SELECTION IN COMPLEX GENETIC SYSTEMS III. AN EFFECT OF ALLELE MULTIPLICITY WITH TWO LOCI

ABSTRACT A two-locus model with three alleles at one locus and two at the other is studied. The viability system is such that all double heterozygotes have fitness unity, all single heterozygotes have fitness w < 1 and all double homozygotes have fitness w2. The following are the major findings: 1. There are more stable equilibria for tight linkage than in the corresponding three-locus model, even though the number of chromosomes is lower. 2. The equilibria stable for tight linkage do not belong to a unique high complementarity class, as is the case for two alleles at each locus. Instead the strength of selection determines the structure of the equilibrium. 3. The increase in number of alleles seems to reduce the possible extent of assocation between the loci. 4. The measure of this association is not well defined, although we have suggested a statistically standard way of getting over this. 5. A mutation introduced while a population is in linkage disequilibrium may, per medium only of the change in number of alleles, destroy the linkage disequilibrium.

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SELECTION IN COMPLEX GENETIC SYSTEMS I. THE SYMMETRIC EQUILIBRIA OF THE THREE-LOCUS SYMMETRIC VIABILITY MODEL

Genetics ◽

10.1093/genetics/76.1.135 ◽

1974 ◽

Vol 76 (1) ◽

pp. 135-162

Author(s):

Marcus W Feldman ◽

Ian Franklin ◽

Glenys J Thomson

Keyword(s):

Linkage Disequilibrium ◽

Linkage Equilibrium ◽

Symmetric Equilibrium ◽

Third Order ◽

Complete Linkage ◽

High Frequencies ◽

New Class ◽

Linkage Disequilibria ◽

Tight Linkage ◽

Stable Equilibria

ABSTRACT The symmetric equilibria of the three-locus symmetric viability model are determined and their stability analyzed. For tight linkage there may be four stable equilibria, each characterized by having one pair of complementary chromosomes in high frequencies, with all others low. For looser linkage the only stable symmetric equilibrium is that with complete linkage equilibrium. For intermediate recombination values both types of equilibria may be stable. A new class of equilibria with all pairwise linkage disequilibria zero, but with third order linkage disequilibrium, has been discovered. It may be stable for tight linkage.

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Selection Intensity Against Deleterious Mutations in RNA Secondary Structures and Rate of Compensatory Nucleotide Substitutions

Genetics ◽

10.1093/genetics/159.1.389 ◽

2001 ◽

Vol 159 (1) ◽

pp. 389-399 ◽

Cited By ~ 1

Author(s):

Hideki Innan ◽

Wolfgang Stephan

Keyword(s):

Linkage Disequilibrium ◽

Natural Populations ◽

Selection Intensity ◽

Deleterious Mutations ◽

Significant Linkage Disequilibrium ◽

Nucleotide Substitutions ◽

Diploid Population ◽

Locus Model ◽

Tight Linkage ◽

Significant Linkage

Abstract A two-locus model of reversible mutations with compensatory fitness interactions is presented; single mutations are assumed to be deleterious but neutral in appropriate combinations. The expectation of the time of compensatory nucleotide substitutions is calculated analytically for the case of tight linkage between sites. It is shown that selection increases the substitution time dramatically when selection intensity Ns > 1, where N is the diploid population size and s the selection coefficient. Computer simulations demonstrate that recombination increases the substitution time, but the effect of recombination is small when selection is weak. The amount of linkage disequilibrium generated in the process of compensatory substitution is also investigated. It is shown that significant linkage disequilibrium is expected to be rare in natural populations. The model is applied to the mRNA secondary structure of the bicoid 3′ untranslated region of Drosophila. It is concluded that average selection intensity Ns against single deleterious mutations is not likely to be much larger than 1.

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The three locus model with multiplicative fitness values

Genetics Research ◽

10.1017/s0016672300012982 ◽

1973 ◽

Vol 22 (2) ◽

pp. 195-200 ◽

Cited By ~ 4

Author(s):

Curtis Strobeck

Keyword(s):

Linkage Disequilibrium ◽

Equilibrium Point ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

The Other ◽

Linkage Equilibrium ◽

Locus Model ◽

Locus System ◽

The Stability ◽

Necessary And Sufficient

SUMMARYThe necessary and sufficient conditions for the stability of the equilibrium point with no linkage disequilibrium are obtained for the three locus model with multiplicative fitnesses. It is shown that there are six inequalities that must be satisfied in order for this equilibrium to be stable. Three of the inequalities require that there be heterozygotic superiority at all loci. The other three are exactly those inequalities which are required for each pair of loci to be stable with linkage equilibrium if they are considered to be an isolated two locus system. Thus, all the information needed to determine the stability of this equilibrium with three loci is contained in one and two locus theory.

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Neutral and Stable Equilibria of Genetic Systems and the Hardy–Weinberg Principle: Limitations of the Chi-Square Test and Advantages of Auto-Correlation Functions of Allele Frequencies

Frontiers in Genetics ◽

10.3389/fgene.2012.00276 ◽

2012 ◽

Vol 3 ◽

Cited By ~ 7

Author(s):

Francisco Bosco ◽

Diogo Castro ◽

Marcelo R. S. Briones

Keyword(s):

Correlation Functions ◽

Allele Frequencies ◽

Chi Square ◽

Auto Correlation ◽

Genetic Systems ◽

Chi Square Test ◽

Stable Equilibria

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Monomorphic and polymorphic enzyme genetic markers of the Waiãpi Indians of Amapá and of inhabitants of Manaus, Amazonas

Genetics and Molecular Biology ◽

10.1590/s1415-47571998000300003 ◽

1998 ◽

Vol 21 (3) ◽

pp. 311-314 ◽

Cited By ~ 1

Author(s):

Moacyr A. Mestriner ◽

Francisco M. Salzano

Keyword(s):

American Indian ◽

Genetic Markers ◽

Skin Color ◽

Genetic Distances ◽

Northern Region ◽

The Other ◽

South American ◽

Genetic Systems ◽

Geographical Distances

One hundred nineteen Waiãpi Indians and 348 inhabitants of Manaus, Amazonas, were tested using nine enzyme genetic systems in the first population and two in the second. The Waiãpi showed some marked differences compared to South American Indian averages in ACP*A (1% vs. 14 ± 9%), GLO1*1 (9% vs. 30 ± 14%) and ESD*1 (99.6% vs. 70 ± 17%), while ESD*1 and CA2*1 prevalences in the Manaus population were within the range previously found in the northern region of Brazil (ESD*1: 85% vs. 80-94%; CA2*1: 98% vs. 89-99.8%). The almost identical frequencies obtained for these two markers in this population, when the sample was subdivided according to skin color, suggest that such morphological classifications have little value in this region. Genetic distances between the Waiãpi and other tribes, obtained using these and other genetic markers, showed good parallelism with the geographical distances which separate these Indians from the other groups considered.

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POPULATION DYNAMICS OF THE SEGREGATION DISTORTER POLYMORPHISM OF DROSOPHILA MELANOGASTER

Genetics ◽

10.1093/genetics/89.1.171 ◽

1978 ◽

Vol 89 (1) ◽

pp. 171-192 ◽

Cited By ~ 2

Author(s):

Brian Charlesworth ◽

Daniel L Hartl

Keyword(s):

Population Genetics ◽

Population Dynamics ◽

Drosophila Melanogaster ◽

The Other ◽

The Core ◽

Segregation Distorter ◽

Tight Linkage ◽

Highly Oscillatory ◽

Approximate Treatment ◽

Special Case

ABSTRACT Two two-locus models of the population dynamics of the segregation distortion (SD) polymorphism of Drosophila melanogaster are described. One model is appropriate for understanding the population genetics of SD in nature, whereas the other is a special case appropriate for understanding an artificial population that has been extensively analysed. The models incorporate the general features of the Sd and Rsp loci which form the core of the SD system. It is shown that the SD polymorphism can be established only when there is sufficiently tight linkage between Sd and Rsp. An approximate treatment, valid for tight linkage, is given of all the equilibria of the system and their stabilities. It is shown that the observed composition of natural and artificial populations with respect to the Sd and Rsp loci is predicted well by the model, provided that restrictions are imposed on the fertilities of certain genotypes. Highly oscillatory paths towards equilibrium are usually to be expected on the basis of this model. The selection pressures on inversions introduced into this system are also investigated.

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Dynamics of genetic variability in two-locus models of stabilizing selection.

Genetics ◽

10.1093/genetics/138.2.519 ◽

1994 ◽

Vol 138 (2) ◽

pp. 519-532

Author(s):

S Gavrilets ◽

A Hastings

Keyword(s):

Linkage Disequilibrium ◽

Initial Conditions ◽

Fitness Function ◽

Stabilizing Selection ◽

Phenotypic Evolution ◽

Phenotypic Characteristics ◽

Locus Model ◽

Straight Line ◽

The Difference ◽

Slow Evolution

Abstract We study a two locus model, with additive contributions to the phenotype, to explore the dynamics of different phenotypic characteristics under stabilizing selection and recombination. We demonstrate that the interaction of selection and recombination results in constraints on the mode of phenotypic evolution. Let Vg be the genic variance of the trait and CL be the contribution of linkage disequilibrium to the genotypic variance. We demonstrate that, independent of the initial conditions, the dynamics of the system on the plane (Vg, CL) are typically characterized by a quick approach to a straight line with slow evolution along this line afterward. We analyze how the mode and the rate of phenotypic evolution depend on the strength of selection relative to recombination, on the form of fitness function, and the difference in allelic effect. We argue that if selection is not extremely weak relative to recombination, linkage disequilibrium generated by stabilizing selection influences the dynamics significantly. We demonstrate that under these conditions, which are plausible in nature and certainly the case in artificial stabilizing selection experiments, the model can have a polymorphic equilibrium with positive linkage disequilibrium that is stable simultaneously with monomorphic equilibria.

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Genome-Wide Patterns of Homozygosity and Relevant Characterizations on the Population Structure in Piétrain Pigs

Genes ◽

10.3390/genes11050577 ◽

2020 ◽

Vol 11 (5) ◽

pp. 577

Author(s):

Huiwen Zhan ◽

Saixian Zhang ◽

Kaili Zhang ◽

Xia Peng ◽

Shengsong Xie ◽

...

Keyword(s):

Linkage Disequilibrium ◽

Population Size ◽

Effective Population Size ◽

Average Length ◽

The Other ◽

Runs Of Homozygosity ◽

Effective Population ◽

Inbreeding Coefficients ◽

Genome Wide ◽

Genomic Regions

Investigating the patterns of homozygosity, linkage disequilibrium, effective population size and inbreeding coefficients in livestock contributes to our understanding of the genetic diversity and evolutionary history. Here we used Illumina PorcineSNP50 Bead Chip to identify the runs of homozygosity (ROH) and estimate the linkage disequilibrium (LD) across the whole genome, and then predict the effective population size. In addition, we calculated the inbreeding coefficients based on ROH in 305 Piétrain pigs and compared its effect with the other two types of inbreeding coefficients obtained by different calculation methods. A total of 23,434 ROHs were detected, and the average length of ROH per individual was about 507.27 Mb. There was no regularity on how those runs of homozygosity distributed in genome. The comparisons of different categories suggested that the formation of long ROH was probably related with recent inbreeding events. Although the density of genes located in ROH core regions is lower than that in the other genomic regions, most of them are related with Piétrain commercial traits like meat qualities. Overall, the results provide insight into the way in which ROH is produced and the identified ROH core regions can be used to map the genes associated with commercial traits in domestic animals.

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