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MAGE - Advanced Mathematical modeling for Evolutionary Genetics

You can refer to the EvoGem website.

Master in Life Sciences, ENS
BIO_M2_E44 | MAGE | Advanced Mathematical modeling for Evolutionary Genetics
Year and Semester : M2 | S1
Where : ENS
Duration : 27 hours
Dates : From mid-October to December, on Wednesdays
Maximum class size : 20-25 students
This course is open to external students ; contact the coordinator.


Amaury Lambert, ENS




Wright-Fisher model | Moran model | Fixation probabilities | Coalescent | Ornstein-Uhlenbeck diffusion | Fisher’s geometric model.

Course prerequisites

Students will have followed MATH1 and have a solid background on population genetics, for example by having followed GPOP of EvoGEM.

Course objectives and description

Aims : To introduce students to the application of mathematical methods and tools in evolutionary genetics.
Themes : We will discuss population genetic dynamics as applied to calculate the probability and time for fixation/extinction and stationary distributions. We will detail the coalescent and characterization of genetic diversity at one and multiple loci with recombination and selection. We will also discuss the coalescent in the context of birth-death models in phylogenetics and random trees. Finally, we will give an overview of quantitative genetics modeling, such as heritability, GWAS and Fisher’s geometric model.
Organisation : The course will have 15h of lectures, each followed by 1.5h practicals (TD).


Students will be evaluated based on their attendance and participation in the lectures and practicals (25%) as well as on an exam together with Math 1 in December, week 50 (50%).

Course material

Lecture handouts and relevant software, research paper prints, etc. will be provided to the students.