Download or read book Mathematical Structures in Population Genetics written by I︠U︡riĭ Ilʹich Li︠u︡bich and published by Springer. This book was released on 1992 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Structures in Population Genetics written by Yuri I. Lyubich and published by Springer. This book was released on 1992 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical methods have been applied successfully to population genet ics for a long time. Even the quite elementary ideas used initially proved amazingly effective. For example, the famous Hardy-Weinberg Law (1908) is basic to many calculations in population genetics. The mathematics in the classical works of Fisher, Haldane and Wright was also not very complicated but was of great help for the theoretical understanding of evolutionary pro cesses. More recently, the methods of mathematical genetics have become more sophisticated. In use are probability theory, stochastic processes, non linear differential and difference equations and nonassociative algebras. First contacts with topology have been established. Now in addition to the tra ditional movement of mathematics for genetics, inspiration is flowing in the opposite direction, yielding mathematics from genetics. The present mono grapll reflects to some degree both patterns but especially the latter one. A pioneer of this synthesis was S. N. Bernstein. He raised-and partially solved- -the problem of characterizing all stationary evolutionary operators, and this work was continued by the author in a series of papers (1971-1979). This problem has not been completely solved, but it appears that only cer tain operators devoid of any biological significance remain to be addressed. The results of these studies appear in chapters 4 and 5. The necessary alge braic preliminaries are described in chapter 3 after some elementary models in chapter 2.
Download or read book Information Geometry and Population Genetics written by Julian Hofrichter and published by Springer. This book was released on 2017-02-23 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Population Genetics written by W.J. Ewens and published by Springer Science & Business Media. This book was released on 2013-03-12 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Genetics and Social Structure Mathematical Structuralism in Population Genetics and Social Theory written by Paul A. Ballonoff and published by . This book was released on 1974 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Population Genetics written by W. J. Ewens and published by Springer. This book was released on 1979-11 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Theories of Populations written by Frank. Hoppensteadt and published by SIAM. This book was released on 1975-01-01 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Genetic Structure and Selection in Subdivided Populations MPB 40 written by François Rousset and published by Princeton University Press. This book was released on 2013-02-15 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various approaches have been developed to evaluate the consequences of spatial structure on evolution in subdivided populations. This book is both a review and new synthesis of several of these approaches, based on the theory of spatial genetic structure. François Rousset examines Sewall Wright's methods of analysis based on F-statistics, effective size, and diffusion approximation; coalescent arguments; William Hamilton's inclusive fitness theory; and approaches rooted in game theory and adaptive dynamics. Setting these in a framework that reveals their common features, he demonstrates how efficient tools developed within one approach can be applied to the others. Rousset not only revisits classical models but also presents new analyses of more recent topics, such as effective size in metapopulations. The book, most of which does not require fluency in advanced mathematics, includes a self-contained exposition of less easily accessible results. It is intended for advanced graduate students and researchers in evolutionary ecology and population genetics, and will also interest applied mathematicians working in probability theory as well as statisticians.
Download or read book The Geometry of Population Genetics written by Ethan Akin and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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].
Download or read book Mathematical Population Genetics written by Warren J. Ewens and published by . This book was released on 1979 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Human Population Genetics written by John H. Relethford and published by John Wiley & Sons. This book was released on 2012-03-27 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory guide to human population genetics and microevolutionary theory Providing an introduction to mathematical population genetics, Human Population Genetics gives basic background on the mechanisms of human microevolution. This text combines mathematics, biology, and anthropology and is best suited for advanced undergraduate and graduate study. Thorough and accessible, Human Population Genetics presents concepts and methods of population genetics specific to human population study, utilizing uncomplicated mathematics like high school algebra and basic concepts of probability to explain theories central to the field. By describing changes in the frequency of genetic variants from one generation to the next, this book hones in on the mathematical basis of evolutionary theory. Human Population Genetics includes: Helpful formulae for learning ease Graphs and analogies that make basic points and relate the evolutionary process to mathematical ideas Glossary terms marked in boldface within the book the first time they appear In-text citations that act as reference points for further research Exemplary case studies Topics such as Hardy-Weinberg equilibrium, inbreeding, mutation, genetic drift, natural selection, and gene flow Human Population Genetics solidifies knowledge learned in introductory biological anthropology or biology courses and makes it applicable to genetic study. NOTE: errata for the first edition can be found at the author's website: http://employees.oneonta.edu/relethjh/HPG/errata.pdf
Download or read book Mathematics of Genetic Diversity written by J. F. C. Kingman and published by SIAM. This book was released on 1980-01-01 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fundamentals of Mathematical Evolutionary Genetics written by Yuri M. Svirezhev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the ~Et moi ..., si j'avait su comment en revenir, human race. It has put common sense back je riy serais point aile.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. o'; 'One service logic has rendered com puter science .. o'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Download or read book The Genetic Structure of Populations written by A. Jacquard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is part of the ideology of science that it is an international enterprise, carried out by a community that knows no barriers of nation or culture. But the reality is somewhat different. Despite the best intentions of scientists to form a single community, unseparated by differences of national and political viewpoint, they are, in fact, separated by language. Scientific literature in German is not generally assimilated by French workers, nor that appearing in French by those whose native language is English. The problem appears to have become more severe since the last war, because the ascendance of the United States as the preeminent economic power led, in a time of big and expensive science, to a pre dominance of American scientific production and a growing tendency (at least among English-speakers) to regard English as the international language of science. International congresses and journals of world circulation have come more and more to take English as their standard or official language. As a result, students and scientific workers in the English speaking world have become more linguistically parochial than ever before and have been cut off from a considerable scientific literature. Population genetics has been no exception to the rule. The elegant and extremely innovative theoreticaI work of Malecot, for example, is only now being properly assimilated by population biologists outside France. It was therefore with some sense of frustration that I read Prof.
Download or read book Mathematical Methods for Population Genetics written by Gunnar Dahlberg and published by . This book was released on 1947 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conception of race and the laws of Mendel. Different form of inheritance. The effect of mutations on the composition of a population in panmixia. The effect of selection on a population. Selection and mutations. The importance of the isolate for the composition of population. Isolates and race. Mutations, selection, and isolates.
