Linkage Disequilibrium in Subdivided Populations

The linkage disequilibrium in a subdivided populaton is shown to be equal to the sum of the average linkage disequilibrium for all subpopulations and the covariance between gene frequencies of the loci concerned. Thus, in a subdivided population the linkage disequilibrium may not be 0 even if the linkage disequilibrium in each subpopulation is 0. If a population is divided into two subpopulations between which migration occurs, the asymptotic rate of approach to linkage equilibrium is equal to either r or 2(m(1) + m(2)) - (m(1) + m(2))(2), whichever is smaller, where r is the recombination value and m(1) and m(2) are the proportions of immigrants in subpopulations 1 and 2, respectively. Thus, if migration rate is high compared with recombination value, the change of linkage disequilibrium in subdivided populations is similar to that of a single random mating population. On the other hand, if migration rate is low, the approach to lnkage equilibrium may be retarded in subdivided populations. If isolated populations begin to exchange genes by migration, linkage disequilibrium may increase temporarily even for neutral loci. If overdominant selection operates and the equilibrium gene frequencies are different in the two subpopulations, a permanent linkage disequilibrium may be produced without epistasis in each subpopulation.     

Linkage Disequilibrium in Natural Populations of DROSOPHILA MELANOGASTER

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.     

Divergence between Human Populations Estimated from Linkage Disequilibrium

Observed linkage disequilibrium (LD) between genetic markers in different populations descended independently from a common ancestral population can be used to estimate their absolute time of divergence, because the correlation of LD between populations will be reduced each generation by an amount that, approximately, depends only on the recombination rate between markers. Although drift leads to divergence in allele frequencies, it has less effect on divergence in LD values. We derived the relationship between LD and time of divergence and verified it with coalescent simulations. We then used HapMap Phase II data to estimate time of divergence between human populations. Summed over large numbers of pairs of loci, we find a positive correlation of LD between African and non-African populations at levels of up to ~0.3 cM. We estimate that the observed correlation of LD is consistent with an effective separation time of approximately 1,000 generations or ~25,000 years before present. The most likely explanation for such relatively low separation times is the existence of substantial levels of migration between populations after the initial separation. Theory and results from coalescent simulations confirm that low levels of migration can lead to a downward bias in the estimate of separation time.     

Linkage Disequilibrium in Natural and Experimental Populations of Drosophila Melanogaster

We have studied linkage disequilibrium in Drosophila melanogaster in two samples from a wild population and in four large laboratory populations derived from the wild samples. We have assayed four polymorphic enzyme loci, fairly closely linked in the third chromosome: Sod Est-6, Pgm, and Odh. The assay method used allows us to identify the allele associations separately in each of the two homologous chromosomes from each male sampled. We have detected significant linkage disequilibrium between two loci in 16.7% of the cases in the wild samples and in 27.8% of the cases in the experimental populations, considerably more than would be expected by chance alone. We have also found three-locus disequilibria in more instances than would be expected by chance. Some disequilibria present in the wild samples disappear in the experimental populations derived from them, but new ones appear over the generations. The effective population sizes required to generate the observed disequilibria by randomness range from 40 to more than 60,000 individuals in the natural population, depending on which locus pair is considered, and from 100 to more than 60,000 in the experimental populations. These population sizes are unrealistic; the fact that different locus-pairs yield disparate estimates within the same population argues against the likelihood that the disequilibria may have arisen as a consequence of population bottlenecks. Migration, or population mixing, cannot be excluded as the process generating the disequilibria in the wild samples, but can in the experimental populations. We conclude that linkage disequilibrium in these populations is most likely due to natural selection acting on the allozymes, or on loci very tightly linked to them.     

ArchiLD: Hierarchical Visualization of Linkage Disequilibrium in Human Populations

Linkage disequilibrium (LD) is an essential metric for selecting single-nucleotide polymorphisms (SNPs) to use in genetic studies and identifying causal variants from significant tag SNPs. The explosion in the number of polymorphisms that can now be genotyped by commercial arrays makes the interpretation of triangular correlation plots, commonly used for visualizing LD, extremely difficult in particular when large genomics regions need to be considered or when SNPs in perfect LD are not adjacent but scattered across a genomic region. We developed ArchiLD, a user-friendly graphical application for the hierarchical visualization of LD in human populations. The software provides a powerful framework for analyzing LD patterns with a particular focus on blocks of SNPs in perfect linkage as defined by r². Thanks to its integration with the UCSC Genome Browser, LD plots can be easily overlapped with additional data on regulation, conservation and expression. ArchiLD is an intuitive solution for the visualization of LD across large or highly polymorphic genomic regions. Its ease of use and its integration with the UCSC Genome Browser annotation potential facilitates the interpretation of association results and enables a more informed selection of tag SNPs for genetic studies.     

A Study of Linkage Disequilibrium in Populations of DROSOPHILA MELANOGASTER

This paper presents the results of a study of linkage disequilibrium between five polymorphic enzyme genes located on chromosome 3 of D. melanogaster. Three sets of chromosomes were examined: two represented samples from successive years of the same natural population, and one came from a large laboratory population. Out of the thirty possible tests for linkage disequilibrium between pairs of loci, two were significant at the 5% level and two at the 1% level. This result cannot reasonably be ascribed to chance alone. The pairs of loci that had a significant correlation in one sample had higher than average correlations in the other samples (though not necessarily in the same direction); this effect was highly significant statistically. There was no tendency for the high correlations to be associated with tightness of linkage between the loci concerned. All five loci were involved in at least one significant effect. It was concluded that these results are difficult to explain on the neutral allele theory of protein polymorphism, but are consistent with the concept of selective control of allele frequencies.     

Linkage Disequilibrium between Allozymes in Natural Populations of Lodgepole Pine

Pairwise linkage disequilibrium values (D) were estimated for 14 allozyme loci in two natural populations of lodgepole pine (Pinus contorta ssp. latifolia). Maternal multilocus genotypes were inferred from samples of (haploid) megagametophytic seed-endosperms. Coupling/repulsion double heterozygotes were distinguished for closely linked pairs of loci. Assays of seven of the loci in seed embryos allowed estimates of D for these loci in the outcross pollen pool (estimates of outcrossing rates indicate no significant departures from random mating in either population). No disequilibrium was observed between unlinked loci in either maternal genotypes or outcross pollen. However, significant disequilibrium was observed within and between gametes for some allelic combinations of four tightly linked loci; the assumption of random association of gamete types within individuals is thus invalid for some loci in lodgepole pine. Possible causes of the observed D were examined using the noncentrality parameter of the general noncentral chi square distribution. We concluded, from estimates of population size, linkage and measurements of population substructure, that neither drift nor population subdivision was responsible for the significant values of D which were observed and that epistatic selection was the most likely cause of the disequilibrium observed.     

Inferring Admixture Histories of Human Populations Using Linkage Disequilibrium

Long-range migrations and the resulting admixtures between populations have been important forces shaping human genetic diversity. Most existing methods for detecting and reconstructing historical admixture events are based on allele frequency divergences or patterns of ancestry segments in chromosomes of admixed individuals. An emerging new approach harnesses the exponential decay of admixture-induced linkage disequilibrium (LD) as a function of genetic distance. Here, we comprehensively develop LD-based inference into a versatile tool for investigating admixture. We present a new weighted LD statistic that can be used to infer mixture proportions as well as dates with fewer constraints on reference populations than previous methods. We define an LD-based three-population test for admixture and identify scenarios in which it can detect admixture events that previous formal tests cannot. We further show that we can uncover phylogenetic relationships among populations by comparing weighted LD curves obtained using a suite of references. Finally, we describe several improvements to the computation and fitting of weighted LD curves that greatly increase the robustness and speed of the calculations. We implement all of these advances in a software package, ALDER, which we validate in simulations and apply to test for admixture among all populations from the Human Genome Diversity Project (HGDP), highlighting insights into the admixture history of Central African Pygmies, Sardinians, and Japanese.     

A Study of Linkage Disequilibrium in British Populations of DROSOPHILA SUBOBSCURA

Data have been obtained concerning the genetic content of samples of O chromosomes from three British populations, and J chromosomes from one population, of Drosophila subobscura. Some improvements to the genetic map of the O and J chromosomes have been made. Allele frequencies at the loci studied do not show much geographical variation, except where associations with geographically varying gene arrangements distort the picture. Striking nonrandom associations between alleles at three enzyme loci and closely linked O chromosome gene arrangements are present. Some historical explanation for these associations cannot at present be ruled out, but it is clear that a very high degree of genetic differentiation must exist between different gene arrangements in this species. There is no convincing direct evidence for linkage disequilibrium between pairs of enzyme loci, although there is a significant association between close linkage and a high value of the linkage disequilibrium measure. This suggests that there may be disequilibria between closely linked enzyme loci that are too small to be individually detectable. These results are in broad agreement with those reported by workers on other Drosophila species. At present there appears to be no evidence to support the concept that selection is sufficiently strong at individual enzyme loci to produce a high degree of nonrandom associations. (Franklin and Lewontin 1970).     

Allozymic Variation and Linkage Disequilibrium in Some Laboratory Populations of DROSOPHILA MELANOGASTER

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 linkage 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 disequilibrum 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 in Natural Populations of DROSOPHILA MELANOGASTER. Seasonal Variation

Linkage disequilibrium among ten polymorphic allozyme loci and polymorphic inversions on chromosomes 2 and 3 in a natural population of Drosophila melanogaster was examined early and late in the annual season. Similar to previous studies, little linkage disequilibrium was observed among allozymes. The two significant cases that were observed in the first sample behaved in a contradictory way. One declined much more rapidly than expected due simply to recombination; the other declined slowly as expected. There was little change in allozyme or inversion frequencies during the season.     

A Model of Functional Epistasis and Linkage Disequilibrium in Populations with Overlapping Generations

A model of functional epistasis is proposed in which it is assumed that coupling and repulsion genotypes differ in metabolic efficiency and thus in development time and net fecundity. The implications of this model are investigated for iteroparous populations with fluctuating rates of increase. It is found that the fluctuations in rate of increase can lead to large fluctuations in gamete frequency and D, the coefficient of linkage disequilibrium, but that D will almost always have a value of zero at some point during the populations' demographic cycle. Some of the model populations would be expected to be in a state of linkage disequilibrium only fleetingly: others would exhibit D-cycles interpretable as random fluctuation. Implications of the model for interpretations of existing data on linkage disequilibrium among enzyme loci in Drosophila are discussed.     

Extensive Long-Range and Nonsyntenic Linkage Disequilibrium in Livestock Populations: Deconstruction of a Conundrum

Great interest was aroused by reports, based on microsatellite markers, of high levels of statistically significant long-range and nonsyntenic linkage disequilibrium (LD) in livestock. Simulation studies showed that this could result from population family structure. In contrast, recent SNP-based studies of livestock populations report much lower levels of LD. In this study we show, on the basis of microsatellite data from four cattle populations, that high levels of long-range LD are indeed obtained when using the multi-allelic D′ measure of LD. Long-range and nonsyntenic LD are exceedingly low, however, when evaluated by the standardized chi-square measure of LD, which stands in relation to the predictive ability of LD. Furthermore, specially constructed study populations provided no evidence for appreciable LD resulting from family structure at the grandparent level. We propose that the high statistical significance and family structure effects observed in the earlier studies are due to the use of large sample sizes, which accord high statistical significance to even slight deviations from asymptotic expectations under the null hypothesis. Nevertheless, even after taking sample size into account, our results indicate that microsatellites testify to the presence of usable LD at considerably wider separation distances than SNPs, suggesting that use of SNP haplotypes may considerably increase the usefulness of a given fixed SNP array.     

The Genetics of DROSOPHILA SUBOBSCURA Populations. IX. Studies on Linkage Disequilibrium in Four Natural Populations

Gametic frequencies were obtained in four natural populations of D. sub-obscura by extracting wild chromosomes and subsequently analyzing them for inversions and allozymes. The genes Lap and Pept-1, both located within the same inversions of chromosome O, were found in striking nonrandom associations with them of the same kind and degree in all populations studied. On the contrary, the gene Acph, also located within the previously mentioned inversions, was found in linkage disequilibrium with them only in two populations and of opposite directions. This is also the case for the genes Est-9 and Hk, both located within chromosome E inversions. While the gene Est-9 was in strong linkage disequilibrium with the inversions, of the same kind and degree in all populations studied, Hk was found to be in linkage equilibrium. Allele frequencies for the 29 genes studied do not show geographical variation except for the genes Lap, Pept-1 and Est-9, the ones found in linkage disequilibria with the geographically varying gene arrangements. Although mechanical or historical explanations for these equilibria cannot be ruled out, these data cannot be explained satisfactorily by the "middle gene explanation," which states that loci displaying such linkage disequilibria are the ones located near the break points of inversions, while the ones displaying linkage equilibria with them are located in the middle of them. There is no evidence for consistent linkage disequilibria between pairs of loci, except for the closely linked genes of the complex locus, Est-9. This would imply, if it is not a peculiarity of the Est-9 complex, that the linkage disequilibria are found only between very closely linked loci or that, for less closely linked genes, the associations are too weak to be detected by the usual samples sizes.     

Evidence for Linkage Disequilibrium Maintained by Selection in Two Natural Populations of DROSOPHILA SUBOBSCURA

One island and one mainland population of Drosophila subobscura were found polymorphic at the XDH (xanthine dehydrogenase) and the AO (aldehyde oxidase) loci. It was observed that one allele at the XDH locus, which has a low frequency in both populations, is nonrandomly associated with the alleles at the AO locus. Two lines of evidence support the thesis that this linkage disequilibrium is due to epistasis rather than random drift: (1) D or r, measures of the disequilibrium, have the same sign and magnitude in both populations. (2) The linkage disequilibrium is not due to inversions. Inversions segregating on the chromosome carrying XDH and AO have been separated into two classes, between which exchange of alleles at the two loci is suppressed. Linkage disequilibrium for XDH and AO was observed within each class. In the absence of any exchange of alleles, these disequilibria must have arisen and been maintained independently. The suggestion is made that the epistatic disequilibrium results from the close structural and physiological relationship which exists between the two enzymes.     

Pairwise Comparisons of Mitochondrial DNA Sequences in Stable and Exponentially Growing Populations

We consider the distribution of pairwise sequence differences of mitochondrial DNA or of other nonrecombining portions of the genome in a population that has been of constant size and in a population that has been growing in size exponentially for a long time. We show that, in a population of constant size, the sample distribution of pairwise differences will typically deviate substantially from the geometric distribution expected, because the history of coalescent events in a single sample of genes imposes a substantial correlation on pairwise differences. Consequently, a goodness-of-fit test of observed pairwise differences to the geometric distribution, which assumes that each pairwise comparison is independent, is not a valid test of the hypothesis that the genes were sampled from a panmictic population of constant size. In an exponentially growing population in which the product of the current population size and the growth rate is substantially larger than one, our analytical and simulation results show that most coalescent events occur relatively early and in a restricted range of times. Hence, the "gene tree" will be nearly a "star phylogeny" and the distribution of pairwise differences will be nearly a Poisson distribution. In that case, it is possible to estimate r, the population growth rate, if the mutation rate, mu, and current population size, N0, are assumed known. The estimate of r is the solution to ri/mu = ln(N0r) - gamma, where i is the average pairwise difference and gamma approximately 0.577 is Euler's constant.     

The Direction of Linkage Disequilibrium

The previous paper (Langley, Tobari and Kojima 1974) reports that the directional linkage disequilibria, D_ω = P_ABP_ab-P_AbP_aB, tend to be negative for data between allozymes and linked to inversions. A and B stand for the two alleles with the greatest frequency in the population. In this paper we show that linkage disequilibrium in this direction is produced at equilibrium when double homozygotes have fitnesses that are a constant fraction of the product of the two component single homozygote fitnesses, a pattern that is frequently observed in experimental data.     

Linkage Disequilibrium in Humans: Models and Data

In this review, we describe recent empirical and theoretical work on the extent of linkage disequilibrium (LD) in the human genome, comparing the predictions of simple population-genetic models to available data. Several studies report significant LD over distances longer than those predicted by standard models, whereas some data from short, intergenic regions show less LD than would be expected. The apparent discrepancies between theory and data present a challenge-both to modelers and to human geneticists-to identify which important features are missing from our understanding of the biological processes that give rise to LD. Salient features may include demographic complications such as recent admixture, as well as genetic factors such as local variation in recombination rates, gene conversion, and the potential segregation of inversions. We also outline some implications that the emerging patterns of LD have for association-mapping strategies. In particular, we discuss what marker densities might be necessary for genomewide association scans.