Modèles aléatoires en Ecologie et Evolution (Mathématiques et Applications) (French Edition) Book PDF, ePub eBook

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Book Descriptions:

Le but du livre est de définir et développer une grande gamme d'outils probabilistes pour la modélisation en biologie des populations, afin de  décrire des dynamiques temporelles de quantités biologiques  telles que la taille d'une ou plusieurs populations, la  proportion d'un allèle dans une population ou la position d'un individu. En partant de modèles markoviens discrets (marches aléatoires, processus de Galton-Watson), nous abordons progressivement le calcul stochastique et les équations différentielles stochastiques, puis les processus markoviens de saut, tels les processus de branchement à temps continu et les processus de naissance et mort. Nous étudions également les processus discret et continu pour l'évolution génétique et les généalogies: processus de Wright-Fisher et coalescent. Le livre détaille systématiquement les calculs  de quantités d'intérêt pour les biologistes.  De nombreux exercices d'application sont proposés.  Le dernier chapitre montre  l'apport de ces outils pour des problématiques biologiques actuelles. Il développe en détail des travaux de recherche très récents.

This book defines and develops probabilistic tools for the modeling of populations in order to describe the dynamics of biological quantities such as population size, allele proportion in a population and individual location. From discrete Markovian models (random walks, Galton-Watson processes), it gradually introduces the stochastic calculus and the stochastic differential equations, as well as the jump Markov processes, such as the branching processes in continuous time and the birth and death processes. It also discusses the discrete and continuous processes of genetic evolution, genealogies and the Wright-Fisher processes and coalescent. The book systematically details the computation of quantities of interest to biologists and provides a number of exercises.  The last chapter shows the use of probabilistic tools for real-world biological problems, and discusses recent research in detail.

Modèles aléatoires en Ecologie et Evolution (Mathématiques et Applications) (French Edition) by Sylvie Méléard

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