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Modeles aleatoires en Ecologie et Evolution (French, Paperback, 1ere ed. 2016)
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Modeles aleatoires en Ecologie et Evolution (French, Paperback, 1ere ed. 2016)
Series: Mathematiques et Applications, 77
Expected to ship within 10 - 15 working days
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Le but du livre est de definir et developper une grande gamme
d'outils probabilistes pour la modelisation en biologie des
populations, afin de decrire des dynamiques temporelles de
quantites biologiques telles que la taille d'une ou plusieurs
populations, la proportion d'un allele dans une population ou la
position d'un individu. En partant de modeles markoviens discrets
(marches aleatoires, processus de Galton-Watson), nous abordons
progressivement le calcul stochastique et les equations
differentielles stochastiques, puis les processus markoviens de
saut, tels les processus de branchement a temps continu et les
processus de naissance et mort. Nous etudions egalement les
processus discret et continu pour l'evolution genetique et les
genealogies: processus de Wright-Fisher et coalescent. Le livre
detaille systematiquement les calculs de quantites d'interet pour
les biologistes. De nombreux exercices d'application sont proposes.
Le dernier chapitre montre l'apport de ces outils pour des
problematiques biologiques actuelles. Il developpe en detail des
travaux de recherche tres recents. 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.
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