Effects of mutation on selection limits in finite populations with multiple alleles.

Abstract The ultimate response to directional selection (i.e., the selection limit) under recurrent mutation is analyzed by a diffusion approximation for a population in which there are k possible alleles at a locus. The limit mainly depends on two scaled parameters S (= 4Ns sigma a) and theta (= 4Nu) and k, the number of alleles, where N is the effective population size, u is the mutation rate, s is the selection coefficient, and sigma 2a is the variance of allelic effects. When the selection pressure is weak (S less than or equal to 0.5), the limit is given approximately by 2S sigma a[1 - (1 + c2)/k]/(theta + 1) for additive effects of alleles, where c is the coefficient of variation of the mutation rates among alleles. For strong selection, other approximations are devised to analyze the limit in different parameter regions. The effect of mutation on selection limits largely relies on the potential of mutation to introduce new and better alleles into the population. This effect is, however, bounded under the present model. Unequal mutation rates among alleles tend to reduce the selection limit, and can have a substantial effect only for small numbers of alleles and weak selection. The selection limit decreases as the mutation rate increases.

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THE DYNAMICS OF FINITE HAPLOID POPULATIONS WITH OVERLAPPING GENERATIONS. II. THE DIFFUSION APPROXIMATION

Genetics ◽

10.1093/genetics/92.1.339 ◽

1979 ◽

Vol 92 (1) ◽

pp. 339-351

Author(s):

Ted H Emigh

Keyword(s):

Population Size ◽

Effective Population Size ◽

Diffusion Approximation ◽

Overlapping Generations ◽

Mutation Rates ◽

Reproductive Value ◽

Selection Coefficient ◽

Effective Population ◽

Haploid Population

ABSTRACT The dynamics of a gene in a haploid population can be explained approximately by considering the average reproductive value of the gene. The dynamics of the average reproductive value are similar to those of a gene in a population with nonoverlapping generations with the following modifications: The effective population size, Ne, replaces N; the average mutation rates,μ* and v* replace μ and v; the average overall selection r*+(T-l)s** replaces s; and time is measured in terms of generations, T. The implications of the average selection coefficient to adaptive life histones are discussed.

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Joint inference of demography and mutation rates from polymorphism data and pedigrees

10.1101/091090 ◽

2016 ◽

Author(s):

Florence Parat ◽

Sándor Miklós Szilágyi ◽

Daniel Wegmann ◽

Aurélien Tellier

Keyword(s):

Mutation Rate ◽

Overlapping Generations ◽

Genetic Data ◽

Mutation Rates ◽

Pedigree Information ◽

Pedigree Data ◽

Computationally Efficient ◽

Effective Population ◽

Joint Inference ◽

Major Interest

ABSTRACTInference of demography and mutation rates is of major interest but difficult because genetic data is only informative about the population mutation rate, the product of the effective population size times the mutation rate, and not about these quantities individually. Here we show that this limitation can be overcome by combining genetic data with pedigree information. To successfully use pedigree data, however, important aspects of real populations such as the presence of two sexes, unbalanced sex ratios and overlapping generations have to be taken into account. We present here an extension of the classic Wright-Fisher model accounting for these effects and show that the coalescent process under this model reduces to the classic Kingman coalescent with specific scaling parameters. We further derive the probability of a pedigree under that model and show how pedigree data can thus be used to infer demographic parameters. Finally, we present a computationally efficient inference approach combining pedigree information and genetic data summarized by the site frequency spectrum (SFS) that allows for the joint inference of the mutation rate, sex-specific population sizes and the fraction of overlapping generations. Using simulations we then show that these parameters can be accurately inferred from pedigrees spanning just a few generations, as are available for many species. We finally discuss future possible extensions of the model and inference framework necessary for applications to wild and domesticated species, namely the account for more complex demographies and the uncertainty in assigning pedigree individuals to specific generations.

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Estimation of universal and taxon-specific parameters of prokaryotic genome evolution

10.1101/137430 ◽

2017 ◽

Author(s):

Itamar Sela ◽

Yuri I. Wolf ◽

Eugene V. Koonin

Keyword(s):

Genome Evolution ◽

Ad Hoc ◽

Prokaryotic Genome ◽

Microbial Genome ◽

Selection Coefficient ◽

Effective Population ◽

Weak Selection ◽

Gene Acquisition ◽

Population Sizes ◽

The Mean

AbstractOur recent study on mathematical modeling of microbial genome evolution indicated that, on average, genomes of bacteria and archaea evolve in the regime of mutation-selection balance defined by positive selection coefficients associated with gene acquisition that is counter-acted by the intrinsic deletion bias. This analysis was based on the strong assumption that parameters of genome evolution are universal across the diversity of bacteria and archaea, and yielded extremely low values of the selection coefficient. Here we further refine the modeling approach by taking into account evolutionary factors specific for individual groups of microbes using two independent fitting strategies, an ad hoc hard fitting scheme and an hierarchical Bayesian model. The resulting estimate of the mean selection coefficient of s∼10-10 associated with the gain of one gene implies that, on average, acquisition of a gene is beneficial, and that microbial genomes typically evolve under a weak selection regime that might transition to strong selection in highly abundant organisms with large effective population sizes. The apparent selective pressure towards larger genomes is balanced by the deletion bias, which is estimated to be consistently greater than unity for all analyzed groups of microbes. The estimated values of s are more realistic than the lower values obtained previously, indicating that global and group-specific evolutionary factors synergistically affect microbial genome evolution that seems to be driven primarily by adaptation to existence in diverse niches.

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Evolution of mutation rates in hypermutable populations of Escherichia coli propagated at very small effective population size

Biology Letters ◽

10.1098/rsbl.2016.0849 ◽

2017 ◽

Vol 13 (3) ◽

pp. 20160849 ◽

Cited By ~ 7

Author(s):

Tanya Singh ◽

Meredith Hyun ◽

Paul Sniegowski

Keyword(s):

Escherichia Coli ◽

Genetic Variation ◽

Mutation Rate ◽

Mutation Rates ◽

Deleterious Mutations ◽

Effective Population ◽

Ultimate Source ◽

Systematic Evolution ◽

Small Effective Size ◽

Small Effective Population Size

Mutation is the ultimate source of the genetic variation—including variation for mutation rate itself—that fuels evolution. Natural selection can raise or lower the genomic mutation rate of a population by changing the frequencies of mutation rate modifier alleles associated with beneficial and deleterious mutations. Existing theory and observations suggest that where selection is minimized, rapid systematic evolution of mutation rate either up or down is unlikely. Here, we report systematic evolution of higher and lower mutation rates in replicate hypermutable Escherichia coli populations experimentally propagated at very small effective size—a circumstance under which selection is greatly reduced. Several populations went extinct during this experiment, and these populations tended to evolve elevated mutation rates. In contrast, populations that survived to the end of the experiment tended to evolve decreased mutation rates. We discuss the relevance of our results to current ideas about the evolution, maintenance and consequences of high mutation rates.

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Modifiers of mutation-selection balance: general approach and the evolution of mutation rates

Genetics Research ◽

10.1017/s001667230003439x ◽

1995 ◽

Vol 66 (1) ◽

pp. 53-69 ◽

Cited By ~ 71

Author(s):

Alexey S. Kondrashov

Keyword(s):

Mutation Rate ◽

Mutant Allele ◽

Deleterious Mutation ◽

Mutation Rates ◽

Quasi Equilibrium ◽

Selection Differential ◽

Selection Coefficient ◽

Modifier Locus ◽

Ratio Of Variances ◽

The Cost

SummaryA general approach is developed to estimate secondary selection at a modifier locus that influences some feature of a population under mutation-selection balance. The approach is based on the assumption that the properties of all available genotypes at this locus are similar. Then mutation-selection balance and weak associations between genotype distributions at selectable loci and the modifier locus are established rapidly. In contrast, changes of frequencies of the modifier genotypes are slow, and lead to only slow and small changes of the other features of the population. Thus, while these changes occur, the population remains in a state of quasi-equilibrium, where the mutation-selection balance and the associations between the selectable loci and the modifier locus are almost invariant. Selection at the modifier locus can be estimated by calculating quasiequilibrium values of these associations. This approach is developed for the situation where distributions of the number of mutations per genome within the individuals with a given modifier genotype are close to Gaussian. The results are used to study the evolution of the mutation rate. Because beneficial mutations are ignored, secondary selection at the modifier locus always diminishes the mutation rate. The coefficient of selection against an allele which increases the mutation rate by υ is approximately υδ2/[U(2−ρ)] = υŝ, where υ is the genomic deleterious mutation rate, δ is the selection differential of the number of mutations per individual in units of the standard deviation of the distribution of this number in the population, ρ is the ratio of variances of the number of mutations after and before selection, and ŝ is the selection coefficient against a mutant allele in the quasiequilibrium population. However, the decline of the mutation rate can be counterbalanced by the cost of fidelity, which can lead to an evolutionary equilibrium mutation rate.

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Evolution of Mutation Rate in Astronomically Large Phytoplankton Populations

Genome Biology and Evolution ◽

10.1093/gbe/evaa131 ◽

2020 ◽

Vol 12 (7) ◽

pp. 1051-1059

Author(s):

Marc Krasovec ◽

Rosalind E M Rickaby ◽

Dmitry A Filatov

Keyword(s):

Genetic Diversity ◽

Population Size ◽

Mutation Rate ◽

Spontaneous Mutation ◽

Large Population ◽

Marine Phytoplankton ◽

Mutation Rates ◽

Effective Population ◽

Spontaneous Mutation Rate ◽

Large Populations

Abstract Genetic diversity is expected to be proportional to population size, yet, there is a well-known, but unexplained lack of genetic diversity in large populations—the “Lewontin’s paradox.” Larger populations are expected to evolve lower mutation rates, which may help to explain this paradox. Here, we test this conjecture by measuring the spontaneous mutation rate in a ubiquitous unicellular marine phytoplankton species Emiliania huxleyi (Haptophyta) that has modest genetic diversity despite an astronomically large population size. Genome sequencing of E. huxleyi mutation accumulation lines revealed 455 mutations, with an unusual GC-biased mutation spectrum. This yielded an estimate of the per site mutation rate µ = 5.55×10−10 (CI 95%: 5.05×10−10 – 6.09×10−10), which corresponds to an effective population size Ne ∼ 2.7×106. Such a modest Ne is surprising for a ubiquitous and abundant species that accounts for up to 10% of global primary productivity in the oceans. Our results indicate that even exceptionally large populations do not evolve mutation rates lower than ∼10−10 per nucleotide per cell division. Consequently, the extreme disparity between modest genetic diversity and astronomically large population size in the plankton species cannot be explained by an unusually low mutation rate.

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Genome wide estimates of mutation rates and spectrum in Schizosaccharomyces pombe indicate CpG sites are highly mutagenic despite the absence of DNA methylation

10.1101/025601 ◽

2015 ◽

Author(s):

Megan G Behringer ◽

David W Hall

Keyword(s):

Schizosaccharomyces Pombe ◽

Mutation Rate ◽

Life Histories ◽

Mutation Rates ◽

Effective Population ◽

Additional Mechanism ◽

Yeast Saccharomyces Cerevisiae ◽

Ascomycetous Yeast ◽

Cpg Dinucleotides ◽

Genome Wide

We accumulated mutations for 1952 generations in 79 initially identical, haploid lines of the fission yeast Schizosaccharomyces pombe and then performed whole-genome sequencing to determine the mutation rates and spectrum. We captured 696 spontaneous mutations across the 79 mutation accumulation lines. We compared the mutation spectrum and rate to another model ascomycetous yeast, the budding yeast Saccharomyces cerevisiae. While the two organisms are approximately 600 million years diverged from each other, they share similar life histories, genome size and genomic G/C content. We found that Sc. pombe and S. cerevisiae have similar mutation rates, contrary to what was expected given Sc. pombe’s smaller reported effective population size. Sc. pombe’s also exhibits a strong insertion bias in comparison to S. cerevisiae,. Intriguingly, we observed an increased mutation rate at cytosine nucleotides, specifically CpG nucleotides, which is also seen in S. cerevisiae. However, the absence of methylation in Sc. pombe and the pattern of mutation at these sites, primarily C→ A as opposed to C→T, strongly suggest that the increased mutation rate is not caused by deamination of methylated cytosines. This result implies that the high mutability of CpG dinucleotides in other species may be caused in part by an additional mechanism than methylation.

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The Effect of Selection on Genealogies

Genetics ◽

10.1093/genetics/166.2.1115 ◽

2004 ◽

Vol 166 (2) ◽

pp. 1115-1131 ◽

Cited By ~ 3

Author(s):

N H Barton ◽

A M Etheridge

Keyword(s):

Allele Frequency ◽

Balancing Selection ◽

Purifying Selection ◽

Mutation Rates ◽

Deleterious Mutations ◽

Selection Coefficient ◽

Weak Selection ◽

Random Drift ◽

Genotype Frequencies ◽

Coalescence Times

Abstract The coalescent process can describe the effects of selection at linked loci only if selection is so strong that genotype frequencies evolve deterministically. Here, we develop methods proposed by Kaplan, Darden, and Hudson to find the effects of weak selection. We show that the overall effect is given by an extension to Price’s equation: the change in properties such as moments of coalescence times is equal to the covariance between those properties and the fitness of the sample of genes. The distribution of coalescence times differs substantially between allelic classes, even in the absence of selection. However, the average coalescence time between randomly chosen genes is insensitive to the current allele frequency and is affected significantly by purifying selection only if deleterious mutations are common and selection is strong (i.e., the product of population size and selection coefficient, Ns > 3). Balancing selection increases mean coalescence times, but the effect becomes large only when mutation rates between allelic classes are low and when selection is extremely strong. Our analysis supports previous simulations that show that selection has surprisingly little effect on genealogies. Moreover, small fluctuations in allele frequency due to random drift can greatly reduce any such effects. This will make it difficult to detect the action of selection from neutral variation alone.

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A phylogenetic estimator of effective population size or mutation rate.

Genetics ◽

10.1093/genetics/136.2.685 ◽

1994 ◽

Vol 136 (2) ◽

pp. 685-692 ◽

Cited By ~ 1

Author(s):

Y X Fu

Keyword(s):

Population Size ◽

Effective Population Size ◽

Mutation Rate ◽

Dna Sequences ◽

High Efficiency ◽

Minimum Variance ◽

Population Subdivision ◽

Effective Population ◽

Fisher Model ◽

Mitochondrial Sequences

Abstract A new estimator of the essential parameter theta = 4Ne mu from DNA polymorphism data is developed under the neutral Wright-Fisher model without recombination and population subdivision, where Ne is the effective population size and mu is the mutation rate per locus per generation. The new estimator has a variance only slightly larger than the minimum variance of all possible unbiased estimators of the parameter and is substantially smaller than that of any existing estimator. The high efficiency of the new estimator is achieved by making full use of phylogenetic information in a sample of DNA sequences from a population. An example of estimating theta by the new method is presented using the mitochondrial sequences from an American Indian population.

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Mutation rate analysis via parent–progeny sequencing of the perennial peach. II. No evidence for recombination-associated mutation

Proceedings of The Royal Society B Biological Sciences ◽

10.1098/rspb.2016.1785 ◽

2016 ◽

Vol 283 (1841) ◽

pp. 20161785 ◽

Cited By ~ 4

Author(s):

Long Wang ◽

Yanchun Zhang ◽

Chao Qin ◽

Dacheng Tian ◽

Sihai Yang ◽

...

Keyword(s):

Mutation Rate ◽

Recombination Rate ◽

Mutation Rates ◽

Recombination Rates ◽

Rate Analysis ◽

A Genome ◽

Break Points ◽

New Mutations

Mutation rates and recombination rates vary between species and between regions within a genome. What are the determinants of these forms of variation? Prior evidence has suggested that the recombination might be mutagenic with an excess of new mutations in the vicinity of recombination break points. As it is conjectured that domesticated taxa have higher recombination rates than wild ones, we expect domesticated taxa to have raised mutation rates. Here, we use parent–offspring sequencing in domesticated and wild peach to ask (i) whether recombination is mutagenic, and (ii) whether domesticated peach has a higher recombination rate than wild peach. We find no evidence that domesticated peach has an increased recombination rate, nor an increased mutation rate near recombination events. If recombination is mutagenic in this taxa, the effect is too weak to be detected by our analysis. While an absence of recombination-associated mutation might explain an absence of a recombination–heterozygozity correlation in peach, we caution against such an interpretation.

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