Measure Of Disequilibrium Research Articles

VivaxGEN: An open access platform for comparative analysis of short tandem repeat genotyping data in Plasmodium vivax populations.

BackgroundThe control and elimination of Plasmodium vivax will require a better understanding of its transmission dynamics, through the application of genotyping and population genetics analyses. This paper describes VivaxGEN (http://vivaxgen.menzies.edu.au), a web-based platform that has been developed to support P. vivax short tandem repeat data sharing and comparative analyses.ResultsThe VivaxGEN platform provides a repository for raw data generated by capillary electrophoresis (FSA files), with fragment analysis and standardized allele calling tools. The query system of the platform enables users to filter, select and differentiate samples and alleles based on their specified criteria. Key population genetic analyses are supported including measures of population differentiation (FST), expected heterozygosity (HE), linkage disequilibrium (IAS), neighbor-joining analysis and Principal Coordinate Analysis. Datasets can also be formatted and exported for application in commonly used population genetic software including GENEPOP, Arlequin and STRUCTURE. To date, data from 10 countries, including 5 publicly available data sets have been shared with VivaxGEN.ConclusionsVivaxGEN is well placed to facilitate regional overviews of P. vivax transmission dynamics in different endemic settings and capable to be adapted for similar genetic studies of P. falciparum and other organisms.

Genetic diversity of a New Zealand multi-breed sheep population and composite breeds\u2019 history revealed by a high-density SNP chip

BackgroundKnowledge about the genetic diversity of a population is a crucial parameter for the implementation of successful genomic selection and conservation of genetic resources. The aim of this research was to establish the scientific basis for the implementation of genomic selection in a composite Terminal sheep breeding scheme by providing consolidated linkage disequilibrium (LD) measures across SNP markers, estimating consistency of gametic phase between breed-groups, and assessing genetic diversity measures, such as effective population size (Ne), and population structure parameters, using a large number of animals (n = 14,845) genotyped with a high density SNP chip (606,006 markers). Information generated in this research will be useful for optimizing molecular breeding values predictions and managing the available genetic resources.ResultsOverall, as expected, levels of pairwise LD decreased with increasing distance between SNP pairs. The mean LD r2 between adjacent SNP was 0.26 ± 0.10. The most recent effective population size for all animals (687) and separately per breed-groups: Primera (974), Lamb Supreme (380), Texel (227) and Dual-Purpose (125) was quite variable. The genotyped animals were outbred or had an average low level of inbreeding. Consistency of gametic phase was higher than 0.94 for all breed pairs at the average distance between SNP on the chip (~4.74 kb). Moreover, there was not a clear separation between the breed-groups based on principal component analysis, suggesting that a mixed-breed training population for calculation of molecular breeding values would be beneficial.ConclusionsThis study reports, for the first time, estimates of linkage disequilibrium, genetic diversity and population structure parameters from a genome-wide perspective in New Zealand Terminal Sire composite sheep breeds. The levels of linkage disequilibrium indicate that genomic selection could be implemented with the high density SNP panel. The moderate to high consistency of gametic phase between breed-groups and overlapping population structure support the pooling of the animals in a mixed training population for genomic predictions. In addition, the moderate to high Ne highlights the need to genotype and phenotype a large training population in order to capture most of the haplotype diversity and increase accuracies of genomic predictions. The results reported herein are a first step toward understanding the genomic architecture of a Terminal Sire composite sheep population and for the optimal implementation of genomic selection and genome-wide association studies in this sheep population.

Genome-wide population structure and evolutionary history of the Frizarta dairy sheep

In the present study, we used genomic data, generated with a medium density single nucleotide polymorphisms (SNP) array, to acquire more information on the population structure and evolutionary history of the synthetic Frizarta dairy sheep. First, two typical measures of linkage disequilibrium (LD) were estimated at various physical distances that were then used to make inferences on the effective population size at key past time points. Population structure was also assessed by both multidimensional scaling analysis and k-means clustering on the distance matrix obtained from the animals’ genomic relationships. The Wright’s fixation FST index was also employed to assess herds’ genetic homogeneity and to indirectly estimate past migration rates. The Wright’s fixation FIS index and genomic inbreeding coefficients based on the genomic relationship matrix as well as on runs of homozygosity were also estimated. The Frizarta breed displays relatively low LD levels with r2 and |Dʹ| equal to 0.18 and 0.50, respectively, at an average inter-marker distance of 31 kb. Linkage disequilibrium decayed rapidly by distance and persisted over just a few thousand base pairs. Rate of LD decay (β) varied widely among the 26 autosomes with larger values estimated for shorter chromosomes (e.g. β=0.057, for OAR6) and smaller values for longer ones (e.g. β=0.022, for OAR2). The inferred effective population size at the beginning of the breed’s formation was as high as 549, was then reduced to 463 in 1981 (end of the breed’s formation) and further declined to 187, one generation ago. Multidimensional scaling analysis and k-means clustering suggested a genetically homogenous population, FST estimates indicated relatively low genetic differentiation between herds, whereas a heat map of the animals’ genomic kinship relationships revealed a stratified population, at a herd level. Estimates of genomic inbreeding coefficients suggested that most recent parental relatedness may have been a major determinant of the current effective population size. A denser than the 50k SNP panel may be more beneficial when performing genome wide association studies in the breed.

The Decay of Disease Association with Declining Linkage Disequilibrium: A Fine Mapping Theorem.

Several important and fundamental aspects of disease genetics models have yet to be described. One such property is the relationship of disease association statistics at a marker site closely linked to a disease causing site. A complete description of this two-locus system is of particular importance to experimental efforts to fine map association signals for complex diseases. Here, we present a simple relationship between disease association statistics and the decline of linkage disequilibrium from a causal site. Specifically, the ratio of Chi-square disease association statistics at a marker site and causal site is equivalent to the standard measure of pairwise linkage disequilibrium, r2. A complete derivation of this relationship from a general disease model is shown. Quite interestingly, this relationship holds across all modes of inheritance. Extensive Monte Carlo simulations using a disease genetics model applied to chromosomes subjected to a standard model of recombination are employed to better understand the variation around this fine mapping theorem due to sampling effects. We also use this relationship to provide a framework for estimating properties of a non-interrogated causal site using data at closely linked markers. Lastly, we apply this way of examining association data from high-density genotyping in a large, publicly-available data set investigating extreme BMI. We anticipate that understanding the patterns of disease association decay with declining linkage disequilibrium from a causal site will enable more powerful fine mapping methods and provide new avenues for identifying causal sites/genes from fine-mapping studies.

Information-theoretic space from simple atomic and molecular systems to biological and pharmacological molecules

In this letter, we present an Information-Theoretic Space generated from the Shannon entropy, the Fisher information, and the disequilibrium measures along with their corresponding Fisher–Shannon and LMC complexity measures, which unveils the unique physical, chemical and biological aspects of a great diversity of many-electron systems, ranging from neutral and ionized atomic systems and simple molecules to much more complex systems such as amino acids and pharmacological molecular ensembles. This endeavour is achieved upon the physical ground that atoms and molecules can be described through the basic information-theoretic notions of delocalization, order, uniformity and complexity, thus revealing that a universal three-dimensional information-theoretic chemical space for all systems of Nature there might exist.

P065 Information theory-based analysis of classical HLA genes

Aim In IMGT/HLA Release 3.24.0, less than 7% of the named classical HLA alleles have curated full-length gene sequences or sequences outside the antigen recognition sites (ARS). This study is to investigate genetic variants, polymorphism, SNPs and linkage disequilibrium (LD) within the entire gene region for the classical HLA genes using information theory. Methods Multiple sequence alignment was performed on full-length HLA Class I alleles (HLA-A, -B, -C) and partial-length (from intron 1 through intron 3) Class II alleles (HLA-DQB1, -DRB1) for 15,865 subjects, followed by a gene annotation pipeline. We analyzed the Shannon entropy of each nucleotide site and mutual information within each of the loci. Conditional asymmetric linkage disequilibrium (ALD) measures were employed to characterize the LD between multiallelic SNPs within a locus. Results For HLA Class I alleles, the untranslated regions generally show high entropy variation. Highly variable sites (entropy >0.01) appear most in the noncoding regions (intron 3 in HLA-A and -B, respectively; intron 4 in HLA-C); while within coding regions, the ARS regions contain the most variants. However, since multiple sequence alignment introduces gaps that are ambiguous, we considered the distribution of variants after removing sites with at least one alignment gap. Consequently, for noncoding regions, intron 5 in HLA-A and -B, respectively, and introns 3 and 4 in HLA-C show the highest entropy variation; for coding regions, ARS regions remain highest entropy variation across all five loci. The ALD measures indicate that highly associated polymorphic sites mostly reside within exons 2, 3 and 4 (ARS regions for class II). Some of these associations also showed high heterogeneity. Conclusions Non-coding regions along with the non-ARS coding regions include many informative sites and the proposed method could be utilized in allele typing, typing validation, SNP association study, as well as matching for stem cell transplant.

Fine-scale spatial genetic structure of a fungal parasite of coffee scale insects

The entomopathogenic fungus Lecanicillium lecanii persists in a highly dynamic network of habitat patches (i.e., a metapopulation) formed by its primary host, the green coffee scale Coccus viridis. Lecanicillium lecanii is an important biological control of both C. viridis and the coffee rust, Hemileia vastatrix. Successfully managing this biocontrol agent will depend on an increased understanding of the characteristics of its dispersal, as migration between occupied and unoccupied patches is essential for the persistence of this metapopulation. In the present study, we employ a population genetics approach, and show that in our study system, a coffee farm in the Soconusco region of southern Mexico, L. lecanii is characterized by clear spatial genetic structure among plots within the farm but a lack of apparent structure at smaller scales. This is consistent with dispersal dominated by highly localized transport, such as by insects or rain splash, and less dependence on longer distance dispersal such as wind transport. The study site was dominated by a few multi-locus microsatellite genotypes, and their identities and large-scale locations persist across both study years, suggesting that local epizootics (outbreaks) are initiated each wet season by residual propagules from the previous wet season, and not by long-distance transport of propagules from other sites. The index of association, a measure of linkage disequilibrium, indicates that epizootics are primarily driven by asexual, clonal reproduction, which is consistent with the apparent lack of a teleomorph in the study site and the presence of only a single mating type across the site (MAT-1-2-1). Although the same predominant clonal genotypes were found across years, a drastic difference in genotypic diversity was witnessed across two sites between the two years, suggesting that interclonal selection was occurring. In light of the dispersal limitation of L. lecanii, spatial structure may be an essential axis of management to ensure the persistence of L. lecanii and preserve the ecosystem services provided by this versatile biocontrol agent in this and similar coffee farms.

Characterization of nine microsatellite loci for Dicrocoelium dendriticum, an emerging liver fluke of ungulates in North America, and their use to detect clonemates and random mating

This study characterizes polymorphic microsatellite loci from adults of the liver fluke Dicrocoelium dendriticum sampled from a population of sympatric beef cattle and wapiti in a region of emergence in southern Alberta, Canada. We also scrutinized the markers to validate their use in studying the population genetics of this complex life cycle parasite. Among the nine loci described, four deviated significantly from Hardy Weinberg Equilibrium (HWE) due to technical artefacts. The remaining five loci were in HWE. These five provided sufficient resolution to identify clonemates produced from the obligate asexual reproduction phase of the life cycle in snails and to assess the impact of non-random transmission of clonemates on measures of FIS, FST and genotypic disequilibrium. Excluding clonemates, we show that the sub-population of worms was in HWE, that average FIS within hosts was 0.003 (p=0.4922) and that there was no population genetic structure among hosts FST=0.001 (p=0.3243). These markers will be useful for studies of Dicrocoelium dendriticum ecology, transmission, and evolution.

Information Theoretical Methods as Discerning Quantifiers of the Equations of State of Neutron Stars

In this work we use the statistical measures of information entropy, disequilibrium and complexity to discriminate different approaches and parametrizations for different equations of state for quark stars. We confirm the usefulness of such quantities to quantify the role of interactions in such stars. We find that within this approach, a quark matter equation of state such as SU(2) NJL with vectorial coupling and phase transition is slightly favoured and deserves deeper studies.

Haplotype synthesis analysis reveals functional variants underlying known genome-wide associated susceptibility loci.

The functional mechanisms underlying disease association remain unknown for Genome-wide Association Studies (GWAS) susceptibility variants located outside coding regions. Synthesis of effects from multiple surrounding functional variants has been suggested as an explanation of hard-to-interpret findings. We define filter criteria based on linkage disequilibrium measures and allele frequencies which reflect expected properties of synthesizing variant sets. For eligible candidate sets, we search for haplotype markers that are highly correlated with associated variants. Via simulations we assess the performance of our approach and suggest parameter settings which guarantee 95% sensitivity at 20-fold reduced computational cost. We apply our method to 1000 Genomes data and confirmed Crohn's Disease (CD) and Type 2 Diabetes (T2D) variants. A proportion of 36.9% allowed explanation by three-variant-haplotypes carrying at least two functional variants, as compared to 16.4% for random variants ([Formula: see text]). Association could be explained by missense variants for MUC19, PER3 (CD) and HMG20A (T2D). In a CD GWAS-imputed using haplotype reference consortium data (64 976 haplotypes)-we could confirm the syntheses of MUC19 and PER3 and identified synthesis by missense variants for 6 further genes (ZGPAZ, GPR65, CLN3/NPIPB8, LOC102723878, rs2872507, GCKR). In all instances, the odds ratios of the synthesizing haplotypes were virtually identical to that of the index SNP. In summary, we demonstrate the potential of synthesis analysis to guide functional follow-up of GWAS findings. All methods are implemented in the C/C ++ toolkit GetSynth, available at http://sourceforge.net/projects/getsynth/ tim.becker@uni-greifswald.de Supplementary data are available at Bioinformatics online.

Association with Spontaneous Hepatitis C Viral Clearance and Genetic Differentiation of IL28B/IFNL4 Haplotypes in Populations from Mexico.

AimTo analyze the genetic heterogeneity of the Amerindian and admixed population (Mestizos) based on the IL28B (rs12979860, rs8099917) and IFNL4 (rs368234815) haplotypes, and their association with spontaneous clearance (SC) and liver damage in patients with hepatitis C infection from West Mexico.MethodsA total of 711 subjects from West Mexico (181 Amerindians and 530 Mestizos) were studied for the prevalence of IL28B (rs12979860C/T, rs8099917G/T) and IFNL4 (rs368234815∆G/TT) genotypes. A case-control study was performed in 234 treatment-naïve HCV Mestizos (149 chronic hepatitis C and 85 with SC) for the association of haplotypes with SC and liver damage. A real-time PCR assay was used for genotyping, and transitional elastography staged liver damage.ResultsSignificant Fst-values indicated differentiation between the studied populations. The frequencies of the protective C, T, TT alleles were significantly lower in the Amerindians than in Mestizos (p<0.05). The r2 measure of linkage disequilibrium was significant for all variants and the T/G/ΔG risk haplotype predominated in Amerindians and secondly in Mestizos. The protective C/T/TT haplotype was associated with SC (OR = 0.46, 95% IC 0.22–0.95, p = 0.03) and less liver damage (OR = 0.32, 95% IC 0.10–0.97, p = 0.04) in chronic patients. The Structure software analysis demonstrated no significant differences in ancestry among SC and chronic patients.ConclusionsWest Mexico´s population is genetically heterogeneous at the IL28B/IFNL4 polymorphisms. The T/G/ΔG high-risk haplotype predominated in Amerindians and the beneficial alternative haplotype in Mestizos. The C/T/TT haplotype was associated with SC and less liver damage in chronically infected Mestizo patients.

Privacy-preserving genome-wide association studies on cloud environment using fully homomorphic encryption.

ObjectiveDeveloped sequencing techniques are yielding large-scale genomic data at low cost. A genome-wide association study (GWAS) targeting genetic variations that are significantly associated with a particular disease offers great potential for medical improvement. However, subjects who volunteer their genomic data expose themselves to the risk of privacy invasion; these privacy concerns prevent efficient genomic data sharing. Our goal is to presents a cryptographic solution to this problem.MethodsTo maintain the privacy of subjects, we propose encryption of all genotype and phenotype data. To allow the cloud to perform meaningful computation in relation to the encrypted data, we use a fully homomorphic encryption scheme. Noting that we can evaluate typical statistics for GWAS from a frequency table, our solution evaluates frequency tables with encrypted genomic and clinical data as input. We propose to use a packing technique for efficient evaluation of these frequency tables.ResultsOur solution supports evaluation of the D′ measure of linkage disequilibrium, the Hardy-Weinberg Equilibrium, the χ2 test, etc. In this paper, we take χ2 test and linkage disequilibrium as examples and demonstrate how we can conduct these algorithms securely and efficiently in an outsourcing setting. We demonstrate with experimentation that secure outsourcing computation of one χ2 test with 10, 000 subjects requires about 35 ms and evaluation of one linkage disequilibrium with 10, 000 subjects requires about 80 ms.ConclusionsWith appropriate encoding and packing technique, cryptographic solutions based on fully homomorphic encryption for secure computations of GWAS can be practical.

Using the variability of linkage disequilibrium between subpopulations to infer sweeps and epistatic selection in a diverse panel of chickens.

A whole-genome scan for identifying selection acting on pairs of linked loci is proposed and implemented. The scan is based on , one of Ohta's 1982 measures of between-population linkage disequilibrium (LD). An approximate empirical null distribution for the statistic is suggested. Although the partitioning of LD into between-population components was originally used to investigate epistatic selection, we demonstrate that values of may also be influenced by single-locus selective sweeps with linkage but no epistasis. The proposed scan is implemented in a diverse panel of chickens including 72 distinct breeds genotyped at 538 298 single-nucleotide polymorphisms. In all, 1723 locus pairs are identified as putatively corresponding to a selective sweep or epistatic selection. These pairs of loci generally cluster to form overlapping or neighboring signals of selection. Known variants that were expected to have been under selection in the panel are identified, as well as an assortment of novel regions that have putatively been under selection in chickens. Notably, a promising pair of genes located 8 MB apart on chromosome 9 are identified based on as demonstrating strong evidence of dispersive epistatic selection between populations.

Asymmetric linkage disequilibrium: Tools for assessing multiallelic LD

Standard measures of linkage disequilibrium (LD) provide an incomplete description of the correlation between two loci. Recently, Thomson and Single (2014) described a new asymmetric pair of LD measures (ALD) that give a more complete description of LD. The ALD measures are symmetric and equivalent to the correlation coefficient r when both loci are bi-allelic. When the numbers of alleles at the two loci differ, the ALD measures capture this asymmetry and provide additional detail about the LD structure. In disease association studies the ALD measures are useful for identifying additional disease genes in a genetic region, by conditioning on known effects. In evolutionary genetic studies ALD measures provide insight into selection acting on individual amino acids of specific genes, or other loci in high LD (see Thomson and Single (2014) for these examples). Here we describe new software for computing and visualizing ALD. We demonstrate the utility of this software using haplotype frequency data from the National Marrow Donor Program (NMDP). This enhances our understanding of LD patterns in the NMDP data by quantifying the degree to which LD is asymmetric and also quantifies this effect for individual alleles.

Contrasting Transmission Dynamics of Co-endemic Plasmodium vivax and P. falciparum: Implications for Malaria Control and Elimination.

BackgroundOutside of Africa, P. falciparum and P. vivax usually coexist. In such co-endemic regions, successful malaria control programs have a greater impact on reducing falciparum malaria, resulting in P. vivax becoming the predominant species of infection. Adding to the challenges of elimination, the dormant liver stage complicates efforts to monitor the impact of ongoing interventions against P. vivax. We investigated molecular approaches to inform the respective transmission dynamics of P. falciparum and P. vivax and how these could help to prioritize public health interventions.Methodology/ Principal FindingsGenotype data generated at 8 and 9 microsatellite loci were analysed in 168 P. falciparum and 166 P. vivax isolates, respectively, from four co-endemic sites in Indonesia (Bangka, Kalimantan, Sumba and West Timor). Measures of diversity, linkage disequilibrium (LD) and population structure were used to gauge the transmission dynamics of each species in each setting. Marked differences were observed in the diversity and population structure of P. vivax versus P. falciparum. In Bangka, Kalimantan and Timor, P. falciparum diversity was low, and LD patterns were consistent with unstable, epidemic transmission, amenable to targeted intervention. In contrast, P. vivax diversity was higher and transmission appeared more stable. Population differentiation was lower in P. vivax versus P. falciparum, suggesting that the hypnozoite reservoir might play an important role in sustaining local transmission and facilitating the spread of P. vivax infections in different endemic settings. P. vivax polyclonality varied with local endemicity, demonstrating potential utility in informing on transmission intensity in this species.Conclusions/ SignificanceMolecular approaches can provide important information on malaria transmission that is not readily available from traditional epidemiological measures. Elucidation of the transmission dynamics circulating in a given setting will have a major role in prioritising malaria control strategies, particularly against the relatively neglected non-falciparum species.

Single-nucleotide polymorphisms in CD8A and their associations with T lymphocyte subpopulations in pig.

Findings from previous studies suggested that the cluster of the differentiation 8 alpha (CD8A) gene plays a prominent role in human T lymphocyte subpopulations. However, the evidence from pig population is still rare. To determine whether the important role of the CD8A gene is conserved in pig, a candidate gene analysis was performed herein through genotype-phenotype associations. Five single-nucleotide polymorphisms (SNPs) locating in the regulatory region of porcine CD8A gene were detected and tested for association analysis with seven T lymphocyte subpopulations (proportion of CD4(-)CD8(-), CD4(+)CD8(+), CD4(+)CD8(-), CD4(-)CD8(+), CD4(+), CD8(+), and the ratio of CD4(+) to CD8(+) T cells in peripheral blood) in 382 Large White piglets. After Bonferroni correction for multiple testing, four SNPs were significantly associated with some or all of the seven T lymphocyte subpopulations. Analyses of pairwise D' measures of linkage disequilibrium between all SNPs were also explored. Two haplotype blocks was inferred and the association study on haplotype level revealed similar effects on T lymphocyte subpopulations. In addition, the tissue-specific RNA expression pattern and electrophoretic mobility shift assay offered further explanation of the link between the CD8A gene with porcine T lymphocyte subpopulations. The findings presented here provide strong evidence for associations of CD8A variants with T lymphocyte subpopulations and may be applied in porcine breeding programs.

The Effect of Interference on the CD8(+) T Cell Escape Rates in HIV.

In early human immunodeficiency virus (HIV) infection, the virus population escapes from multiple CD8+ cell responses. The later an escape mutation emerges, the slower it outgrows its competition, i.e., the escape rate is lower. This pattern could indicate that the strength of the CD8+ cell responses is waning, or that later viral escape mutants carry a larger fitness cost. In this paper, we investigate whether the pattern of decreasing escape rates could also be caused by genetic interference among different escape strains. To this end, we developed a mathematical multi-epitope model of HIV dynamics, which incorporates stochastic effects, recombination, and mutation. We used cumulative linkage disequilibrium measures to quantify the amount of interference. We found that nearly synchronous, similarly strong immune responses in two-locus systems enhance the generation of genetic interference. This effect, combined with a scheme of densely spaced sampling times at the beginning of infection and sparse sampling times later, leads to decreasing successive escape rate estimates, even when there were no selection differences among alleles. These predictions are supported by empirical data from one HIV-infected patient. Thus, interference could explain why later escapes are slower. Considering escape mutations in isolation, neglecting their genetic linkage, conceals the underlying haplotype dynamics and can affect the estimation of the selective pressure exerted by CD8+ cells. In systems in which multiple escape mutations appear, the occurrence of interference dynamics should be assessed by measuring the linkage between different escape mutations.

Information theoretical methods as discerning quantifiers of the equations of state of neutron stars

Abstract In this work we use the statistical measures of information entropy, disequilibrium and complexity to discriminate different approaches and parametrizations for different equations of state for quark stars. We confirm the usefulness of such quantities to quantify the role of interactions in such stars. We find that within this approach, a quark matter equation of state such as SU(2) NJL with vectorial coupling and phase transition is slightly favoured and deserves deeper studies.

Analysis of spontaneous MEG activity in mild cognitive impairment and Alzheimer's disease using Jensen's divergence.

The aim of this study was to analyze the changes that mild cognitive impairment (MCI) and Alzheimer's disease (AD) elicit in brain dynamics. For this task, the spontaneous magnetoencephalographic (MEG) activity from 36 AD patients, 18 MCI subjects and 24 healthy controls was analyzed. A disequilibrium measure, Jensen's divergence, was used to estimate the irregularity of neural dynamics. Results revealed that AD patients displayed significant changes (p<;0.05) in the patterns of irregularity in comparison with MCI subjects and healthy controls. Slight differences between MCI subjects and elderly controls were also found. Our results suggest that AD progression is accompanied by region-specific patterns of abnormalities in the neural activity.

Conditional asymmetric linkage disequilibrium (ALD): extending the biallelic r2 measure.

For multiallelic loci, standard measures of linkage disequilibrium provide an incomplete description of the correlation of variation at two loci, especially when there are different numbers of alleles at the two loci. We have developed a complementary pair of conditional asymmetric linkage disequilibrium (ALD) measures. Since these measures do not assume symmetry, they more accurately describe the correlation between two loci and can identify heterogeneity in genetic variation not captured by other symmetric measures. For biallelic loci the ALD are symmetric and equivalent to the correlation coefficient r. The ALD measures are particularly relevant for disease-association studies to identify cases in which an analysis can be stratified by one of more loci. A stratified analysis can aid in detecting primary disease-predisposing genes and additional disease genes in a genetic region. The ALD measures are also informative for detecting selection acting independently on loci in high linkage disequilibrium or on specific amino acids within genes. For SNP data, the ALD statistics provide a measure of linkage disequilibrium on the same scale for comparisons among SNPs, among SNPs and more polymorphic loci, among haplotype blocks of SNPs, and for fine mapping of disease genes. The ALD measures, combined with haplotype-specific homozygosity, will be increasingly useful as next-generation sequencing methods identify additional allelic variation throughout the genome.