Some Stochastic Processes In Population Genetics With Their Diffusion Approximations
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Some Stochastic Processes In Population Genetics With Their Diffusion Approximations
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Author : David William Mott
language : en
Publisher:
Release Date : 1973
Some Stochastic Processes In Population Genetics With Their Diffusion Approximations written by David William Mott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with categories.
Stochastic Methods In Biology
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Author : Motoo Kimura
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-13
Stochastic Methods In Biology written by Motoo Kimura and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-13 with Mathematics categories.
The use of probabilistic methods in the biological sciences has been so well established by now that mathematical biology is regarded by many as a distinct dis cipline with its own repertoire of techniques. The purpose of the Workshop on sto chastic methods in biology held at Nagoya University during the week of July 8-12, 1985, was to enable biologists and probabilists from Japan and the U. S. to discuss the latest developments in their respective fields and to exchange ideas on the ap plicability of the more recent developments in stochastic process theory to problems in biology. Eighteen papers were presented at the Workshop and have been grouped under the following headings: I. Population genetics (five papers) II. Measure valued diffusion processes related to population genetics (three papers) III. Neurophysiology (two papers) IV. Fluctuation in living cells (two papers) V. Mathematical methods related to other problems in biology, epidemiology, population dynamics, etc. (six papers) An important feature of the Workshop and one of the reasons for organizing it has been the fact that the theory of stochastic differential equations (SDE's) has found a rich source of new problems in the fields of population genetics and neuro biology. This is especially so for the relatively new and growing area of infinite dimensional, i. e. , measure-valued or distribution-valued SDE's. The papers in II and III and some of the papers in the remaining categories represent these areas.
Diffusion Models In Population Genetics
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Author : Motoo Kimura
language : en
Publisher:
Release Date : 1964
Diffusion Models In Population Genetics written by Motoo Kimura and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Diffusion categories.
Approximation Of Population Processes
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Author : Thomas G. Kurtz
language : en
Publisher: SIAM
Release Date : 1981-02-01
Approximation Of Population Processes written by Thomas G. Kurtz and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-02-01 with Mathematics categories.
This monograph considers approximations that are possible when the number of particles in population processes is large
Stochastic Models For Structured Populations
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Author : Sylvie Meleard
language : en
Publisher: Springer
Release Date : 2015-09-03
Stochastic Models For Structured Populations written by Sylvie Meleard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-03 with Mathematics categories.
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.
Stochastic Processes In Population Genetics
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Author : Motoo Kimura
language : en
Publisher:
Release Date : 1956
Stochastic Processes In Population Genetics written by Motoo Kimura and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956 with Population genetics categories.
Stochastic Problems In Population Genetics
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Author : T. Maruyama
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-13
Stochastic Problems In Population Genetics written by T. Maruyama and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-13 with Mathematics categories.
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.
Stochastic Models In Biology
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Author : Narendra S. Goel
language : en
Publisher: Elsevier
Release Date : 2013-10-22
Stochastic Models In Biology written by Narendra S. Goel and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Science categories.
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.
Stochastic Processes In Genetics And Evolution
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Author : Charles J. Mode
language : en
Publisher: World Scientific
Release Date : 2012
Stochastic Processes In Genetics And Evolution written by Charles J. Mode and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
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.
Some Mathematical Models From Population Genetics
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Author : Alison Etheridge
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-07
Some Mathematical Models From Population Genetics written by Alison Etheridge and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-07 with Mathematics categories.
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.