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Author : Warren J. Ewens
Publisher : Unknown
Page : 86 pages
File Size : 55,9 Mb
Release : 2014-11-08
Category : Electronic
ISBN : 1503139727
Mathematical Population Genetics: Lecture NotesBy Warren J Ewens
Author : W.J. Ewens
Publisher : Springer Science & Business Media
Page : 153 pages
File Size : 42,9 Mb
Release : 2013-03-12
Category : Science
ISBN : 9789401033558
Population genetics is the mathematical investigation of the changes in the genetic structure of populations brought about by selection, mutation, inbreeding, migration, and other phenomena, together with those random changes deriving from chance events. These changes are the basic components of evolutionary progress, and an understanding of their effect is therefore necessary for an informed discussion of the reasons for and nature of evolution. It would, however, be wrong to pretend that a mathematical theory, depending as it must on a large number of simplifying assump tions, should be accepted unreservedly and that its conclusions should be accepted uncritically. No-one would pretend that in the event of disagreement between observation and mathematical prediction, the discrepancy is due to anything other than the inadequacy of the mathematical treatment. The biological world is, of course, far too complex for the study of population genetics to be simply a branch of applied mathematics, so that while we are concerned here with the mathematical theory, I have tried to indicate which of our results should continue to apply in a context wider than that in which they are formally derived. The difficulties involved in the joint discussions of mathematical and genetical problems are obvious enough. I have tried to aim this book rather more at the mathematician than at the geneticist, and for this reason a brief glossary of common genetical terms is included.
Author : Alison Etheridge
Publisher : Springer Science & Business Media
Page : 129 pages
File Size : 55,6 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 : Warren J. Ewens
Publisher : Springer Science & Business Media
Page : 435 pages
File Size : 42,5 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.
Author : W. J. Ewens
Publisher : Springer
Page : 354 pages
File Size : 44,6 Mb
Release : 1979-11
Category : Mathematics
ISBN : CORNELL:31924001937170
Author : J. F. C. Kingman
Publisher : SIAM
Page : 77 pages
File Size : 54,7 Mb
Release : 1980-01-01
Category : Science
ISBN : 1611970350
This book draws together some mathematical ideas that are useful in population genetics, concentrating on a few aspects which are both biologically relevant and mathematically interesting.
Author : Anthony William Fairbank Edwards
Publisher : Cambridge University Press
Page : 138 pages
File Size : 40,9 Mb
Release : 2000-01-13
Category : Science
ISBN : 0521775442
A definitive account of the origins of modern mathematical population genetics, first published in 2000.
Author : Thomas Nagylaki
Publisher : Springer Science & Business Media
Page : 381 pages
File Size : 48,5 Mb
Release : 2013-03-12
Category : Science
ISBN : 9783642762147
This book covers those areas of theoretical population genetics that can be investigated rigorously by elementary mathematical methods. I have tried to formulate the various models fairly generally and to state the biological as sumptions quite explicitly. I hope the choice and treatment of topics will en able the reader to understand and evaluate detailed analyses of many specific models and applications in the literature. Models in population genetics are highly idealized, often even over idealized, and their connection with observation is frequently remote. Further more, it is not practicable to measure the parameters and variables in these models with high accuracy. These regrettable circumstances amply justify the use of appropriate, lucid, and rigorous approximations in the analysis of our models, and such approximations are often illuminating even when exact solu tions are available. However, our empirical and theoretical limitations justify neither opaque, incomplete formulations nor unconvincing, inadequate analy ses, for these may produce uninterpretable, misleading, or erroneous results. Intuition is a principal source of ideas for the construction and investigation of models, but it can replace neither clear formulation nor careful analysis. Fisher (1930; 1958, pp. x, 23-24, 38) not only espoused similar ideas, but he recognized also that our concepts of intuition and rigor must evolve in time. The book is neither a review of the literature nor a compendium of results. The material is almost entirely self-contained. The first eight chapters are a thoroughly revised and greatly extended version of my published lecture notes (Nagylaki, 1977a).
Author : J.F. Crow
Publisher : Scientific Publishers
Page : 609 pages
File Size : 45,5 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 : Ken-ichi Kojima
Publisher : Unknown
Page : 414 pages
File Size : 48,8 Mb
Release : 1970
Category : Science
ISBN : MINN:319510000188398
Author : Frank. Hoppensteadt
Publisher : SIAM
Page : 79 pages
File Size : 52,7 Mb
Release : 1975-01-01
Category : Social Science
ISBN : 1611970482
Mathematical theories of populations have appeared both implicitly and explicitly in many important studies of populations, human populations as well as populations of animals, cells and viruses. They provide a systematic way for studying a population's underlying structure. A basic model in population age structure is studied and then applied, extended and modified, to several population phenomena such as stable age distributions, self-limiting effects, and two-sex populations. Population genetics are studied with special attention to derivation and analysis of a model for a one-locus, two-allele trait in a large randomly mating population. The dynamics of contagious phenomena in a population are studied in the context of epidemic diseases.
Author : Warren J. Ewens
Publisher : Unknown
Page : 325 pages
File Size : 42,6 Mb
Release : 1979
Category : Population genetics
ISBN : LCCN:79018938
Author : Ethan Akin
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 49,9 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9783642931284
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].
Author : Simon A. Levin
Publisher : American Mathematical Soc.
Page : 113 pages
File Size : 45,6 Mb
Release : 1984
Category : Science
ISBN : 9780821800836
Contains lecture notes that were presented at the AMS Short Course on Population Biology, held August 6-7, 1983, in Albany, New York in conjunction with the summer meeting of the American Mathematical Society. This title acquaints the reader with the mathematical ideas that pervade various levels of thinking in population biology.
Author : Avner Friedman
Publisher : Springer
Page : 210 pages
File Size : 52,6 Mb
Release : 2007-11-21
Category : Mathematics
ISBN : 3540743286
This book offers an introduction to fast growing research areas in evolution of species, population genetics, ecological models, and population dynamics. It reviews the concept and methodologies of phylogenetic trees, introduces ecological models, examines a broad range of ongoing research in population dynamics, and deals with gene frequencies under the action of migration and selection. The book features computational schemes, illustrations, and mathematical theorems.
