation conditions for PE&RC courses and activities.

Note: If you would like to cancel your registration, ALWAYS inform us. By NOT paying the participation fee, your registration is NOT automatically cancelled (and do note that you will be kept to the cancellation conditions)

More information

Dr. Sanja Selaković (PE&RC)
Phone: +31 (0) 317 480269
Email: sanja.selakovic@wur.nl

Registration

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