[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-956073","data":"\u003Cdiv class=\u0022container content-rte\u0022\u003E\n  \u003Cdiv class=\u0022row\u0022\u003E\n    \u003Cdiv class=\u0022box col-md-6 bg-primary text-white\u0022\u003E\n      \u003Ch2 class=\u0022h1 text-left\u0022\u003E  Mod\u00e8les al\u00e9atoires en Ecologie et en Evolution\n\u003C\/h2\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n          3\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ESemester:\n          Semestre 1\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ED\u00e9tail du volume horaire\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ELecture:\u003C\/span\u003E\n                                      \u003Cspan\u003E15\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                              \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003EDirected study:\u003C\/span\u003E\n                                      \u003Cspan\u003E12\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                                            \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ELangue d\u0026#039;enseignement\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EFran\u00e7ais\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EEnseignement \u00e0 distance\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003Enon\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n    \u003Cdiv class=\u0022box col-md-6\u0022\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EPr\u00e9requis\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cul\u003E\n\u003Cli\u003E\u003Cstrong\u003EPrerequisites:\u003C\/strong\u003E\u003C\/li\u003E\n\u003Cli\u003EA student enrolling in the course should know:\u003C\/li\u003E\n\u003Cli\u003Ewhat a matrix is and the elementary operations that apply to it (multiplication, diagonalization, inversion);\u003C\/li\u003E\n\u003Cli\u003Ewhat a discrete and continuous random variable is, and the related concepts (law, density, distribution function, expectation, variance);\u003C\/li\u003E\n\u003Cli\u003EKnowledge of deterministic models of evolution, notably based on ordinary differential equations, is a plus;\u003C\/li\u003E\n\u003Cli\u003EFor those who are interested in the course but for whom these notions are unknown or remote, don\u0027t panic: you can acquire this knowledge by first taking the DYST module.\\\u003C\/li\u003E\n\u003C\/ul\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n                \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EObjectifs d\u0026#039;apprentissage\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003E\u003Cstrong\u003EContents:\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cp\u003EIntroduction to classical probabilistic dynamic models in ecology and evolution, i.e. Markov processes:\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003Ein discrete time and space (Markov chains);\u003C\/li\u003E\n\u003Cli\u003Ein continuous time and discrete space (Poisson processes, birth and death);\u003C\/li\u003E\n\u003Cli\u003Ein discrete time and continuous space (Gaussian random walk);\u003C\/li\u003E\n\u003Cli\u003Ein discrete time and continuous space (Brownian motion and stochastic differential equations);\u003C\/li\u003E\n\u003C\/ul\u003E\n\u003Cp\u003E\u003Cstrong\u003EGoals:\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cp\u003EAt the end of the module, the student will be able to:\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EDefine classical probabilistic dynamical models (random walks, birth-and-death processes, coalescent, Brownian motion);\u003C\/li\u003E\n\u003Cli\u003EDeduce Markov chain characteristics (ergodicity, stationarity, periodicity) in discrete time and space from its transition law;\u003C\/li\u003E\n\u003Cli\u003ENumerically implement a simulation code (exact or approximate) of a Markov process to study its properties empirically;\\\u003C\/li\u003E\n\u003C\/ul\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n                                        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ENature de l\u0026#039;\u00e9valuation\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EEvaluation Continue non Int\u00e9grale\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n  \u003C\/div\u003E\n\u003C\/div\u003E\n","settings":null}]