scholarly journals Pleiotropic Model of Maintenance of Quantitative Genetic Variation at Mutation-Selection Balance

Genetics ◽  
2002 ◽  
Vol 161 (1) ◽  
pp. 419-433 ◽  
Author(s):  
Xu-Sheng Zhang ◽  
Jinliang Wang ◽  
William G Hill
Keyword(s):  
Genetic Variation ◽  
Genetic Variance ◽  
Large Population ◽  
Stabilizing Selection ◽  
Fitness Effect ◽  
Environmental Variance ◽  
Quantitative Genetic ◽  
Phenotypic Standard Deviation ◽  
Bivariate Gamma Distribution ◽  
Mutational Variance

AbstractA pleiotropic model of maintenance of quantitative genetic variation at mutation-selection balance is investigated. Mutations have effects on a metric trait and deleterious effects on fitness, for which a bivariate gamma distribution is assumed. Equations for calculating the strength of apparent stabilizing selection (Vs) and the genetic variance maintained in segregating populations (VG) were derived. A large population can hold a high genetic variance but the apparent stabilizing selection may or may not be relatively strong, depending on other properties such as the distribution of mutation effects. If the distribution of mutation effects on fitness is continuous such that there are few nearly neutral mutants, or a minimum fitness effect is assumed if most mutations are nearly neutral, VG increases to an asymptote as the population size increases. Both VG and Vs are strongly affected by the shape of the distribution of mutation effects. Compared with mutants of equal effect, allowing their effects on fitness to vary across loci can produce a much higher VG but also a high Vs (Vs in phenotypic standard deviation units, which is always larger than the ratio VP/Vm), implying weak apparent stabilizing selection. If the mutational variance Vm is ∼10-3  Ve (Ve, environmental variance), the model can explain typical values of heritability and also apparent stabilizing selection, provided the latter is quite weak as suggested by a recent review.

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 Linkage and the maintenance of variation for quantitative traits by mutation–selection balance: an infinitesimal model

1998 ◽  
Vol 71 (2) ◽  
pp. 161-170 ◽  
Author(s):  
ENRIQUE SANTIAGO
Keyword(s):  
Quantitative Traits ◽  
Genetic Variance ◽  
Chromosome Length ◽  
Stabilizing Selection ◽  
Effective Population ◽  
Environmental Variance ◽  
Homologous Chromosomes ◽  
Quadratic Equations ◽  
Mutational Variance ◽  
The Continuum

The infinitesimal model is extended to cover linkage in finite populations. General equations to predict the dynamics of the genetic variation under the joint effects of mutation, selection and drift are derived. Under truncation and stabilizing selection, the quadratic equations for the asymptotic genetic variance (VG) are respectivelyV2G(1+kS)+VG (Ve−2NeVm) −2NeVmVe=0andV2G(1+S)+VG (Ve+γ−2NeVm) −2NeVm(Ve+γ)=0,where Ne is the effective population size, Vm is the mutational variance, Ve is the environmental variance, γ is the parameter that measures the spread of fitness around the optimum under stabilizing selection, k is equal to i(i−x) where i is the selection intensity and x is the cut-off point under truncation selection. The term S is a function of the number of chromosomes (v) and the average chromosome length (l):formula hereThese predictions are accurate when compared with results of simulations of small populations unless the number of genes is small. The infinitesimal model reduces to the continuum of alleles model if there is no recombination between homologous chromosomes.

Is Function of the Drosophila Homeotic Gene Ultrabithorax Canalized?

Genetics ◽  
1997 ◽  
Vol 147 (3) ◽  
pp. 1155-1168 ◽  
Author(s):  
Greg Gibson ◽  
Sylvie van Helden
Keyword(s):  
Genetic Variance ◽  
Population Level ◽  
Homeotic Gene ◽  
Stabilizing Selection ◽  
Homeotic Genes ◽  
Wild Type ◽  
Isofemale Lines ◽  
Environmental Variance ◽  
Quantitative Genetic ◽  
Genetic Contributions

Genetic variation affecting the expressivity of an amorphic allele of the homeotic gene Ultrabithorax, (Ubx1) was characterized after 11 generations of introgression into 29 different isofemale lines. Heterozygotes display a range of haploinsufficient phenotypes, from overlap with wild-type halteres to dramatic transformations such as a 50% increase in area and the presence of over 20 bristles on the anterior margin of each haltere. In both the wild-type and mutant genetic backgrounds, there is moderate genetic variance and low environmental variance/developmental asymmetry, as expected of a trait under stabilizing selection pressure. Surprisingly, there is little evidence that mutant halteres are more variable than wild-type ones, so it is unclear that haltere development is also canalized. The correlation between wild-type and Ubx haltere size is very low, indicating that interactions among modifiers of Ubx are complex, and in some cases sex-specific. The potential quantitative genetic contributions of homeotic genes to appendage morphology are discussed, noting that population-level effects of variation in key regulatory genes may be prevalent and complex but cannot be readily extrapolated to macroevolutionary diversification.

scholarly journals Quantitative genetic variability maintained by mutation-stabilizing selection balance in finite populations

1988 ◽  
Vol 52 (1) ◽  
pp. 33-43 ◽  
Author(s):  
Peter D. Keightley ◽  
William G. Hill
Keyword(s):  
Standard Deviation ◽  
Quantitative Traits ◽  
Genetic Variance ◽  
Finite Population ◽  
Stabilizing Selection ◽  
Infinite Population ◽  
Quantitative Genetic ◽  
Optimum Model ◽  
Mutational Variance ◽  
Allele Model

SummaryModels of variability in quantitative traits maintained by a balance between mutation and stabilizing selection are investigated. The effects of mutant alleles are assumed to be additive and to be randomly sampled from a stationary distribution. With a two-allele model the equilibrium genetic variance in an infinite population is independent of the distribution of mutant effects, and dependent only on the total number of mutants appearing per generation. In a finite population, however, both the shape and standard deviation of the distribution of mutant effects are important. The equilibrium variance is lower when most of the mutational variance is contributed by few genes of large effect. Genes of small effect can eventually contribute substantially to the variance with increasing population size (N.) The equilibrium variance can be higher in a finite than an infinite population since near-neutral alleles can drift to intermediate frequencies where selection is weakest. Linkage leads to a reduction in the maintained variance which is small unless linkage is very tight and selection is strong, but the reduction becomes greater with increasing N since more mutants segregate. A multi-allele model is simulated and it is concluded that the two-allele model gives a good approximation of its behaviour. It is argued that the total number of loci capable of influencing most quantitative traits is large, and that the distribution of mutant effects is highly leptokurtic with the effects of most mutants very small, and such mutants are important in contributing to the maintained variance since selection against them is slight. The weakness of the simple optimum model is discussed in relation to the likely consequences of pleiotropy.

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 Characterization of Deleterious Mutations in Outcrossing Populations

Genetics ◽  
1998 ◽  
Vol 150 (2) ◽  
pp. 945-956 ◽  
Author(s):  
Hong-Wen Deng
Keyword(s):  
Genetic Variation ◽  
Genetic Variance ◽  
Estimation Bias ◽  
Deleterious Mutations ◽  
Environmental Variance ◽  
Higher Power ◽  
Sib Mating ◽  
The Mean ◽  
Simulation Results

Abstract Deng and Lynch recently proposed estimating the rate and effects of deleterious genomic mutations from changes in the mean and genetic variance of fitness upon selfing/outcrossing in outcrossing/highly selfing populations. The utility of our original estimation approach is limited in outcrossing populations, since selfing may not always be feasible. Here we extend the approach to any form of inbreeding in outcrossing populations. By simulations, the statistical properties of the estimation under a common form of inbreeding (sib mating) are investigated under a range of biologically plausible situations. The efficiencies of different degrees of inbreeding and two different experimental designs of estimation are also investigated. We found that estimation using the total genetic variation in the inbred generation is generally more efficient than employing the genetic variation among the mean of inbred families, and that higher degree of inbreeding employed in experiments yields higher power for estimation. The simulation results of the magnitude and direction of estimation bias under variable or epistatic mutation effects may provide a basis for accurate inferences of deleterious mutations. Simulations accounting for environmental variance of fitness suggest that, under full-sib mating, our extension can achieve reasonably well an estimation with sample sizes of only ∼2000-3000.

scholarly journals Quantitative genetic variability maintained by mutation-stabilizing selection balance: sampling variation and response to subsequent directional selection

1989 ◽  
Vol 54 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Peter D. Keightley ◽  
William G. Hill
Keyword(s):  
Genetic Variance ◽  
Directional Selection ◽  
Quantitative Character ◽  
Stabilizing Selection ◽  
Effective Population ◽  
Selection Responses ◽  
Quantitative Genetic ◽  
Before And After ◽  
Cage Population ◽  
Selection Of

SummaryA model of genetic variation of a quantitative character subject to the simultaneous effects of mutation, selection and drift is investigated. Predictions are obtained for the variance of the genetic variance among independent lines at equilibrium with stabilizing selection. These indicate that the coefficient of variation of the genetic variance among lines is relatively insensitive to the strength of stabilizing selection on the character. The effects on the genetic variance of a change of mode of selection from stabilizing to directional selection are investigated. This is intended to model directional selection of a character in a sample of individuals from a natural or long-established cage population. The pattern of change of variance from directional selection is strongly influenced by the strengths of selection at individual loci in relation to effective population size before and after the change of regime. Patterns of change of variance and selection responses from Monte Carlo simulation are compared to selection responses observed in experiments. These indicate that changes in variance with directional selection are not very different from those due to drift alone in the experiments, and do not necessarily give information on the presence of stabilizing selection or its strength.

scholarly journals Genetic constraints predict evolutionary divergence in Dalechampia blossoms

2014 ◽  
Vol 369 (1649) ◽  
pp. 20130255 ◽  
Author(s):  
Geir H. Bolstad ◽  
Thomas F. Hansen ◽  
Christophe Pélabon ◽  
Mohsen Falahati-Anbaran ◽  
Rocío Pérez-Barrales ◽  
...  
Keyword(s):  
Genetic Variance ◽  
Floral Morphology ◽  
Additive Genetic Variance ◽  
Genetic Data ◽  
Stabilizing Selection ◽  
Evolutionary Divergence ◽  
Genetic Constraints ◽  
Quantitative Genetic ◽  
Rates Of Evolution ◽  
Genetic Constraint

If genetic constraints are important, then rates and direction of evolution should be related to trait evolvability. Here we use recently developed measures of evolvability to test the genetic constraint hypothesis with quantitative genetic data on floral morphology from the Neotropical vine Dalechampia scandens (Euphorbiaceae). These measures were compared against rates of evolution and patterns of divergence among 24 populations in two species in the D. scandens species complex. We found clear evidence for genetic constraints, particularly among traits that were tightly phenotypically integrated. This relationship between evolvability and evolutionary divergence is puzzling, because the estimated evolvabilities seem too large to constitute real constraints. We suggest that this paradox can be explained by a combination of weak stabilizing selection around moving adaptive optima and small realized evolvabilities relative to the observed additive genetic variance.

scholarly journals Spontaneous mutations and the origin and maintenance of quantitative genetic variation

eLife ◽  
2016 ◽  
Vol 5 ◽  
Author(s):  
Wen Huang ◽  
Richard F Lyman ◽  
Rachel A Lyman ◽  
Mary Anna Carbone ◽  
Susan T Harbison ◽  
...  
Keyword(s):  
Genetic Variation ◽  
Natural Selection ◽  
Quantitative Traits ◽  
Spontaneous Mutation ◽  
Natural Populations ◽  
Empirical Work ◽  
Stabilizing Selection ◽  
Spontaneous Mutation Rate ◽  
Evolutionary Forces ◽  
Quantitative Genetic

Mutation and natural selection shape the genetic variation in natural populations. Here, we directly estimated the spontaneous mutation rate by sequencing new Drosophila mutation accumulation lines maintained with minimal natural selection. We inferred strong stabilizing natural selection on quantitative traits because genetic variation among wild-derived inbred lines was much lower than predicted from a neutral model and the mutational effects were much larger than allelic effects of standing polymorphisms. Stabilizing selection could act directly on the traits, or indirectly from pleiotropic effects on fitness. However, our data are not consistent with simple models of mutation-stabilizing selection balance; therefore, further empirical work is needed to assess the balance of evolutionary forces responsible for quantitative genetic variation.

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