Linkage maps have been invaluable for the positional cloning of many genes involved in severe human diseases. Standard genetic linkage maps have been constructed for this purpose from the Centre d'Etude du Polymorphisme Humain and other panels, and have been widely used. Now that attention has shifted towards identifying genes predisposing to common disorders using linkage disequilibrium (LD) and maps of single nucleotide polymorphisms (SNPs), it is of interest to consider a standard LD map which is somewhat analogous to the corresponding map for linkage. We have constructed and evaluated a cosmopolitan LD map by combining samples from a small number of populations using published data from a 10-megabase region on chromosome 20. In support of a pilot study, which examined a number of small genomic regions with a lower density of markers, we have found that a cosmopolitan map, which serves all populations when appropriately scaled, recovers 91 to 95 per cent of the information within population-specific maps. Recombination hot spots appear to have a dominant role in shaping patterns of LD. The success of the cosmopolitan map might be attributed to the co-localisation of hot spots in all populations. Although there must be finer scale differences between populations due to other processes (mutation, drift, selection), the results suggest that a whole-genome standard LD map would indeed be a useful resource for disease gene mapping.

The maximum likelihood estimator of D'--a standard measure of linkage disequilibrium--is biased toward disequilibrium, and the bias is particularly evident in small samples and rare haplotypes.

Assortative mating has been suggested to result in an increase in heritability and additive genetic variance through an increase in linkage disequilibrium. The impact of assortative mating on linkage disequilibrium was explicitly examined for the two-locus model of Wright (1921) and two selective assortative mating models. For the Wright (1921) model, when the proportion of assortative mating was high, positive linkage disequilibrium was generated. However, when the proportion of assortative mating was similar to that found in some studies, the amount of linkage disequilibrium was quite low. In addition, the amount of linkage disequilibrium was independent of the level of recombination. For two selective assortative models, the amount of linkage disequilibrium was a function of the amount of recombination. For these models, the linkage disequilibrium generated was negative mainly because repulsion heterozygotes were favored over coupling heterozygotes. From these findings, the impact of assortative mating on linkage disequilibrium, and consequently heritability and additive genetic variance, appears to be small and model-specific.

Recently, metric linkage disequilibrium (LD) maps that assign an LD unit (LDU) location for each marker have been developed (Maniatis et al. 2002). Here we present a multiple pairwise method for positional cloning by LD within a composite likelihood framework and investigate the operating characteristics of maps in physical units (kb) and LDU for two bodies of data (Daly et al. 2001; Jeffreys et al. 2001) on which current ideas of blocks are based. False-negative indications of a disease locus (type II error) were examined by selecting one single-nucleotide polymorphism (SNP) at a time as causal and taking its allelic count (0, 1, or 2, for the three genotypes) as a pseudophenotype, Y. By use of regression and correlation, association between every pseudophenotype and the allelic count of each SNP locus (X) was based on an adaptation of the Malecot model, which includes a parameter for location of the putative gene. By expressing locations in kb or LDU, greater power for localization was observed when the LDU map was fitted. The efficiency of the kb map, relative to the LDU map, to describe LD varied from a maximum of 0.87 to a minimum of 0.36, with a mean of 0.62. False-positive indications of a disease locus (type I error) were examined by simulating an unlinked causal SNP and the allele count was used as a pseudophenotype. The type I error was in good agreement with Wald's likelihood theorem for both metrics and all models that were tested. Unlike tests that select only the most significant marker, haplotype, or haploset, these methods are robust to large numbers of markers in a candidate region. Contrary to predictions from tagging SNPs that retain haplotype diversity, the sample with smaller size but greater SNP density gave less error. The locations of causal SNPs were estimated with the same precision in blocks and steps, suggesting that block definition may be less useful than anticipated for mapping a causal SNP. These results provide a guide to efficient positional cloning by SNPs and a benchmark against which the power of positional cloning by haplotype-based alternatives may be measured.

Crosses between laboratory strains of mice provide a powerful way of detecting quantitative trait loci for complex traits related to human disease. Hundreds of these loci have been detected, but only a small number of the underlying causative genes have been identified. The main difficulty is the extensive linkage disequilibrium (LD) in intercross progeny and the slow process of fine-scale mapping by traditional methods. Recently, new approaches have been introduced, such as association studies with inbred lines and multigenerational crosses. These approaches are very useful for interval reduction, but generally do not provide single-gene resolution because of strong LD extending over one to several megabases. Here, we investigate the genetic structure of a natural population of mice in Arizona to determine its suitability for fine-scale LD mapping and association studies. There are three main findings: (1) Arizona mice have a high level of genetic variation, which includes a large fraction of the sequence variation present in classical strains of laboratory mice; (2) they show clear evidence of local inbreeding but appear to lack stable population structure across the study area; and (3) LD decays with distance at a rate similar to human populations, which is considerably more rapid than in laboratory populations of mice. Strong associations in Arizona mice are limited primarily to markers less than 100 kb apart, which provides the possibility of fine-scale association mapping at the level of one or a few genes. Although other considerations, such as sample size requirements and marker discovery, are serious issues in the implementation of association studies, the genetic variation and LD results indicate that wild mice could provide a useful tool for identifying genes that cause variation in complex traits.

The presence of linkage disequilibrium violates the underlying assumption of linkage equilibrium in most traditional multipoint linkage approaches. Studies have shown that such violation leads to bias in qualitative trait linkage analysis when parental genotypes are unavailable. Appropriate handling of marker linkage disequilibrium can avoid such false positive evidence. Using the rheumatoid arthritis simulated data from Genetic Analysis Workshop 15, we examined and compared the following three approaches to handle linkage disequilibrium among dense markers in both qualitative and quantitative trait linkage analyses: a simple algorithm; SNPLINK, methods for marker selection; and MERLIN-LD, a method for modeling linkage disequilibrium by creating marker clusters. In analysis ignoring linkage disequilibrium between markers, we observed LOD score inflation only in the affected sib-pair linkage analysis without parental genotypes; no such inflation was present in the quantitative trait locus linkage analysis with severity as our phenotype with or without parental genotypes. Using methods to model or adjust for linkage disequilibrium, we found a substantial reduction of inflation of LOD score in affected sib-pair linkage analysis. Greater LOD score reduction was observed by decreasing the amount of tolerable linkage disequilibrium among markers selected or marker clusters using MERLIN-LD; the latter approach showed most reduction. SNPLINK performed better with selected markers based on the D' measure of linkage disequilibrium as opposed to the r2 measure and outperformed the simple algorithm. Our findings reiterate the necessity of properly handling dense markers in linkage analysis, especially when parental genotypes are unavailable.

The guppy Y chromosome has been considered a model system for the evolution of suppressed recombination between sex chromosomes, and it has been proposed that complete sex-linkage has evolved across about 3 Mb surrounding this fish's sex-determining locus, followed by recombination suppression across a further 7 Mb of the 23 Mb XY pair, forming younger "evolutionary strata". Sequences of the guppy genome show that Y is very similar to the X chromosome. Knowing which parts of the Y are completely nonrecombining, and whether there is indeed a large completely nonrecombining region, are important for understanding its evolution. Here, we describe analyses of PoolSeq data in samples from within multiple natural populations from Trinidad, yielding new results that support previous evidence for occasional recombination between the guppy Y and X. We detected recent demographic changes, notably that downstream populations have higher synonymous site diversity than upstream ones and other expected signals of bottlenecks. We detected evidence of associations between sequence variants and the sex-determining locus, rather than divergence under a complete lack of recombination. Although recombination is infrequent, it is frequent enough that associations with SNPs can suggest the region in which the sex-determining locus must be located. Diversity is elevated across a physically large region of the sex chromosome, conforming to predictions for a genome region with infrequent recombination that carries one or more sexually antagonistic polymorphisms. However, no consistently male-specific variants were found, supporting the suggestion that any completely sex-linked region may be very small.

Current efforts to find disease-causing genes depend on patterns of linkage disequilibrium in human populations. Recent work has shown that linkage disequilibrium can extend over much larger genomic regions than expected, and that the patterns of linkage disequilibrium can differ markedly among populations.

Bovine whole genome linkage disequilibrium maps were constructed for eight breeds of cattle. These data provide fundamental information concerning bovine genome organization which will allow the design of studies to associate genetic variation with economically important traits and also provides background information concerning the extent of long range linkage disequilibrium in cattle.

Genome-wide association studies with single nucleotide polymorphisms (SNPs) show great promise to identify genetic determinants of complex human traits. In current analyses, genotype calling and imputation of missing genotypes are usually considered as two separated tasks. The genotypes of SNPs are first determined one at a time from allele signal intensities. Then the missing genotypes, i.e., no-calls caused by not perfectly separated signal clouds, are imputed based on the linkage disequilibrium (LD) between multiple SNPs. Although many statistical methods have been developed to improve either genotype calling or imputation of missing genotypes, treating the two steps independently can lead to loss of genetic information.

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

Recent migrations and inter-ethnic mating of long isolated populations have resulted in genetically admixed populations. To understand the complex population admixture process, which is critical to both evolutionary and medical studies, here we used admixture induced linkage disequilibrium (LD) to infer continuous admixture events, which is common for most existing admixed populations. Unlike previous studies, we expanded the typical continuous admixture model to a more general scenario with isolation after a certain duration of continuous gene flow. Based on the new models, we developed a method, CAMer, to infer the admixture history considering continuous and complex demographic process of gene flow between populations. We evaluated the performance of CAMer by computer simulation and further applied our method to real data analysis of a few well-known admixed populations.

We performed whole-genome amplification followed by hybridization of custom-designed resequencing arrays to resequence 303 kb of genomic sequence from a worldwide panel of 39 Bacillus anthracis strains. We used an efficient algorithm contained within a custom software program, UniqueMER, to identify and mask repetitive sequences on the resequencing array to reduce false-positive identification of genetic variation, which can arise from cross-hybridization. We discovered a total of 240 single nucleotide variants (SNVs) and showed that B. anthracis strains have an average of 2.25 differences per 10,000 bases in the region we resequenced. Common SNVs in this region are found to be in complete linkage disequilibrium. These patterns of variation suggest there has been little if any historical recombination among B. anthracis strains since the origin of the pathogen. This pattern of common genetic variation suggests a framework for recognizing new or genetically engineered strains.

Detailed study of genetic variation at the population level in humans and other species is now possible due to the availability of large sets of single nucleotide polymorphism data. Alleles at two or more loci are said to be in linkage disequilibrium (LD) when they are correlated or statistically dependent. Current efforts to understand the genetic basis of complex phenotypes are based on the existence of such associations, making study of the extent and distribution of linkage disequilibrium central to this endeavour. The objective of this paper is to develop methods to study fine-scale patterns of allelic association using probabilistic graphical models.

Chromatin interactions and linkage disequilibrium (LD) are both pairwise measurements between genomic loci that show block patterns along mammalian chromosomes. Their values are generally high for sites that are nearby in the linear genome but abruptly drop across block boundaries. One function of chromatin boundaries is to insulate regulatory domains from one another. Since recombination is depressed within genes and between distal regulatory elements and their promoters, we hypothesized that LD and chromatin contact frequency might be correlated genome-wide with the boundaries of LD blocks and chromatin domains frequently coinciding. To comprehensively address this question, we compared chromatin contacts in 22 cell types to LD across billions of pairs of loci in the human genome. These computationally intensive analyses revealed that there is no concordance between LD and chromatin interactions, even at genomic distances below 25 kilobases (kb) where both tend to be high. At genomic distances where LD is approximately zero, chromatin interactions are frequent. While LD is somewhat elevated between distal regulatory elements and their promoters, LD block boundaries are depleted-not enriched-at chromatin boundaries. Finally, gene expression and ontology data suggest that chromatin contacts identify regulatory variants more reliably than do LD and genomic proximity. We conclude that the genomic architectures of genetic and physical interactions are independent, with important implications for gene regulatory evolution, interpretation of genetic association studies, and precision medicine.

Long-range linkage disequilibria (LRLD) between sites that are widely separated on chromosomes may suggest that population admixture, epistatic selection, or other evolutionary forces are at work. We quantified patterns of LRLD on a chromosome-wide level in the YRI population of the HapMap dataset of single nucleotide polymorphisms (SNPs). We calculated the disequilibrium between all pairs of SNPs on each chromosome (a total of >2×10(11) values) and evaluated significance of overall disequilibrium using randomization. The results show an excess of associations between pairs of distant sites (separated by >0.25 cM) on all of the 22 autosomes. We discuss possible explanations for this observation.

Software tools for linkage disequilibrium (LD) analyses are designed to calculate LD among all genetic variants in a single region. Since compute and memory requirements grow quadratically with the distance between variants, using these tools for long-range LD calculations leads to long execution times and increased allocation of memory resources. Furthermore, widely used tools do not fully utilize the computational resources of modern processors and/or graphics processing cards, limiting future large-scale analyses on thousands of samples. We present quickLD, a stand-alone and open-source software that computes several LD-related statistics, including the commonly used r2 . quickLD calculates pairwise LD between genetic variants in a single region or in arbitrarily distant regions with negligible memory requirements. Moreover, quickLD achieves up to 95% and 97% of the theoretical peak performance of a CPU and a GPU, respectively, enabling 21.5× faster processing than current state-of-the-art software on a multicore processor and 49.5× faster processing when the aggregate processing power of a multicore CPU and a GPU is harnessed. quickLD can also be used in studies of selection, recombination, genetic drift, inbreeding and gene flow. The software is available at https://github.com/pephco/quickLD.

Both genome-wide association (GWA) studies and genomic selection depend on the level of non-random association of alleles at different loci, i.e. linkage disequilibrium (LD), across the genome. Therefore, characterizing LD is of fundamental importance to implement both approaches. In this study, using a 60K single nucleotide polymorphism (SNP) panel, we estimated LD and haplotype structure in crossbred broiler chickens and their component pure lines (one male and two female lines) and calculated the consistency of LD between these populations.

Peach (Prunus persica (L.) Batsch) is one of the most important model fruits in the Rosaceae family. Native to the west of China, where peach has been domesticated for more than 4,000 years, its cultivation spread from China to Persia, Mediterranean countries and to America. Chinese peach has had a major impact on international peach breeding programs due to its high genetic diversity. In this research, we used 48 highly polymorphic SSRs, distributed over the peach genome, to investigate the difference in genetic diversity, and linkage disequilibrium (LD) among Chinese cultivars, and North American and European cultivars, and the evolution of current peach cultivars.

The extent of linkage disequilibrium (LD) was studied in two small food-gathering populations-Evenki and Saami-and two larger food-producing populations-Finns and Swedes-in northern Eurasia. In total, 50 single-nucleotide polymorphisms (SNPs) from five genes were genotyped using real-time pyrophosphate DNA sequencing, whereas 14 microsatellites were genotyped in two X-chromosomal regions. In addition, hypervariable region I of the mtDNA was sequenced to shed light on the demographic history of the populations. The SNP data, as well as the microsatellite data, reveal extensive levels of LD in Evenki and Saami when compared to Finns and Swedes. mtDNA-sequence variation is compatible with constant population size over time in Evenki and Saami but indicates population expansion in Finns and Swedes. Furthermore, the similarity between Finns and Swedes in SNP allele- and haplotype-frequency distributions indicate that these two populations may share a recent common origin. These findings suggest that populations such as the Evenki and the Saami, rather than the Finns, may be particularly suited for the initial coarse mapping of common complex diseases.