scholarly journals The divergence of a polygenic system subject to stabilizing selection, mutation and drift

1989 ◽  
Vol 54 (1) ◽  
pp. 59-78 ◽  
Author(s):  
Nick Barton
Keyword(s):  
Genetic Variance ◽  
Gaussian Approximation ◽  
Stabilizing Selection ◽  
Small Populations ◽  
Underlying Distribution ◽  
Wide Range ◽  
Population Sizes ◽  
Polygenic System ◽  
Gene Frequency Distribution ◽  
Polygenic Variation

SummaryPolygenic variation can be maintained by a balance between mutation and stabilizing selection. When the alleles responsible for variation are rare, many classes of equilibria may be stable. The rate at which drift causes shifts between equilibria is investigated by integrating the gene frequency distribution W̅2NΠ(pq)4Nμ−1. This integral can be found exactly, by numerical integration, or can be approximated by assuming that the full distribution of allele frequencies is approximately Gaussian. These methods are checked against simulations. Over a wide range of population sizes, drift will keep the population near an equilibrium which minimizes the genetic variance and the deviation from the selective optimum. Shifts between equilibria in this class occur at an appreciable rate if the product of population size and selection on each locus is small (Nsα2 < 10). The Gaussian approximation is accurate even when the underlying distribution is strongly skewed. Reproductive isolation evolves as populations shift to new combinations of alleles: however, this process is slow, approaching the neutral rate (≈ μ) in small populations.

scholarly journals Pleiotropic models of polygenic variation, stabilizing selection, and epistasis.

Genetics ◽  
1993 ◽  
Vol 134 (2) ◽  
pp. 609-625 ◽  
Author(s):  
S Gavrilets ◽  
G de Jong
Keyword(s):  
Genetic Variance ◽  
Genetic Load ◽  
Genetic System ◽  
Stabilizing Selection ◽  
Selection System ◽  
Genotypic Variance ◽  
Epistatic Model ◽  
Polygenic System ◽  
Polygenic Variation ◽  
Total Selection

Abstract We show that in polymorphic populations many polygenic traits pleiotropically related to fitness are expected to be under apparent "stabilizing selection" independently of the real selection acting on the population. This occurs, for example, if the genetic system is at a stable polymorphic equilibrium determined by selection and the nonadditive contributions of the loci to the trait value either are absent, or are random and independent of those to fitness. Stabilizing selection is also observed if the polygenic system is at an equilibrium determined by a balance between selection and mutation (or migration) when both additive and nonadditive contributions of the loci to the trait value are random and independent of those to fitness. We also compare different viability models that can maintain genetic variability at many loci with respect to their ability to account for the strong stabilizing selection on an additive trait. Let Vm be the genetic variance supplied by mutation (or migration) each generation, Vg be the genotypic variance maintained in the population, and n be the number of the loci influencing fitness. We demonstrate that in mutation (migration)-selection balance models the strength of apparent stabilizing selection is order Vm/Vg. In the overdominant model and in the symmetric viability model the strength of apparent stabilizing selection is approximately 1/(2n) that of total selection on the whole phenotype. We show that a selection system that involves pairwise additive by additive epistasis in maintaining variability can lead to a lower genetic load and genetic variance in fitness (approximately 1/(2n) times) than an equivalent selection system that involves overdominance. We show that, in the epistatic model, the apparent stabilizing selection on an additive trait can be as strong as the total selection on the whole phenotype.

scholarly journals Joint Effects of Pleiotropic Selection and Stabilizing Selection on the Maintenance of Quantitative Genetic Variation at Mutation-Selection Balance

Genetics ◽  
2002 ◽  
Vol 162 (1) ◽  
pp. 459-471 ◽  
Author(s):  
Xu-Sheng Zhang ◽  
William G Hill
Keyword(s):  
Genetic Variation ◽  
Genetic Variance ◽  
Stabilizing Selection ◽  
Limited Impact ◽  
Quantitative Genetic ◽  
High Heritability ◽  
Selection For ◽  
Selection Parameters ◽  
Mutation And Selection ◽  
Polygenic Variation

AbstractIn quantitative genetics, there are two basic “conflicting” observations: abundant polygenic variation and strong stabilizing selection that should rapidly deplete that variation. This conflict, although having attracted much theoretical attention, still stands open. Two classes of model have been proposed: real stabilizing selection directly on the metric trait under study and apparent stabilizing selection caused solely by the deleterious pleiotropic side effects of mutations on fitness. Here these models are combined and the total stabilizing selection observed is assumed to derive simultaneously through these two different mechanisms. Mutations have effects on a metric trait and on fitness, and both effects vary continuously. The genetic variance (VG) and the observed strength of total stabilizing selection (Vs,t) are analyzed with a rare-alleles model. Both kinds of selection reduce VG but their roles in depleting it are not independent: The magnitude of pleiotropic selection depends on real stabilizing selection and such dependence is subject to the shape of the distributions of mutational effects. The genetic variation maintained thus depends on the kurtosis as well as the variance of mutational effects: All else being equal, VG increases with increasing leptokurtosis of mutational effects on fitness, while for a given distribution of mutational effects on fitness, VG decreases with increasing leptokurtosis of mutational effects on the trait. The VG and Vs,t are determined primarily by real stabilizing selection while pleiotropic effects, which can be large, have only a limited impact. This finding provides some promise that a high heritability can be explained under strong total stabilizing selection for what are regarded as typical values of mutation and selection parameters.

scholarly journals The maintenance of polygenic variation through a balance between mutation and stabilizing selection

1986 ◽  
Vol 47 (3) ◽  
pp. 209-216 ◽  
Author(s):  
N. H. Barton
Keyword(s):  
Gaussian Approximation ◽  
Previous History ◽  
Stabilizing Selection ◽  
A Value ◽  
House Of Cards ◽  
History Of ◽  
Stable Equilibria ◽  
The Mean ◽  
Continuous Range ◽  
Polygenic Variation

SummaryThe maintenance of polygenic variation through a balance between mutation and stabilizing selection can be approximated in two ways. In the ‘Gaussian’ approximation, a normal distribution of allelic effects is assumed at each locus. In the ‘House of Cards’ approximation, the effect of new mutations is assumed to be large compared with the spread of the existing distribution. These approximations were developed to describe models where alleles may have a continuous range of effects. However, previous analyses of models with only two alleles have predicted an equilibrium variance equal to that given by the ‘House of Cards’ approximation. These analyses of biallelic models have assumed that, at equilibrium, the population mean is at the optimum. Here, it is shown that many stable equilibria may coexist, each giving a slight deviation from the optimum. Though the variance is given by the ‘House of Cards’ approximation when the mean is at the optimum, it increases towards a value of the same order as that given by the ‘Gaussian’ approximation when the mean deviates from the optimum. Thus, the equilibrium variance cannot be predicted by any simple model, but depends on the previous history of the population.

scholarly journals Heritable variation and heterozygosity under a balance between mutations and stabilizing selection

1987 ◽  
Vol 50 (1) ◽  
pp. 53-62 ◽  
Author(s):  
Montgomery Slatkin
Keyword(s):  
Genetic Variance ◽  
Normal Approximation ◽  
Quantitative Character ◽  
Stabilizing Selection ◽  
Heritable Variation ◽  
House Of Cards ◽  
Wide Range ◽  
Electrophoretic Data ◽  
Haploid Species ◽  
Parameter Values

SummaryA model of the balance between mutations and stabilizing selection affecting a quantitative character is developed and analysed. This model is essentially a discretized version of the continuum-of-alleles models analysed previously by Kimura, Lande, Turelli and others, and is formally similar to the stepwise mutation models used to interpret electrophoretic data. The complete model cannot be solved even for a haploid species, but there are useful approximations for most parameter values of interest. The ‘house-of-cards’ approximation can be used when selection is strong relative to mutation, and a normal approximation can be used when selection is relatively weak. For intermediate levels of selection a new ‘five-allele’ approximation provides accurate results over a wide range of parameter values. The house-of-cards and five-allele approximations applied to recessive alleles in a diploid population show that, for a given mutation rate, a somewhat larger genetic variance is maintained at equilibrium than in a comparable model of additive alleles. Under directional selection, the increase in genetic variance is largest for alleles of large effect and is much smaller for alleles of intermediate or small effect. At an equilibrium under stabilizing selection, homozygotes would tend to have a higher average fitness than heterozygotes when each mutation has a relatively large effect (the house-of-cards approximation), with the reverse if each mutation has a small effect (the normal approximation).

Maintenance of Quantitative Genetic Variation

2018 ◽  
Author(s):  
Bruce Walsh ◽  
Michael Lynch
Keyword(s):  
Genetic Variation ◽  
Quantitative Genetics ◽  
Stabilizing Selection ◽  
Quantitative Genetic ◽  
Wide Range

One of the major unresolved issues in quantitative genetics is what accounts for the amount of standing genetic variation in traits. A wide range of models, all reviewed in this chapter, have been proposed, but none fit the data, either giving too much variation or too little apparent stabilizing selection.

scholarly journals Recombination Can Evolve in Large Finite Populations Given Selection on Sufficient Loci

Genetics ◽  
2003 ◽  
Vol 165 (4) ◽  
pp. 2249-2258 ◽  
Author(s):  
Mark M Iles ◽  
Kevin Walters ◽  
Chris Cannings
Keyword(s):  
Experimental Evidence ◽  
Genetic Drift ◽  
Finite Population ◽  
Selective Advantage ◽  
Indirect Selection ◽  
Small Populations ◽  
Finite Populations ◽  
Population Sizes ◽  
Population Recombination

AbstractIt is well known that an allele causing increased recombination is expected to proliferate as a result of genetic drift in a finite population undergoing selection, without requiring other mechanisms. This is supported by recent simulations apparently demonstrating that, in small populations, drift is more important than epistasis in increasing recombination, with this effect disappearing in larger finite populations. However, recent experimental evidence finds a greater advantage for recombination in larger populations. These results are reconciled by demonstrating through simulation without epistasis that for m loci recombination has an appreciable selective advantage over a range of population sizes (am, bm). bm increases steadily with m while am remains fairly static. Thus, however large the finite population, if selection acts on sufficiently many loci, an allele that increases recombination is selected for. We show that as selection acts on our finite population, recombination increases the variance in expected log fitness, causing indirect selection on a recombination-modifying locus. This effect is enhanced in those populations with more loci because the variance in phenotypic fitnesses in relation to the possible range will be smaller. Thus fixation of a particular haplotype is less likely to occur, increasing the advantage of recombination.

scholarly journals 2000 Fleming Lecture. The origin and evolution of hepatitis viruses in humans

2001 ◽  
Vol 82 (4) ◽  
pp. 693-712 ◽  
Author(s):  
Peter Simmonds
Keyword(s):  
Large Population ◽  
Human Populations ◽  
Hepatitis Viruses ◽  
Hepatitis G Virus ◽  
Origin And Evolution ◽  
Wide Range ◽  
Population Sizes ◽  
History Of ◽  
Virus C ◽  
Time Of Divergence

The spread and origins of hepatitis C virus (HCV) in human populations have been the subject of extensive investigations, not least because of the importance this information would provide in predicting clinical outcomes and controlling spread of HCV in the future. However, in the absence of historical and archaeological records of infection, the evolution of HCV and other human hepatitis viruses can only be inferred indirectly from their epidemiology and by genetic analysis of contemporary virus populations. Some information on the history of the latter may be obtained by dating the time of divergence of various genotypes of HCV, hepatitis B virus (HBV) and the non-pathogenic hepatitis G virus (HGV)/GB virus-C (GBV-C). However, the relatively recent times predicted for the origin of these viruses fit poorly with their epidemiological distributions and the recent evidence for species-associated variants of HBV and HGV/GBV-C in a wide range of non-human primates. The apparent conservatism of viruses over long periods implied by these latter observations may be the result of constraints on sequence change peculiar to viruses with single-stranded genomes, or with overlapping reading frames. Large population sizes and intense selection pressures that optimize fitness may be the factors that set virus evolution apart from that of their hosts.

scholarly journals Direct Optimal Control Approach to Laser-Driven Quantum Particle Dynamics

2021 ◽  
Vol 9 ◽  
Author(s):  
A. R. Ramos Ramos ◽  
O. Kühn
Keyword(s):  
Optimal Control ◽  
Gaussian Approximation ◽  
Gaussian Function ◽  
Dynamical Equations ◽  
Control Approach ◽  
Wide Range ◽  
Bistable Potential ◽  
Wavepacket Dynamics ◽  
Direct Optimal Control ◽  
Backward Propagation

Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets. Here, we propose direct optimal control as a robust and flexible alternative. It is based on a discretization of the dynamical equations resulting in a nonlinear optimization problem. The method is illustrated for the case of laser-driven wavepacket dynamics in a bistable potential. The wavepacket is parameterized in terms of a single Gaussian function and field optimization is performed for a wide range of particle masses and lengths of the control interval. Using the optimized field in a full quantum propagation still yields reasonable control yields for most of the considered cases. Analysis of the deviations leads to conditions which have to be fulfilled to make the semiclassical single Gaussian approximation meaningful for field optimization.

Genetic and statistical analyses of strong selection on polygenic traits: what, me normal?

Genetics ◽  
1994 ◽  
Vol 138 (3) ◽  
pp. 913-941 ◽  
Author(s):  
M Turelli ◽  
N H Barton
Keyword(s):  
Allele Frequency ◽  
Genetic Variance ◽  
Gaussian Approximation ◽  
Selection Response ◽  
Disruptive Selection ◽  
Breeding Values ◽  
Central Moments ◽  
Linkage Disequilibria ◽  
The Mean ◽  
Frequency Changes

Abstract We develop a general population genetic framework for analyzing selection on many loci, and apply it to strong truncation and disruptive selection on an additive polygenic trait. We first present statistical methods for analyzing the infinitesimal model, in which offspring breeding values are normally distributed around the mean of the parents, with fixed variance. These show that the usual assumption of a Gaussian distribution of breeding values in the population gives remarkably accurate predictions for the mean and the variance, even when disruptive selection generates substantial deviations from normality. We then set out a general genetic analysis of selection and recombination. The population is represented by multilocus cumulants describing the distribution of haploid genotypes, and selection is described by the relation between mean fitness and these cumulants. We provide exact recursions in terms of generating functions for the effects of selection on non-central moments. The effects of recombination are simply calculated as a weighted sum over all the permutations produced by meiosis. Finally, the new cumulants that describe the next generation are computed from the non-central moments. Although this scheme is applied here in detail only to selection on an additive trait, it is quite general. For arbitrary epistasis and linkage, we describe a consistent infinitesimal limit in which the short-term selection response is dominated by infinitesimal allele frequency changes and linkage disequilibria. Numerical multilocus results show that the standard Gaussian approximation gives accurate predictions for the dynamics of the mean and genetic variance in this limit. Even with intense truncation selection, linkage disequilibria of order three and higher never cause much deviation from normality. Thus, the empirical deviations frequently found between predicted and observed responses to artificial selection are not caused by linkage-disequilibrium-induced departures from normality. Disruptive selection can generate substantial four-way disequilibria, and hence kurtosis; but even then, the Gaussian assumption predicts the variance accurately. In contrast to the apparent simplicity of the infinitesimal limit, data suggest that changes in genetic variance after 10 or more generations of selection are likely to be dominated by allele frequency dynamics that depend on genetic details.

Sign in / Sign up

Export Citation Format

Share Document