The Mathematical Theory Of Selection Recombination And Mutation

Author : R. Bürger
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 432 pages
Book Rating : 4.99/5 ( download)

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Download or read book The Mathematical Theory of Selection, Recombination, and Mutation written by R. Bürger and published by John Wiley & Sons. This book was released on 2000-11-02 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: "It is close to being a masterpiece...could well be the classic presentation of the area." Warren J. Ewens, University of Pennsylvania, USA Population genetics is concerned with the study of the genetic, ecological, and evolutionary factors that influence and change the genetic composition of populations. The emphasis here is on models that have a direct bearing on evolutionary quantitative genetics. Applications concerning the maintenance of genetic variation in quantitative traits and their dynamics under selection are treated in detail. * Provides a unified, self-contained and in-depth study of the theory of multilocus systems * Introduces the basic population-genetic models * Explores the dynamical and equilibrium properties of the distribution of quantitative traits under selection * Summarizes important results from more demanding sections in a comprehensible way * Employs a clear and logical presentation style Following an introduction to elementary population genetics and discussion of the general theory of selection at two or more loci, the author considers a number of mutation-selection models, and derives the dynamical equations for polygenic traits under general selective regimes. The final chapters are concerned with the maintenance of quantitative-genetic variation, the response to directional selection, the evolutionary role of deleterious mutations, and other topics. Graduate students and researchers in population genetics, evolutionary theory, and biomathematics will benefit from the in-depth coverage. This text will make an excellent reference volume for the fields of quantitative genetics, population and theoretical biology.

Author : Steven Neil Evans
Publisher :
ISBN 13 : 9780821895115
Total Pages : 128 pages
Book Rating : 4.17/5 ( download)

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Download or read book A Mutation-selection Model with Recombination for General Genotypes written by Steven Neil Evans and published by . This book was released on 2013 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate a continuous time, probability measure-valued dynamical system that describes the process of mutation-selection balance in a context where the population is infinite, there may be infinitely many loci, and there are weak assumptions on selective costs. Our model arises when we incorporate very general recombination mechanisms into an earlier model of mutation and selection presented by Steinsaltz, Evans and Wachter in 2005 and take the relative strength of mutation and selection to be sufficiently small. The resulting dynamical system is dynamical system a flow of measures on the space of loci. Each such measure is the intensity measure of a Poisson random measure on the space of loci: intensity measure the points of a realization of the random measure record the set of loci at which the genotype of a uniformly chosen individual differs from a reference wild type due to an accumulation of ancestral mutations. Our motivation for working in such a general setting is to provide a basis for understanding mutation-driven changes in age-specific demographic schedules that arise from the complex interaction of many genes, and hence to develop a framework for understanding the evolution of aging. We establish the existence and uniqueness of the dynamical system, provide conditions for the existence and stability of equilibrium states, and prove that our continuous-time dynamical system is the limit of a sequence of discrete-time infinite population mutation-selection-recombination models in the standard asymptotic regime where selection and mutation are weak relative to recombination and both scale at the same infinitesimal rate in the limit.

Author : Michael George Bulmer
Publisher : Clarendon Press
ISBN 13 :
Total Pages : 272 pages
Book Rating : 4.28/5 ( download)

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Download or read book The Mathematical Theory of Quantitative Genetics written by Michael George Bulmer and published by Clarendon Press. This book was released on 1985 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes discussion of the underlying principles of the theory of quantitative genetics which provides the bridge between the observable statistical properties of a character and the gentic factors, which together with environmental factors, determine the expression of the character. "An essential reference for anyone concerned with quantitative genetics. . . . Provides the only review available of the parts of quantitative genetics relevant to evolutionary theory."--Science

Author : Igor M. Rouzine
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110615452
Total Pages : 181 pages
Book Rating : 4.56/5 ( download)

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Download or read book Mathematical Modeling of Evolution written by Igor M. Rouzine and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-11-23 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book will benefit a reader with a background in physical sciences and applied mathematics interested in the mathematical models of genetic evolution. In the first chapter, we analyze several thought experiments based on a basic model of stochastic evolution of a single genomic site in the presence of the factors of random mutation, directional natural selection, and random genetic drift. In the second chapter, we present a more advanced theory for a large number of linked loci. In the third chapter, we include the effect of genetic recombination into account and find out the advantage of sexual reproduction for adaptation. These models are useful for the evolution of a broad range of asexual and sexual populations, including virus evolution in a host and a host population.

Author : Ken-ichi Kojima
Publisher : Springer Science & Business Media
ISBN 13 : 3642462448
Total Pages : 408 pages
Book Rating : 4.43/5 ( download)

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Download or read book Mathematical Topics in Population Genetics written by Ken-ichi Kojima and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: A basic method of analyzing particulate gene systems is the proba bilistic and statistical analyses. Mendel himself could not escape from an application of elementary probability analysis although he might have been unaware of this fact. Even Galtonian geneticists in the late 1800's and the early 1900's pursued problems of heredity by means of mathe matics and mathematical statistics. They failed to find the principles of heredity, but succeeded to establish an interdisciplinary area between mathematics and biology, which we call now Biometrics, Biometry, or Applied Statistics. A monumental work in the field of popUlation genetics was published by the late R. A. Fisher, who analyzed "the correlation among relatives" based on Mendelian gene theory (1918). This theoretical analysis over came "so-called blending inheritance" theory, and the orientation of Galtonian explanations for correlations among relatives for quantitative traits rapidly changed. We must not forget the experimental works of Johanson (1909) and Nilsson-Ehle (1909) which supported Mendelian gene theory. However, a large scale experiment for a test of segregation and linkage of Mendelian genes affecting quantitative traits was, prob ably for the first time, conducted by K. Mather and his associates and Panse in the 1940's.

Author : Institute of Mathematics and Its Applications
Publisher :
ISBN 13 :
Total Pages : 368 pages
Book Rating : 4.80/5 ( download)

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Download or read book The Mathematical Theory of the Dynamics of Biological Populations written by Institute of Mathematics and Its Applications and published by . This book was released on 1973 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Steven Neil Evans
Publisher : American Mathematical Soc.
ISBN 13 : 0821875698
Total Pages : 142 pages
Book Rating : 4.98/5 ( download)

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Download or read book A Mutation-Selection Model with Recombination for General Genotypes written by Steven Neil Evans and published by American Mathematical Soc.. This book was released on 2013-02-26 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors investigate a continuous time, probability measure-valued dynamical system that describes the process of mutation-selection balance in a context where the population is infinite, there may be infinitely many loci, and there are weak assumptions on selective costs. Their model arises when they incorporate very general recombination mechanisms into an earlier model of mutation and selection presented by Steinsaltz, Evans and Wachter in 2005 and take the relative strength of mutation and selection to be sufficiently small. The resulting dynamical system is a flow of measures on the space of loci. Each such measure is the intensity measure of a Poisson random measure on the space of loci: the points of a realization of the random measure record the set of loci at which the genotype of a uniformly chosen individual differs from a reference wild type due to an accumulation of ancestral mutations. The authors' motivation for working in such a general setting is to provide a basis for understanding mutation-driven changes in age-specific demographic schedules that arise from the complex interaction of many genes, and hence to develop a framework for understanding the evolution of aging.

Author : Charles J. Mode
Publisher : World Scientific
ISBN 13 : 9814350680
Total Pages : 695 pages
Book Rating : 4.86/5 ( download)

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Download or read book Stochastic Processes in Genetics and Evolution written by Charles J. Mode and published by World Scientific. This book was released on 2012 with total page 695 pages. Available in PDF, EPUB and Kindle. Book excerpt: Prologue; Acknowledgments; Contents; 1. An Introduction to Mathematical Probability with Applications in Mendelian Genetics; 1.1 Introduction; 1.2 Mathematical Probability in Mendelian Genetics; 1.3 Examples of Finite Probability Spaces; Example 1.3.1: An Equal Frequency Model; Example 1.3.2: Partitions of an Abstract Set; Example 1.3.3: A Deterministic Case; Example 1.3.4: Inheritance of Eye Color and Sex; 1.4 Elementary Combinatorial Analysis; 1.5 The Binomial Distribution; Example 1.5.1: Distribution of Boys and Girls in Families of Size N.

Author : Warren J. Ewens
Publisher : Springer Science & Business Media
ISBN 13 : 038721822X
Total Pages : 435 pages
Book Rating : 4.29/5 ( download)

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Download or read book Mathematical Population Genetics 1 written by Warren J. Ewens and published by Springer Science & Business Media. This book was released on 2012-10-01 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of a planned two-volume work discussing the mathematical aspects of population genetics with an emphasis on evolutionary theory. This volume draws heavily from the author’s 1979 classic, but it has been revised and expanded to include recent topics which follow naturally from the treatment in the earlier edition, such as the theory of molecular population genetics.

Author : Josef Hofbauer
Publisher :
ISBN 13 : 9780521352888
Total Pages : 341 pages
Book Rating : 4.86/5 ( download)

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Download or read book Evolutionstheorie und Dynamische Systeme written by Josef Hofbauer and published by . This book was released on 1988 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to dynamical systems and its applications to evolutionary game theory, mathematical ecology, and population genetics. This first English edition is a translation from the authors' successful German edition which has already made an enormous impact on the teaching and study of mathematical biology. The book's main theme is to discuss the solution of differential equations that arise from examples in evolutionary biology. Topics covered include the Hardy–Weinberg law, the Lotka–Volterra equations for ecological models, genetic evolution, aspects of sociobiology, and mutation and recombination. There are numerous examples and exercises throughout and the reader is led up to some of the most recent developments in the field. Thus the book will make an ideal introduction to the subject for graduate students in mathematics and biology coming to the subject for the first time. Research workers in evolutionary theory will also find much of interest here in the application of powerful mathematical techniques to the subject.