scholarly journals A theoretical analysis of linkage disequilibrium produced by genetic drift in Drosophila populations

1986 ◽  
Vol 48 (3) ◽  
pp. 161-166 ◽  
Author(s):  
Catherine Montchamp-Moreau ◽  
Mariano Katz
Keyword(s):  
Linkage Disequilibrium ◽  
Genetic Drift ◽  
Statistical Tests ◽  
Burst Size ◽  
Natural Populations ◽  
Finite Size ◽  
Gene Frequencies ◽  
Accurate Knowledge ◽  
Maximum Value ◽  
Cyclical Fluctuations

SummaryWe analyse the progression of linkage disequilibrium produced by random genetic drift in populations subject to cyclical fluctuations in size. Our model is applied to natural populations of Drosophila which show an annual demographic cycle of bottleneck (finite size) and demographic burst (size supposed to be infinite). In these populations, linkage disequilibrium stabilizes in such a way that, at equilibrium, the expected square of the correlation of gene frequencies E(r2) shows a stable cycle from year to year. If two loci are tightly linked, E(r2) barely varies during the annual cycle. Its values remain close to the value expected in a population of the same but constant effective size. If two loci are loosely linked, fluctuations in E(r2) are large. The maximum value, reached at the end of the bottleneck, is 10 to 100 times greater than the value obtained at the end of the burst. Our results show that the interpretation of observed linkage disequilibrium, by means of statistical tests, requires an accurate knowledge of population demography.

scholarly journals Linkage disequilibrium in experimental populations of Drosophila simulans: a test of the random drift hypothesis

1987 ◽  
Vol 50 (3) ◽  
pp. 187-193
Author(s):  
Catherine Montchamp-Moreau ◽  
Mariano Katz
Keyword(s):  
Linkage Disequilibrium ◽  
Genetic Drift ◽  
Natural Populations ◽  
Aldehyde Oxidase ◽  
Drosophila Simulans ◽  
Random Drift ◽  
Esterase 6 ◽  
Experimental Populations ◽  
Experimental Values ◽  
Neutralist Hypothesis

SummaryLinkage disequilibrium between five polymorphic enzymic loci of the third chromosome (Esterase-6, Phosphoglucomutase, Esterase-C, Aldehyde Oxidase and Acid Phosphatase) was studied in experimental populations of Drosophila simulans. Gametic data were obtained by mating sampled males with homozygous females at the five loci. Four cage populations were initiated with flies caught from natural populations. Extensive linkage disequilibrium was detected after 25 or 34 generations. The effective size of these populations was estimated about 400. Monte-Carlo simulations were performed in order to determine whether the observed disequilibria could be due to genetic drift. The observed probability distribution of the experimental values of r (the gametic correlation coefficient) was consistent with the distribution expected under random genetic drift. Our results are thus in accordance with the neutralist hypothesis.

scholarly journals Uncorrelated genetic drift of gene frequencies and linkage disequilibrium in some models of linked overdominant polymorphisms

1974 ◽  
Vol 24 (3) ◽  
pp. 281-294 ◽  
Author(s):  
Joseph Felsenstein
Keyword(s):  
Linkage Disequilibrium ◽  
Covariance Matrix ◽  
Genetic Drift ◽  
Conditional Distribution ◽  
Large Population ◽  
Multivariate Normal ◽  
Gene Frequencies ◽  
Constant Variance ◽  
Population Sizes ◽  
Multiplicative Family

SUMMARYFor large population sizes, gene frequencies p and q at two linked over-dominant loci and the linkage disequilibrium parameter D will remain close to their equilibrium values. We can treat selection and recombination as approximately linear forces on p, q and D, and we can treat genetic drift as a multivariate normal perturbation with constant variance-covariance matrix. For the additive-multiplicative family of two-locus models, p, q and D are shown to be (approximately) uncorrelated. Expressions for their variances are obtained. When selection coefficients are small the variances of p and q are those previously given by Robertson for a single locus. For small recombination fractions the variance of D is that obtained for neutral loci by Ohta & Kimura. For larger recombination fractions the result differs from theirs, so that for unlinked loci r2 ≃ 2/(3N) instead of 1/(2N). For the Lewontin-Kojima and Bodmer symmetric viability models, and for a model symmetric at only one of the loci, a more exact argument is possible. In the asymptotic conditional distribution in these cases, various of p, q and D are uncorrelated, depending on the type of symmetiy in the model.

scholarly journals LINKAGE DISEQUILIBRIUM IN NATURAL POPULATIONS OF DROSOPHILA MELANOGASTER

Genetics ◽  
1974 ◽  
Vol 78 (3) ◽  
pp. 921-936
Author(s):  
Charles H Langley ◽  
Yoshiko N Tobari ◽  
Ken-Ichi Kojima
Keyword(s):  
Drosophila Melanogaster ◽  
Genetic Variation ◽  
Linkage Disequilibrium ◽  
Natural Populations ◽  
Chromosomal Gene ◽  
Gene Frequencies ◽  
Linkage Disequilibria ◽  
Allozyme Loci ◽  
Two Populations ◽  
Stable Populations

ABSTRACT Two large, stable populations (Texas and Japan) of Drosophila melanogaster were surveyed at 21 allozyme loci on the second and third chromosomes and for chromosomal gene arrangements on those two chromosomes. Over 220 independent gametes were sampled from each population. The types and frequencies of the surveyed genetic variation are similar to those observed previously and suggest only slight differentiation among geographically distant populations. Linkage disequilibrium among linked allozymes loci is only slightly, if at all, detectable with these sample sizes. Linkage disequilibrium between linked inversions and allozymes loci is common especially when located in the same arm. These disequilibria appear to be in the same direction for most comparisons in the two population samples. This result is interpreted as evidence of similar selective environments (ecological and genetic) in the two populations. It is also noted that the direction of these linkage disequilibria appears to be oriented with respect to the gene frequencies at the component loci.

scholarly journals The effect of finite population size on models of linked overdominant loci

1978 ◽  
Vol 31 (3) ◽  
pp. 239-254 ◽  
Author(s):  
P. J. Avery
Keyword(s):  
Linkage Disequilibrium ◽  
Population Size ◽  
Genetic Drift ◽  
High Probability ◽  
Finite Population ◽  
Equilibrium Points ◽  
Gene Frequencies ◽  
Wide Range ◽  
Stable Equilibria ◽  
Range Of Values

SUMMARYModels of two linked overdominant loci in moderately large, but finite, populations are examined by looking at the variance-covariance matrix of the two gene frequencies and the linkage disequilibrium around stable deterministic equilibrium points. In particular, the effect of genetic drift is examined in cases where, in infinite populations, two stable equilibria with non-zero linkage disequilibrium, D, are maintained. Theoretical formulae are produced and checked by computer simulation. In general, the results show that unless the population size is very large indeed, genetic drift causes the values of D to vary considerably about the equilibrium values and that for many models, where stable equilibria exist at non-zero D values, a wide range of values of D have a high probability. Thus it is very difficult to draw conclusions about the selection regime by measuring Linkage disequilibrium in a finite population.

scholarly journals THE EFFECT OF A SELECTED LOCUS ON LINKED NEUTRAL LOCI

Genetics ◽  
1977 ◽  
Vol 85 (4) ◽  
pp. 753-788 ◽  
Author(s):  
Glenys Thomson
Keyword(s):  
Linkage Disequilibrium ◽  
Natural Populations ◽  
Recombination Fraction ◽  
Gene Frequencies ◽  
Order Of Magnitude

ABSTRACT The effects produced on linked neutral loci as a selected locus evolves towards its equilibrium value are considered. Significant effects on the neutral loci arise if the recombination fraction between the neutral and selected loci is smaller than the order of magnitude of the selective differences at the selected locus. The effect on gene frequencies at the neutral loci, that is, the hitchhiking effect, is determined, as well as the linkage disequilibrium generated by this hitchhiking effect. One of the more important findings is that significant disequilibrium can be generated between two neutral loci by the evolution of a linked selected locus. Consideration is given to the problem of determining how the effect of selection operating in natural populations can be detected, the question of the establishment of inversions in populations, and also to the nonequilibrium properties of populations.

scholarly journals Inferring Linkage Disequilibrium Between a Polymorphic Marker Locus and a Trait Locus in Natural Populations

Genetics ◽  
2000 ◽  
Vol 156 (1) ◽  
pp. 457-467 ◽  
Author(s):  
Z W Luo ◽  
S H Tao ◽  
Z-B Zeng
Keyword(s):  
Linkage Disequilibrium ◽  
Allele Frequency ◽  
Random Mating ◽  
Natural Populations ◽  
Polymorphic Marker ◽  
Marker Locus ◽  
Model Parameters ◽  
Phenotypic Variance ◽  
Wide Range ◽  
Trait Locus

Abstract Three approaches are proposed in this study for detecting or estimating linkage disequilibrium between a polymorphic marker locus and a locus affecting quantitative genetic variation using the sample from random mating populations. It is shown that the disequilibrium over a wide range of circumstances may be detected with a power of 80% by using phenotypic records and marker genotypes of a few hundred individuals. Comparison of ANOVA and regression methods in this article to the transmission disequilibrium test (TDT) shows that, given the genetic variance explained by the trait locus, the power of TDT depends on the trait allele frequency, whereas the power of ANOVA and regression analyses is relatively independent from the allelic frequency. The TDT method is more powerful when the trait allele frequency is low, but much less powerful when it is high. The likelihood analysis provides reliable estimation of the model parameters when the QTL variance is at least 10% of the phenotypic variance and the sample size of a few hundred is used. Potential use of these estimates in mapping the trait locus is also discussed.

scholarly journals Joint Linkage and Linkage Disequilibrium Mapping in Natural Populations

Genetics ◽  
2001 ◽  
Vol 157 (2) ◽  
pp. 899-909
Author(s):  
Rongling Wu ◽  
Zhao-Bang Zeng
Keyword(s):  
Linkage Disequilibrium ◽  
Complex Traits ◽  
Positional Cloning ◽  
Genome Structure ◽  
Natural Populations ◽  
Linkage Disequilibrium Mapping ◽  
Linkage Disequilibria ◽  
Time Simulation ◽  
New Strategy ◽  
Fisher Scoring Algorithm

Abstract A new strategy for studying the genome structure and organization of natural populations is proposed on the basis of a combined analysis of linkage and linkage disequilibrium using known polymorphic markers. This strategy exploits a random sample drawn from a panmictic natural population and the open-pollinated progeny of the sample. It is established on the principle of gene transmission from the parental to progeny generation during which the linkage between different markers is broken down due to meiotic recombination. The strategy has power to simultaneously capture the information about the linkage of the markers (as measured by recombination fraction) and the degree of their linkage disequilibrium created at a historic time. Simulation studies indicate that the statistical method implemented by the Fisher-scoring algorithm can provide accurate and precise estimates for the allele frequencies, recombination fractions, and linkage disequilibria between different markers. The strategy has great implications for constructing a dense linkage disequilibrium map that can facilitate the identification and positional cloning of the genes underlying both simple and complex traits.

NUMERICAL ANALYSIS OF RANDOM DRIFT IN A CLINE

Genetics ◽  
1980 ◽  
Vol 94 (2) ◽  
pp. 497-517
Author(s):  
Thomas Nagylaki ◽  
Bradley Lucier
Keyword(s):  
Natural Populations ◽  
The Other ◽  
Random Genetic Drift ◽  
Gene Frequencies ◽  
Random Drift ◽  
Linear Habitat ◽  
Asymptotic Formulae ◽  
A Chain ◽  
Average Position ◽  
Uniform Population

ABSTRACT The equilibrium state of a diffusion model for random genetic drift in a cline is analyzed numerically. The monoecious organism occupies an unbounded linear habitat with constant, uniform population density. Migration is homogeneouq symmetric and independent of genotype. A single diallelic locus with a step environment is investigated in the absence of dominance and mutation. The flattening of the expected cline due to random drift is very slight in natural populations. The ratio of the variance of either gene frequency to the product of the expected gene frequencies decreases monotonically to a nonzero constant. The correlation between the gene frequencies at two points decreases monotonically to zero as the separation is increased with the average position fixed; the decrease is asymptotically exponential. The correlation decreases monotonically to a positive constant depending on the separation as the average position increasingly deviates from the center of the cline with the separation fixed. The correlation also decreases monotonically to zero if one of the points is fixed and the other is moved outward in the habitat, the ultimate decrease again being exponential. Some asymptotic formulae are derived analytically.—The loss of an allele favored in an environmental pocket is investigated by simulating a chain of demes exchanging migrants, the other assumptions being the same as above. For most natural populations, provided the allele would be maintained in the population deterministically, this process is too slow to have evolutionary importance.

scholarly journals Network Analysis of Linkage Disequilibrium Reveals Genome Architecture in Chum Salmon

2020 ◽  
Vol 10 (5) ◽  
pp. 1553-1561 ◽  
Author(s):  
Garrett McKinney ◽  
Megan V. McPhee ◽  
Carita Pascal ◽  
James E. Seeb ◽  
Lisa W. Seeb
Keyword(s):  
Population Structure ◽  
Linkage Disequilibrium ◽  
Network Analysis ◽  
Chum Salmon ◽  
Sex Chromosome ◽  
Natural Populations ◽  
Population Substructure ◽  
Chromosome Inversion ◽  
Genomic Features ◽  
Chromosome Inversions

Many studies exclude loci that exhibit linkage disequilibrium (LD); however, high LD can signal reduced recombination around genomic features such as chromosome inversions or sex-determining regions. Chromosome inversions and sex-determining regions are often involved in adaptation, allowing for the inheritance of co-adapted gene complexes and for the resolution of sexually antagonistic selection through sex-specific partitioning of genetic variants. Genomic features such as these can escape detection when loci with LD are removed; in addition, failing to account for these features can introduce bias to analyses. We examined patterns of LD using network analysis to identify an overlapping chromosome inversion and sex-determining region in chum salmon. The signal of the inversion was strong enough to show up as false population substructure when the entire dataset was analyzed, while the effect of the sex-determining region on population structure was only obvious after restricting analysis to the sex chromosome. Understanding the extent and geographic distribution of inversions is now a critically important part of genetic analyses of natural populations. Our results highlight the importance of analyzing and understanding patterns of LD in genomic dataset and the perils of excluding or ignoring loci exhibiting LD. Blindly excluding loci in LD would have prevented detection of the sex-determining region and chromosome inversion while failing to understand the genomic features leading to high-LD could have resulted in false interpretations of population structure.

Linkage disequilibrium between neutral genes in finite populations

1974 ◽  
Vol 6 (01) ◽  
pp. 13-15
Author(s):  
William G. Hill
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linkage Disequilibrium ◽  
Finite Populations ◽  
Gene Frequencies ◽  
Infinite Population ◽  
Asymptotic Values

There is now a large literature on linkage disequilibrium between pairs of loci, both for selection in infinite populations and for neutral genes in finite populations, but there have been few studies with more loci. Bennett (1954) showed how the frequencies of chromosomes with any number of neutral genes would change in an infinite population, and the author (unpublished) has extended Bennett's results to find expected changes in chromosome frequencies with up to six loci in finite populations. For two linked neutral genes in finite populations the expected disequilibrium is zero, but the variance of the disequilibrium or the correlation of gene frequencies in segregating populations has been found. This has been done by Monte Carlo simulation (Hill and Robertson (1968)), but an approximation can be obtained by diffusion methods (Ohta and Kimura (1969)) and the asymptotic values using inbreeding theory (Sved (1971)). In this note we discuss the case of disequilibrium between three neutral loci and show how it relates to that between two loci.

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