Probability Models for DNA Sequence Evolution

As a starting point the authors address the fundamental question "What underlying forces are responsible for the observed patterns of variability, given a collection of DNA sequences?" In approaching this question they introduce and analyze a number of probability models: the Wright-Fisher model, the coalescent, the infinite alleles model, and the infinite sites model. They then discuss 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."

Many researchers in statistics, biology, mathematics, and computer science are working in the area of genetics. This book presents mathematical techniques for understanding sequence evolution. This book is written for mathematicians and for biologists alike. It assumes no previous knowledge of concepts from biology and only a basic knowledge of probability.

Second edition of a successful book Genetics is one of the fastest growing areas of active research Durrett is a very well-known probabilist Assumes no previous knowledge of biology and only a basic knowledge of probability Includes data from numerous experimental studies from the biological literature Includes supplementary material: sn.pub/extras

Autorentext
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.

Klappentext

How is genetic variability shaped by natural selection, demographic factors, and random genetic drift? To approach this question, we introduce and analyze a number of probability models beginning with the basics, and ending at the frontiers of current research. Throughout the book, the theory is developed in close connection with examples from the biology literature that illustrate the use of these results. Along the way, there are many numerical examples and graphs to illustrate the conclusions.

This is the second edition and is twice the size of the first one. The material on recombination and the stepping stone model have been greatly expanded, there are many results form the last five years, and two new chapters on diffusion processes develop that viewpoint. This book is written for mathematicians and for biologists alike. No previous knowledge of concepts from biology is assumed, and only a basic knowledge of probability, including some familiarity with Markov chains and Poisson processes. The book has been restructured into a large number of subsections and written in a theorem-proof style, to more clearly highlight the main results and allow readers to find the results they need and to skip the proofs if they desire.

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 eight books and 160 research papers, most of which concern the use of probability models in genetics and ecology. He is the academic father of 39 Ph.D. students and was recently elected to the National Academy of Sciences.

Zusammenfassung
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.

Inhalt
Basic Models.- Estimation and Hypothesis Testing.- Recombination.- Population Complications.- Stepping Stone Model.- Natural Selection.- Diffusion Processes.- Multidimensional Diffusions.- Genome Rearrangement.