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.

scholarly journals Clines in polygenic traits

1999 ◽  
Vol 74 (3) ◽  
pp. 223-236 ◽  
Author(s):  
N. H. BARTON
Keyword(s):  
Allele Frequency ◽  
Gaussian Distribution ◽  
Genetic Variance ◽  
Theoretical Models ◽  
Stabilizing Selection ◽  
Strong Selection ◽  
Linkage Disequilibria ◽  
Polygenic Traits ◽  
Frequency Changes ◽  
Spatially Varying

This article outlines theoretical models of clines in additive polygenic traits, which are maintained by stabilizing selection towards a spatially varying optimum. Clines in the trait mean can be accurately predicted, given knowledge of the genetic variance. However, predicting the variance is difficult, because it depends on genetic details. Changes in genetic variance arise from changes in allele frequency, and in linkage disequilibria. Allele frequency changes dominate when selection is weak relative to recombination, and when there are a moderate number of loci. With a continuum of alleles, gene flow inflates the genetic variance in the same way as a source of mutations of small effect. The variance can be approximated by assuming a Gaussian distribution of allelic effects; with a sufficiently steep cline, this is accurate even when mutation and selection alone are better described by the ‘House of Cards’ approximation. With just two alleles at each locus, the phenotype changes in a similar way: the mean remains close to the optimum, while the variance changes more slowly, and over a wider region. However, there may be substantial cryptic divergence at the underlying loci. With strong selection and many loci, linkage disequilibria are the main cause of changes in genetic variance. Even for strong selection, the infinitesimal model can be closely approximated by assuming a Gaussian distribution of breeding values. Linkage disequilibria can generate a substantial increase in genetic variance, which is concentrated at sharp gradients in trait means.

58 Integrating Quantitative Genetics and Epidemiology: Why Selection Against Infectious Diseases Is More Promising Than We Think

2021 ◽  
Vol 99 (Supplement_3) ◽  
pp. 31-32
Author(s):  
Piter Bijma ◽  
Piter Bijma
Keyword(s):  
Infectious Diseases ◽  
Genetic Parameters ◽  
Genetic Variance ◽  
Disease Status ◽  
Genetic Theory ◽  
Breeding Values ◽  
Quantitative Genetic ◽  
The Mean ◽  
Low Prevalence ◽  
Simple Average

Abstract Pathogens have profound effects on livestock. The low heritabilities of individual binary disease status suggest limited prospects for genetic improvement. However, a proper quantitative genetic theory for infectious diseases, including transmission dynamics, is currently lacking. Here we present a quantitative genetic theory for endemic infectious diseases, focussing on the genetic factors that determine the prevalence (P; the mean fraction of the population that is infected). We present simple expressions for breeding values and genetic parameters for the prevalence. Without genetic variation in infectiousness, breeding values for prevalence are a factor 1/P greater than the ordinary breeding values for individual binary disease status (0/1). Hence, even though prevalence is the simple average of individual binary disease status, breeding values for prevalence show much greater variation than our ordinary breeding values. This implies that the genetic variance that determines the potential response of prevalence to selection is largely due to indirect genetic effects (IGE), and thus hidden to ordinary genetic analysis and selection. Hence, the genetic variance that determines the potential of livestock populations to respond to selection must be much greater than currently believed, particularly at low prevalence. We evaluated this implication using simulation of endemics following standard methods in epidemiology. Results show that response of prevalence to selection increases very strongly when prevalence decreases, and is much greater than predicted by our ordinary breeding values. These results supports our theoretical findings, and show that selection against infectious diseases is much more promising than currently believed.

scholarly journals Evolution of genetic variability in a spatially heterogeneous environment: effects of genotype–environment interaction

1987 ◽  
Vol 49 (2) ◽  
pp. 147-156 ◽  
Author(s):  
Sara Via ◽  
Russell Lande
Keyword(s):  
Genetic Variability ◽  
Genetic Correlation ◽  
Genetic Variance ◽  
Genetic Correlations ◽  
Covariance Structure ◽  
Genetic Models ◽  
Quantitative Character ◽  
Disruptive Selection ◽  
Environment Interaction ◽  
The Mean

SummaryClassical population genetic models show that disruptive selection in a spatially variable environment can maintain genetic variation. We present quantitative genetic models for the effects of disruptive selection between environments on the genetic covariance structure of a polygenic trait. Our models suggest that disruptive selection usually does not alter the equilibrium genetic variance, although transient changes are predicted. We view a quantitative character as a set of character states, each expressed in one environment. The genetic correlation between character states expressed in different environments strongly affects the evolution of the genetic variability. (1) If the genetic correlation between character states is not ± 1, then the mean phenotype expressed in each environment will eventually attain the optimum value for that environment; this is the evolution of phenotypic plasticity (Via & Lande, 1985). At the joint phenotypic optimum, there is no disruptive selection between environments and thus no increase in the equilibrium genetic variability over that maintained by a balance between mutation and stabilizing selection within each environment. (2) If, however, the genetic correlation between character states is ± 1, the mean phenotype will not evolve to the joint phenotypic optimum and a persistent force of disruptive selection between environments will increase the equilibrium genetic variance. (3) Numerical analyses of the dynamic equations indicate that the mean phenotype can usually be perturbed several phenotypic standard deviations from the optimum without producing transient changes of more than a few per cent in the genetic variances or correlations. It may thus be reasonable to assume a roughly constant covariance structure during phenotypic evolution unless genetic correlations among character states are extremely high or populations are frequently perturbed. (4) Transient changes in the genetic correlations between character states resulting from disruptive selection act to constrain the evolution of the mean phenotype rather than to facilitate it.

Short-term Changes in the Variance: 1. Changes in the Additive Variance

2018 ◽  
Author(s):  
Bruce Walsh ◽  
Michael Lynch
Keyword(s):  
Linkage Disequilibrium ◽  
Assortative Mating ◽  
Genetic Variance ◽  
Additive Genetic Variance ◽  
Allele Frequencies ◽  
Disruptive Selection ◽  
Stabilizing Selection ◽  
Short Term ◽  
Additive Variance ◽  
The Mean

Selection changes the additive-genetic variance (and hence the response in the mean) by both changing allele frequencies and by generating correlations among alleles at different loci (linkage disequilibrium). Such selection-induced correlations can be generated even between unlinked loci, and (generally) are negative, such that alleles increasing trait values tend to become increasingly negative correlated under direction or stabilizing selection, and positively correlated under disruptive selection. Such changes in the additive-genetic variance from disequilibrium is called the Bulmer effects. For a large number of loci, the amount of change can be predicted from the Bulmer equation, the analog of the breeder's equation, but now for the change in the variance. Upon cessation of selection, any disequilibrium decays away, and the variances revert back to their additive-genic variances (the additive variance in the absence of disequilibrium). Assortative mating also generates such disequilibrium.

scholarly journals The effects of stabilizing selection on the time of development in Drosophila melanogaster

1962 ◽  
Vol 3 (3) ◽  
pp. 364-382 ◽  
Author(s):  
Timothy Prout
Keyword(s):  
Drosophila Melanogaster ◽  
Development Time ◽  
Genetic Variance ◽  
Additive Genetic Variance ◽  
Parallel Line ◽  
Total Variance ◽  
Disruptive Selection ◽  
Stabilizing Selection ◽  
Environmental Component ◽  
The Mean

The length of time of development, from oviposition to emergence in Drosophila melanogaster was subjected to stabilizing selection. In each generation only the individuals emerging close to the mean development time were used as parents of the next generation. This line was designated the ‘S’ line. In a parallel line disruptive selection was practised; where in each generation the earliest flies to emerge were mated to the flies last to emerge; those emerging at intermediate times were discarded. This line was designated the ‘D’ line. Two control lines were also carried, where the flies were mated at random with respect to time of emergence. The experiment extended for 40 generations and produced the following results:(1) The variance of development time decreased in the S line and increased in the D line, relative to the control lines.(2) The mean development time decreased in the S line and increased in the D line.(3) The coefficients of variation decreased in the S line and increased in the D line.(4) The viability, measured as per cent flies emerging, decreased in the D line.Toward the end of the experiment the amount of additive genetic variance in the selected lines and in the control lines was estimated from the response to directional selection. The estimates showed that (i) the loss of total variance in the S line can be accounted for completely by a loss in additive genetic variance, and (ii) the increase in the total variance of the D line cannot be ascribed to an increase in the additive genetic variance. It was probably due to an increase in the environmental component of variance, i.e. to a loss of ‘buffering capacity’.

scholarly journals Ohana: detecting selection in multiple populations by modelling ancestral admixture components

2019 ◽  
Author(s):  
Jade Yu Cheng ◽  
Fernando Racimo ◽  
Rasmus Nielsen
Keyword(s):  
Native American ◽  
Allele Frequency ◽  
Mexican Americans ◽  
Gaussian Approximation ◽  
Simulated Data ◽  
Fat Distribution ◽  
Likelihood Method ◽  
Multiple Populations ◽  
Frequency Changes ◽  
Candidate Regions

AbstractOne of the most powerful and commonly used methods for detecting local adaptation in the genome is the identification of extreme allele frequency differences between populations. In this paper, we present a new maximum likelihood method for finding regions under positive selection. The method is based on a Gaussian approximation to allele frequency changes and it incorporates admixture between populations. The method can analyze multiple populations simultaneously and retains power to detect selection signatures specific to ancestry components that are not representative of any extant populations. We evaluate the method using simulated data and compare it to related methods based on summary statistics. We also apply it to human genomic data and identify loci with extreme genetic differentiation between major geographic groups. Many of the genes identified are previously known selected loci relating to hair pigmentation and morphology, skin and eye pigmentation. We also identify new candidate regions, including various selected loci in the Native American component of admixed Mexican-Americans. These involve diverse biological functions, like immunity, fat distribution, food intake, vision and hair development.

scholarly journals The alternative fitness sets which preserve allele trajectories: a general treatment.

Genetics ◽  
1994 ◽  
Vol 138 (4) ◽  
pp. 1323-1330
Author(s):  
M Lachmann-Tarkhanov ◽  
S Sarkar
Keyword(s):  
Population Dynamics ◽  
General Solution ◽  
Allele Frequency ◽  
General Treatment ◽  
Fitness Set ◽  
Mean Fitness ◽  
The Mean ◽  
Frequency Changes ◽  
The One ◽  
Fitness Sets

Abstract A general solution is presented of the problem of specifying all alternative, generally frequency-dependent, (absolute) fitness sets which give rise to the same allele frequency changes and population dynamics as a given fitness set. The one- and two-locus cases are analyzed in detail and the method is then extended to the n-locus case. It is shown that if biological constraints can be used to specify the mean fitness of the population and the relative fitnesses of the heterozygotes, then the allele frequency trajectories determine a unique fitness set.

scholarly journals Recombination and Gene Conversion in a 170-kb Genomic Region of Arabidopsis thaliana

Genetics ◽  
2002 ◽  
Vol 161 (3) ◽  
pp. 1269-1278 ◽  
Author(s):  
Bernhard Haubold ◽  
Jürgen Kroymann ◽  
Andreas Ratzka ◽  
Thomas Mitchell-Olds ◽  
Thomas Wiehe
Keyword(s):  
Genetic Diversity ◽  
Arabidopsis Thaliana ◽  
Linkage Disequilibrium ◽  
Gene Conversion ◽  
Genomic Sequence ◽  
Genomic Region ◽  
Resistance To Herbivory ◽  
Linkage Disequilibria ◽  
Coalescent Simulations ◽  
The Mean

Abstract Arabidopsis thaliana is a highly selfing plant that nevertheless appears to undergo substantial recombination. To reconcile its selfing habit with the observations of recombination, we have sampled the genetic diversity of A. thaliana at 14 loci of ~500 bp each, spread across 170 kb of genomic sequence centered on a QTL for resistance to herbivory. A total of 170 of the 6321 nucleotides surveyed were polymorphic, with 169 being biallelic. The mean silent genetic diversity (πs) varied between 0.001 and 0.03. Pairwise linkage disequilibria between the polymorphisms were negatively correlated with distance, although this effect vanished when only pairs of polymorphisms with four haplotypes were included in the analysis. The absence of a consistent negative correlation between distance and linkage disequilibrium indicated that gene conversion might have played an important role in distributing genetic diversity throughout the region. We tested this by coalescent simulations and estimate that up to 90% of recombination is due to gene conversion.

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.

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