Linkage Disequilibrium Measures Research Articles

Recent and historical recombination in the admixed Norwegian Red cattle breed

BackgroundComparison of recent patterns of recombination derived from linkage maps to historical patterns of recombination from linkage disequilibrium (LD) could help identify genomic regions affected by strong artificial selection, appearing as reduced recent recombination. Norwegian Red cattle (NRF) make an interesting case study for investigating these patterns as it is an admixed breed with an extensively recorded pedigree. NRF have been under strong artificial selection for traits such as milk and meat production, fertility and health.While measures of LD is also crucial for determining the number of markers required for association mapping studies, estimates of recombination rate can be used to assess quality of genomic assemblies.ResultsA dataset containing more than 17,000 genome-wide distributed SNPs and 2600 animals was used to assess recombination rates and LD in NRF. Although low LD measured by r2 was observed in NRF relative to some of the breeds from which this breed originates, reports from breeds other than those assessed in this study have described more rapid decline in r2 at short distances than what was found in NRF. Rate of decline in r2 for NRF suggested that to obtain an expected r2 between markers and a causal polymorphism of at least 0.5 for genome-wide association studies, approximately one SNP every 15 kb or a total of 200,000 SNPs would be required. For well known quantitative trait loci (QTLs) for milk production traits on Bos Taurus chromosomes 1, 6 and 20, map length based on historic recombination was greater than map length based on recent recombination in NRF.Further, positions for 130 previously unpositioned contigs from assembly of the bovine genome sequence (Btau_4.0) found using comparative sequence analysis were validated by linkage analysis, and 28% of these positions corresponded to extreme values of population recombination rate.ConclusionWhile LD is reduced in NRF compared to some of the breeds from which this admixed breed originated, it is elevated over short distances compared to some other cattle breeds. Genomic regions in NRF where map length based on historic recombination was greater than map length based on recent recombination coincided with some well known QTL regions for milk production traits.Linkage analysis in combination with comparative sequence analysis and detection of regions with extreme values of population recombination rate proved to be valuable for detecting problematic regions in the Btau_4.0 genome assembly.

On the Uses and Applications of the Most Commonly Used Measures of Linkage Disequilibrium from the Comparative Analysis of Their Statistical Properties

Background/Objective: The analysis of linkage disequilibrium is relevant for the exploration of the structure and evolution of genomes and for the gene mapping of quantitative characters and human diseases. The strength of linkage disequilibrium between diallelic loci is commonly measured by the coefficients D′ and r. Recent studies suggest that r is more useful than D′ as a general measure of the strength of disequilibrium because it provides much more precise (lower sampling variance) and accurate (lower bias) estimates of disequilibrium. We compared for the first time the statistical properties of D′ and r taking into account their differences in range. Methods: The sampling properties of D′ and r were evaluated by simulation under a variety of realistic population conditions and varying sample sizes using standardised statistics that allow for comparisons of the precision, accuracy and efficiency of estimates with different ranges. Results: Simulations revealed that estimates of r do not tend to be significantly more precise, accurate or efficient than those of D′ when compared by means of standardised statistics. Conclusion: The supposed advantage of r over D′ based on direct comparisons of their sampling distributions is more apparent than real. The obtained results are useful to assess the uses and applications of these widely used disequilibrium measures.

A Method to Assess Linkage Disequilibrium between CNVs and SNPs Inside Copy Number Variable Regions

Since the discovery of the ubiquitous contribution of copy number variation to genetic variability, researchers have commonly used metrics such as r2 to quantify linkage disequilibrium (LD) between copy number variants (CNVs) and single nucleotide polymorphisms (SNPs). However, these reports have been restricted to SNPs outside copy number variable regions (CNVR) as current methods have not been adapted to account for SNPs displaying variable copy number. We show that traditional LD metrics inappropriately quantify SNP/CNV covariance when SNPs lie within CNVR. We derive a new method for measuring LD that solves this issue, and defaults to traditional metrics otherwise. Finally, we present a procedure to estimate CNV–SNP allele frequencies from unphased CNV–SNP genotypes. Our method allows researchers to include all SNPs in SNP/CNV LD measurements, regardless of copy number.

Interleukin 7 receptor gene polymorphisms and haplotypes are associated with susceptibility to IgA nephropathy in Korean children

An abnormal T-cell response is involved in the pathogenesis of various renal diseases. Survival of naïve T cells is dependent on interleukin 7 (IL7) and its receptor (IL7R). Thus, we investigated the association between IL7R single nucleotide polymorphisms (SNPs) and childhood IgA nephropathy (IgAN). We analyzed the genotypic distributions of two missense SNPs of IL7R, rs1494558 (Ile66Thr) and rs1494555 (Val138Ile), among 198 pediatric IgAN patients and 288 healthy controls. Haplotype analysis and measurement of pair-wise linkage disequilibrium were performed. In addition, the genotypes of patient subgroups, determined by the presence of nephrotic range proteinuria (>40 mg/m(2)/h) and pathological advancement, were analyzed. The genotyping data of IgAN patients and controls showed significant differences in rs1494558 (codominant, P=0.0003; dominant, P=0.0003) and rs1494555 (codominant, P=0.0038; dominant, P=0.0099). In the haplotype analysis, AC (codominant, P=0.0066) and GT (codominant, P=0.0005; dominant, P=0.0006) were significantly associated with susceptibility to IgAN. Furthermore, in the analysis of clinical subgroups of IgAN patients, rs1494558 was associated with nephrotic range proteinuria (codominant, P=0.027; recessive, P=0.023). Our results suggest that IL7R may be associated with disease susceptibility and proteinuria in childhood IgAN.

Contrasting linkage disequilibrium as a multilocus family-based association test

Linkage disequilibrium (LD) of genetic loci is routinely estimated and graphically illustrated in genetic association studies. It has been suggested that the information in LD is also useful for association mapping and genetic association can be detected by comparing LD patterns between cases and controls. Here, we extend this idea to analyze case-parents data by comparing LD patterns between transmitted and nontransmitted genotypes. We provide the condition when contrasting LD is valid for testing gene-gene interactions. A permutation procedure is given to assess statistical significance. One advantage of our proposed methods is that haplotype information is not required. Thus, the implementation of our methods is straightforward and the resulted tests are free from potential bias caused by assumptions made to estimate haplotypes in silico. Since our test statistics use pairwise LD measurements, they are less affected by missing data than many other multilocus methods. With simulated data, we demonstrate that examining LD patterns of case-parents data is a useful multilocus association mapping strategy and it complements existing association mapping methods. The application of our methods to a Crohn's disease data set shows that our methods can detect multilocus association that might be missed by other association methods. Our permutation procedure can also be modified to allow multiple offspring from a family to be analyzed.

Extent of linkage disequilibrium and effective population size in Finnish Landrace and Finnish Yorkshire pig breeds1

The extent of linkage disequilibrium (LD) and effective population size in Finnish Landrace and Finnish Yorkshire pig populations were studied using a whole genome SNP panel (Illumina PorcineSNP60 BeadChip) and pedigree data. Genotypic data included 86 Finnish Landrace and 32 Finnish Yorkshire boars. Pedigree data included 608,138 Finnish Landrace 554,237 and Finnish Yorkshire pigs, and on average 15 ancestral generations were known for the reference animals, born in 2005 to 2009. The breeding animals of the 2 populations have been kept separate in the breeding programs. Based on the pedigree data, the current effective population size for Finnish Landrace is 91 and for Finnish Yorkshire 61. Linkage disequilibrium measures (D' and r(2)) were estimated for over 1.5 million pairs of SNP. Average r(2) for SNP 30 kb apart was 0.47 and 0.49 and for SNP 5 Mb apart 0.09 and 0.12 for Finnish Landrace and Finnish Yorkshire, respectively. Average LD (r(2)) between adjacent SNP in the Illumina PorcineSNP60 BeadChip was 0.43 (57% of the adjacent SNP pairs had r(2) > 0.2) for Finnish Landrace and 0.46 (60% of the adjacent SNP pairs had r(2) > 0.2) for Finnish Yorkshire, and average r(2) > 0.2 extended to 1.0 and 1.5 Mb for Finnish Landrace and Finnish Yorkshire, respectively. Effective population size estimates based on the decay of r(2) with distance were similar to those based on the pedigree data: 80 and 55 for Finnish Landrace and Finnish Yorkshire, respectively. Thus, the results indicate that the effective population size of Finnish Yorkshire is smaller than of Finnish Landrace and has a clear effect on the extent of LD. The current effective population size of both breeds is above the recommended minimum of 50 but may get smaller than that in the near future, if no action is taken to balance the inbreeding rate and selection response. Because a moderate level of LD extends over a long distance, selection based on whole genome SNP markers (genomic selection) is expected to be efficient for both breeds.

You've Gotta Be Lucky: Coverage and the Elusive Gene-Gene Interaction

Genome-wide association studies (GWAS) have led to a large number of single-SNP association findings, but there has been, so far, no investigation resulting in the discovery of a replicable gene-gene interaction. In this paper, we examine some of the possible explanations for the lack of findings, and argue that coverage of causal variation not only has a large effect on the loss in power, but that the effect is larger than in the single-SNP analyses. We show that the product of linkage disequilibrium measures, r², between causal and tested SNPs offers a good approximation to the loss in efficiency as defined by the ratio of sample sizes that lead to similar power. We also demonstrate that, in addition to the huge search space, the loss in power due to coverage when using commercially available platforms makes the search for gene-gene interactions daunting.

A gene‐based SNP linkage map for pacific white shrimp, Litopenaeus vannamei

Pacific white shrimp (Litopenaeus vannamei) are of particular economic importance to the global shrimp aquaculture industry. However, limited genomics information is available for the penaeid species. We utilized the limited public information available, mainly single nucleotide polymorphisms (SNPs) and expressed sequence tags, to discover markers for the construction of the first SNP genetic map for Pacific white shrimp. In total, 1344 putative SNPs were discovered, and out of 825 SNPs genotyped, 418 SNP markers from 347 contigs were mapped onto 45 sex-averaged linkage groups, with approximate coverage of 2071 and 2130 cm for the female and male maps, respectively. The average-squared correlation coefficient (r(2)), a measure of linkage disequilibrium, for markers located more than 50 cm apart on the same linkage group, was 0.15. Levels of r(2) increased with decreasing inter-marker distance from approximately 80 cm, and increased more rapidly from approximately 30 cm. A QTL for shrimp gender was mapped on linkage group 13. Comparative mapping to model organisms, Daphnia pulex and Drosophila melanogaster, revealed extensive rearrangement of genome architecture for L. vannamei, and that L. vannamei was more related to Daphnia pulex. This SNP genetic map lays the foundation for future shrimp genomics studies, especially the identification of genetic markers or regions for economically important traits.

Summarizing and Quantifying Multilocus Linkage Disequilibrium Patterns with Multi-Order Markov Chain Models

Studies on linkage disequilibrium (LD) are important in mapping disease genes. A novel statistical method, the multi-order Markov chain model has been recently developed to quantify the complexity level of multilocus LD patterns among single nucleotide polymorphism markers (Kim et al., 2008). In this study, mathematical relationships between two types of LD measures are derived to understand the Markov chain model parameters in terms of conventional LD measures. Statistical sample properties of the Markov chain order estimates are investigated by simulations. Two published data sets are reanalyzed to illustrate the proposed approach.

Comparison of Estimators for Measures of Linkage Disequilibrium

The measurement of biallelic pair-wise association called linkage disequilibrium (LD) is an important issue in order to understand the genomic architecture. A plethora of measures of association in two by two tables have been proposed in the literature. Beside the problem of choosing an appropriate measure, the problem of their estimation has been neglected in the literature. It needs to be emphasized that the definition of a measure and the choice of an estimator function for it are conceptually unrelated tasks. In this paper, we compare the performance of various estimators for the three popular LD measures D', r and Y in a simulation study for small to moderate samples sizes (N<=500). The usual frequency-plug-in estimators can lead to unreliable or undefined estimates. Estimators based on the computationally expensive volume measures have been proposed recently as a remedy to this well-known problem. We confirm that volume estimators have better expected mean square error than the naive plug-in estimators. But they are outperformed by estimators plugging-in easy to calculate non-informative Bayesian probability estimates into the theoretical formulae for the measures. Fully Bayesian estimators with non-informative Dirichlet priors have comparable accuracy but are computationally more expensive. We recommend the use of non-informative Bayesian plug-in estimators based on Jeffreys' prior, in particular when dealing with SNP array data where the occurrence of small table entries and table margins is likely.

Risk haplotype pattern discovery for gene mapping by recursive partitioning method based on weighted classification trees

In this paper, we present a combinatorial approach based on recursive weighted longest prefix trees (RWLPT) for mining a massive genetic marker data. Given a case and a control chromosome dataset, we develop a fast recursive permutation algorithm for building an RWLPT. This algorithm provides an optimal solution to find a privileged order of classifiers for constructing optimum haplotype clusters and biclusters. Using RWLPT model, extracting haplotype clusters and haplotype patterns will be performed in linear time on the number of markers. Employing the measure of linkage disequilibrium and the statistical test, we examine the case-control association analysis for identifying risk haplotype patterns associated with the disease permitting likely location of disease susceptibility genes. We demonstrate that the case-control association test based on haplotype patterns reduces degrees of freedom and number of tests while increasing the power of disease-haplotype association analysis. The experimental results through the real published SNP dataset show that our approach tends to be more effective and powerful than the sliding window approach, classification and regression trees and single marker analysis.

Inference of disease associations with unmeasured genetic variants by combining results from genome-wide association studies with linkage disequilibrium patterns in a reference data set

Results from whole-genome association studies of many common diseases are now available. Increasingly, these are being incorporated into meta-analyses to increase the power to detect weak associations with measured single-nucleotide polymorphisms (SNPs). Imputation of genotypes at unmeasured loci has been widely applied using patterns of linkage disequilibrium (LD) observed in the HapMap panels, but there is a need for alternative methods that can utilize the pooled effect estimates from meta-analyses and explore possible associations with SNPs and haplotypes that are not included in HapMap.By a weighted average technique, we show that association results for common SNPs in an observed data set can be scaled and combined to infer the effect of a genetic variant that has been measured only in an independent reference data set. We show that the ratio p(R-1)/[1 + p(R-1)], where R is the relative risk associated with a measured or unmeasured allele of frequency p, is appropriately scaled by 1/D' and weighted in proportion to r2, both common measures of LD being derived from the reference data set.We illustrate this computationally simple method by combining the results of a genome-wide association screen from the North American Rheumatoid Arthritis Consortium with LD measures from the British 1958 Birth Cohort, and explore the validity of underlying assumptions about the generalizability of LD from one population to another, and from healthy subjects to subjects with clinical disease.

A Unified Framework for Detecting Genetic Association with Multiple SNPs in a Candidate Gene or Region: Contrasting Genotype Scores and LD Patterns between Cases and Controls

It is critical to develop and apply powerful statistical tests for genetic association studies due to typically weak associations with complex human diseases or phenotypes. For population-based case-control studies with unphased multilocus genotype data, most of the existing methods are based on comparing genotype scores, e.g. allele frequencies, between the case and control groups. Another class of approaches are motivated to contrast linkage disequilibrium (LD) patterns between the two groups. It is expected that no single test can be uniformly most powerful across all situations, and different tests may perform better under different scenarios. A recent effort has been devoted to combining the above two classes of approaches, which however has some potential drawbacks. Here we propose a general and simple framework to unify the above two classes of approaches: it is based on the simple idea to incorporate LD measurements, in addition to genotype scores, as covariates in a logistic regression model, from which various tests can be constructed by taking advantage of the nice properties of the score statistics for the logistic model. It also has an advantage in easily accommodating covariates and other study designs. We use simulated data to show that our proposed tests performed well across several scenarios. In particular, in contrast to either of the two classes of the tests that is only powerful in detecting only one, but not both, of the two types of the distributional differences between cases and controls, our proposed tests are sensitive to both.

A multilocus linkage disequilibrium measure based on mutual information theory and its applications

Evaluating the patterns of linkage disequilibrium (LD) is important for association mapping study as well as for studying the genomic architecture of human genome (e.g., haplotype block structures). Commonly used bi-allelic pairwise measures for assessing LD between two loci, such as r(2) and D', may not make full and efficient use of modern multilocus data. Though extended to multilocus scenarios, their performance is still questionable. Meanwhile, most existing measures for an entire multilocus region, such as normalized entropy difference, do not consider existence of LD heterogeneity across the region under investigation. Additionally, these existing multilocus measures cannot handle distant regions where long-range LD patterns may exist. In this study, we proposed a novel multilocus LD measure developed based on mutual information theory. Our proposed measure described LD pattern between two chromosome regions each of which may consist of multiple loci (including multi-allele loci). As such, the proposed measure can better characterize LD patterns between two arbitrary regions. As potential applications, we developed algorithms on the proposed measure for partitioning haplotype blocks and for selecting haplotype tagging SNPs (htSNPs), which were helpful for follow-up association tests. The results on both simulated and empirical data showed that our LD measure had distinct advantages over pairwise and other multilocus measures. First, our measure was more robust, and can capture comprehensively the LD information between neighboring as well as disjointed regions. Second, haplotype blocks were better described via our proposed measure. Furthermore, association tests with htSNPs from the proposed algorithm had improved power over tests on single markers and on haplotypes.

Extent and distribution of linkage disequilibrium in the Old Order Amish

Knowledge of the extent and distribution of linkage disequilibrium (LD) is critical to the design and interpretation of gene mapping studies. Because the demographic history of each population varies and is often not accurately known, it is necessary to empirically evaluate LD on a population-specific basis. Here we present the first genome-wide survey of LD in the Old Order Amish (OOA) of Lancaster County Pennsylvania, a closed population derived from a modest number of founders. Specifically, we present a comparison of LD between OOA individuals and US Utah participants in the International HapMap project (abbreviated CEU) using a high-density single nucleotide polymorphism (SNP) map. Overall, the allele (and haplotype) frequency distributions and LD profiles were remarkably similar between these two populations. For example, the median absolute allele frequency difference for autosomal SNPs was 0.05, with an inter-quartile range of 0.02–0.09, and for autosomal SNPs 10–20 kb apart with common alleles (minor allele frequency≥0.05), the LD measure r2 was at least 0.8 for 15 and 14% of SNP pairs in the OOA and CEU, respectively. Moreover, tag SNPs selected from the HapMap CEU sample captured a substantial portion of the common variation in the OOA (∼88%) at r2≥0.8. These results suggest that the OOA and CEU may share similar LD profiles for other common but untyped SNPs. Thus, in the context of the common variant-common disease hypothesis, genetic variants discovered in gene mapping studies in the OOA may generalize to other populations.

Correlation measures for linkage disequilibrium within and between populations

Correlation statistics can be used to measure the amount of linkage disequilibrium (LD) between two loci in subdivided populations. Within populations, the square of the correlation of gene frequencies, r2, is a convenient measure of LD. Between populations, the statistic rirj, for populations i and j, measures the relatedness of LD. Recurrence relationships for these two parameters are derived for the island model of population subdivision, under the assumptions of the linked identity-by-descent (LIBD) model in which correlation measures are equated to probability measures. The recurrence relationships closely predict the build-up of r2 and rirj following population subdivision in computer simulations. The LIBD model predicts that a steady state will be reached with r2 equal to 1/[1+4Nec(1+(k-1)rho)], where k is the number of island populations, Ne is the effective local population (island) size, and rho measures the ratio of migration (m) to recombination (c) and is equal to m/[c(k-1)+m]. For low values of m/c, rho=0, and E(r2) is equal to 1/(1+4Nec). For high values of m/c, rho=1, and E(r2) is equal to 1/(1+4kNec). The value of rirj following separation eventually settles down to a steady state whose expectation, E(rirj), is equal to E(r2) multiplied by rho. Equations predicting the change in rirj values are applied to the separation of African (Yoruba - YRI) and non-African (European - CEU) populations, using data from Hapmap. The primary data lead to an estimate of separation time of less than 1000 generations if there has been no migration, which is around one-third of minimum current estimates. Ancient rather than recent migration can explain the form of the data.

Modelling evolutionary processes in small populations: not as ideal as you think

Evolutionary processes are routinely modelled using 'ideal' Wright-Fisher populations of constant size N in which each individual has an equal expectation of reproductive success. In a hypothetical ideal population, variance in reproductive success (V(k)) is binomial and effective population size (N(e)) = N. However, in any actual implementation of the Wright-Fisher model (e.g., in a computer), V(k) is a random variable and its realized value in any given replicate generation (V(k)*) only rarely equals the binomial variance. Realized effective size (N(e)*) thus also varies randomly in modelled ideal populations, and the consequences of this have not been adequately explored in the literature. Analytical and numerical results show that random variation in V(k)* and N(e)* can seriously distort analyses that evaluate precision or otherwise depend on the assumption that N(e)* is constant. We derive analytical expressions for Var(V(k)) [4(2N - 1)(N - 1)/N(3)] and Var(N(e)) [N(N - 1)/(2N - 1) approximately N/2] in modelled ideal populations and show that, for a genetic metric G = f(N(e)), Var(G) has two components: Var(Gene) (due to variance across replicate samples of genes, given a specific N(e)*) and Var(Demo) (due to variance in N(e)*). Var(G) is higher than it would be with constant N(e) = N, as implicitly assumed by many standard models. We illustrate this with empirical examples based on F (standardized variance of allele frequency) and r(2) (a measure of linkage disequilibrium). Results demonstrate that in computer models that track multilocus genotypes, methods of replication and data analysis can strongly affect consequences of variation in N(e)*. These effects are more important when sampling error is small (large numbers of individuals, loci and alleles) and with relatively small populations (frequently modelled by those interested in conservation).

Association of peroxisome proliferator-activated receptor-gamma gene polymorphisms with the development of asthma

The peroxisome proliferator-activated receptors (PPAR) are the nuclear hormone receptor superfamily of ligand-activated transcriptional factors. PPAR-gamma (PPARG) activation downregulates production of Th2 type cytokines and eosinophil function. Additionally, treatment with a synthetic PPARG ligand can reduce lung inflammation and IFN-gamma, IL-4, and IL-2 production in experimental allergic asthma. In patients with asthma, PPARG gene expression is known to be associated with the airway inflammatory and remodeling responses. Thus, genetic variants of PPARG may be associated with the development of asthma. We genotyped two single nucleotide polymorphisms on the PPARG gene, +34C>G (Pro12Ala) and +82466C>T (His449His), in Korean subjects (839 subjects with asthma and 449 normal controls). Association analysis using logistic regression analysis showed that +82466C>T and haplotypes 1(CC) and 2(CT) were associated with the development of asthma (p=0.01-0.04). The frequency of PPARG-ht2 was significantly lower in the patients with asthma compared to the normal controls in codominant and dominant models (p=0.01, p(corr)=0.03 and p=0.02, p(corr)=0.03, respectively). Conversely, the frequency of PPARG-ht1 was significantly higher in the patients with asthma compared to the normal controls in the codominant model [p=0.04, OR: 1.27 (1.01-1.6)]. In addition, the rare allele frequency of +82466C>T was significantly lower in patients with asthma in comparison to normal controls in the codominant model (OR: 0.78, p=0.04). Thus, polymorphism of the PPARG gene may be linked to an increased risk of asthma development.

Extensive Long-Range and Nonsyntenic Linkage Disequilibrium in Livestock Populations: Deconstruction of a Conundrum

Great interest was aroused by reports, based on microsatellite markers, of high levels of statistically significant long-range and nonsyntenic linkage disequilibrium (LD) in livestock. Simulation studies showed that this could result from population family structure. In contrast, recent SNP-based studies of livestock populations report much lower levels of LD. In this study we show, on the basis of microsatellite data from four cattle populations, that high levels of long-range LD are indeed obtained when using the multi-allelic D' measure of LD. Long-range and nonsyntenic LD are exceedingly low, however, when evaluated by the standardized chi-square measure of LD, which stands in relation to the predictive ability of LD. Furthermore, specially constructed study populations provided no evidence for appreciable LD resulting from family structure at the grandparent level. We propose that the high statistical significance and family structure effects observed in the earlier studies are due to the use of large sample sizes, which accord high statistical significance to even slight deviations from asymptotic expectations under the null hypothesis. Nevertheless, even after taking sample size into account, our results indicate that microsatellites testify to the presence of usable LD at considerably wider separation distances than SNPs, suggesting that use of SNP haplotypes may considerably increase the usefulness of a given fixed SNP array.

Testing for linkage and Hardy-Weinberg disequilibrium

This paper concerns several important points when testing for Hardy-Weinberg equilibrium (HWE) and linkage disequilibrium (LD) in genetics. First, we challenge the necessity of using exclusively two-sided tests for LD. Next, we show that the exact 2-sided tests based on the most popular measures of LD are not equivalent, and neither are the standard statistical tests even though the 1-sided tests are equivalent. We show how this results in different inference about LD for two data sets consisting of small groups of markers. Finally, we advocate the use of the conditional p-value for both LD and HWE testing. An important advantage of this p-value is that equivalent 1-sided tests are transformed into equivalent 2-sided tests.