Measure Linkage Disequilibrium Research Articles

Correlated Allele Frequency Changes Reveal Clonal Structure and Selection in Temporal Genetic Data.

In evolving populations where the rate of beneficial mutations is large, subpopulations of individuals with competing beneficial mutations can be maintained over long times. Evolution with this kind of clonal structure is commonly observed in a wide range of microbial and viral populations. However, it can be difficult to completely resolve clonal dynamics in data. This is due to limited read lengths in high-throughput sequencing methods, which are often insufficient to directly measure linkage disequilibrium or determine clonal structure. Here, we develop a method to infer clonal structure using correlated allele frequency changes in time-series sequence data. Simulations show that our method recovers true, underlying clonal structures when they are known and accurately estimate linkage disequilibrium. This information can then be combined with other inference methods to improve estimates of the fitness effects of individual mutations. Applications to data suggest novel clonal structures in an E. coli long-term evolution experiment, and yield improved predictions of the effects of mutations on bacterial fitness and antibiotic resistance. Moreover, our method is computationally efficient, requiring orders of magnitude less run time for large data sets than existing methods. Overall, our method provides a powerful tool to infer clonal structures from data sets where only allele frequencies are available, which can also improve downstream analyses.

Covariation of viral recombination with single nucleotide variants during virus evolution revealed by CoVaMa.

Adaptation of viruses to their environments occurs through the acquisition of both novel single-nucleotide variants (SNV) and recombination events including insertions, deletions, and duplications. The co-occurrence of SNVs in individual viral genomes during their evolution has been well-described. However, unlike covariation of SNVs, studying the correlation between recombination events with each other or with SNVs has been hampered by their inherent genetic complexity and a lack of bioinformatic tools. Here, we expanded our previously reported CoVaMa pipeline (v0.1) to measure linkage disequilibrium between recombination events and SNVs within both short-read and long-read sequencing datasets. We demonstrate this approach using long-read nanopore sequencing data acquired from Flock House virus (FHV) serially passaged in vitro. We found SNVs that were either correlated or anti-correlated with large genomic deletions generated by nonhomologous recombination that give rise to Defective-RNAs. We also analyzed NGS data from longitudinal HIV samples derived from a patient undergoing antiretroviral therapy who proceeded to virological failure. We found correlations between insertions in the p6Gag and mutations in Gag cleavage sites. This report confirms previous findings and provides insights on novel associations between SNVs and specific recombination events within the viral genome and their role in viral evolution.

Associations between TMEM196 polymorphisms and NSAID-exacerbated respiratory disease in asthma.

We previously found differences in the minor allele frequency (MAF) of single-nucleotide polymorphisms (SNPs) in transmembrane protein 196 (TMEM196) between 995 patients with aspirin-tolerant asthma (ATA) and 141 asthmatic patients with NSAID-exacerbated respiratory disease (NERD). In this study, we statistically analyzed the distributions of the genotypes and haplotypes of these SNPs to determine the exact association between TMEM196 genetic variants and the risk for NERD. Lewontin's D' and r values were used to measure linkage disequilibrium between the biallelic loci having MAFs more than 0.05, and haplotypes were inferred using the PHASE algorithm (version 2.0). The genotype distribution was analyzed by logistic regression models using age of onset, smoking status (nonsmoker=0, ex-smoker=1, smoker=2), and BMI as covariates. Regression analysis of the association between SNPs and the risk of NERD was analyzed using SPSS version 12.0 and PLINK version 1.9. The MAF of rs9886152 C>T was significantly lower in NERD than in ATA [24.8 vs. 34.0%, odds ratio=0.64 (0.48-0.85), P=2.07×10, Pcorr=0.048]. The rate of the rs9886152 C>T minor allele was significantly lower in NERD than in ATA [44.0 vs. 56.4% in the codominant model, P=0.002, Pcorr=0.049, odds ratio=0.64 (0.48-0.85)]. An additional three SNPs (rs9639334 A>G, rs9638765 A>G, and rs2097811 G>A) showed similar associations with the risk of NERD. NERD patients had lower frequencies of the rs9639334 A>G minor allele (51.1 vs. 64.4%, P=0.002, Pcorr=0.043), rs9638765 A>G (49.7 vs. 64.2%, P=0.001, Pcorr=0.017), and rs2097811 G>A (51.1 vs. 64.5%, P=0.002, Pcorr=0.04) compared with ATA patients. Patients homozygous for the minor alleles of the four SNPs showed significantly less of an aspirin-induced decrease in forced expiratory volume in one second compared with those homozygous for the common alleles (P=0.003-0.012). The minor alleles of the four SNPs in TMEM196 may exert a protective effect against the development of NERD and may be useful genetic markers to predict the risk of NERD.

Mathematical Properties of Linkage Disequilibrium Statistics Defined by Normalization of the Coefficient D = pAB – pApB

Background: Many statistics for measuring linkage disequilibrium (LD) take the form of a normalization of the LD coefficient D. Different normalizations produce statistics with different ranges, interpretations, and arguments favoring their use. Methods: Here, to compare the mathematical properties of these normalizations, we consider 5 of these normalized statistics, describing their upper bounds, the mean values of their maxima over the set of possible allele frequency pairs, and the size of the allele frequency regions accessible given specified values of the statistics. Results: We produce detailed characterizations of these properties for the statistics d and ρ, analogous to computations previously performed for r². We examine the relationships among the statistics, uncovering conditions under which some of them have close connections. Conclusion: The results contribute insight into LD measurement, particularly the understanding of differences in the features of different LD measures when computed on the same data.

Genome-wide association study for somatic cell score in Argentinean dairy cattle

This study aimed to understand the genomic architecture of Argentinean dairy herds by measuring linkage disequilibrium (LD) and identifying loci associated with parameters calculated from somatic cell count (SCC). Phenotypic data consisted of 3530 SCC records from 544 Holstein and Holstein x Jersey cows owned by a single dairy company located in the Central dairy area of Argentina. SCC was recorded every 40 days. After quality control, genotypic data consisted in 38,872 single nucleotide polymorphisms (SNP). The squared correlation of the alleles at two loci (r2) was computed for all SNP pairs on each chromosome. At marker distances less than 10kb the average r2 was 0.40. Between 40 and 50kb the average r2 was 0.25 and 0.18 for 100kb apart. Three different variables were calculated from the somatic cell score (SCS): the arithmetic mean (AM), the maximum value (MAX) and the arithmetic mean of the top 3 values (TOP3). Few significant SNP associations were found. As expected, polygenic traits such as SCC are influenced by multiple loci throughout the genome, each with a relatively small effect. AM on one side and TOP3 and MAX on the other, showed different SNP associated showing that they capture different aspects of mastitis response. AM was significantly associated with two SNP: ARS-BFGL-NGS-114608 (BTA1) and Hapmap60306-rs29023088 (BTA5). MAX and TOP3 were significantly associated with four SNP: ARS-BFGL-NGS-107594, ARS-BFGL-NGS-104220 (BTA10), BTA-43543-no-rs (BTA18) and ARS-BFGL-NGS-109705 (BTA26). MAX and TOP3 were equivalent phenotypic variables to be used in a GWAS. These results contribute to gain insight into the genomic regions influencing the SCC in Argentinean herds.

Measuring linkage disequilibrium by the partial correlation coefficient

Measuring linkage disequilibrium by the partial correlation coefficient

The Extent of Linkage Disequilibrium and Computational Challenges of Single Nucleotide Polymorphisms in Genome-Wide Association Studies

Single Nucleotide Polymorphisms (SNPs) are the most abundant form of genetic variations observed in the human genome. With the advent of high-throughput genotyping arrays and next-generation sequencing (NGS) platforms, tens of millions of SNPs have been uncovered in several human populations. However, the huge amount of SNPs bring new challenges in subsequent analysis. In reality, a number of SNPs may not be genotyped, and non-mutant bases may be falsely reported as SNPs in the microarray and NGS platforms. Furthermore, the identification of disease susceptibility genes are often confounded by numerous SNPs correlated by chance. In this paper, we review existing approaches for calling SNPs using microarrays and next-generation sequencing (NGS) platforms. Methods for measuring linkage disequilibrium (LD) and applications of the LD structure are discussed. Finally, we compare methods for inferring haplotypes from genotypes using microarray and NGS platforms and present the challenges of using SNPs in large-scale association studies.

A novel method to express SNP‐based genetic heterogeneity, Ψ, and its use to measure linkage disequilibrium for multiple SNPs, Dg, and to estimate absolute maximum of haplotype frequency

Single nucleotide polymorphisms (SNPs) are important markers to investigate genetic heterogeneity of population and to perform linkage disequilibrium (LD) mapping. We propose a new method, Psi, to express frequency of 2(N(s)) haplotypes for N(s) di-allelic SNPs. Using the new expression of haplotype frequency, we propose a novel measure of LD, D(g), not only for SNP pairs but also for multiple markers. The values of D(g) for SNP pairs were revealed to be similar to values of conventional pairwise LD indices, D' and r(2), and it was revealed that D(g) quantitated components of LD that were not measured by conventional LD indices for SNP pairs. Also we propose a distinct method, D(g)-based absolute estimation, to infer the absolute maximum estimates of haplotype frequency. The result of the D(g)-based absolute estimation of haplotype frequency for SNP pairs were compared with the conventional expectation-maximization (EM) algorithm and reported that the new method gave better inference than the EM algorithm which converged infrequently to a local extreme.

Association of specific haplotypes of GAS6 gene with stroke

The product of the growth arrest-specific gene 6 (GAS6), a ligand for tyrosine kinase receptors, is a vitamin K-dependent protein, structurally related to anticoagulant protein S. Gas6-deficient mice are protected against thrombosis, demonstrating the importance of this protein in the cardiovascular system. In a preliminary study on GAS6 polymorphisms and atherothrombotic disease we found an association between the AA genotype of the c.834 + 7G > A GAS6 polymorphism and stroke. In order to further explore this association by considering GAS6 haplotypes and the main stroke subtypes, 457 patients with ischemic stroke, 199 with hemorrhagic stroke and 150 asymptomatic controls were genotyped for eight GAS6 polymorphisms and other genetic markers in the same genome region. Association was measured by logistic regression analysis. The THESIAS program was used to measure linkage disequilibrium and haplotype frequencies. In univariate analysis, the GAS6 c.834 + 7AA genotype was found associated with decreased risk for stroke (OR: 0.59; 95%CI: 0.37-0.93). After adjustment for vascular risk factors, association was maintained when stroke subtypes affecting the microvasculature such as lacunar stroke and deep haemorrhage, were grouped together (OR: 0.44; 95%CI: 0.21-0.90). Furthermore, haplotype analysis revealed that association was even stronger when the c.834 + 7A allele was present in a specific haplotype (CACA) of four GAS6 polymorphisms. From these results we conclude that the A allele of the GAS6 c.834 + 7G > A polymorphism and more specifically, the CACA haplotype, is less prevalent in patients with stroke, suggesting a protective role for stroke of this haplotype.

Sampling properties of homozygosity-based statistics for linkage disequilibrium

Homozygosity-based statistics such as Ohta’s identity-in-state (IIS) excess offer the potential to measure linkage disequilibrium for multiallelic loci in small samples. However, previous observations have suggested that for independent loci, in small samples these statistics might produce values that more frequently lie on one side rather than on the other side of zero. Here we investigate the sampling properties of the IIS excess. We find that for any pair of independent polymorphic loci, as sample size n approaches infinity, the sampling distribution of the IIS excess approaches a normal distribution. For large samples, the IIS excess tends towards symmetry around zero, and the probabilities of positive and of negative IIS excess both approach 1/2. Surprisingly, however, we also find that for sufficiently large n, independent loci can be chosen so that the probability of a sample having positive IIS excess is arbitrarily close to either 0 or 1. The results are applied to interpretation of data from human populations, and we conclude that before employing homozygosity-based statistics to measure LD in a particular sample, especially for loci with either very small or very large homozygosities, it is useful to verify that loci with the observed homozygosity values are not likely to produce a large bias in IIS excess in samples of the given size.

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.

Efficiency of DNA pooling to estimate joint allele frequencies and measure linkage disequilibrium.

Pooling DNA samples can yield efficient estimates of the prevalence of genetic variants. We extend methods of analyzing pooled DNA samples to estimate the joint prevalence of variants at two or more loci. If one has a sample from the general population, one can adapt the method for joint prevalence estimation to estimate allele frequencies and D, the measure of linkage disequilibrium. The parameter D is fundamental in population genetics and in determining the power of association studies. In addition, joint allelic prevalences can be used in case-control studies to estimate the relative risks of disease from joint exposures to the genetic variants. Our methods allow for imperfect assay sensitivity and specificity. The expected savings in numbers of assays required when pooling is utilized compared to individual testing are quantified.

What do patterns of genetic variability reveal about mitochondrial recombination?

Recent claims that patterns of genetic variability in human mitochondria show evidence for recombination, have provoked considerable argument and much correspondence concerning the quality of the data, the nature of the analyses, and the biological realism of mitochondrial recombination. While the majority of evidence now points towards a lack of effective recombination, at least in humans, the debate has highlighted how difficult the detection of recombination can be in genomes with unusual mutation processes and complex demographic histories. A major difficulty is the lack of consensus about how to measure linkage disequilibrium. I show that measures differ in the way they treat data that are uninformative about recombination, and that when just those pairwise comparisons that are informative about recombination are used, there is agreement between different statistics. In this light, the significant negative correlation between linkage disequilibrium and distance, in at least some of the data sets, is a real pattern that requires explanation. I discuss whether plausible mutational and selective processes can give rise to such a pattern.

Statistical methods for assessing linkage disequilibrium at the HLA-A, B, C loci.

SUMMARYA number of standard and new statistics for measuring linkage disequilibrium are introduced applicable to any multilocus system. Included are the usual pairwise gametic disequilibrium function, D, the Lewontin disequilibrium index, DL, a Euclidean disequilibrium distance, DE, a hierarchy of stratified linkage disequilibrium functions (e.g. a pairwise disequilibrium value conditioned on the value of a third locus) and an averaged conditional disequilibrium expression, DW. Various global second order measures of disequilibrium are proposed partly based on contingency table statistics and weighted pairwise disequilibrium quantities. A non‐parametric (stochastic) comparison assessment for global linkage disequilibrium is also developed. These measures are compared and contrasted at the HLA‐A, B, C gene complex for a sample of 2000 haplotypes from a healthy Austrian population.Several results from applying these methods include: (1) Of the various pairwise disequilibrium measures examined, D, DE and DW correlated very closely with each other but differ from DL. (2) The ‘third‐order interaction’ between two loci conditional on an allele (or group of alleles) at a third locus indicated that HLA‐AB maintains the classical disequilibrium pairings only for conditioning on CX (the blank allele at locus C), and they mostly disappear for conditioning on C1 to C5. (3) Subpopulations involving C3 or C4 alleles exhibit the significant new combinations A33B17 and A2B15. (4) The B, C loci have a higher total linkage disequilibrium than A, B and A, C; more than expected by mapping distance relationships. (5) The total linkage disequilibrium was significantly larger for conditioning on CX compared to CX (non‐CX), but smaller for the population conditioned by {C3, C4}.A number of interpretations of the results with respect to heterogeneity classifications of populations are discussed.

The effect of finite population size on models of linked overdominant loci

SUMMARYModels of two linked overdominant loci in moderately large, but finite, populations are examined by looking at the variance-covariance matrix of the two gene frequencies and the linkage disequilibrium around stable deterministic equilibrium points. In particular, the effect of genetic drift is examined in cases where, in infinite populations, two stable equilibria with non-zero linkage disequilibrium,D, are maintained. Theoretical formulae are produced and checked by computer simulation. In general, the results show that unless the population size is very large indeed, genetic drift causes the values ofDto vary considerably about the equilibrium values and that for many models, where stable equilibria exist at non-zeroDvalues, a wide range of values ofDhave a high probability. Thus it is very difficult to draw conclusions about the selection regime by measuring Linkage disequilibrium in a finite population.