The influence of gene conversion on linkage disequilibrium around a selective sweep

In a 2007 article, McVean studied the effect of recombination on linkage disequilibrium (LD) between two neutral loci located near a third locus that has undergone a selective sweep. The results demonstrated that two loci on the same side of a selected locus might show substantial LD, whereas the expected LD for two loci on opposite sides of a selected locus is zero. In this article, we extend McVean's model to include gene conversion. We show that one of the conclusions is strongly affected by gene conversion: when gene conversion is present, there may be substantial LD between two loci on opposite sides of a selective sweep.     

The effect of recurrent mutation on the linkage disequilibrium under a selective sweep

A selective sweep describes the reduction of diversity due to strong positive selection. If the mutation rate to a selectively beneficial allele is sufficiently high, Pennings and Hermisson (Mol Biol Evol 23(5):1076–1084, 2006a) have shown, that it becomes likely, that a selective sweep is caused by several individuals. Such an event is called a soft sweep and the complementary event of a single origin of the beneficial allele, the classical case, a hard sweep. We give analytical expressions for the linkage disequilibrium (LD) between two neutral loci linked to the selected locus, depending on the recurrent mutation to the beneficial allele, measured by D and ${\widehat{\sigma_D^2}}$ , a quantity introduced by Ohta and Kimura (Genetics 63(1):229–238, 1969), and conclude that the LD-pattern of a soft sweep differs substantially from that of a hard sweep due to haplotype structure. The analytical results are compared with simulations.     

High nucleotide diversity and limited linkage disequilibrium in Helicoverpa armigera facilitates the detection of a selective sweep

Insecticides impose extreme selective pressures on populations of target pests and so insecticide resistance loci of these species may provide the footprints of ‘selective sweeps''. To lay the foundation for future genome-wide scans for selective sweeps and inform genome-wide association study designs, we set out to characterize some of the baseline population genomic parameters of one of the most damaging insect pests in agriculture worldwide, Helicoverpa armigera. To this end, we surveyed nine Z-linked loci in three Australian H. armigera populations. We find that estimates of π are in the higher range among other insects and linkage disequilibrium decays over short distances. One of the surveyed loci, a cytochrome P450, shows an unusual haplotype configuration with a divergent allele at high frequency that led us to investigate the possibility of an adaptive introgression around this locus.     

The extent of linkage disequilibrium and haplotype sharing around a polymorphic site

Various expressions related to the length of a conserved haplotype around a polymorphism of known frequency are derived. We obtain exact expressions for the probability that no recombination has occurred in a sample or subsample. We obtain an approximation for the probability that no recombination that could give rise to a detectable recombination event (through the four-gamete test) has occurred. The probabilities can be used to obtain approximate distributions for the length of variously defined haplotypes around a polymorphic site. The implications of our results for data analysis, and in particular for detecting selection, are discussed.     

Haplotype diversity and the block structure of linkage disequilibrium

Several recent studies indicate that patterns of linkage disequilibrium in the human genome cannot be reconciled with a uniform distribution of recombination events, but crossovers appear to be localized in short hot-spots that separate longer stretches of DNA. Markers within these low-recombination blocks show increased levels of linkage disequilibrium and very low haplotype diversity. This could simplify study of the genetic basis of complex diseases if causal variants are common.     

The posterior probability of linkage allowing for linkage disequilibrium and a new estimate of disequilibrium between a trait and a marker

The posterior probability of linkage (PPL) statistic has been developed as a method for the rigorous accumulation of evidence for or against linkage allowing for both intra- and inter-sample heterogeneity. To date, the method has assumed linkage equilibrium between alleles at the trait locus and the marker locus. We now generalize the PPL to allow for linkage disequilibrium (LD), by incorporating variable phase probabilities into the underlying linkage likelihood. This enables us to recover the marginal posterior density of the recombination fraction, integrating out nuisance parameters of the trait model, including the locus heterogeneity (admixture) parameter, as well as a vector of LD parameters. The marginal posterior density can then be updated across data subsets or new data as they become available, while allowing parameters of the trait model to vary between data sets. The method applies immediately to general pedigree structures and to markers with multiple alleles. In the case of SNPs, the likelihood is parameterized in terms of the standard single LD parameter D'; and it therefore affords a mechanism for estimation of D' between the marker and the trait, again, without fixing the parameters of the trait model and allowing for updating across data sets. It is even possible to allow for a different associated allele in different populations, while accumulating information regarding the strength of LD. While a computationally efficient implementation for multi-allelic markers is still in progress, we have implemented a version of this new LD-PPL for SNPs and evaluated its performance in nuclear families. Our simulations show that LD-PPLs tend to be larger than PPLs (stronger evidence in favor of linkage/LD) with increased LD level, under a variety of generating models; while in the absence of linkage and LD, LD-PPLs tend to be smaller than PPLs (stronger evidence against linkage). The estimate of D' also behaves well even in relatively small, heterogeneous samples.     

Exploring linkage disequilibrium

Linkage disequilibrium (LD, association of allelic states across loci) is poorly understood by many evolutionary biologists, but as technology for multilocus sampling improves, we ignore LD at our peril. If we sample variation at 10 loci in an organism with 20 chromosomes, we can reasonably treat them as 10 ‘independent witnesses’ of the evolutionary process. If instead, we sample variation at 1000 loci, many are bound to be close together on a chromosome. With only one or two crossovers per meiosis, associations between close neighbours decay so slowly that even LD created far in the past will not have dissipated, so we cannot treat the 1000 loci as independent witnesses (Barton 2011 ). This means that as marker density on genomes increases classic analyses assuming independent loci become mired in the problem of overconfidence: if 1000 independent witnesses are assumed, and that number should be much lower, any conclusion will be overconfident. This is of special concern because our literature suffers from a strong publication bias towards confident answers, even when they turn out to be wrong (Knowles 2008 ). In contrast, analyses that take into account associations across loci both control for overconfidence and can inform us about LD generating events far in the past, for example human/Neanderthal admixture (Fu et al. 2014 ). With increased marker density, biologists must increase their awareness of LD and, in this issue of Molecular Ecology Resources, Kemppainen et al. ( 2015 ) make software available that can only help in this process: LDna allows patterns of LD in a data set to be explored using tools borrowed from network analysis. This has great potential, but realizing that potential requires understanding LD.     

Population structure and linkage disequilibrium unravelled in tetraploid potato

Association mapping is considered to be an important alternative strategy for the identification of quantitative trait loci (QTL) as compared to traditional QTL mapping. A necessary prerequisite for association analysis to succeed is detailed information regarding hidden population structure and the extent of linkage disequilibrium. A collection of 430 tetraploid potato cultivars, comprising two association panels, has been analysed with 41 AFLP^® and 53 SSR primer combinations yielding 3364 AFLP fragments and 653 microsatellite alleles, respectively. Polymorphism information content values and detected number of alleles for the SSRs studied illustrate that commercial potato germplasm seems to be equally diverse as Latin American landrace material. Genome-wide linkage disequilibrium (LD)—reported for the first time for tetraploid potato—was observed up to approximately 5 cM using r ² higher than 0.1 as a criterion for significant LD. Within-group LD, however, stretched on average twice as far when compared to overall LD. A Bayesian approach, a distance-based hierarchical clustering approach as well as principal coordinate analysis were adopted to enquire into population structure. Groups differing in year of market release and market segment (starch, processing industry and fresh consumption) were repeatedly detected. The observation of LD up to 5 cM is promising because the required marker density is not likely to disable the possibilities for association mapping research in tetraploid potato. Population structure appeared to be weak, but strong enough to demand careful modelling of genetic relationships in subsequent marker-trait association analyses. There seems to be a good chance that linkage-based marker-trait associations can be identified at moderate marker densities.     

Population structure and long-range linkage disequilibrium in a durum wheat elite collection

A collection of 134 durum wheat accessions, mainly including cultivars (cvs.) representative of the major gene pools, was assembled and characterized with 70 SSRs for genetic diversity and level of long-range linkage disequilibrium (LD). Results of both a distance-based and a model-based (Bayesian) cluster analysis evidenced the presence of a structured diversity. In the model-based analysis, six to eight main distinct subpopulations were identified based on the molecular data. Only a relatively small portion (20%) of the molecular variation was accounted for by the geographical origin of the accessions. Major differences were detected between the North American and the Mediterranean cvs., while a considerable overlap characterized the cvs. from CIMMYT-ICARDA and Italy. The North American cvs. showed the highest within group mean genetic similarity (GS_m = 0.68). French cvs. revealed sizeable similarities with both the North American as well as the Italian and CIMMYT-ICARDA pools. Considering the germplasm as a whole, high levels of LD were found both at locus pairs with an intrachromosomal distance <50 cM as well as at those with distances more than 50 cM and independent (86, 52 and 54% of SSR pairs at p < 0.01, respectively). After re-evaluating LD within each of the three main subgroups identified through the analysis of the germplasm structure, the LD level remained high for tightly to moderately linked locus pairs (<20 cM apart), but was greatly reduced in the loosely linked (more than 50 cM apart) and independent locus pairs. The implications of these findings as to the possibility of using association mapping for gene/QTL discovery in durum wheat are discussed.     

The trimmed-haplotype test for linkage disequilibrium

Single-marker linkage-disequilibrium (LD) methods cannot fully describe disequilibrium in an entire chromosomal region surrounding a disease allele. With the advent of myriad tightly linked microsatellite markers, we have an opportunity to extend LD analysis from single markers to multiple-marker haplotypes. Haplotype analysis has increased statistical power to disclose the presence of a disease locus in situations where it correctly reflects the historical process involved. For maximum efficiency, evidence of LD ought to come not just from a single haplotype, which may well be rare, but in addition from many similar haplotypes that could have descended from the same ancestral founder but have been trimmed in succeeding generations. We present such an analysis, called the "trimmed-haplotype method." We focus on chromosomal regions that are small enough that disequilibrium in significant portions of them may have been preserved in some pedigrees and yet that contain enough markers to minimize coincidental occurrence of the haplotype in the absence of a disease allele: perhaps regions 1-2 cM in length. In general, we could have no idea what haplotype an ancestral founder carried generations ago, nor do we usually have a precise chromosomal location for the disease-susceptibility locus. Therefore, we must search through all possible haplotypes surrounding multiple locations. Since such repeated testing obliterates the sampling distribution of the test, we employ bootstrap methods to calculate significance levels. Trimmed-haplotype analysis is performed on family data in which genotypes have been assembled into haplotypes. It can be applied either to conventional parent-affected-offspring triads or to multiplex pedigrees. We present a method for summarizing the LD evidence, in any pedigree, that can be employed in trimmed-haplotype analysis as well as in other methods.     

The effect of linkage disequilibrium on linkage analysis of incomplete pedigrees

Dense SNP maps can be highly informative for linkage studies. But when parental genotypes are missing, multipoint linkage scores can be inflated in regions with substantial marker-marker linkage disequilibrium (LD). Such regions were observed in the Affymetrix SNP genotypes for the Genetic Analysis Workshop 14 (GAW14) Collaborative Study on the Genetics of Alcoholism (COGA) dataset, providing an opportunity to test a novel simulation strategy for studying this problem. First, an inheritance vector (with or without linkage present) is simulated for each replicate, i.e., locations of recombinations and transmission of parental chromosomes are determined for each meiosis. Then, two sets of founder haplotypes are superimposed onto the inheritance vector: one set that is inferred from the actual data and which contains the pattern of LD; and one set created by randomly selecting parental alleles based on the known allele frequencies, with no correlation (LD) between markers. Applying this strategy to a map of 176 SNPs (66 Mb of chromosome 7) for 100 replicates of 116 sibling pairs, significant inflation of multipoint linkage scores was observed in regions of high LD when parental genotypes were set to missing, with no linkage present. Similar inflation was observed in analyses of the COGA data for these affected sib pairs with parental genotypes set to missing, but not after reducing the marker map until r2 between any pair of markers was 相似文献   

Homozygosity and linkage disequilibrium

We illustrate how homozygosity of haplotypes can be used to measure the level of disequilibrium between two or more markers. An excess of either homozygosity or heterozygosity signals a departure from the gametic phase equilibrium: We describe the specific form of dependence that is associated with high (low) homozygosity and derive various linkage disequilibrium measures. They feature a clear biological interpretation, can be used to construct tests, and are standardized to allow comparison across loci and populations. They are particularly advantageous to measure linkage disequilibrium between highly polymorphic markers.     

Decomposing multilocus linkage disequilibrium

We present a mathematically precise formulation of total linkage disequilibrium between multiple loci as the deviation from probabilistic independence and provide explicit formulas for all higher-order terms of linkage disequilibrium, thereby combining J. Dausset et al.'s 1978 definition of linkage disequilibrium with H. Geiringer's 1944 approach. We recursively decompose higher-order linkage disequilibrium terms into lower-order ones. Our greatest simplification comes from defining linkage disequilibrium at a single locus as allele frequency at that locus. At each level, decomposition of linkage disequilibrium is mathematically equivalent to number theoretic compositions of positive integers; i.e., we have converted a genetic decomposition into a mathematical decomposition.     

Visualization of pairwise and multilocus linkage disequilibrium structure using latent forests

Linkage disequilibrium study represents a major issue in statistical genetics as it plays a fundamental role in gene mapping and helps us to learn more about human history. The linkage disequilibrium complex structure makes its exploratory data analysis essential yet challenging. Visualization methods, such as the triangular heat map implemented in Haploview, provide simple and useful tools to help understand complex genetic patterns, but remain insufficient to fully describe them. Probabilistic graphical models have been widely recognized as a powerful formalism allowing a concise and accurate modeling of dependences between variables. In this paper, we propose a method for short-range, long-range and chromosome-wide linkage disequilibrium visualization using forests of hierarchical latent class models. Thanks to its hierarchical nature, our method is shown to provide a compact view of both pairwise and multilocus linkage disequilibrium spatial structures for the geneticist. Besides, a multilocus linkage disequilibrium measure has been designed to evaluate linkage disequilibrium in hierarchy clusters. To learn the proposed model, a new scalable algorithm is presented. It constrains the dependence scope, relying on physical positions, and is able to deal with more than one hundred thousand single nucleotide polymorphisms. The proposed algorithm is fast and does not require phase genotypic data.     

Hierarchical modeling of linkage disequilibrium: genetic structure and spatial relations

Linkage disequilibrium (LD) mapping offers much promise for the positional cloning of disease-causing genes. However, conventional estimates of LD may fluctuate substantially across contiguous genomic regions, because of population-specific phenomena such as mutation, genetic drift, population structure, and variations in allele frequencies. This fluctuation makes it difficult to interpret patterns of LD and distinguish where a causal gene is located. To address this issue, we propose hierarchical modeling of LD (HLD) for fine-scale mapping. This approach incorporates information on haplotype block structure and chromosomal spatial relations to refine the pattern of LD, increasing the ability to localize disease genes. Here, we present a framework for HLD, a simulation study assessing the performance of HLD under various scenarios, and an application of HLD to existing data. This work demonstrates that hierarchical modeling of linkage disequilibrium is a valuable and flexible approach for fine-scale mapping.     

GOLD--graphical overview of linkage disequilibrium

SUMMARY: We describe a software package that provides a graphical summary of linkage disequilibrium in human genetic data. It allows for the analysis of family data and is well suited to the analysis of dense genetic maps. AVAILABILITY: http://www.well.ox.ac.uk/asthma/GOLD CONTACT: goncalo@well.ox.ac.uk     

Significant admixture linkage disequilibrium across 30 cM around the FY locus in African Americans

Scientists, to understand the importance of allelic polymorphisms on phenotypes that are quantitative and environmentally interacting, are now turning to population-association screens, especially in instances in which pedigree analysis is difficult. Because association screens require linkage disequilibrium between markers and disease loci, maximizing the degree of linkage disequilibrium increases the chances of discovering functional gene-marker associations. One theoretically valid approach-mapping by admixture linkage disequilibrium (MALD), using recently admixed African Americans-is empirically evaluated here by measurement of marker associations with 15 short tandem repeats (STRs) and an insertion/deletion polymorphism of the AT3 locus in a 70-cM segment at 1q22-23, around the FY (Duffy) locus. The FY polymorphism (-46T-->C) disrupts the GATA promoter motif, specifically blocking FY erythroid expression and has a nearly fixed allele-frequency difference between European Americans and native Africans that is likely a consequence of a selective advantage of FY-/- in malaria infections. Analysis of linkage disequilibrium around the FY gene has indicated that there is strong and consistent linkage disequilibrium between FY and three flanking loci (D1S303, SPTA1, and D1S484) spanning 8 cM. We observed significant linkage-disequilibrium signals over a 30-cM region from -4.4 to 16.3 cM (from D1S2777 to D1S196) for STRs and at 26.4 cM (AT3), which provided quantitative estimates of centimorgan limits, by MALD assessment in African American population-association analyses, of 5-10 cM.     

An approach to incorporate linkage disequilibrium structure into genomic association analysis

In this study, we propose to use the principal component analysis (PCA) and regression model to incorporate linkage disequilibrium (LD) in genomic association data analysis. To accommodate LD in genomic data and reduce multiple testing, we suggest performing PCA and extracting the PCA score to capture the variation of genomic data, after which regression analysis is used to assess the association of the disease with the principal component score. An empirical analysis result shows that both genotype-basod correlation matrix and haplotype-based LD matrix can produce similar results for PCA. Principal component score seems to be more powerful in detecting genetic association because the principal component score is quantitatively measured and may be able to capture the effect of multiple loci.     

Population structure and linkage disequilibrium in barley assessed by DArT markers

Diversity Array Technology (DArT) markers were used to investigate the genetic diversity, population structure, and extent of linkage disequilibrium (LD) on a genome-wide level in Canadian barley (Hordeum vulgare L.). Approximately 1,000 DArT markers were polymorphic and scored with high confidence among a collection of 170 barley lines composed mostly of Canadian cultivars and breeding lines. The reproducibility of DArT markers proved very high, as 99.9% of allele calls were identical among seven replicated samples. The polymorphism information content (PIC) of DArT markers ranged between 0.04 and 0.50 with an average of 0.38. Using principal coordinate analysis (PCoA), most lines fell into one of two major groups reflecting inflorescence type (two-row versus six-row). Within these two large groups, evidence of geographic clustering of genotypes was also observed. A cluster analysis Unweighted Pair Group Method with Algorithmic Mean suggested the existence of three subgroups within the two-row group and four subgroups within the six-row group. An analysis of molecular variance (AMOVA) revealed highly significant (P < 0.001) genetic variance within subgroups, among subgroups, and among groups. Values of LD, expressed as r ², declined with increasing genetic distance, and mean values of r ² fell below 0.2 for markers located 2.6 cM apart. Approximately 8% of marker pairs located on the same chromosome and 3.4% of pairs located on different chromosomes were in LD (r ²  > 0.2). Within both the subsets of two-row and six-row lines, LD extended slightly further (3.5 cM) than for the entire set, while 7.5% of intra-chromosomal locus pairs and <2% of inter-chromosomal pairs were in LD. We discuss the implications of these findings with regard to the prospects of association mapping of complex traits in barley.