King's formula for the mutation load with epistasis.

Abstract A formula by J. L. King gives the equilibrium mutation load as L = 2 sigma ui(1 - qi)/z - x) in which ui is the mutation rate to deleterious alleles at the ith locus, qi is the frequency of mutant alleles at this locus, x is the mean number of such mutant genes per individual before selection, z is the mean number in individuals eliminated by selection, and the summation is over all relevant loci. We show that this rule is inaccurate for intense selection and that a correct formula is L = 2 sigma ui(1 - qi) w/(z - x) = 2U w/(z - x) = 2U/(z - x + 2U) in which U is the mean number of new mutations per haploid genome in the population and w is the mean relative fitness before selection. If w/(z - x) less than 1/2, the mutation load is less than the Haldane value (U less than or equal to L less than or equal to 2U) and can be considerably less. In a diploid asexual population, however, with independent occurrence of mutations, L = 1 - e-2U regardless of the mode of selection.

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Accumulation of mutations in sexual and asexual populations

Genetics Research ◽

10.1017/s0016672300026938 ◽

1987 ◽

Vol 49 (2) ◽

pp. 135-146 ◽

Cited By ~ 98

Author(s):

Pekka Pamilo ◽

Masatoshi Nei ◽

Wen-Hsiung Li

Keyword(s):

Weak Selection ◽

Population Variance ◽

Asexual Population ◽

Term Evolution ◽

A Genome ◽

Analytical Formulae ◽

The Mean ◽

Asexual Populations ◽

Mutant Genes

SummaryThe accumulation of beneficial and harmful mutations in a genome is studied by using analytical methods as well as computer simulation for different modes of reproduction. The modes of reproduction examined are biparental (bisexual, hermaphroditic), uniparental (selfing, automictic, asexual) and mixed (partial selfing, mixture of hermaphroditism and parthenogenesis). It is shown that the rates of accumulation of both beneficial and harmful mutations with weak selection depend on the within-population variance of the number of mutant genes per genome. Analytical formulae for this variance are derived for neutral mutant genes for hermaphroditic, selfing and asexual populations; the neutral variance is largest in a selfing population and smallest in an asexual population. Directional selection reduces the population variance in most cases, whereas recombination partially restores the reduced variance. Therefore, biparental organisms accumulate beneficial mutations at the highest rate and harmful mutations at the lowest rate. Selfing organisms are intermediate between biparental and asexual organisms. Even a limited amount of outcrossing in largely selfing and parthenogenetic organisms markedly affects the accumulation rates. The accumulation of mutations is likely to affect the mean population fitness only in long-term evolution.

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Selection, Load and Inbreeding Depression in a Large Metapopulation

Genetics ◽

10.1093/genetics/160.3.1191 ◽

2002 ◽

Vol 160 (3) ◽

pp. 1191-1202 ◽

Cited By ~ 1

Author(s):

Michael C Whitlock

Keyword(s):

Population Structure ◽

Inbreeding Depression ◽

Population Subdivision ◽

Response To Selection ◽

Mutation Load ◽

Deleterious Alleles ◽

Subdivided Population ◽

Soft Selection ◽

Mean Fitness ◽

The Mean

Abstract The subdivision of a species into local populations causes its response to selection to change, even if selection is uniform across space. Population structure increases the frequency of homozygotes and therefore makes selection on homozygous effects more effective. However, population subdivision can increase the probability of competition among relatives, which may reduce the efficacy of selection. As a result, the response to selection can be either increased or decreased in a subdivided population relative to an undivided one, depending on the dominance coefficient FST and whether selection is hard or soft. Realistic levels of population structure tend to reduce the mean frequency of deleterious alleles. The mutation load tends to be decreased in a subdivided population for recessive alleles, as does the expected inbreeding depression. The magnitude of the effects of population subdivision tends to be greatest in species with hard selection rather than soft selection. Population structure can play an important role in determining the mean fitness of populations at equilibrium between mutation and selection.

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Multilocus models of inbreeding depression with synergistic selection and partial self-fertilization

Genetics Research ◽

10.1017/s0016672300029256 ◽

1991 ◽

Vol 57 (2) ◽

pp. 177-194 ◽

Cited By ~ 112

Author(s):

B. Charlesworth ◽

M. T. Morgan ◽

D. Charlesworth

Keyword(s):

Inbreeding Depression ◽

Mutation Rate ◽

Approximate Expression ◽

Heterozygote Advantage ◽

Selfing Rate ◽

Deleterious Alleles ◽

Plausible Model ◽

Computer Calculations ◽

Mean Fitness ◽

The Mean

SummaryMean fitness and inbreeding depression values in multi-locus models of the control of fitness were studied, using both a model of mutation to deleterious alleles, and a model of heterozygote advantage. Synergistic fitness interactions between loci were assumed, to find out if this more biologically plausible model altered the conclusions we obtained previously using a model of multiplicative interactions. Systems of unlinked loci were assumed. We used deterministic computer calculations, and approximations based on normal or Poisson theory. These approximations gave good agreement with the exact results for some regions of the parameter space. In the mutational model, we found that the effect of synergism was to lower the number of mutant alleles per individual, and thus to increase the mean fitness, compared with the multiplicative case. Inbreeding depression, however, was increased. Similar effects on mean fitness and inbreeding depression were found for the case of heterozygote advantage. For that model, the results were qualitatively similar to those previously obtained assuming multiplicativity. With the mutational load model, however, the mean fitness sometimes decreased, and the inbreeding depression increased, at high selfing rates, after declining as the selfing rate increased from zero. We also studied the behaviour of modifier alleles that changed the selfing rate, introduced into equilibrium populations. In general, the results were similar to those with the multiplicative model, but in some cases an ESS selfing rate, with selfing slightly below one, existed. Finally, we derive an approximate expression for the inbreeding depression in completely selfing populations. This depends only on the mutation rate and the dominance coefficient and can therefore be used to obtain estimates of the mutation rate to mildly deleterious alleles for plant species.

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The Effect of Deleterious Alleles on Adaptation in Asexual Populations

Genetics ◽

10.1093/genetics/162.1.395 ◽

2002 ◽

Vol 162 (1) ◽

pp. 395-411 ◽

Cited By ~ 2

Author(s):

Toby Johnson ◽

Nick H Barton

Keyword(s):

Selective Sweep ◽

Deleterious Mutation ◽

Short Interval ◽

Selective Advantage ◽

Asexual Population ◽

Restrictive Assumption ◽

Deleterious Alleles ◽

Fixation Probabilities ◽

Asexual Populations ◽

Beneficial Allele

Abstract We calculate the fixation probability of a beneficial allele that arises as the result of a unique mutation in an asexual population that is subject to recurrent deleterious mutation at rate U. Our analysis is an extension of previous works, which make a biologically restrictive assumption that selection against deleterious alleles is stronger than that on the beneficial allele of interest. We show that when selection against deleterious alleles is weak, beneficial alleles that confer a selective advantage that is small relative to U have greatly reduced probabilities of fixation. We discuss the consequences of this effect for the distribution of effects of alleles fixed during adaptation. We show that a selective sweep will increase the fixation probabilities of other beneficial mutations arising during some short interval afterward. We use the calculated fixation probabilities to estimate the expected rate of fitness improvement in an asexual population when beneficial alleles arise continually at some low rate proportional to U. We estimate the rate of mutation that is optimal in the sense that it maximizes this rate of fitness improvement. Again, this analysis relaxes the assumption made previously that selection against deleterious alleles is stronger than on beneficial alleles.

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The mutation load under tetrasomic inheritance and its consequences for the evolution of the selfing rate in autotetraploid species

Genetics Research ◽

10.1017/s0016672399003845 ◽

1999 ◽

Vol 74 (1) ◽

pp. 31-42 ◽

Cited By ~ 59

Author(s):

J. RONFORT

Keyword(s):

Inbreeding Depression ◽

Deleterious Mutation ◽

Stable State ◽

Approximate Solutions ◽

Balance Model ◽

Deleterious Mutations ◽

Selfing Rate ◽

Mutation Load ◽

Mean Fitness ◽

The Mean

Single-locus equilibrium frequencies of a partially recessive deleterious mutation under the mutation–selection balance model are derived for partially selfing autotetraploid populations. Assuming multiplicative fitness interactions among loci, approximate solutions for the mean fitness and inbreeding depression values are also derived for the multiple locus case and compared with expectations for the diploid model. As in diploids, purging of deleterious mutations through consanguineous matings occurs in autotetraploid populations, i.e. the equilibrium mutation load is a decreasing function of the selfing rate. However, the variation of inbreeding depression with the selfing rate depends strongly on the dominance coefficients associated with the three heterozygous genotypes. Inbreeding depression can either increase or decrease with the selfing rate, and does not always vary monotonically. Expected issues for the evolution of the selfing rate consequently differ depending on the dominance coefficients. In some cases, expectations for the evolution of the selfing rate resemble expectations in diploids; but particular sets of dominance coefficients can be found that lead to either complete selfing or intermediate selfing rates as unique evolutionary stable state.

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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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GENETIC VARIABILITY MAINTAINED BY MUTATION AND OVERDOMINANT SELECTION IN FINITE POPULATIONS

Genetics ◽

10.1093/genetics/98.2.441 ◽

1981 ◽

Vol 98 (2) ◽

pp. 441-459 ◽

Cited By ~ 2

Author(s):

Takeo Maruyama ◽

Masatoshi Nei

Keyword(s):

Mutation Rate ◽

Allozyme Polymorphism ◽

Random Genetic Drift ◽

Effective Population ◽

Mathematical Properties ◽

Overdominant Selection ◽

Mean And Variance ◽

The Mean ◽

Neutral Mutations ◽

The Relationship

ABSTRACT Mathematical properties of the overdominance model with mutation and random genetic drift are studied by using the method of stochastic differential equations (Itô and McKean 1974). It is shown that overdominant selection is very powerful in increasing the mean heterozygosity as compared with neutral mutations, and if 2Ns (N = effective population size; s = selective disadvantage for homozygotes) is larger than 10, a very low mutation rate is sufficient to explain the observed level of allozyme polymorphism. The distribution of heterozygosity for overdominant genes is considerably different from that of neutral mutations, and if the ratio of selection coefficient (s) to mutation rate (ν) is large and the mean heterozygosity (h) is lower than 0.2, single-locus heterozygosity is either approximately 0 or 0.5. If h increases further, however, heterozygosity shows a multiple-peak distribution. Reflecting this type of distribution, the relationship between the mean and variance of heterozygosity is considerably different from that for neutral genes. When s/v is large, the proportion of polymorphic loci increases approximately linearly with mean heterozygosity. The distribution of allele frequencies is also drastically different from that of neutral genes, and generally shows a peak at the intermediate gene frequency. Implications of these results on the maintenance of allozyme polymorphism are discussed.

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Extension of the Haldane-Muller principle of mutation load with application for estimating a possible range of relative evolution rate

Genetics Research ◽

10.1017/s0016672300022461 ◽

1985 ◽

Vol 46 (1) ◽

pp. 75-84 ◽

Cited By ~ 3

Author(s):

Kazushige Ishii ◽

Hirotsugu Matsuda

Keyword(s):

Mutation Rate ◽

Time Variation ◽

Evolution Rate ◽

Mutation Load ◽

Weak Selection ◽

Diploid Population ◽

Malthusian Parameter ◽

Haploid Population ◽

Range Of Values

SUMMARYThe Haldane-Muller principle of mutation load is generalized so as to be applicable to both cases of strong and very weak selection with any time variation. It is proved that in an infinite asexual haploid population, the average Malthusian parameter m¯ of a population, the evolution rate ν, and the total mutation rate μ satisfy the relation ∂m¯/∂/∂μ = ν/μ−1, so long as each Malthusian parameter is independent of μ. A similar result is also true in a diploid population under genie selection. It is discussed how the above relation gives a restriction on the possible range of values of relative evolution rate ν/μ.

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Predicting evolution from the shape of genealogical trees

eLife ◽

10.7554/elife.03568 ◽

2014 ◽

Vol 3 ◽

Cited By ~ 94

Author(s):

Richard A Neher ◽

Colin A Russell ◽

Boris I Shraiman

Keyword(s):

Influenza A ◽

Seasonal Influenza ◽

Historical Data ◽

Relative Fitness ◽

H3n2 Virus ◽

Asexual Population ◽

Genealogical Trees ◽

Branching Patterns ◽

Species Specific ◽

Evolution Proceeds

Given a sample of genome sequences from an asexual population, can one predict its evolutionary future? Here we demonstrate that the branching patterns of reconstructed genealogical trees contains information about the relative fitness of the sampled sequences and that this information can be used to predict successful strains. Our approach is based on the assumption that evolution proceeds by accumulation of small effect mutations, does not require species specific input and can be applied to any asexual population under persistent selection pressure. We demonstrate its performance using historical data on seasonal influenza A/H3N2 virus. We predict the progenitor lineage of the upcoming influenza season with near optimal performance in 30% of cases and make informative predictions in 16 out of 19 years. Beyond providing a tool for prediction, our ability to make informative predictions implies persistent fitness variation among circulating influenza A/H3N2 viruses.

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A stability property of the Ewens sampling formula

Journal of Applied Probability ◽

10.1017/s002190020002372x ◽

1983 ◽

Vol 20 (03) ◽

pp. 449-459

Author(s):

Stanley Sawyer

Keyword(s):

Population Size ◽

Error Bound ◽

Mutation Rate ◽

Stability Property ◽

Ewens Sampling Formula ◽

Sampling Formula ◽

Deleterious Alleles

An error bound for convergence to the Ewens sampling formula is given where the population size or mutation rate may vary from generation to generation, or the population is not yet at equilibrium. An application is given to a model of Hartl and Campbell about selectively-equivalent subtypes within a class of deleterious alleles, and a theorem is proven showing that the size of the deleterious class stays within bounds sufficient to apply the first result. Generalizations are discussed.

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