The variance of linkage disequilibrium between three loci in a finite population

1983 ◽  
Vol 25 (2) ◽  
pp. 139-145 ◽  
Author(s):  
C. Strobeck ◽  
G. B. Golding
Keyword(s):  
Linkage Disequilibrium ◽  
Finite Population ◽  
Intragenic Recombination ◽  
Random Drift ◽  
Third Order ◽  
Linkage Disequilibria ◽  
Order Of Magnitude ◽  
Infinite Alleles Model

The variance of three-locus linkage disequilibria for an equilibrium infinite alleles model is solved numerically on a computer, using identity coefficients. It is shown that the variance of three-locus linkage disequilibrium created by random drift, although smaller than the variance of two-locus linkage disequilibrium, is of the same order of magnitude. Hence third-order disequilibria are not necessarily good indications of selection. The formula for the variance of linkage disequilibrium is given when there is no recombination between the genes. This model can also be interpreted as intragenic recombination between three sites within a gene.

scholarly journals THE EFFECT OF COMBINING ALLELES INTO ELECTROPHORETIC CLASSES ON DETECTING LINKAGE DISEQUILIBRIUM

Genetics ◽  
1977 ◽  
Vol 85 (3) ◽  
pp. 543-556
Author(s):  
E Zouros ◽  
G B Golding ◽  
Trudy F C MacKay
Keyword(s):  
Linkage Disequilibrium ◽  
Sample Size ◽  
Natural Populations ◽  
Epistatic Interactions ◽  
Detection Power ◽  
Linkage Disequilibria ◽  
Allelic Distribution ◽  
Order Of Magnitude ◽  
Actual Degree

ABSTRACT When alleles are combined into few detectable classes, linkage correlations are underestimated most of the time. The probability that the linkage correlation will be underestimated is a function of the actual degree of correlation and the evenness of the allelic distribution, but is mainly determined by the distribution of alleles into distinguishable classes. With only two alleles per class this probability will usually be higher than 0.7. Also, the consistency in the sign of the linkage disequilibrium over many populations may escape detection. An increase of sample size by one order of magnitude or more may be required to compensate for the loss in detection power. It follows that the available electrophoretic studies of linkage correlations, although negative in their majority, do not suggest that epistatic interactions and linkage disequilibria are rare in natural populations.

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

Genetics ◽  
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.

scholarly journals LINKAGE DISEQUILIBRIUM IN A FINITE POPULATION THAT IS PARTIALLY SELFING

Genetics ◽  
1980 ◽  
Vol 94 (3) ◽  
pp. 777-789 ◽  
Author(s):  
G B Golding ◽  
C Strobeck
Keyword(s):  
Linkage Disequilibrium ◽  
Population Size ◽  
Finite Population ◽  
Random Mating ◽  
Effective Population ◽  
Infinite Allele Model ◽  
Inbreeding Coefficients ◽  
Linkage Disequilibria ◽  
Recombination Value ◽  
Allele Model

ABSTRACT The linkage disequilibrium expected in a finite, partially selfing population is analyzed, assuming the infinite allele model. Formulas for the expected sum of squares of the linkage disequilibria and the squared standard linkage disequilibrium are derived from the equilibrium values of sixteen inbreeding coefficients required to describe the behavior of the system. These formulas are identical to those obtained with random mating if the effective population size Ne = (l—½S)N and the effective recombination value re = (l-S)r/(l-½S), where S is the proportion of selfing, are substituted for the population size and the recombination value, Therefore, the effect of partial selfing at equilibrium is to reduce the population size by a factor 1 — ½S and the recombination value by a factor (l-S)/(l—½S).

scholarly journals EXPECTED LINKAGE DISEQUILIBRIUM FOR A NEUTRAL LOCUS LINKED TO A CHROMOSOMAL ARRANGEMENT

Genetics ◽  
1983 ◽  
Vol 103 (3) ◽  
pp. 545-555
Author(s):  
Curtis Strobeck
Keyword(s):  
Linkage Disequilibrium ◽  
Balancing Selection ◽  
Natural Populations ◽  
Transient Behavior ◽  
Random Drift ◽  
Strong Linkage ◽  
Linkage Disequilibria ◽  
Chromosomal Arrangement ◽  
Neutral Locus ◽  
Selection For

ABSTRACT The expected value of the squared linkage disequilibrium is derived for a neutral locus associated with a chromosomal arrangement that is maintained in the population by strong balancing selection. For a given value of recombination, the expected squared linkage disequilibrium is shown to decrease as the intensity of selection maintaining the arrangement increases. The transient behavior of the expected square linkage disequilibrium is also derived. This theory applies to loci that are closely linked to inversions in Drosophila species and to loci closely linked to the differential segments of the translocation complexes in ring-forming species of Oenothera. In both cases the strong linkage disequilibria that have been observed in natural populations can be explained by random drift.

scholarly journals ALLOZYMIC VARIATION AND LINKAGE DISEQUILIBRIUM IN SOME LABORATORY POPULATIONS OF DROSOPHILA MELANOGASTER

Genetics ◽  
1979 ◽  
Vol 92 (4) ◽  
pp. 1295-1314
Author(s):  
C C Laurie-Ahlberg ◽  
B S Weir
Keyword(s):  
Linkage Disequilibrium ◽  
Gel Electrophoresis ◽  
Natural Populations ◽  
Starch Gel Electrophoresis ◽  
Random Drift ◽  
Linkage Disequilibria ◽  
Laboratory Populations ◽  
Rate Of Decay ◽  
Starch Gel ◽  
Selective Effects

ABSTRACT Nine laboratory populations of D. melanogaster were surveyed by starch gel electrophoresis for variation at 17 enzyme loci. A single-fly extract could be assayed for all 17 enzymes, so that the data consist of 17-locus genotypes.— Pairwise linkage disequilibria were estimated from the multilocus genotypic frequencies, using both BURROWS' and HILL'S methods. Large amounts of link-age disequilibrium were found, in contrast to the results reported for natural populations.—Knowledge of the approximate sizes of these populations was used to compare the observed heterozygosities and linkage disequilibria with predictions of the neutral allele hypothesis. The relatively large amount of linkage disequilibrium is consistent with the small sizes of the populations. However, the levels of heterozygosity in at least some populations suggest that some mechanism has been operating to retard the rate of decay by random drift. Several examples of significant deviation from Hardy-Weinberg frequencies and the large amount of linkage disequilibnim present in these populations indicate that a likely mechanism is selective effects associated with neutral alleles because of linkage disequilibrium with selected loci (e.g., "associative overdominance"). The results are therefore consistent with both neutralist, and selectionist hypotheses, but suggest the importance of considering linkage disequilibrium between neutral and selected loci when attempting to explain the dynamics of enzyme polymorphisms.

LINKAGE DISEQUILIBRIUM WITH THE ISLAND MODEL

Genetics ◽  
1982 ◽  
Vol 101 (1) ◽  
pp. 139-155
Author(s):  
Tomoko Ohta
Keyword(s):  
Population Structure ◽  
Linkage Disequilibrium ◽  
Total Population ◽  
Finite Population ◽  
Inbreeding Coefficient ◽  
Island Model ◽  
Mutation Rates ◽  
Linkage Disequilibria ◽  
Histocompatibility Complex ◽  
Subdivided Population

ABSTRACT Linkage disequilibrium between two linked loci was studied for a finite population with a subdivided population structure. Wright's island model was used; extinction and replacement of colonies were also incorporated. Two alleles (A  1 and A  2 at the first locus, and B  1 and B  2 at the second locus) with symmetric mutation rates were assumed, and equilibrium properties of linkage disequilibrium coefficients were analyzed. In terms of analogy with the subdivision of inbreeding coefficient, the variance of linkage disequilibrium is divided into several components: D  2  IS (variance of within-colony disequilibrium), D  2  ST (variance of correlation of A  1 and B  1 of different gametes of one colony relative to that of the total population), and D  2  IT (total variance of disequilibrium). Other subdivisions are D′2  IS (variance of correlation of A  1 and B  1 of one gamete of a colony relative to that of the average gamete of the population) and D′2  ST (variance of the ordinary disequilibrium of the whole population). When migration is limited, the variance becomes large if the correlation of A  1 and B  1 of one colony is taken relative to that of the whole population (D  2  ST and D′2  IS). Also, when the rate of extinction-replacement of colonies is high, the whole-population disequilibrium coefficient (D′2  ST) can become fairly large. Observed linkage disequilibria, such as those among markers in the major histocompatibility complex of man and mouse, may well be explained by limited migration, without assuming epistatic natural selection.

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 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.

scholarly journals Recombination and Selection at Brassica Self-Incompatibility Loci

Genetics ◽  
1999 ◽  
Vol 152 (1) ◽  
pp. 413-425 ◽  
Author(s):  
Philip Awadalla ◽  
Deborah Charlesworth
Keyword(s):  
Linkage Disequilibrium ◽  
Balancing Selection ◽  
Brassica Species ◽  
Selective Constraint ◽  
Intragenic Recombination ◽  
Self Incompatibility ◽  
History Of ◽  
Unknown Gene ◽  
Slg Gene ◽  
High Diversity

Abstract In Brassica species, self-incompatibility is controlled genetically by haplotypes involving two known genes, SLG and SRK, and possibly an as yet unknown gene controlling pollen incompatibility types. Alleles at the incompatibility loci are maintained by frequency-dependent selection, and diversity at SLG and SRK appears to be very ancient, with high diversity at silent and replacement sites, particularly in certain “hypervariable portions of the genes. It is important to test whether recombination occurs in these genes before inferences about function of different parts of the genes can be made from patterns of diversity within their sequences. In addition, it has been suggested that, to maintain the relationship between alleles within a given S-haplotype, recombination is suppressed in the S-locus region. The high diversity makes many population genetic measures of recombination inapplicable. We have analyzed linkage disequilibrium within the SLG gene of two Brassica species, using published coding sequences. The results suggest that intragenic recombination has occurred in the evolutionary history of these alleles. This is supported by patterns of synonymous nucleotide diversity within both the SLG and SRK genes, and between domains of the SRK gene. Finally, clusters of linkage disequilibrium within the SLG gene suggest that hypervariable regions are under balancing selection, and are not merely regions of relaxed selective constraint.

A multitechnique investigation of the second order NLO response of a 10,20-diphenylporphyrinato nickel(II) complex carrying a phenylethynyl based push-pull system in the 5- and 15-positions

2004 ◽  
Vol 08 (11) ◽  
pp. 1311-1324 ◽  
Author(s):  
Maddalena Pizzotti ◽  
Elisabetta Annoni ◽  
Renato Ugo ◽  
Silvia Bruni ◽  
Silvio Quici ◽  
...  
Keyword(s):  
Ab Initio ◽  
Planar Structure ◽  
Third Order ◽  
Incident Wavelength ◽  
Pull System ◽  
Nlo Response ◽  
Self Consistent ◽  
Order Of Magnitude ◽  
Zero Frequency

A multitechnique investigation of the determination of the order of magnitude of the second and third order NLO response of [5-[(4-dimethylaminophenyl)ethynyl]-15-[(4-nitrophenyl)ethynyl]-10,20-diphenylporphyrinato]nickel(II) (1) is reported with the aim to produce self consistent evidence for a significant NLO response of this kind of push-pull porphyrin chromophore. The experimental multitechnique approach is based on the EFISH technique, working with a non-resonant incident wavelength of 1.907 μm, on the solvatochromic method and finally on a vibrational method, avoiding any fluorescence or resonance interference. A theoretical MNDO-TDHF evaluation of the zero-frequency quadratic and cubic hyperpolarizabilities of an ab initio optimized planar structure is also reported. The order of magnitude of the quadratic hyperpolarizability of (1) at zero frequency (β0), was found to be significantly lower than that reported for the corresponding Cu (II) or Zn (II) complexes with the same push-pull porphyrin chromophore.

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