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.
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.
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.
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.
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.
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.
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.
Download or read book Probability Models for DNA Sequence Evolution written by Rick Durrett and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: "What underlying forces are responsible for the observed patterns of variability, given a collection of DNA sequences?" In approaching this question a number of probability models are introduced and anyalyzed.Throughout the book, the theory is developed in close connection with data from more than 60 experimental studies that illustrate the use of these results.
Download or read book Evolutionary Algorithms written by William M. Spears and published by Springer Science & Business Media. This book was released on 2000-06-15 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite decades of work in evolutionary algorithms, there remains an uncertainty as to the relative benefits and detriments of using recombination or mutation. This book provides a characterization of the roles that recombination and mutation play in evolutionary algorithms. It integrates important prior work and introduces new theoretical techniques for studying evolutionary algorithms. Consequences of the theory are explored and a novel method for comparing search and optimization algorithms is introduced. The focus allows the book to bridge multiple communities, including evolutionary biologists and population geneticists.
Download or read book Mathematical Evolutionary Theory written by Marcus Feldman and published by Princeton University Press. This book was released on 2014-07-14 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: An international group of distinguished scientists presents an up-to-date survey of quantitative problems at the forefront of modern evolutionary theory. Their articles illustrate results from the latest research in population and behavioral genetics, molecular evolution, and ecology. Each author gives careful attention to the exposition of the models, the logic of their analysis, and the legitimacy of qualitative biological inferences. The topics covered include stochastic models of finite populations and the sorts of diffusion approximations that are valid for their study, models of migration, kin selection, geneculture coevolution, sexual selection, life-history evolution, the statistics of linkage disequilibrium, and the molecular evolution of repeated DNA sequences and the HLA system in humans. The fourteen contributions are presented in two sections: Part I, Stochastic and Deterministic Genetic Theory, and Part II, Behavior, Ecology, and Evolutionary Genetics. Marcus W. Feldman provides an introduction to each part. The contributors are J. G. Bodmer, W. F. Bodmer, L. L. Cavalli Sforza, F. B. Christiansen, C. Cockerham, W. J. Ewens, M. W. Feldman, J. H. Gillespie, R. R. Hudson, N. L. Kaplan, S. Lessard, U. Liberman, M.E.N. Majerus, P. O'Donald, J. Roughgarden, S. Tavar, M. K. Uyenoyama, G. A. Watterson, and B. Weir. Originally published in 1989. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book A Biologist s Guide to Mathematical Modeling in Ecology and Evolution written by Sarah P. Otto and published by Princeton University Press. This book was released on 2011-09-19 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available
Download or read book The Geometry of Population Genetics written by Ethan Akin and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The differential equations which model the action of selection and recombination are nonlinear equations which are impossible to It is even difficult to describe in general the solve explicitly. Recently, Shahshahani began using qualitative behavior of solutions. differential geometry to study these equations [28]. with this mono graph I hope to show that his ideas illuminate many aspects of pop ulation genetics. Among these are his proof and clarification of Fisher's Fundamental Theorem of Natural Selection and Kimura's Maximum Principle and also the effect of recombination on entropy. We also discover the relationship between two classic measures of 2 genetic distance: the x measure and the arc-cosine measure. There are two large applications. The first is a precise definition of the biological concept of degree of epistasis which applies to general (i.e. frequency dependent) forms of selection. The second is the unexpected appearance of cycling. We show that cycles can occur in the two-locus-two-allele model of selection plus recombination even when the fitness numbers are constant (i.e. no frequency dependence). This work is addressed to two different kinds of readers which accounts for its mode of organization. For the biologist, Chapter I contains a description of the entire work with brief indications of a proof for the harder results. I imagine a reader with some familiarity with linear algebra and systems of differential equations. Ideal background is Hirsch and Smale's text [15].
Download or read book Mutation and Evolution written by Ronny C. Woodruff and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although debated since the time of Darwin, the evolutionary role of mutation is still controversial. In over 40 chapters from leading authorities in mutation and evolutionary biology, this book takes a new look at both the theoretical and experimental measurement and significance of new mutation. Deleterious, nearly neutral, beneficial, and polygenic mutations are considered in their effects on fitness, life history traits, and the composition of the gene pool. Mutation is a phenomenon that draws attention from many different disciplines. Thus, the extensive reviews of the literature will be valuable both to established researchers and to those just beginning to study this field. Through up-to-date reviews, the authors provide an insightful overview of each topic and then share their newest ideas and explore controversial aspects of mutation and the evolutionary process. From topics like gonadal mosaicism and mutation clusters to adaptive mutagenesis, mutation in cell organelles, and the level and distribution of DNA molecular changes, the foundation is set for continuing the debate about the role of mutation, fitness, and adaptability. It is a debate that will have profound consequences for our understanding of evolution.
Download or read book Theoretical Aspects of Population Genetics written by Motoo Kimura and published by Princeton University Press. This book was released on 1971-10-21 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: To show the importance of stochastic processes in the change of gene frequencies, the authors discuss topics ranging from molecular evolution to two-locus problems in terms of diffusion models. Throughout their discussion, they come to grips with one of the most challenging problems in population genetics--the ways in which genetic variability is maintained in Mendelian populations. R.A. Fisher, J.B.S. Haldane, and Sewall Wright, in pioneering works, confirmed the usefulness of mathematical theory in population genetics. The synthesis their work achieved is recognized today as mathematical genetics, that branch of genetics whose aim is to investigate the laws governing the genetic structure of natural populations and, consequently, to clarify the mechanisms of evolution. For the benefit of population geneticists without advanced mathematical training, Professors Kimura and Ohta use verbal description rather than mathematical symbolism wherever practicable. A mathematical appendix is included.
Download or read book Evolution and Selection of Quantitative Traits written by Bruce Walsh and published by Oxford University Press. This book was released on 2018-06-21 with total page 1504 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantitative traits-be they morphological or physiological characters, aspects of behavior, or genome-level features such as the amount of RNA or protein expression for a specific gene-usually show considerable variation within and among populations. Quantitative genetics, also referred to as the genetics of complex traits, is the study of such characters and is based on mathematical models of evolution in which many genes influence the trait and in which non-genetic factors may also be important. Evolution and Selection of Quantitative Traits presents a holistic treatment of the subject, showing the interplay between theory and data with extensive discussions on statistical issues relating to the estimation of the biologically relevant parameters for these models. Quantitative genetics is viewed as the bridge between complex mathematical models of trait evolution and real-world data, and the authors have clearly framed their treatment as such. This is the second volume in a planned trilogy that summarizes the modern field of quantitative genetics, informed by empirical observations from wide-ranging fields (agriculture, evolution, ecology, and human biology) as well as population genetics, statistical theory, mathematical modeling, genetics, and genomics. Whilst volume 1 (1998) dealt with the genetics of such traits, the main focus of volume 2 is on their evolution, with a special emphasis on detecting selection (ranging from the use of genomic and historical data through to ecological field data) and examining its consequences.
Download or read book Mathematical and Statistical Developments of Evolutionary Theory written by S. Lessard and published by Springer. This book was released on 1990 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical and statistical approaches to evolutionary theory are numerous. The NATO Advanced Study Institute (ASI) held at the Universite de Montreal, Montreal, August 3-21, 1987, was an opportunity to review most of the classical approaches and to study the more recent developments. The participation of theoretical biologists and geneticists as well as applied mathematicians and statisticians made possible exchanges of ideas between students and scholars having different views on the subject. These Proceedings contain the lecture notes of seven (7) of the eleven (11) series of lectures that were given. ESS (Evolutionarily Stable Stragety) theory is considered from many perspectives, from a game-theoretic approach to understanding behavior and evolution (W.G.S. Hines), and a systematic classification of properties and patterns of ESS's (C. Cannings) to particular applications of the differential geometry of the Shahshahani metric (E. Akin). Extensions of ESS theory to sexual populations and finite populations, not to mention games between relatives, are presented (W.G.S. Hines). Special attention is given to the classical game called the War of Attrition but with n players and random rewards (C. Cannings). The Shahshahani metric is also used to show the occurrence of cycling in the two-locus, two-allele model (E. Akin). Various inference problems in population genetics are adressed. Procedures to detect and measure selection components and polymorphism (in particular, the Wahlund effect) at one or several loci from mother-offspring combinations in natural populations are discussed at length (F.B. Christiansen).
