Download Full eBooks in PDF
Stochastic Models In Population Genetics Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Stochastic Models In Population Genetics book. This book definitely worth reading, it is an incredibly well-written.
Author : Wen-Hsiung Li
Publisher : Unknown
Page : 504 pages
File Size : 47,7 Mb
Release : 1977
Category : Mathematical models
ISBN : UCAL:B4284996
Author : Narendra S. Goel,Nira Richter-Dyn
Publisher : Elsevier
Page : 282 pages
File Size : 47,6 Mb
Release : 2013-10-22
Category : Science
ISBN : 9781483278100
Stochastic Models in Biology describes the usefulness of the theory of stochastic process in studying biological phenomena. The book describes analysis of biological systems and experiments though probabilistic models rather than deterministic methods. The text reviews the mathematical analyses for modeling different biological systems such as the random processes continuous in time and discrete in state space. The book also discusses population growth and extinction through Malthus' law and the work of MacArthur and Wilson. The text then explains the dynamics of a population of interacting species. The book also addresses population genetics under systematic evolutionary pressures known as deterministic equations and genetic changes in a finite population known as stochastic equations. The text then turns to stochastic modeling of biological systems at the molecular level, particularly the kinetics of biochemical reactions. The book also presents various useful equations such as the differential equation for generating functions for birth and death processes. The text can prove valuable for biochemists, cellular biologists, and researchers in the medical and chemical field who are tasked to perform data analysis.
Author : T. Maruyama
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 51,9 Mb
Release : 2013-03-13
Category : Mathematics
ISBN : 9783642930652
These are" notes based on courses in Theoretical Population Genetics given at the University of Texas at Houston during the winter quarter, 1974, and at the University of Wisconsin during the fall semester, 1976. These notes explore problems of population genetics and evolution involving stochastic processes. Biological models and various mathematical techniques are discussed. Special emphasis is given to the diffusion method and an attempt is made to emphasize the underlying unity of various problems based on the Kolmogorov backward equation. A particular effort was made to make the subject accessible to biology students who are not familiar with stochastic processes. The references are not exhaustive but were chosen to provide a starting point for the reader interested in pursuing the subject further. Acknowledgement I would like to use this opportunity to express my thanks to Drs. J. F. Crow, M. Nei and W. J. Schull for their hospitality during my stays at their universities. I am indebted to Dr. M. Kimura for his continuous encouragement. My thanks also go to the small but resolute groups of.students, visitors and colleagues whose enthusiasm was a great source of encouragement. I am especially obliged to Dr. Martin Curie-Cohen and Dr. Crow for reading a large part eX the manuscript and making many valuable comments. Special gratitude is expressed to Miss Sumiko Imamiya for her patience and endurance and for her efficient preparation of the manuscript.
Author : Alison Etheridge
Publisher : Springer Science & Business Media
Page : 129 pages
File Size : 45,9 Mb
Release : 2011-01-07
Category : Mathematics
ISBN : 9783642166310
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.
Author : T Maruyama
Publisher : Unknown
Page : 260 pages
File Size : 43,9 Mb
Release : 1977-08-01
Category : Electronic
ISBN : 3642930662
Author : Sylvie Meleard,Vincent Bansaye
Publisher : Springer
Page : 107 pages
File Size : 50,9 Mb
Release : 2015-09-03
Category : Mathematics
ISBN : 9783319217116
In this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long time behavior of some classes of limiting processes. Structured population dynamics are modeled by measure-valued processes describing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading to infinite-dimensional deterministic or stochastic large-population approximations. Biologically relevant questions are considered, such as extinction criteria, the effect of large birth events, the impact of environmental catastrophes, the mutation-selection trade-off, recovery criteria in parasite infections, genealogical properties of a sample of individuals. These notes originated from a lecture series on Structured Population Dynamics at Ecole polytechnique (France). Vincent Bansaye and Sylvie Méléard are Professors at Ecole Polytechnique (France). They are a specialists of branching processes and random particle systems in biology. Most of their research concerns the applications of probability to biodiversity, ecology and evolution.
Author : Anonim
Publisher : Unknown
Page : 245 pages
File Size : 47,8 Mb
Release : 1977
Category : Biomathematics
ISBN : 0387083499
Author : Julian Hofrichter,Jürgen Jost,Tat Dat Tran
Publisher : Springer
Page : 320 pages
File Size : 46,5 Mb
Release : 2017-02-23
Category : Mathematics
ISBN : 9783319520452
The present monograph develops a versatile and profound mathematical perspective of the Wright--Fisher model of population genetics. This well-known and intensively studied model carries a rich and beautiful mathematical structure, which is uncovered here in a systematic manner. In addition to approaches by means of analysis, combinatorics and PDE, a geometric perspective is brought in through Amari's and Chentsov's information geometry. This concept allows us to calculate many quantities of interest systematically; likewise, the employed global perspective elucidates the stratification of the model in an unprecedented manner. Furthermore, the links to statistical mechanics and large deviation theory are explored and developed into powerful tools. Altogether, the manuscript provides a solid and broad working basis for graduate students and researchers interested in this field.
Author : Sergio Albeverio,Philip Blanchard,Michiel Hazewinkel,L. Streit
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400928930
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. O. K. Chesterton. The Scandal of Father 'The Hermit Qad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Author : J.F. Crow
Publisher : Scientific Publishers
Page : 609 pages
File Size : 42,7 Mb
Release : 2017-01-01
Category : Technology & Engineering
ISBN : 9789388148061
This text book, originally published in 1970, presents the field of population genetics, starting with elementary concepts and leading the reader well into the field. It is concerned mainly with population genetics in a strict sense and deals primarily with natural populations and less fully with the rather similar problems that arise in breading live stock and cul t i vat ed plans . The emphasis is on the behavior of genes and population attributes under natural selection where the most important measure is Darwinian fitness. This text is intended for graduatestudents and advanced undergraduates in genetics and population biology. This book steers a middle course between completely verbal biological arguments and the rigor of the mathematician. The first two-thirds of the book do not require advanced mathematical background. An ordinary knowledge of calculus will suffice. The latter parts of the book, which deal with population stochastically, use more advanced methods.
Author : Motoo Kimura
Publisher : Unknown
Page : 70 pages
File Size : 55,8 Mb
Release : 1964
Category : Diffusion
ISBN : UOM:39015017343487
Author : Charles J Mode,Candace K Sleeman
Publisher : World Scientific
Page : 696 pages
File Size : 52,6 Mb
Release : 2012-02-13
Category : Mathematics
ISBN : 9789814397070
The scope of this book is the field of evolutionary genetics. The book contains new methods for simulating evolution at the genomic level. It sets out applications using up to date Monte Carlo simulation methods applied in classical population genetics, and sets out new fields of quantifying mutation and selection at the Mendelian level. A serious limitation of Wright-Fisher process, the assumption that population size is constant, motivated the introduction of self regulating branching processes in this book. While providing a short review of the principles of probability and its application and using computer intensive methods whilst applying these principles, this book explains how it is possible to derive new formulas expressed in terms of matrix algebra providing new insights into the classical Wright-Fisher processes of evolutionary genetics. Also covered are the development of new methods for studying genetics and evolution, simulating nucleotide substitutions of a DNA molecule and on self regulating branching processes. Components of natural selection are studied in terms of reproductive success of each genotype whilst also studying the differential ability of genotypes to compete for resources and sexual selection. The concept of the gene is also reviewed in this book, and it provides a current definition of a gene based on very recent experiments with micro-array technologies. A development of stochastic models for simulating the evolution of model genomes concludes the studies in this book. Deserving of a place on the book shelves of workers in biomathematics, applied probability, stochastic processes and statistics, as well as in bioinformatics and phylogenetics, it will also be relevant to those interested in computer simulation, and evolutionary biologists interested in quantitative methods. Contents:An Introduction to Mathematical Probability with Applications in Mendelian GeneticsLinkage and Recombination at Multiple LociLinkage and Recombination in Large Random Mating Diploid Populations Random Mating Diploid PopulationsTwo Allele Wright-Fisher Process with Mutation and SelectionMultitype Gamete Sampling Processes, Generation of Random Numbers and Monte Carlo Simulation MethodsNucleotide Substitution Models Formulated as Markov Processes in Continuous TimeMixtures of Markov Processes as Models of Nucleotide Substitutions at Many SitesComputer Implementations and Applications of Nucleotide Substitution Models at Many Sites — Other Non-SNP Types of MutationGenealogies, Coalescence and Self-Regulating Branching ProcessesEmergence, Survival and Extinction of Mutant Types in Populations of Self Replicating Individuals Evolving From Small Founder PopulationsTwo Sex Multitype Self Regulating Branching Processes in Evolutionary GeneticsMultitype Self-Regulatory Branching Process and the Evolutionary Genetics of Age Structured Two Sex PopulationsAn Overview of the History of the Concept of a Gene and Selected Topics in Molecular GeneticsDetecting Genomic Signals of Selection and the Development of Models for Simulating the Evolution of GenomesSuggestions for Further Research, Reading and Viewing Readership: Professionals, researchers in mathematical and theoretical genetics and biology, graduate students in applied stochastic processes. Keywords:Mutation;Selection;Genes;Genomes;Stochastic Processes;Self Regulating Branching Processes;Models of GenomesKey Features:Provides many examples of applying Monte Carlo simulation methods to models that are not tractable mathematicallyRaises the study of evolution to new levels by using computer intensive methods when compared to classical and widely read population genetics books such as those by Ewens and Hartl and ClarkAll models, rooted within a formal framework of stochastic processes, enable any reader to write code in a programming language of his choice, to duplicate any of the experiments reported in the bookReviews: "Evolutionary biologists today need enough mathematical training to be able to assess the power and limits of evolutionary genetic models and to develop theories and models themselves. This book, based on very extensive—and impressive—research work, serves that purpose." Mathematical Reviews
Author : D. Ludwig
Publisher : Springer Science & Business Media
Page : 117 pages
File Size : 44,6 Mb
Release : 2013-03-07
Category : Mathematics
ISBN : 9783642808838
These notes serve as an introduction to stochastic theories which are useful in population biology; they are based on a course given at the Courant Institute, New York, in the Spring of 1974. In order to make the material. accessible to a wide audience, it is assumed that the reader has only a slight acquaintance with probability theory and differential equations. The more sophisticated topics, such as the qualitative behavior of nonlinear models, are approached through a succession of simpler problems. Emphasis is placed upon intuitive interpretations, rather than upon formal proofs. In most cases, the reader is referred elsewhere for a rigorous development. On the other hand, an attempt has been made to treat simple, useful models in some detail. Thus these notes complement the existing mathematical literature, and there appears to be little duplication of existing works. The authors are indebted to Miss Jeanette Figueroa for her beautiful and speedy typing of this work. The research was supported by the National Science Foundation under Grant No. GP-32996X3. CONTENTS I. LINEAR MODELS •••••. •••••••••••••••. . ••••••••••••••••••••••••••••••••••••••• 1 1. The Poisson Process ••••••••••••••••••••••••••. ••. •••••••••••. •••••••••• 1 2. Birth and Death Processes 5 2. 1 Linear Birth Process 5 2. 2 Linear Birth and Death Process •••••. ••••••. ••••••••••••••. •••••••• 7 2. 3 Birth and Death with Carrying Capacity ••••••••. •••. ••••••. ••••••. • 16 3. Branching Processes •••••••••••••••••••. •••••••. ••••••••. ••••••••••••••• 20 3. 1 Continuous Time . •••. ••••••••••. •••••••••••••••••••. ••••••••. ••••.
Author : W. Y. Tan
Publisher : World Scientific
Page : 464 pages
File Size : 49,6 Mb
Release : 2002
Category : Science
ISBN : 9810248695
This book presents a systematic treatment of Markov chains, diffusion processes and state space models, as well as alternative approaches to Markov chains through stochastic difference equations and stochastic differential equations. It illustrates how these processes and approaches are applied to many problems in genetics, carcinogenesis, AIDS epidemiology and other biomedical systems.One feature of the book is that it describes the basic MCMC (Markov chain and Monte Carlo) procedures and illustrates how to use the Gibbs sampling method and the multilevel Gibbs sampling method to solve many problems in genetics, carcinogenesis, AIDS and other biomedical systems.As another feature, the book develops many state space models for many genetic problems, carcinogenesis, AIDS epidemiology and HIV pathogenesis. It shows in detail how to use the multilevel Gibbs sampling method to estimate (or predict) simultaneously the state variables and the unknown parameters in cancer chemotherapy, carcinogenesis, AIDS epidemiology and HIV pathogenesis. As a matter of fact, this book is the first to develop many state space models for many genetic problems, carcinogenesis and other biomedical problems.
Author : Warren J. Ewens
Publisher : Springer Science & Business Media
Page : 435 pages
File Size : 44,5 Mb
Release : 2012-10-01
Category : Science
ISBN : 9780387218229
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.