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.     

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.     

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.     

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 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.     

Linkage Disequilibrium in Growing and Stable Populations

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 ``starlike' genealogies making significant linkage disequilibrium unlikely.     

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.     

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.     

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.     

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.     

The Genetics of DROSOPHILA SUBOBSCURA Populations. V. a Study of Linkage Disequilibrium in Natural Populations between Genes and Inversions of the E Chromosome

The genetics of Hk and Est-9 complex gene have been studied in Drosophila subobscura. While Hk alleles mendelize normally, Est-9 is a complex locus consisting of several very closely linked genes with active and silent alleles. Both genes are located on chromosome E; a detailed genetic map was constructed with the help of visible markers and inversions. Both Hk and Est-9 are included in or are very near to inversions of the E chromosome. While Hk does not show linkage disequilibrium either with Est-9 or inversions, Est-9 does show disequilibrium in two ways: both with inversions and between different Est-9 genes. All natural populations studied show the same kind of association between Est-9 gene combinations and inversions. It is argued that these results are better explained by selection than by neutrality.     

The Genetic Structure of Natural Populations of DROSOPHILA MELANOGASTER Xiii. Further Studies on Linkage Disequilibrium

The Raleigh, North Carolina, population of Drosophila melanogaster was examined for linkage disequilibrium in 1974, several years after previous analyses in 1968, 1969, and 1970. alphaglycerol-3-phosphate dehydrogenase-1 (alphaGpdh-1), malate dehydrogenase-1 (Mdh-1), alcohol dehydrogenase (Adh), and hexokinase-C (Hex-C, tentative name, F. M. Johnson, unpublished; position determined by the present authors to be 2-74.5) were assayed for 617 second chromosomes, and esterase-C (Est-C) and octanol dehydrogenase (Odh) were assayed for 526 third chromosomes. In addition, two polymorphic inversions in the second chromosomes [In(2L)t and In(2R)NS] were examined, and the following findings were obtained: (1) No linkage disequilibrium between isozyme genes was detected. Significant linkage disequilibria were found only between the polymorphic inversions and isozyme genes [In(2L)t vs. Adh, and In(2R)NS vs. Hex-C]. Significant disequilibrium was not detected between In(2L)t and alphaGpdh-1, which is included in the inversion, but a tendency toward disequilibrium was consistently found from 1968 to 1974. The frequency of two-strand double crossovers within inversion In(2L)t involving a single crossover on each side of alphaGpdh-1 was estimated to be 0.00022. Thus, the consistent but not significant linkage disequilibrium between the two factors can be explained by recombination after the inversion occurred. (2) Previously existing linkage disequilibrium between Adh and In(2R)NS (the distance is about 30 cM, but the effective recombination value is about 1.75%) was found to have disappeared. (3) No higher-order linkage disequilibrium was detected. (4) Linkage disequilibrium between Odh and Est-C (the distance of which was estimated to be 0.0058 +/- 0.002) could not be detected (chi(2) (df=1) = 0.9).-From the above results, it was concluded that linkage disequilibria among isozyme genes are very rare in D. melanogaster, so that the Franklin-Lewontin model (Franklin and Lewontin 1970) is not applicable to these genes. The linkage disequilibria between some isozyme genes and polymorphic inversions may be explained by founder effect.     

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).     

Spatial Autocorrelation Analysis of the Distribution of Genotypes within Populations of Lodgepole Pine

Spatial autocorrelation analyses of point samples within two populations of lodgepole pine (Pinus contorta ssp. latifolia) indicate that single-locus mature tree and pollen genotypes are distributed in a nearly random fashion for most of the allozyme loci assayed. This lack of structure in the distributions of most genotypes is consistent with outcrossing rates that are very nearly 1.0 and with estimates indicating that both pollen and seed are dispersed over long distances in lodgepole pine. However, spatial autocorrelation of genotypes for a few loci suggests that genotypes at these loci may be under natural selection.     

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 Trypanosoma cruzi (Flagellate), the Agent of Chagas’ Disease1

ABSTRACT. We have studied linkage disequilibrium in natural populations of Trypanosoma cruzi, the agent of Chagas’ disease, by analyzing (i) a set of 524 stocks from the whole geographical range of the parasite, characterized at four gene loci coding for enzymes; (ii) a subsample of 121 stocks characterized at 12 enzyme loci; and (iii) a subset of 386 stocks from six locations in Bolivia, characterized by four enzyme loci. Our results show that the linkage disequilibrium reaches the maximum possible value, given the observed allelic frequencies, for almost all the locus pairs. This result is most consistent with the hypothesis that genetic recombination is absent or very rare in T. cruzi natural populations. Partition of the linkage disequilibrium variance for the six Bolivian populations shows that both inter- and intrapopulation components are substantial and that the relationships among the components are D_IS² < D_ST², and D'_IS² < D'_ST². These inequalities are interpreted as the result of an interplay between genetic drift, rare or absent mating, and clonal selection in generating linkage disequilibrium in T. cruzi populations.     

The Genetic Structure of Natural Populations of DROSOPHILA MELANOGASTER. Xii. Linkage Disequilibrium in a Large Local Population

Seven hundred and three second chromosomes were extracted from a Raleigh, North Carolina population of Drosophila melanogaster in 1970. Additionally, four hundred and eighty-nine third chromosomes were extracted from a large cage population founded from the flies in the 1970 Raleigh collection. The alpha glycerol-3-phosphate dehydrogenase-1, malate dehydrogenase-1, alcohol dehydrogenase, and alpha amylase loci were studied from the second chromosomes, and the esterase-6, esterase-C, and octanol dehydrogenase loci were analyzed from the third chromosomes. Inversions, relative viability and fecundity were studied for both classes of chromosomes. The following significant findings were obtained: (1) All loci examined were polymorphic or had at least two alleles at appreciable frequencies. Analysis of the combined data from this experiment with that of Mukai, Mettler and Chigusa (1971) revealed that the frequencies of the genes in the second chromosomes collected in early August were approximately the same over three years. (2) Linkage disequilibria between and among isozyme genes inter se were not detected except in a few cases which can be considered due to non-random sampling. (3) Linkage disequilibria between isozyme genes and polymorphic inversions were detected when the recombination values between the breakage points of the inversions and the genes in question were small. In only a few cases, were second and third order linkage disequilibria including polymorphic inversions detected. (4) Evidence for either variation among genotypes within loci or cumulative effects of heterozygosity was found for viability and fecundity. As a result of these findings, it was tentatively concluded that although selection might be perceptibly operating on some polymorphic isozyme loci, most of the polymorphic isozyme genes are selectively neutral or near-neutral in the populations studied.