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 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
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 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:
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 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 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.
Download or read book Population Genetics written by W.J. Ewens and published by Springer. This book was released on 1969-02-28 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The hardy-weinberg law; Selection and mutation; The fundamental teorem of natural selection; Stochastic treatment; discrete processes; Diffusion approximations; Applications; Results derived from branching processes; Two-locus behaviour; Linkage; Dominance.
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 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 Introduction to the Mathematical Theory of Genetic Linkage written by Norman T. J. Bailey and published by . This book was released on 1961 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Mathematical Models from Population Genetics written by Alison Etheridge and published by Springer Science & Business Media. This book was released on 2011-01-07 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour summer school in probability. It provides a rapid introduction to a range of mathematical models that have their origins in theoretical population genetics. The models fall into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time (coalescent) models that trace out the genealogical relationships between individuals in a sample from the population. Some, like the classical Wright-Fisher model, date right back to the origins of the subject. Others, like the multiple merger coalescents or the spatial Lambda-Fleming-Viot process are much more recent. All share a rich mathematical structure. Biological terms are explained, the models are carefully motivated and tools for their study are presented systematically.
Download or read book A Quest Towards a Mathematical Theory of Living Systems written by Nicola Bellomo and published by Birkhäuser. This book was released on 2017-07-13 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph aims to lay the groundwork for the design of a unified mathematical approach to the modeling and analysis of large, complex systems composed of interacting living things. Drawing on twenty years of research in various scientific fields, it explores how mathematical kinetic theory and evolutionary game theory can be used to understand the complex interplay between mathematical sciences and the dynamics of living systems. The authors hope this will contribute to the development of new tools and strategies, if not a new mathematical theory. The first chapter discusses the main features of living systems and outlines a strategy for their modeling. The following chapters then explore some of the methods needed to potentially achieve this in practice. Chapter Two provides a brief introduction to the mathematical kinetic theory of classical particles, with special emphasis on the Boltzmann equation; the Enskog equation, mean field models, and Monte Carlo methods are also briefly covered. Chapter Three uses concepts from evolutionary game theory to derive mathematical structures that are able to capture the complexity features of interactions within living systems. The book then shifts to exploring the relevant applications of these methods that can potentially be used to derive specific, usable models. The modeling of social systems in various contexts is the subject of Chapter Five, and an overview of modeling crowd dynamics is given in Chapter Six, demonstrating how this approach can be used to model the dynamics of multicellular systems. The final chapter considers some additional applications before presenting an overview of open problems. The authors then offer their own speculations on the conceptual paths that may lead to a mathematical theory of living systems hoping to motivate future research activity in the field. A truly unique contribution to the existing literature, A Quest Toward a Mathematical Theory of Living Systems is an important book that will no doubt have a significant influence on the future directions of the field. It will be of interest to mathematical biologists, systems biologists, biophysicists, and other researchers working on understanding the complexities of living systems.
Download or read book Evolutionary Algorithms written by William M. Spears and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 224 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 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
