A Mutation Selection Model With Recombination For General Genotypes
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| Author | : Steven Neil Evans |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 142 |
| Release | : 2013-02-26 |
| Genre | : Mathematics |
| ISBN | : 0821875698 |
The authors investigate a continuous time, probability measure-valued dynamical system that describes the process of mutation-selection balance in a context where the population is infinite, there may be infinitely many loci, and there are weak assumptions on selective costs. Their model arises when they incorporate very general recombination mechanisms into an earlier model of mutation and selection presented by Steinsaltz, Evans and Wachter in 2005 and take the relative strength of mutation and selection to be sufficiently small. The resulting dynamical system is a flow of measures on the space of loci. Each such measure is the intensity measure of a Poisson random measure on the space of loci: the points of a realization of the random measure record the set of loci at which the genotype of a uniformly chosen individual differs from a reference wild type due to an accumulation of ancestral mutations. The authors' motivation for working in such a general setting is to provide a basis for understanding mutation-driven changes in age-specific demographic schedules that arise from the complex interaction of many genes, and hence to develop a framework for understanding the evolution of aging.
| Author | : Steven Neil Evans |
| Publisher | : |
| Total Pages | : 128 |
| Release | : 2013 |
| Genre | : Evolutionary genetics |
| ISBN | : 9780821895115 |
We investigate a continuous time, probability measure-valued dynamical system that describes the process of mutation-selection balance in a context where the population is infinite, there may be infinitely many loci, and there are weak assumptions on selective costs. Our model arises when we incorporate very general recombination mechanisms into an earlier model of mutation and selection presented by Steinsaltz, Evans and Wachter in 2005 and take the relative strength of mutation and selection to be sufficiently small. The resulting dynamical system is dynamical system a flow of measures on the space of loci. Each such measure is the intensity measure of a Poisson random measure on the space of loci: intensity measure the points of a realization of the random measure record the set of loci at which the genotype of a uniformly chosen individual differs from a reference wild type due to an accumulation of ancestral mutations. Our motivation for working in such a general setting is to provide a basis for understanding mutation-driven changes in age-specific demographic schedules that arise from the complex interaction of many genes, and hence to develop a framework for understanding the evolution of aging. We establish the existence and uniqueness of the dynamical system, provide conditions for the existence and stability of equilibrium states, and prove that our continuous-time dynamical system is the limit of a sequence of discrete-time infinite population mutation-selection-recombination models in the standard asymptotic regime where selection and mutation are weak relative to recombination and both scale at the same infinitesimal rate in the limit.
| Author | : Brian Charlesworth |
| Publisher | : Roberts |
| Total Pages | : 776 |
| Release | : 2010-02-03 |
| Genre | : Science |
| ISBN | : |
This textbook shows readers how models of the genetic processes involved in evolution are made (including natural selection, migration, mutation, and genetic drift in finite populations), and how the models are used to interpret classical and molecular genetic data. The material is intended for advanced level undergraduate courses in genetics and evolutionary biology, graduate students in evolutionary biology and human genetics, and researchers in related fields who wish to learn evolutionary genetics. The topics covered include genetic variation, DNA sequence variability and its measurement, the different types of natural selection and their effects (e.g. the maintenance of variation, directional selection, and adaptation), the interactions between selection and mutation or migration, the description and analysis of variation at multiple sites in the genome, genetic drift, and the effects of spatial structure.
| Author | : John Maynard Smith |
| Publisher | : Cambridge University Press |
| Total Pages | : 236 |
| Release | : 1978-08-24 |
| Genre | : Science |
| ISBN | : 9780521218870 |
The question of why organisms reproduce sexually is still a matter of controversy. In this account, Professor Maynard Smith considers the selective forces responsible for the origin and evolution of sexual reproduction and genetic recombination, using quantitative population genetics arguments to support his ideas. The relative importance of individual and group selection processes are also considered. the aim is to give a clear statement of the theoretical issues, and present enough of the evidence to show what kinds of facts are relevant. It is hoped that where crucial evidence is missing, experimentalists and field workers may be encouraged to collect the relevant data. The author does not claim to solve all the problems he raises, but this clear and well-argued account should provide stimulating reading for advanced undergraduate students and research workers in evolutionary theory.
| Author | : Rama S. Singh |
| Publisher | : Oxford University Press |
| Total Pages | : 309 |
| Release | : 2012-06-28 |
| Genre | : Science |
| ISBN | : 0199642273 |
A range of theories on the rates of evolution-from static to gradual to punctuated to quantum-have been developed, mostly by comparing morphological changes over geological timescales as described in the fossil record.
| Author | : Julien Y Dutheil |
| Publisher | : |
| Total Pages | : 464 |
| Release | : 2020-10-08 |
| Genre | : Science |
| ISBN | : 9781013271403 |
This open access volume presents state-of-the-art inference methods in population genomics, focusing on data analysis based on rigorous statistical techniques. After introducing general concepts related to the biology of genomes and their evolution, the book covers state-of-the-art methods for the analysis of genomes in populations, including demography inference, population structure analysis and detection of selection, using both model-based inference and simulation procedures. Last but not least, it offers an overview of the current knowledge acquired by applying such methods to a large variety of eukaryotic organisms. Written in the highly successful Methods in Molecular Biology series format, chapters include introductions to their respective topics, pointers to the relevant literature, step-by-step, readily reproducible laboratory protocols, and tips on troubleshooting and avoiding known pitfalls. Authoritative and cutting-edge, Statistical Population Genomics aims to promote and ensure successful applications of population genomic methods to an increasing number of model systems and biological questions. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
| Author | : |
| Publisher | : World Scientific |
| Total Pages | : 1131 |
| Release | : |
| Genre | : |
| ISBN | : |
| Author | : Ioan Bejenaru |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 120 |
| Release | : 2014-03-05 |
| Genre | : Mathematics |
| ISBN | : 0821892150 |
The authors consider the Schrödinger Map equation in 2+1 dimensions, with values into \mathbb{S}^2. This admits a lowest energy steady state Q, namely the stereographic projection, which extends to a two dimensional family of steady states by scaling and rotation. The authors prove that Q is unstable in the energy space \dot H^1. However, in the process of proving this they also show that within the equivariant class Q is stable in a stronger topology X \subset \dot H^1.
| Author | : Victor Reiner |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 121 |
| Release | : 2014-03-05 |
| Genre | : Mathematics |
| ISBN | : 0821890956 |
For a finite real reflection group W and a W -orbit O of flats in its reflection arrangement - or equivalently a conjugacy class of its parabolic subgroups - the authors introduce a statistic noninv O (w) on w in W that counts the number of O -noninversions of w . This generalises the classical (non-)inversion statistic for permutations w in the symmetric group S n. The authors then study the operator ? O of right-multiplication within the group algebra CW by the element that has noninv O (w) as its coefficient on w.
| Author | : Robert J. Buckingham |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 148 |
| Release | : 2013-08-23 |
| Genre | : Mathematics |
| ISBN | : 0821885456 |
The authors study the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and also high-frequency librational motion in the tails. They show that for small times independent of the semiclassical scaling parameter, both types of motion are accurately described by explicit formulae involving elliptic functions. These formulae demonstrate consistency with predictions of Whitham's formal modulation theory in both the hyperbolic (modulationally stable) and elliptic (modulationally unstable) cases.
