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Author: Ziad Taib
Publisher: Springer Science & Business Media
ISBN: 3642515363
Category : Mathematics
Languages : en
Pages : 120
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Book Description
The Galton-Watson branching process has its roots in the problem of extinction of family names which was given a precise formulation by F. Galton as problem 4001 in the Educational Times (17, 1873). In 1875, an attempt to solve this problem was made by H. W. Watson but as it turned out, his conclusion was incorrect. Half a century later, R. A. Fisher made use of the Galton-Watson process to determine the extinction probability of the progeny of a mutant gene. However, it was J. B. S. Haldane who finally gave the first sketch of the correct conclusion. J. B. S. Haldane also predicted that mathematical genetics might some day develop into a "respectable branch of applied mathematics" (quoted in M. Kimura & T. Ohta, Theoretical Aspects of Population Genetics. Princeton, 1971). Since the time of Fisher and Haldane, the two fields of branching processes and mathematical genetics have attained a high degree of sophistication but in different directions. This monograph is a first attempt to apply the current state of knowledge concerning single-type branching processes to a particular area of mathematical genetics: neutral evolution. The reader is assumed to be familiar with some of the concepts of probability theory, but no particular knowledge of branching processes is required. Following the advice of an anonymous referee, I have enlarged my original version of the introduction (Chapter Zero) in order to make it accessible to a larger audience. G6teborg, Sweden, November 1991.
Author: Ziad Taib
Publisher: Springer Science & Business Media
ISBN: 3642515363
Category : Mathematics
Languages : en
Pages : 120
Get Book Here
Book Description
The Galton-Watson branching process has its roots in the problem of extinction of family names which was given a precise formulation by F. Galton as problem 4001 in the Educational Times (17, 1873). In 1875, an attempt to solve this problem was made by H. W. Watson but as it turned out, his conclusion was incorrect. Half a century later, R. A. Fisher made use of the Galton-Watson process to determine the extinction probability of the progeny of a mutant gene. However, it was J. B. S. Haldane who finally gave the first sketch of the correct conclusion. J. B. S. Haldane also predicted that mathematical genetics might some day develop into a "respectable branch of applied mathematics" (quoted in M. Kimura & T. Ohta, Theoretical Aspects of Population Genetics. Princeton, 1971). Since the time of Fisher and Haldane, the two fields of branching processes and mathematical genetics have attained a high degree of sophistication but in different directions. This monograph is a first attempt to apply the current state of knowledge concerning single-type branching processes to a particular area of mathematical genetics: neutral evolution. The reader is assumed to be familiar with some of the concepts of probability theory, but no particular knowledge of branching processes is required. Following the advice of an anonymous referee, I have enlarged my original version of the introduction (Chapter Zero) in order to make it accessible to a larger audience. G6teborg, Sweden, November 1991.
Author: Charles Swanton
Publisher: Perspectives Cshl
ISBN: 9781621821434
Category : Medical
Languages : en
Pages : 350
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Book Description
Tumor progression is driven by mutations that confer growth advantages to different subpopulations of cancer cells. As a tumor grows, these subpopulations expand, accumulate new mutations, and are subjected to selective pressures from the environment, including anticancer interventions. This process, termed clonal evolution, can lead to the emergence of therapy-resistant tumors and poses a major challenge for cancer eradication efforts. Written and edited by experts in the field, this collection from Cold Spring Harbor Perspectives in Medicine examines cancer progression as an evolutionary process and explores how this way of looking at cancer may lead to more effective strategies for managing and treating it. The contributors review efforts to characterize the subclonal architecture and dynamics of tumors, understand the roles of chromosomal instability, driver mutations, and mutation order, and determine how cancer cells respond to selective pressures imposed by anticancer agents, immune cells, and other components of the tumor microenvironment. They compare cancer evolution to organismal evolution and describe how ecological theories and mathematical models are being used to understand the complex dynamics between a tumor and its microenvironment during cancer progression. The authors also discuss improved methods to monitor tumor evolution (e.g., liquid biopsies) and the development of more effective strategies for managing and treating cancers (e.g., immunotherapies). This volume will therefore serve as a vital reference for all cancer biologists as well as anyone seeking to improve clinical outcomes for patients with cancer.
Author: Naruya Saitou
Publisher: Springer Science & Business Media
ISBN: 1447153049
Category : Computers
Languages : en
Pages : 476
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Book Description
This book is the first of its kind to explain the fundamentals of evolutionary genomics. The comprehensive coverage includes concise descriptions of a variety of genome organizations, a thorough discussion of the methods used, and a detailed review of genome sequence processing procedures. The opening chapters also provide the necessary basics for readers unfamiliar with evolutionary studies. Features: introduces the basics of molecular biology, DNA replication, mutation, phylogeny, neutral evolution, and natural selection; presents a brief evolutionary history of life from the primordial seas to the emergence of humans; describes the genomes of prokaryotes, eukaryotes, vertebrates, and humans; reviews methods for genome sequencing, phenotype data collection, homology searches and analysis, and phylogenetic tree and network building; discusses databases of genome sequences and related information, evolutionary distances, and population genomics; provides supplementary material at an associated website.
Author: Marek Kimmel
Publisher: Springer Science & Business Media
ISBN: 038795340X
Category : Mathematics
Languages : en
Pages : 242
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Book Description
Biological examples of branching processes from molecular and cellular biology are introduced in this volume, as well as from the fields of human evolution and medicine. It will interest scientists who work in quantitative modeling of biological systems, particularly probabilists, mathematical biologists, and others. 54 illustrations.
Author: Charles J. Mode
Publisher: World Scientific
ISBN: 9814350680
Category : Mathematics
Languages : en
Pages : 695
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Book Description
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: Patsy Haccou
Publisher: Cambridge University Press
ISBN: 9780521832205
Category : Mathematics
Languages : en
Pages : 342
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Book Description
This book covers the mathematical idea of branching processes, and tailors it for a biological audience.
Author: J.S. Gale
Publisher: Springer Science & Business Media
ISBN: 9400903871
Category : Science
Languages : en
Pages : 428
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Book Description
The rise of the neutral theory of molecular evolution seems to have aroused a renewed interest in mathematical population genetics among biologists, who are primarily experimenters rather than theoreticians. This has encouraged me to set out the mathematics of the evolutionary process in a manner that, I hope, will be comprehensible to those with only a basic knowledge of calculus and matrix algebra. I must acknowledge from the start my great debt to my students. Equipped initially with rather limited mathematics, they have pursued the subject with much enthusiasm and success. This has enabled me to try a number of different approaches over the years. I was particularly grateful to Dr L. J. Eaves and Professor W. E. Nance for the opportunity to give a one-semester course at the Medical College of Virginia, and I would like to thank them, their colleagues and their students for the many kindnesses shown to me during my visit. I have concentrated almost entirely on stochastic topics, since these cause the greatest problems for non-mathematicians. The latter are particularly concerned with the range of validity of formulae. A sense of confidence in applying these formulae is, almost certainly, best gained by following their derivation. I have set out proofs in fair detail, since, in my experience, minor points of algebraic manipulation occasionally cause problems. To avoid loss of continuity, I have sometimes put material in notes at the end of chapters.
Author: Sándor Suhai
Publisher: Springer Science & Business Media
ISBN: 1461559030
Category : Science
Languages : en
Pages : 332
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Book Description
The application ofcomputational methods to solve scientific and practical problems in genome research created a new interdisciplinary area that transcends boundaries tradi tionally separating genetics, biology, mathematics, physics, and computer science. Com puters have, of course, been intensively used in the field of life sciences for many years, even before genome research started, to store and analyze DNA or protein sequences; to explore and model the three-dimensional structure, the dynamics, and the function of biopolymers; to compute genetic linkage or evolutionary processes; and more. The rapid development of new molecular and genetic technologies, combined with ambitious goals to explore the structure and function ofgenomes ofhigher organisms, has generated, how ever, not only a huge and exponentially increasing body of data but also a new class of scientific questions. The nature and complexity of these questions will also require, be yond establishing a new kind ofalliance between experimental and theoretical disciplines, the development of new generations both in computer software and hardware technolo gies. New theoretical procedures, combined with powerful computational facilities, will substantially extend the horizon of problems that genome research can attack with suc cess. Many of us still feel that computational models rationalizing experimental findings in genome research fulfill their promises more slowly than desired. There is also an uncer tainty concerning the real position of a "theoretical genome research" in the network of established disciplines integrating their efforts in this field.
Author: Naruya Saitou
Publisher: Springer
ISBN: 331992642X
Category : Computers
Languages : en
Pages : 518
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Book Description
This authoritative textbook/reference presents a comprehensive introduction to the field of evolutionary genomics. The opening chapters describe the fundamental concepts in molecular biology and genome evolution for readers without any prior background in this area. This is followed by a detailed examination of genome evolution in various different groups of organisms. The text then concludes with a review of practical methods essential to researchers in the field. This updated and revised new edition also features historical perspectives on contributions to evolutionary genomics from related fields such as molecular evolution, genetics, and numerical taxonomy. Topics and features: introduces the basics of molecular biology, covering protein structure and diversity, as well as DNA replication, transcription, and translation; examines the phylogenetic relationships of DNA sequences, and the processes of mutation, neutral evolution, and natural selection; presents a brief evolutionary history of life, surveying the key features of the genomes of prokaryotes, eukaryotes, viruses and phages, vertebrates, and humans; reviews the various biological “omic” databases, and discusses the analysis of homologous nucleotide and amino acid sequences; provides an overview of the experimental sequencing of genomes and transcriptomes, and the construction of phylogenetic trees; describes methods for estimating of evolutionary distances, and performing studies of population genetics; supplies additional supporting material at an associated website. Serving as an indispensable textbook for graduate and advanced undergraduate courses on evolutionary genomics, this accessible overview will also prove invaluable to researchers from both computer science and the biological sciences seeking a primer on the field.
Author: Denis Mollison
Publisher: Cambridge University Press
ISBN: 9780521475365
Category : Mathematics
Languages : en
Pages : 458
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Book Description
Surveys the state of epidemic modelling, resulting from the NATO Advanced Workshop at the Newton Institute in 1993.
