Mathematical Population Genetics

Ewens, Warren J.

doi:10.1007/978-0-387-21822-9

Cited by 1,167 publications

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“…However, they are incompatible with the timescale of neutral evolution. With an effective population size of N e ~ 10 7 , new mutations would require Δt ~ 0.1 N e ~ 10 6 generations to reach the 10% detection threshold by genetic drift alone 22 . Thus, the mutations in Fig.…”

Section: Reconstructing the Molecular Fossil Recordmentioning

confidence: 99%

The dynamics of molecular evolution over 60,000 generations

Good

McDonald

Barrick

et al. 2017

Nature

645

839

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The outcomes of evolution are determined by a stochastic dynamical process that governs how mutations arise and spread through a population. Here, we analyze the dynamics of molecular evolution in twelve experimental populations of Escherichia coli, using whole-genome metagenomic sequencing at 500-generation intervals through 60,000 generations. Despite a declining rate of fitness gain, molecular evolution continues to be characterized by signatures of rapid adaptation, with multiple beneficial variants simultaneously competing for dominance in each population. Interactions between ecological and evolutionary processes play an important role, as long-term quasi-stable coexistence arises spontaneously in most populations, and evolution continues within each clade. We also present new evidence that the targets of natural selection change over time, as epistasis and historical contingency alter the strength of selection on different genes. Together, these results show that long-term adaptation to a constant environment can be a more complex and dynamic process than is often assumed.

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Section: Reconstructing the Molecular Fossil Recordmentioning

confidence: 99%

The dynamics of molecular evolution over 60,000 generations

Good

McDonald

Barrick

et al. 2017

Nature

645

839

View full text Add to dashboard Cite

show abstract

“…Under weak and constant selection, using diffusion theory (Nei & Roychoudhury, 1973;Maruyama, 1974Maruyama, , 1977Ewens, 2004) showed that a selectively disadvantageous mutant, if destined for fixation, spends as much time, on average, in any frequency range as a correspondingly advantageous mutant destined for fixation. In particular, the conditional mean fixation time of a single advantageous mutant is the same as that of a corresponding deleterious mutant.…”

Section: Fixation Time In a Wright-fisher Processmentioning

confidence: 99%

“…Let P i,i+1 = λ i , and P i,i−1 = μ i , λ 0 = μ N = 0. We can write down the expressions for , , , and explicitly [Karlin & Taylor, 1975;Ewens, 2004]. Let then (A.6) Using these formulae, we can calculate t A ,t B in Appendix B.…”

Section: Proof Of Propositionmentioning

confidence: 99%

“…The probability of fixation and the mean time to fixation of a single mutant are important quantities. There is an extensive literature on this topic using diffusion theory to calculate both the fixation probability and the conditional mean time to fixation (Kimura, 1994;Ewens, 2004).…”

Section: Introductionmentioning

confidence: 99%

“…calculations of (Nei & Roychoudhury, 1973;Maruyama, 1974Maruyama, , 1977Ewens, 2004); furthermore, it requires no limiting assumption on population size or selection factor.…”

Section: Introductionmentioning

confidence: 99%

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A symmetry of fixation times in evoultionary dynamics

Taylor

Iwasa

Nowak

2006

Journal of Theoretical Biology

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In this paper, we show that for evolutionary dynamics between two types that can be described by a Moran process, the conditional fixation time of either type is the same irrespective of the selective scenario. With frequency dependent selection between two strategies A and B of an evolutionary game, regardless of whether A dominates B, A and B are best replies to themselves, or A and B are best replies to each other, the conditional fixation times of a single A and a single B mutant are identical. This does not hold for Wright-Fisher models, nor when the mutants start from multiple copies.

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Population Genetics: Overview

Ewens

2010

Encyclopedia of Life Sciences

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Population genetics is concerned with the nature of, and the forces determining, the genetic composition of a population. Since any presently observed population is the outcome of an evolutionary process, the subject is in large part concerned with evolutionary questions. Indeed the evolutionary component of population genetics may be thought of as the rewriting of the Darwinian theory in terms of the Mendelian hereditary mechanism. This involves, for example, determining the rate of incorporation of favourable new alleles into a population, and the evolutionary effects of mutation. These activities are prospective , that is they discuss changes in the structure of a population forwards in time. However population genetics theory is currently largely retrospective , assessing the past history of a population (‘When and where did the most recent common ancestor of all currently living humans live?’) and investigating what forces led to the currently observed genetic composition of a population. Key Concepts: The additive genetic variance is that component of the variation in any character which is explained by ‘genes within genotypes’. The blending theory asserts that the value of any characteristic of any child is approximately the average of the corresponding characteristics in that child's parents. The correlation between relatives is the correlation in some character between close relatives (e.g. mother–daughter). The Fundamental Theorem of Natural Selection relates aspects of the change in the mean fitness of a population from one generation to the next to the parental generation additive genetic variance in fitness. The Hardy–Weinberg law shows that, in the absence of selection, genetic variation is maintained from one generation to the next. The neutral theory claim that most of presently observed genetic variation in a population, and most of the variation from one population to another, did not arise as a result of selection but arose rather as a result of purely random changes in allelic frequencies. Retrospective population genetics theory focuses on the past history of a population rather than its future evolution.

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Mathematical Population Genetics

Cited by 1,167 publications

References 0 publications

The dynamics of molecular evolution over 60,000 generations

The dynamics of molecular evolution over 60,000 generations

A symmetry of fixation times in evoultionary dynamics

Population Genetics: Overview

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