Effects of the Ordering of Natural Selection and Population Regulation Mechanisms on Wright-Fisher Models

Abstract We explore the effect of different mechanisms of natural selection on the evolution of populations for one- and two-locus systems. We compare the effect of viability and fecundity selection in the context of the Wright-Fisher model with selection under the assumption of multiplicative fitness. We show that these two modes of natural selection correspond to different orderings of the processes of population regulation and natural selection in the Wright-Fisher model. We find that under the Wright-Fisher model these two different orderings can affect the distribution of trajectories of haplotype frequencies evolving with genetic recombination. However, the difference in the distribution of trajectories is only appreciable when the population is in significant linkage disequilibrium. We find that as linkage disequilibrium decays the trajectories for the two different models rapidly become indistinguishable. We discuss the significance of these findings in terms of biological examples of viability and fecundity selection, and speculate that the effect may be significant when factors such as gene migration maintain a degree of linkage disequilibrium.

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Effects of the Ordering of Natural Selection and Population Regulation Mechanisms on Wright-Fisher Models

10.1101/061911 ◽

2016 ◽

Author(s):

Zhangyi He ◽

Mark Beaumont ◽

Feng Fu

Keyword(s):

Population Dynamics ◽

Life Cycle ◽

Natural Selection ◽

Population Regulation ◽

Genetic Research ◽

Natural Populations ◽

Gene Migration ◽

Local Selection ◽

Fisher Model ◽

Regulation Mechanisms

AbstractThe Wright-Fisher model and its extensions are of central importance in population genetics, and so far, they have formed the basis of most theoretical and applied population genetic research. In the present work, we explore the effect that the ordering of natural selection and population regulation in the life cycle has on the resulting population dynamics under the Wright-Fisher model, especially for the evolution of one- and two-locus systems. With weak natural selection, the details of how to order natural selection and population regulation in the life cycle do not matter in the Wright-Fisher model and its diffusion approximation. By contrast, we show that when there is strong natural selection and the population is in linkage disequilibrium, there can be appreciable differences in the resulting population dynamics under the Wright-Fisher model, depending on whether natural selection occurs before or after population regulation in the life cycle. We argue that this effect may be of significance in natural populations subject to gene migration and local selection.F.Y. supported in part by EPSRC Grant EP/I028498/1.

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Moment-based approximations for the Wright-Fisher model of population dynamics under natural selection at two linked loci

10.1101/2021.01.01.424882 ◽

2021 ◽

Author(s):

Zhangyi He ◽

Wenyang Lyu ◽

Mark Beaumont ◽

Feng Yu

Keyword(s):

Population Dynamics ◽

Natural Selection ◽

Probability Distribution ◽

Diffusion Approximation ◽

Normal Approximation ◽

Genetic Recombination ◽

Transition Probability ◽

Computational Cost ◽

Fisher Model ◽

Support Issue

AbstractProperly modelling genetic recombination and local linkage has been shown to bring a significant improvement to the inference of natural selection from time series genetic data under a Wright-Fisher model. Existing approaches that can take genetic recombination effect and local linkage information into account are built upon either the diffusion approximation or the moment-based approximation of the Wright-Fisher model. However, such approximations are either limited to the increased computational cost like the diffusion approximation or suffer from the distribution support issue like the normal approximation, which can seriously affect computational efficiency and accuracy. In this work, we propose two novel moment-based approximations for the Wright-Fisher model of population dynamics subject to natural selection at a pair of linked loci. Our key innovation is that we extend existing approaches to calculate the mean and (co)variance of the two-locus Wright-Fisher model with selection and suggest a logistic normal distribution or a hierarchical beta distribution as a parametric continuous probability distribution to approximate the Wright-Fisher model by matching its first two moments to those of the Wright-Fisher model. Compared with the diffusion approximation, our approximations enable the computation of the transition probability distribution of the Wright-Fisher model at a far smaller computational cost and also allow us to avoid the distribution support issue found in the normal approximation.

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Linkage disequilibrium, natural selection, and epistatic gene interaction in Drosophila nasuta

Genome ◽

10.1139/g88-082 ◽

1988 ◽

Vol 30 (4) ◽

pp. 495-498 ◽

Cited By ~ 2

Author(s):

Arun Kumar ◽

J. P. Gupta

Keyword(s):

Linkage Disequilibrium ◽

Natural Selection ◽

Natural Populations ◽

Gene Interaction ◽

Significant Linkage Disequilibrium ◽

Linked Gene ◽

Significant Linkage ◽

Drosophila Nasuta ◽

Main Factor

The data of linkage disequilibrium between III-2 and 111-35 gene arrangements in natural populations of Drosophila nasuta is presented. The results demonstrated that there was significant linkage disequilibrium between the above gene arrangements in natural populations. Among all nine possible karyotypic combinations, only four combinations were seen. The absence of some combinations might be because of sublethal combinations of genes that reduced the viabilities of their carriers. The frequency of double inversion heterozygotes was always in excess and only 1.29% single hetrozygotes were observed. Based on these findings, we suggest that natural selection acting through the suppression of recombination and epistatic gene interaction providing fitness are the main factor for the maintenance of linkage disequilibrium between the above linked gene arrangements in natural populations of D. nasuta.Key words: linkage disequilibrium, selection, epistasis, Drosophila nasuta.

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SHOULD INDIVIDUAL FITNESS INCREASE WITH HETEROZYGOSITY?

Genetics ◽

10.1093/genetics/104.1.191 ◽

1983 ◽

Vol 104 (1) ◽

pp. 191-209

Author(s):

Michael Turelli ◽

Lev R Ginzburg

Keyword(s):

Linkage Disequilibrium ◽

Natural Selection ◽

Empirical Literature ◽

Correlated Traits ◽

Individual Fitness ◽

Stable Product ◽

Theoretical Results ◽

Average Fitness

ABSTRACT Natural selection influences not only gamete frequencies in populations but also the multilocus fitness structures associated with segregating gametes. In particular, only certain patterns of multilocus fitnesses are consistent with the maintenance of stable multilocus polymorphisms. This paper offers support for the proposition that, at stable, viability-maintained, multilocus polymorphisms, the fitness of a genotype tends to increase with the number of heterozygous loci it contains. Average fitness always increases with heterozygosity at stable product equilibria (i.e., those without linkage disequilibrium) maintained by either additive or multiplicative fitness schemes. Simulations suggest that it "generally" increases for arbitrary fitness schemes. The empirical literature correlating allozyme heterozygosity with fitness-correlated traits is discussed in the light of these and other theoretical results.

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Protein Variation in ADH and ADH-RELATED in Drosophila pseudoobscura: Linkage Disequilibrium Between Single Nucleotide Polymorphisms and Protein Alleles

Genetics ◽

10.1093/genetics/159.2.673 ◽

2001 ◽

Vol 159 (2) ◽

pp. 673-687

Author(s):

Stephen W Schaeffer ◽

C Scott Walthour ◽

Donna M Toleno ◽

Anna T Olek ◽

Ellen L Miller

Keyword(s):

Linkage Disequilibrium ◽

Single Nucleotide Polymorphisms ◽

Drosophila Pseudoobscura ◽

Linkage Disequilibrium Mapping ◽

Nucleotide Polymorphisms ◽

Neutral Model ◽

Significant Linkage Disequilibrium ◽

Single Nucleotide ◽

Synonymous Sites ◽

Significant Linkage

Abstract A 3.5-kb segment of the alcohol dehydrogenase (Adh) region that includes the Adh and Adh-related genes was sequenced in 139 Drosophila pseudoobscura strains collected from 13 populations. The Adh gene encodes four protein alleles and rejects a neutral model of protein evolution with the McDonald-Kreitman test, although the number of segregating synonymous sites is too high to conclude that adaptive selection has operated. The Adh-related gene encodes 18 protein haplotypes and fails to reject an equilibrium neutral model. The populations fail to show significant geographic differentiation of the Adh-related haplotypes. Eight of 404 single nucleotide polymorphisms (SNPs) in the Adh region were in significant linkage disequilibrium with three ADHR protein alleles. Coalescent simulations with and without recombination were used to derive the expected levels of significant linkage disequilibrium between SNPs and 18 protein haplotypes. Maximum levels of linkage disequilibrium are expected for protein alleles at moderate frequencies. In coalescent models without recombination, linkage disequilibrium decays between SNPs and high frequency haplotypes because common alleles mutate to haplotypes that are rare or that reach moderate frequency. The implication of this study is that linkage disequilibrium mapping has the highest probability of success with disease-causing alleles at frequencies of 10%.

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Estimates of linkage disequilibrium and the recombination parameter determined from segregating nucleotide sites in the alcohol dehydrogenase region of Drosophila pseudoobscura.

Genetics ◽

10.1093/genetics/135.2.541 ◽

1993 ◽

Vol 135 (2) ◽

pp. 541-552 ◽

Cited By ~ 5

Author(s):

S W Schaeffer ◽

E L Miller

Keyword(s):

Linkage Disequilibrium ◽

Alcohol Dehydrogenase ◽

Distance Effect ◽

Theoretical Distribution ◽

Drosophila Pseudoobscura ◽

Significant Linkage Disequilibrium ◽

Effective Population ◽

Nucleotide Distance ◽

Significant Linkage ◽

Recombination Parameter

Abstract The alcohol dehydrogenase (Adh) region of Drosophila pseudoobscura, which includes the two genes Adh and Adh-Dup, was used to examine the pattern and organization of linkage disequilibrium among pairs of segregating nucleotide sites. A collection of 99 strains from the geographic range of D. pseudoobscura were nucleotide-sequenced with polymerase chain reaction-mediated techniques. All pairs of the 359 polymorphic sites in the 3.5-kb Adh region were tested for significant linkage disequilibrium with Fisher's exact test. Of the 74,278 pairwise comparisons of segregating sites, 127 were in significant linkage disequilibrium at the 5% level. The distribution of five linkage disequilibrium estimators D(ij), D2, r(ij), r2 and D(ij) were compared to theoretical distributions. The observed distributions of D(ij), D2, r(ij) and r2 were consistent with the theoretical distribution given an infinite sites model. The observed distribution of D(ij) differed from the theoretical distribution because of an excess of values at -1 and 1. No spatial pattern was observed in the linkage disequilibrium pattern in the Adh region except for two clusters of sites nonrandomly associated in the adult intron and intron 2 of Adh. The magnitude of linkage disequilibrium decreases significantly as nucleotide distance increases, or a distance effect. Adh-Dup had a larger estimate of the recombination parameter, 4Nc, than Adh, where N is the effective population size and c is the recombination rate. A comparison of the mutation and recombination parameters shows that 7-17 recombination events occur for each mutation event. The heterogeneous estimates of the recombination parameter and the inverse relationship between linkage disequilibrium and nucleotide distance are no longer significant when the two clusters of Adh intron sites are excluded from analyses. The most likely explanation for the two clusters of linkage disequilibria is epistatic selection between sites in the cluster to maintain pre-mRNA secondary structure.

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GWAS revealed effect of genotype × environment interactions for grain yield of Nebraska winter wheat

BMC Genomics ◽

10.1186/s12864-020-07308-0 ◽

2021 ◽

Vol 22 (1) ◽

Author(s):

Shamseldeen Eltaher ◽

P. Stephen Baenziger ◽

Vikas Belamkar ◽

Hamdy A. Emara ◽

Ahmed A. Nower ◽

...

Keyword(s):

Linkage Disequilibrium ◽

Winter Wheat ◽

Grain Yield ◽

Genome Wide Association Study ◽

Phenotypic Selection ◽

Wheat Breeding ◽

Wheat Genotypes ◽

Genome Wide ◽

Genomic Regions ◽

Significant Linkage

Abstract Background Improving grain yield in cereals especially in wheat is a main objective for plant breeders. One of the main constrains for improving this trait is the G × E interaction (GEI) which affects the performance of wheat genotypes in different environments. Selecting high yielding genotypes that can be used for a target set of environments is needed. Phenotypic selection can be misleading due to the environmental conditions. Incorporating information from phenotypic and genomic analyses can be useful in selecting the higher yielding genotypes for a group of environments. Results A set of 270 F3:6 wheat genotypes in the Nebraska winter wheat breeding program was tested for grain yield in nine environments. High genetic variation for grain yield was found among the genotypes. G × E interaction was also highly significant. The highest yielding genotype differed in each environment. The correlation for grain yield among the nine environments was low (0 to 0.43). Genome-wide association study revealed 70 marker traits association (MTAs) associated with increased grain yield. The analysis of linkage disequilibrium revealed 16 genomic regions with a highly significant linkage disequilibrium (LD). The candidate parents’ genotypes for improving grain yield in a group of environments were selected based on three criteria; number of alleles associated with increased grain yield in each selected genotype, genetic distance among the selected genotypes, and number of different alleles between each two selected parents. Conclusion Although G × E interaction was present, the advances in DNA technology provided very useful tools and analyzes. Such features helped to genetically select the highest yielding genotypes that can be used to cross grain production in a group of environments.

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Ecological Divergence and the Origins of Intrinsic Postmating Isolation with Gene Flow

International Journal of Ecology ◽

10.1155/2011/435357 ◽

2011 ◽

Vol 2011 ◽

pp. 1-15 ◽

Cited By ~ 24

Author(s):

Aneil F. Agrawal ◽

Jeffrey L. Feder ◽

Patrik Nosil

Keyword(s):

Linkage Disequilibrium ◽

Gene Flow ◽

Natural Selection ◽

Theoretical Models ◽

Ecological Speciation ◽

Divergent Selection ◽

Postmating Isolation ◽

Divergent Natural Selection ◽

Mathematical Exploration ◽

Neutral Gene

The evolution of intrinsic postmating isolation has received much attention, both historically and in recent studies of speciation genes. Intrinsic isolation often stems from between-locus genetic incompatibilities, where alleles that function well within species are incompatible with one another when brought together in the genome of a hybrid. It can be difficult for such incompatibilities to originate when populations diverge with gene flow, because deleterious genotypic combinations will be created and then purged by selection. However, it has been argued that if genes underlying incompatibilities are themselves subject to divergent selection, then they might overcome gene flow to diverge between populations, resulting in the origin of incompatibilities. Nonetheless, there has been little explicit mathematical exploration of such scenarios for the origin of intrinsic incompatibilities during ecological speciation with gene flow. Here we explore theoretical models for the origin of intrinsic isolation where genes subject to divergent natural selection also affect intrinsic isolation, either directly or via linkage disequilibrium with other loci. Such genes indeed overcome gene flow, diverge between populations, and thus result in the evolution of intrinsic isolation. We also examine barriers to neutral gene flow. Surprisingly, we find that intrinsic isolation sometimes weakens this barrier, by impeding differentiation via ecologically based divergent selection.

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Linkage disequilibrium in growing and stable populations.

Genetics ◽

10.1093/genetics/137.1.331 ◽

1994 ◽

Vol 137 (1) ◽

pp. 331-336 ◽

Cited By ~ 9

Author(s):

M Slatkin

Keyword(s):

Linkage Disequilibrium ◽

Sequence Data ◽

Significant Linkage Disequilibrium ◽

Rapid Population Growth ◽

Exact Test ◽

Dna Sequence Data ◽

Constant Size ◽

Significant Linkage ◽

Stable Populations ◽

Growing Population

Abstract Nonrandom associations between alleles at different loci can be tested for using Fisher's exact test. Extensive simulations show that there is a substantial probability of obtaining significant nonrandom associations between closely or completely linked polymorphic neutral loci in a population of constant size at equilibrium under mutation and genetic drift. In a rapidly growing population, however, there will be little chance of finding significant nonrandom associations even between completely linked loci if the growth has been sufficiently rapid. This result is illustrated by the analysis of mitochondrial DNA sequence data from humans. In comparing all pairs of informative sites, fewer than 5% of the pairs show significant disequilibrium in Sardinians, which have apparently undergone rapid population growth, while 20% to 30% in !Kung and Pygmies, which apparently have not undergone rapid growth, show significance. The extent of linkage disequilibrium in a population is closely related to the gene genealogies of the loci examined, with "star-like" genealogies making significant linkage disequilibrium unlikely.

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Numerical simulation of the two-locus Wright-Fisher stochastic differential equation with application to approximating transition probability densities

10.1101/2020.07.21.213769 ◽

2020 ◽

Cited By ~ 2

Author(s):

Zhangyi He ◽

Mark Beaumont ◽

Feng Yu

Keyword(s):

Differential Equation ◽

Natural Selection ◽

Probability Density Function ◽

Stochastic Differential Equation ◽

Probability Density ◽

Density Function ◽

Genetic Recombination ◽

Transition Probability ◽

Superior Performance ◽

Transition Probability Density

AbstractOver the past decade there has been an increasing focus on the application of the Wright-Fisher diffusion to the inference of natural selection from genetic time series. A key ingredient for modelling the trajectory of gene frequencies through the Wright-Fisher diffusion is its transition probability density function. Recent advances in DNA sequencing techniques have made it possible to monitor genomes in great detail over time, which presents opportunities for investigating natural selection while accounting for genetic recombination and local linkage. However, most existing methods for computing the transition probability density function of the Wright-Fisher diffusion are only applicable to one-locus problems. To address two-locus problems, in this work we propose a novel numerical scheme for the Wright-Fisher stochastic differential equation of population dynamics under natural selection at two linked loci. Our key innovation is that we reformulate the stochastic differential equation in a closed form that is amenable to simulation, which enables us to avoid boundary issues and reduce computational costs. We also propose an adaptive importance sampling approach based on the proposal introduced by Fearnhead (2008) for computing the transition probability density of the Wright-Fisher diffusion between any two observed states. We show through extensive simulation studies that our approach can achieve comparable performance to the method of Fearnhead (2008) but can avoid manually tuning the parameter ρ to deliver superior performance for different observed states.

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