Adaptive Dynamics Modeling
Master in Life Sciences, ENS – M2
2026-2027 - Semester 1
UNBIO1-073 | Adaptive Dynamics modeling
3 ECTS
—2025-2026 program & syllabus—
Level | Semester : M2 | S1
Where : ENS Biology Department, 3rd floor, room 321
Duration : 1 week | 30 hours (including personal work)
Dates : October 26th-30th, 2026
Maximum class size : 20 students
Coordination
Régis Ferrière (IBENS & UMI iGLOBES CNRS, ENS, Univ. Arizona)
Chloé Dumeige
Credits
3 ECTS
Keywords
Adaptive dynamics | Eco-evolutionary feedbacks | Invasion fitness | Evolutionary stability | Evolutionary branching | Coevolutionary dynamics.
Targeted audience and Course pre-requisites
The targeted audience is advanced undergraduates and graduate students in ecology and evolutionary biology and related fields, with a strong interest in mathematical modeling.
Participants trained in other fields are welcome provided they had exposure to notions of population and community ecology and have sufficient mathematical training (advanced calculus).
Enrolled students are expected to feel comfortable with basic population and community theory (e.g. logistic population growth, Lotka-Volterra competition...) and calculus applied to the natural sciences (modeling with differential equations, notion of equilibrium and stability analysis).
Course objectives and description
Course summary
Adaptive dynamics modeling has become the dominant theoretical framework for ‘Darwinian ecology’, i.e. the investigation of the ecological causes and consequences of evolution.
The course will present the key concepts underlying the adaptive dynamics approach : environmental feedback loop, invasion fitness, evolutionary singularity, evolutionary stability, evolutionary branching, evolutionary suicide, pairwise invasibility plots and canonical equations.
The general framework will be applied to study the eco-evolutionary dynamics of populations competing for resources, predator-prey interactions, and mutualistic systems. Hands-on tutorial sessions will aim at simulations of specific examples and the development of individual mini-projects.
Course content and learning objectives :
Lecture 1 : Introduction to AD : biological motivation. Modeling approach : ecological model, model of resident-mutant interaction, derivation of invasion fitness and selection gradient, evolutionary singularity. First example : How microbial adaptation reshapes soil carbon feedback to climate warming.
Lecture 2 : Analysis of evolutionary singularities in 1D trait space : trait substitution sequence, pairwise invasibility plot, stability properties discussed graphically. Example of Doebeli- Dieckmann model. Evolutionary dynamics : trait substitution sequence, stochastic process of birth with mutation – interaction – death. Evolutionary branching.
Lectures 3 : Evolutionary suicide, evolutionary rescue. Multidimensional trait evolution. Canonical equation. Examples. Extension to polymorphic populations.
Tutorial 1 : Introduction of Claessen’s model (2007) : one predator-two prey model, evolution of specialization. Equilibrium analysis of ecological model, approximation, Python code for PIP construction.
Tutorial 2 : Influence of tradeoff shape on ES stability properties. Stochastic simulations (Gillespie algorithm). Numerical evidence of evolutionary branching. Simulations under assumptions of TSS.
Tutorial 3 : Simulations of canonical equation. Comparison with stochastic simulations.
Course format :
This is a one-week intensive course.
Lecture-style presentations will be complemented with computer-based tutorials.
In the tutorial sessions, students will work to implement the theory and study model examples numerically, as well as develop a simple case study based on their own research interest.
This will involve the guided writing of simple code in Python.
We will use MOODLE to communicate about the class and provide teaching support material.
Prior to class
• Check access to course site and course material on Moodle.
• Familiarize with Moodle tools.
• Set up softwares and download notebooks for tutorials and project.
Evaluation
Student evaluation is based on individual oral presentations of the exploratory work carried out in the tutorial/project sessions.
Course material
Readings, slides, computer simulation tutorial, and video-recorded presentations will be made available to enrolled students.
Suggested readings - Supporting references
• Brännström A, Johansson J, von Festenberg N (2013) The hitchhiker’s guide to adaptive dynamics. Games 4 : 304-328. doi:10.3390/g4030304
• Dieckmann U, Law R (1996) The dynamical theory of coevolution : a derivation from stochastic ecological processes. Journal of Mathematical Biology 34 : 579-612.
• Dieckmann U, Ferriere R (2004) Adaptive Dynamics and Evolving Biodiversity. In : Evolutionary Conservation Biology, eds. Ferrière R, Dieckmann U & Couvet D, pp. 188–224. Cambridge University Press.
• Diekmann O (2003) A beginner’s guide to adaptive dynamics. Banach Center Publications 63 : 47-86.
• Doebeli M, Dieckmann U (2000) Evolutionary branching and sympatric speciation caused by different types of ecological interactions. Am. Nat. 156 : S77-S101.
• Geritz SAH, Kisdi E , Meszéna G , Metz JAJ (1998) Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evolutionnary Ecology 12 : 35-37.
• Geritz SAH, van der Meijden E, Metz JAJ (1997) Evolutionary dynamics of seed size and seedling competitive ability. Theoretical Population Biology 55 : 324-343.
• IIASA (coll.) (2000) Studying the evolution of complex adaptive systems : the Adaptive Dynamics Network project. Options Spring 2000 : 1-22.
• Kisdi E (1999) Evolutionary branching under asymmetric competition. Journal of Theoretical Biology 197 : 149-162.