MAEE - Stochastic Models in Ecology and Evolution
You can refer to the EvoGem website.
Master in Life Sciences, ENS
BIO_M2_E43 | MAEE | Stochastic Models in Ecology and Evolution
Year and Semester : M2 | S1
Where : Sorbonne Université, to be confirmed
Duration : 30 hours
Dates : October 7-11, 2024
Maximum class size : 20-25 students
This course is open to external students ; contact the coordinator.
Coordination
Stéphane Robin, Agro ParisTech
Credits
3 ECTS
Keywords
Differential equations | Perron-Frobenius theorem | Poisson processes | Markov chains | Bayes inference.
Course prerequisites
Students will have basic education in mathematical modeling, for example by having followed MATH 0 of EvoGEM. Notions of probability theory, calculus and linear algebra are necessary.
Course objectives and description
Aims : To introduce students to the basic mathematical methods and tools to analyze classical models of evolutionary genetics, with special emphasis on population genetics modeling.
Themes : We will introduce students to differential non-linear equations and characterization of equilibrium dynamics, positive matrices and the Perron-Frobenius theorem, the Central Limit theorem, Markov chains in discrete and continuous time, transition matrices, Poisson processes, diffusion and infinitesimal generators, algorithms for simulation, sampling and Bayes inference. We will discuss the concepts of likelihood and introduce tools such as MCMC, Gibbs sampling and ABC.
Organisation : The course will have 3h of lectures in the mornings only.
Assessment
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 2 in December, week 50 (50%).
Course material
Lecture handouts and relevant software, research paper prints, etc. will be provided to the students.