THE TIME REQUIRED FOR ALLELE FREQUENCY CHANGE

2017 ◽  
Vol 58 (3-4) ◽  
pp. 464-473
Author(s):  
TAI-HE FAN ◽  
SHUHAO SUN ◽  
PING-AN HE
Keyword(s):  
Stochastic Process ◽  
Population Genetics ◽  
Allele Frequency ◽  
Evolutionary Theory ◽  
Directional Selection ◽  
Selection Model ◽  
Frequency Change ◽  
Weak Selection ◽  
Expected Time ◽  
Time Required

In evolutionary theory, a key issue in selection theory is the expected time for a given amount of allele frequency change to occur. Crow and Kimura, by assuming weak selection, presented explicit results for several important cases of the directional selection and of the stochastic process. Those results played an important role in the theory of population genetics. In this paper, first we show that the weak selection assumption can be removed from most of the results of Crow and Kimura, and then we generalize those results to the most general selection model. Next, we estimate the errors of the deterministic formulae produced by proving that the deterministic formulae are limits of the corresponding stochastic formulae when the size of the population tends to infinity. Finally, we present a result which removes the restriction of Kimura’s corresponding results for a favourite recessive selection model, and we also observe that the conclusion made by Kimura about the favourite dominant selection might not be correct.

Estimating the Ratios of the Stationary Distribution Values for Markov Chains Modeling Evolutionary Algorithms

2009 ◽  
Vol 17 (3) ◽  
pp. 343-377 ◽  
Author(s):  
Boris Mitavskiy ◽  
Chris Cannings
Keyword(s):  
Stochastic Process ◽  
Population Genetics ◽  
Markov Chain ◽  
Evolutionary Algorithms ◽  
Markov Chains ◽  
Evolutionary Algorithm ◽  
Stationary Distribution ◽  
Genetic Load ◽  
Construction Method ◽  
Expected Time

The evolutionary algorithm stochastic process is well-known to be Markovian. These have been under investigation in much of the theoretical evolutionary computing research. When the mutation rate is positive, the Markov chain modeling of an evolutionary algorithm is irreducible and, therefore, has a unique stationary distribution. Rather little is known about the stationary distribution. In fact, the only quantitative facts established so far tell us that the stationary distributions of Markov chains modeling evolutionary algorithms concentrate on uniform populations (i.e., those populations consisting of a repeated copy of the same individual). At the same time, knowing the stationary distribution may provide some information about the expected time it takes for the algorithm to reach a certain solution, assessment of the biases due to recombination and selection, and is of importance in population genetics to assess what is called a “genetic load” (see the introduction for more details). In the recent joint works of the first author, some bounds have been established on the rates at which the stationary distribution concentrates on the uniform populations. The primary tool used in these papers is the “quotient construction” method. It turns out that the quotient construction method can be exploited to derive much more informative bounds on ratios of the stationary distribution values of various subsets of the state space. In fact, some of the bounds obtained in the current work are expressed in terms of the parameters involved in all the three main stages of an evolutionary algorithm: namely, selection, recombination, and mutation.

Introduction

2019 ◽  
pp. 1-10
Author(s):  
Asher D. Cutter
Keyword(s):  
Population Genetics ◽  
Allele Frequency ◽  
Dna Sequences ◽  
Population Genetic ◽  
Historical Context ◽  
Frequency Change ◽  
Molecular Population Genetics ◽  
Probability Of Fixation

Chapter 1, “Introduction: What is molecular population genetics?,” presents the motivations, applications, and historical context for molecular population genetics as a subdiscipline within biology. It describes how changes to DNA are inextricably woven into thinking about evolution and how molecular population genetics can be used to transport our thinking backward and forward through time. Key classic theoretical ideas summarizing allele frequency change, probability of fixation, and the time to fixation are encapsulated in brief vignettes. Both fundamental and applied uses of molecular population genetic perspectives are summarized in this survey of the historical, conceptual, and empirical development of the branch of science that we call population genetics and its integration with DNA sequences.

The Population Genetics of Selection

2018 ◽  
Author(s):  
Bruce Walsh ◽  
Michael Lynch
Keyword(s):  
Population Genetics ◽  
Genetic Variation ◽  
Linkage Disequilibrium ◽  
Equilibrium Structure ◽  
Single Locus ◽  
Stabilizing Selection ◽  
Frequency Change ◽  
Single Generation ◽  
Expected Time ◽  
Locus Selection

This chapter examines models of one- and two-locus selection in the absence of drift and mutation. Expressions for the per-generation rate of allele-frequency change and the expected time for a specified amount of change are developed for single-locus models, and their equilibrium structure is examined for those settings where selection retains more than one allele. The presence of selection-generated linkage disequilibrium greatly complicates the extension of single-locus results to two loci, and the chapter examines some of the resulting complications. Finally, it examines the nature of selection on a locus that underlies a trait under selection, and then uses this to develop the breeder's equation for the single-generation response in a trait under selection. One important result is that the loci for a trait under stabilizing selection experience fitness underdominance, and thus trait selection removes, rather than retains, genetic variation.

Time required for allele frequency change

2017 ◽  
Vol 58 ◽  
pp. 464
Author(s):  
Taihe Fan ◽  
Shuhao Sun ◽  
Pingan He
Keyword(s):  
Allele Frequency ◽  
Frequency Change ◽  
Time Required

scholarly journals The Rate of Compensatory Evolution

Genetics ◽  
1996 ◽  
Vol 144 (1) ◽  
pp. 419-426 ◽  
Author(s):  
Wolfgang Stephan
Keyword(s):  
Diffusion Theory ◽  
Secondary Structures ◽  
Compensatory Mutation ◽  
Weak Selection ◽  
Mutation Pressure ◽  
Theory Of Evolution ◽  
Compensatory Evolution ◽  
Expected Time ◽  
Individual Fitness ◽  
Shifting Balance

Abstract A two-locus model is presented to analyze the evolution of compensatory mutations occurring in stems of RNA secondary structures. Single mutations are assumed to be deleterious but harmless (neutral) in appropriate combinations. In proceeding under mutation pressure, natural selection and genetic drift from one fitness peak to another one, a population must therefore pass through a valley of intermediate deleterious states of individual fitness. The expected time for this transition is calculated using diffusion theory. The rate of compensatory evolution, kc, is then defined as the inverse of the expected transition time. When selection against deleterious single mutations is strong, kc, depends on the recombination fraction r between the two loci. Recombination generally reduces the rate of compensatory evolution because it breaks up favorable combinations of double mutants. For complete linkage, kc, is given by the rate at which favorable combinations of double mutantS are produced by compensatory mutation. For r > 0, kc, decreases exponentially with r. In contrast, kc, becomes independent of r for weak selection. We discuss the dynamics of evolutionary substitutions of compensatory mutants in relation to Wright'S shifting balance theory of evolution and use our results to analyze the substitution process in helices of mRNA secondary structures.

scholarly journals LevioSAM: Fast lift-over of alternate reference alignments

2021 ◽  
Author(s):  
Taher Mun ◽  
Nae-Chyun Chen ◽  
Ben Langmead
Keyword(s):  
Population Genetics ◽  
Coordinate System ◽  
Data Structures ◽  
Succinct Data Structures ◽  
Reference Coordinate System ◽  
Link Type ◽  
A Chain ◽  
Time Required ◽  
Effective Use

AbstractMotivationAs more population genetics datasets and population-specific references become available, the task of translating (“lifting”) read alignments from one reference coordinate system to another is becoming more common. Existing tools generally require a chain file, whereas VCF files are the more common way to represent variation. Existing tools also do not make effective use of threads, creating a post-alignment bottleneck.ResultsLevioSAM is a tool for lifting SAM/BAM alignments from one reference to another using a VCF file containing population variants. LevioSAM uses succinct data structures and scales efficiently to many threads. When run downstream of a read aligner, levioSAM completes in less than 13% the time required by an aligner when both are run with 16 threads.Availabilityhttps://github.com/alshai/[email protected], [email protected]

Risk Based Strategy for the Development of an Emergency Pipeline Repair System (EPRS)

2016 ◽  
Author(s):  
Ali Alani ◽  
Graham D. Goodfellow ◽  
Dennis Keen
Keyword(s):  
Economic Consequences ◽  
Third Party ◽  
Repair System ◽  
Pipeline Network ◽  
Expected Time ◽  
Emergency Repair ◽  
Offshore Pipeline ◽  
Timely Access ◽  
The Individual ◽  
Time Required

This paper presents an overview of the various components of an emergency pipeline repair system which should be in place in order to act effectively and efficiently during an emergency pipeline repair scenario. The condition of pipelines during operation is typically monitored by means of external and internal inspections. These inspections allow for planned intervention when a pipeline is found to be deteriorating. A failure to inspect adequately for time dependent threats, or randomly occurring events such as third party interaction, could result in a pipeline failure, leading to a requirement to rapidly return to operation and thus the need for an emergency repair. An Emergency Pipeline Repair System (EPRS) is therefore an essential part of a pipeline integrity management system. The primary purpose of the EPRS is to ensure that pipeline operators have the necessary level of readiness to allow an emergency repair to be carried out, thus minimising the economic consequences of having a pipeline out of service, whilst optimising the cost of purchasing and maintaining equipment and spares. In general, pipeline operators will have some emergency repair procedures to cater for unplanned or unexpected incidents. However, to complete an emergency repair efficiently and effectively, the availability of adequate spare materials and timely access to the damage location is required. For a large pipeline network, satisfying these requirements can be challenging. This paper discusses some basic elements of an EPRS and describes a case study of the development of a risk based EPRS strategy for an offshore pipeline operator. This approach involves the identification of credible hazards that can lead to damage requiring an emergency repair, and identification of repair options. The relative importance of the individual pipelines, in terms of their availability requirement, and the expected time required to complete an emergency repair are then taken into account. This enables the pipelines to be ranked based on the consequence of failure. Pipelines with consequence rankings that are considered unacceptable are therefore highlighted, and EPRS readiness related to those pipelines can subsequently be optimised. Recommendations for the development of an EPRS for an onshore or offshore pipeline network are also made.

scholarly journals Combining Experimental Evolution and Genomics to Understand How Seed Beetles Adapt to a Marginal Host Plant

Genes ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 400 ◽  
Author(s):  
Alexandre Rêgo ◽  
Samridhi Chaturvedi ◽  
Amy Springer ◽  
Alexandra M. Lish ◽  
Caroline L. Barton ◽  
...  
Keyword(s):  
Gene Expression ◽  
Allele Frequency ◽  
Development Time ◽  
Callosobruchus Maculatus ◽  
Parallel Evolution ◽  
Frequency Change ◽  
Multiple Traits ◽  
Population Genomic ◽  
Performance Traits ◽  
Frequency Changes

Genes that affect adaptive traits have been identified, but our knowledge of the genetic basis of adaptation in a more general sense (across multiple traits) remains limited. We combined population-genomic analyses of evolve-and-resequence experiments, genome-wide association mapping of performance traits, and analyses of gene expression to fill this knowledge gap and shed light on the genomics of adaptation to a marginal host (lentil) by the seed beetle Callosobruchus maculatus. Using population-genomic approaches, we detected modest parallelism in allele frequency change across replicate lines during adaptation to lentil. Mapping populations derived from each lentil-adapted line revealed a polygenic basis for two host-specific performance traits (weight and development time), which had low to modest heritabilities. We found less evidence of parallelism in genotype-phenotype associations across these lines than in allele frequency changes during the experiments. Differential gene expression caused by differences in recent evolutionary history exceeded that caused by immediate rearing host. Together, the three genomic datasets suggest that genes affecting traits other than weight and development time are likely to be the main causes of parallel evolution and that detoxification genes (especially cytochrome P450s and beta-glucosidase) could be especially important for colonization of lentil by C. maculatus.

scholarly journals An inclusive fitness analysis of synergistic interactions in structured populations

2012 ◽  
Vol 279 (1747) ◽  
pp. 4596-4603 ◽  
Author(s):  
Peter Taylor ◽  
Wes Maciejewski
Keyword(s):  
Frequency Dependence ◽  
Allele Frequency ◽  
Inclusive Fitness ◽  
Selective Advantage ◽  
Structured Populations ◽  
Weak Selection ◽  
Synergistic Interactions ◽  
Fitness Effects ◽  
Structured Population

We study the evolution of a pair of competing behavioural alleles in a structured population when there are non-additive or ‘synergistic’ fitness effects. Under a form of weak selection and with a simple symmetry condition between a pair of competing alleles, Tarnita et al. provide a surprisingly simple condition for one allele to dominate the other. Their condition can be obtained from an analysis of a corresponding simpler model in which fitness effects are additive. Their result uses an average measure of selective advantage where the average is taken over the long-term—that is, over all possible allele frequencies—and this precludes consideration of any frequency dependence the allelic fitness might exhibit. However, in a considerable body of work with non-additive fitness effects—for example, hawk–dove and prisoner's dilemma games—frequency dependence plays an essential role in the establishment of conditions for a stable allele-frequency equilibrium. Here, we present a frequency-dependent generalization of their result that provides an expression for allelic fitness at any given allele frequency p . We use an inclusive fitness approach and provide two examples for an infinite structured population. We illustrate our results with an analysis of the hawk–dove game.

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