Probability Models for DNA Sequence Evolution by Richard Durrett
Our basic question is: Given a collection of DNA sequences, what underlying forces are responsible for the observed patterns of variability? To approach this question we introduce and analyze a number of probability models: the Wright-Fisher model, the coalescent, the infinite alleles model, and the infinite sites model. We study the complications that come from nonconstant population size, recombination, population subdivision, and three forms of natural selection: directional selection, balancing selection, and background selection. These theoretical results set the stage for the investigation of various statistical tests to detect departures from "neutral evolution." The final chapter studies the evolution of whole genomes by chromosomal inversions, reciprocal translocations, and genome duplication.Throughout the book, the theory is developed in close connection with data from more than 60 experimental studies from the biology literature that illustrate the use of these results. This book is written for mathematicians and for biologists alike. We assume no previous knowledge of concepts from biology and only a basic knowledge of probability: a one semester undergraduate course and some familiarity with Markov chains and Poisson processes. Rick Durrett received his Ph.D. in operations research from Stanford University in 1976. He taught in the UCLA mathematics department before coming to Cornell in 1985. He is the author of six books and 125 research papers, and is the academic father of more than 30 Ph.D. students. His current interests are the use of probability models in genetics and ecology, and decreasing the mean and variance of his golf.-
An Introduction to Stochastic Integration
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Invariant Probabilities of Transition Functions
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Associated Sequences, Demimartingales and Nonparametric Inference
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Continuous-Time Markov Jump Linear Systems
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Quasi-Stationary Distributions
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Normal Approximation by Stein's Method
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Stochastic Partial Differential Equations
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Self-Normalized Processes
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Laws of Chaos
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Stochastic Differential Equations in Infinite Dimensions
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Invariant Random Fields on Spaces with a Group Action
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Noise-Induced Phenomena in Slow-Fast Dynamical Systems
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Schrodinger Diffusion Processes
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Probability Measures on Semigroups
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Stochastic Control in Insurance
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Measure-Valued Branching Markov Processes
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Stochastic Processes
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The Doctrine of Chances
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An Introduction to the Theory of Point Processes
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Eigenvalues, Inequalities, and Ergodic Theory
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Theory of Random Sets
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Feynman-Kac Formulae
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Mass Transportation Problems
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Stochastic Calculus for Fractional Brownian Motion and Applications
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Renewal Theory for Perturbed Random Walks and Similar Processes
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Discrete-Time Markov Jump Linear Systems
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Basics of Applied Stochastic Processes
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Limit Theorems for Randomly Stopped Stochastic Processes
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Point Process Theory and Applications
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Excursions of Markov Processes
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Decoupling
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The Malliavin Calculus and Related Topics
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Discrete-Time Semi-Markov Random Evolutions and Their Applications
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Stochastic Neutron Transport
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Diffusions and Elliptic Operators
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| ISBN 13 | |
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| Title | Probability Models for DNA Sequence Evolution |
| Author | Richard Durrett |
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| Condition | Unavailable |
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| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
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