MAEE

Localisation :

Sorbonne Université

Contents:

Introduction to classical probabilistic dynamic models in ecology and evolution, i.e. Markov processes:

• in discrete time and space (Markov chains);

• in continuous time and discrete space (Poisson processes, birth and death);

• in discrete time and continuous space (Gaussian random walk);

• in discrete time and continuous space (Brownian motion and stochastic differential equations);

Goals:

At the end of the module, the student will be able to:

• Define classical probabilistic dynamical models (random walks, birth-and-death processes, coalescent, Brownian motion);

• Deduce Markov chain characteristics (ergodicity, stationarity, periodicity) in discrete time and space from its transition law;

• Numerically implement a simulation code (exact or approximate) of a Markov process to study its properties empirically;\

Prerequisites:

A student enrolling in the course should know:

• what a matrix is and the elementary operations that apply to it (multiplication, diagonalization, inversion);

• what a discrete and continuous random variable is, and the related concepts (law, density, distribution function, expectation, variance);

• Knowledge of deterministic models of evolution, notably based on ordinary differential equations, is a plus;

• For those who are interested in the course but for whom these notions are unknown or remote, don't panic: you can acquire this knowledge by first taking the DYST module.\

Assesment:

Standard exam