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Adaptive Dynamics modeling

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PSL Master in Life Sciences - ENS IMaLiS
Bio-M2_E11 | Adaptive Dynamics modeling
Year and Semester : M2 | S1
Venue : ENS Biology Department
Duration : 30 hours
First and last day of class : October 24th-28th, 2022
Hours : 9:00-12:00 | 14:00-17:00
Maximum class size : 20 students


Régis Ferrière (IBENS & UMI iGLOBES CNRS, ENS, Univ. Arizona)




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 experience and 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

Adaptive dynamics modeling has become the dominant theoretical framework for ‘Darwinian ecology’, i.e. the investigation of the ecological causes and consequences of evolution.
Aims : 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.
Course format : This is a one-week intensive course. Lecture-style presentations will be complemented by computer-based tutorials.
In the tutorial sessions, students will work to implement the theory and study model examples numerically. This will involve the guided writing of simple code in Python.


Student evaluation is based on presenting the exploratory work carried out in the tutorial sessions. The presentations will take place at the end of the week.
Depending on the Covid-19 situation, presentations may be recorded and submitted at the end of the course on the course website.

Course material

Readings, slides, computer simulation tutorial, and video-recorded presentations will be made available to enrolled students.

Prior 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.

Suggested readings

• 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, Ferrière R (2004) Adaptive Dynamics and Evolving Biodiversity. In : Evolutionary Conservation Biology, eds. Ferrière R, Dieckmann U & Couvet D, pp. 188-224. Cambridge University Press.
• 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.
• Kisdi E (1999) Evolutionary branching under asymmetric competition. Journal of Theoretical Biology 197 : 149-162.