PSEUDOMARKER: a powerful program for joint linkage and/or linkage disequilibrium analysis on mixtures of singletons and related individuals

A decade ago, there was widespread enthusiasm for the prospects of genome-wide association studies to identify common variants related to common chronic diseases using samples of unrelated individuals from populations. Although technological advancements allow us to query more than a million SNPs across the genome at low cost, a disappointingly small fraction of the genetic portion of common disease etiology has been uncovered. This has led to the hypothesis that less frequent variants might be involved, stimulating a renaissance of the traditional approach of seeking genes using multiplex families from less diverse populations. However, by using the modern genotyping and sequencing technology, we can now look not just at linkage, but jointly at linkage and linkage disequilibrium (LD) in such samples. Software methods that can look simultaneously at linkage and LD in a powerful and robust manner have been lacking. Most algorithms cannot jointly analyze datasets involving families of varying structures in a statistically or computationally efficient manner. We have implemented previously proposed statistical algorithms in a user-friendly software package, PSEUDOMARKER. This paper is an announcement of this software package. We describe the motivation behind the approach, the statistical methods, and software, and we briefly demonstrate PSEUDOMARKER's advantages over other packages by example.     

Accommodating linkage disequilibrium in genetic-association analyses via ridge regression

Large-scale genetic-association studies that take advantage of an extremely dense set of genetic markers have begun to produce very compelling statistical associations between multiple makers exhibiting strong linkage disequilibrium (LD) in a single genomic region and a phenotype of interest. However, the ultimate biological or "functional" significance of these multiple associations has been difficult to discern. In fact, the LD relationships between not only the markers found to be associated with the phenotype but also potential functionally or causally relevant genetic variations that reside near those markers have been exploited in such studies. Unfortunately, LD, especially strong LD, between variations at neighboring loci can make it difficult to distinguish the functionally relevant variations from nonfunctional variations. Although there are (rare) situations in which it is impossible to determine the independent phenotypic effects of variations in LD, there are strategies for accommodating LD between variations at different loci, and they can be used to tease out their independent effects on a phenotype. These strategies make it possible to differentiate potentially causative from noncausative variations. We describe one such approach involving ridge regression. We showcase the method by using both simulated and real data. Our results suggest that ridge regression and related techniques have the potential to distinguish causative from noncausative variations in association studies.     

The effect of genotyping errors on the robustness of composite linkage disequilibrium measures

We conclude that composite linkage disequilibrium (LD) measures be adopted in population-based LD mapping or association mapping studies since it is unaffected by Hardy-Weinberg disequilibrium. Although some properties of composite LD measures have been recently studied, the effects of genotyping errors on composite LD measures have not been examined. In this report, we derived deterministic formulas to evaluate the impact of genotyping errors on the composite LD measures Δ'AB and rAB, and compared the robustness of Δ'AB and rAB in the presence of genotyping errors. The results showed that Δ'AB and rAB depend on the allele frequencies and the assumed error model, and show varying degrees of robustness in the presence of errors. In general, whether there is HWD or not, rAB is more robust than Δ'AB except some special cases and the difference of robustness between Δ'AB and rAB becomes less severe as the difference between the frequencies of two SNP alleles A and B becomes smaller.     

Joint modeling of linkage and association: identifying SNPs responsible for a linkage signal

Once genetic linkage has been identified for a complex disease, the next step is often association analysis, in which single-nucleotide polymorphisms (SNPs) within the linkage region are genotyped and tested for association with the disease. If a SNP shows evidence of association, it is useful to know whether the linkage result can be explained, in part or in full, by the candidate SNP. We propose a novel approach that quantifies the degree of linkage disequilibrium (LD) between the candidate SNP and the putative disease locus through joint modeling of linkage and association. We describe a simple likelihood of the marker data conditional on the trait data for a sample of affected sib pairs, with disease penetrances and disease-SNP haplotype frequencies as parameters. We estimate model parameters by maximum likelihood and propose two likelihood-ratio tests to characterize the relationship of the candidate SNP and the disease locus. The first test assesses whether the candidate SNP and the disease locus are in linkage equilibrium so that the SNP plays no causal role in the linkage signal. The second test assesses whether the candidate SNP and the disease locus are in complete LD so that the SNP or a marker in complete LD with it may account fully for the linkage signal. Our method also yields a genetic model that includes parameter estimates for disease-SNP haplotype frequencies and the degree of disease-SNP LD. Our method provides a new tool for detecting linkage and association and can be extended to study designs that include unaffected family members.     

Linkage disequilibrium fine mapping of quantitative trait loci: A simulation study

Recently, the use of linkage disequilibrium (LD) to locate genes which affect quantitative traits (QTL) has received an increasing interest, but the plausibility of fine mapping using linkage disequilibrium techniques for QTL has not been well studied. The main objectives of this work were to (1) measure the extent and pattern of LD between a putative QTL and nearby markers in finite populations and (2) investigate the usefulness of LD in fine mapping QTL in simulated populations using a dense map of multiallelic or biallelic marker loci. The test of association between a marker and QTL and the power of the test were calculated based on single-marker regression analysis. The results show the presence of substantial linkage disequilibrium with closely linked marker loci after 100 to 200 generations of random mating. Although the power to test the association with a frequent QTL of large effect was satisfactory, the power was low for the QTL with a small effect and/or low frequency. More powerful, multi-locus methods may be required to map low frequent QTL with small genetic effects, as well as combining both linkage and linkage disequilibrium information. The results also showed that multiallelic markers are more useful than biallelic markers to detect linkage disequilibrium and association at an equal distance.     

Contribution of an additive locus to genetic variance when inheritance is multi-factorial with implications on interpretation of GWAS

Although the effects of linkage disequilibrium (LD) on partition of genetic variance have received attention in quantitative genetics, there has been little discussion on how this phenomenon affects attribution of variance to a given locus. This paper reinforces the point that standard metrics used for assessing the contribution of a locus to variance can be misleading when there is linkage LD and that factors such as distribution of effects and of allelic frequencies over loci, or existence of frequency-dependent effects, play a role as well. An apparently new metric is proposed for measuring how much of the variability is contributed by a locus when LD exists. Effects of intervening factors, such as type and extent of LD, number of loci, distribution of effects, and of allelic frequencies over loci, as well as a model for generating frequency-dependent effects, are illustrated via hypothetical simulation scenarios. Implications on the interpretation of genome-wide association studies (GWAS), as typically carried out in human genetics, where single marker regression and the assumption of a sole quantitative trait locus (QTL) are common, are discussed. It is concluded that the standard attributions to variance contributed by a single QTL from a GWAS analysis may be misleading, conceptually and statistically, when a trait is complex and affected by sets of many genes in linkage disequilibrium. Yet another factor to consider in the “missing heritability” saga?.     

"Sexual" population structure and genetics of the malaria agent P. falciparum

The population genetics and structure of P. falciparum determine the rate at which malaria evolves in response to interventions such as drugs and vaccines. This has been the source of considerable recent controversy, but here we demonstrate the organism to be essentially sexual, in an area of moderately high transmission in the Lower Shire Valley, Malawi. Seven thousand mosquitoes were collected and dissected, and genetic data were obtained on 190 oocysts from 56 infected midguts. The oocysts were genotyped at three microsatellite loci and the MSP1 locus. Selfing rate was estimated as 50% and there was significant genotypic linkage disequilibrium (LD) in the pooled oocysts. A more appropriate analysis searching for genotypic LD in outcrossed oocysts and/or haplotypic LD in the selfed oocysts found no evidence for LD, indicating that the population was effectively sexual. Inbreeding estimates at MSP1 were higher than at the microsatellites, possibly indicative of immune action against MSP1, but the effect was confounded by the probable presence of null mutations. Mating appeared to occur at random in mosquitoes and evidence regarding whether malaria clones in the same host were related (presumably through simultaneous inoculation in the same mosquito bite) was ambiguous. This is the most detailed genetic analysis yet of P. falciparum sexual stages, and shows P. falciparum to be a sexual organism whose genomes are in linkage equilibrium, which acts to slow the emergence of drug resistance and vaccine insensitivity, extending the likely useful therapeutic lifespan of drugs and vaccines.     

A potential bias in the temporal method for estimating Ne in admixed populations under natural selection

Indirect genetic methods are frequently used to estimate the effective population size (N(e)) or effective number of breeders (N(b)) in natural populations. Although assumptions behind these methods are often violated, there have been few attempts to evaluate how accurate these estimates really are in practice. Here we investigate the influence of natural selection following a population admixture on the temporal method for estimating N(e). Our analytical and simulation results suggest that N(e) is often underestimated in this method when subpopulations differ substantially in allele frequencies and in reproductive success. The underestimation is exacerbated when true N(e) and the fraction of the low-fitness group are large. As an empirical example, we compared N(b) estimated in natural populations of steelhead trout (Oncorhynchus mykiss) using the temporal method (N(b[temp])) with estimates based on direct demographic methods (N(b[demo])) and the linkage disequilibrium method (N(b[LD])). While N(b[LD]) was generally in close agreement with N(b[demo]), N(b[temp]) was much lower in sample sets that were dominated by nonlocal hatchery fish with low reproductive success, as predicted by the analytical results. This bias in the temporal method, which arises when genes associated with a particular group of parents are selected against in the offspring sample, has not been widely appreciated before. Such situations may be particularly common when artificial propagation or translocations are used for conservation. The linkage disequilibrium method, which requires data from only one sample, is robust to this type of bias, although it can be affected by other factors.     

Identifying disease polymorphisms from case–control genetic association data

In case-control association studies, it is typical to observe several associated polymorphisms in a gene region. Often the most significantly associated polymorphism is considered to be the disease polymorphism; however, it is not clear whether it is the disease polymorphism or there is more than one disease polymorphism in the gene region. Currently, there is no method that can handle these problems based on the linkage disequilibrium (LD) relationship between polymorphisms. To distinguish real disease polymorphisms from markers in LD, a method that can detect disease polymorphisms in a gene region has been developed. Relying on the LD between polymorphisms in controls, the proposed method utilizes model-based likelihood ratio tests to find disease polymorphisms. This method shows reliable Type I and Type II error rates when sample sizes are large enough, and works better with re-sequenced data. Applying this method to fine mapping using re-sequencing or dense genotyping data would provide important information regarding the genetic architecture of complex traits.     

Detecting population structure using STRUCTURE software: effect of background linkage disequilibrium

STRUCTURE is the most widely used clustering software to detect population genetic structure. The last version of this software (STRUCTURE 2.1) has been enhanced recently to take into account the occurrence of linkage disequilibrium (LD) caused by admixture between populations. This last version, however, still does not consider the effects of strong background LD caused by genetic drift, and which may cause spurious results. STRUCTURE authors have, therefore, suggested a rough threshold value of the distance (1.0 cM) between two loci below which the pair of loci should not be used. Because of the sensitiveness of LD to demographic events, the distance between loci is not always a good indicator of the strength of LD. In this study, we examine the link between genomic distance and the strength of the correlation between loci (r(LD)) in a free-ranging population of mouflon (Ovis aries), and we present an empirical test of effect of r(LD) on the clustering results provided by the linkage model in STRUCTURE. We showed that a high r(LD) value increases the probability of detecting spurious clustering. We propose to use r(LD) as an index to base a decision on whether or not to use a pair of loci in a clustering analysis.     

Levels of linkage disequilibrium in a wild bird population

Population-based mapping approaches are attractive for tracing the genetic background to phenotypic traits in wild species, given that it is often difficult to gather extensive and well-defined pedigrees needed for quantitative trait locus analysis. However, the feasibility of association or hitch-hiking mapping is dependent on the degree of linkage disequilibrium (LD) in the population, on which there is yet limited information for wild species. Here we use single nucleotide polymorphism (SNP) markers from 23 genes in a recently established linkage map of the Z chromosome of the collared flycatcher, to study the extent of LD in a natural bird population. In most but not all cases we find SNPs within the same intron (less than 500 bp) to be in perfect LD. However, LD then decays to background level at a distance 1cM or 400-500 kb. Although LD seems more extensive than in other species, if the observed pattern is representative for other regions of the genome and turns out to be a general feature of natural bird populations, dense marker maps might be needed for genome scans aimed at identifying association between marker and trait loci.     

Score tests of genetic association in the presence of linkage based on the additive genetic gamma frailty model

Nuclear families with multiple affected sibs are often collected for genetic linkage analysis of complex diseases. Once linkage evidence is established, dense markers are often typed in the linked region for genetic association analysis based on linkage disequilibrium (LD). Detection of association in the presence of linkage localizes disease genes more accurately than the methods that rely on linkage alone. However, test of association due to LD in the linked region needs to account for dependency of the allele transmissions to different sibs within a family. In this paper, we define a joint model for genetic linkage and association and derive the corresponding joint survival function of age of onset for the sibs within a sibship. The joint survival function is a function of both the inheritance vector and the genotypes at the candidate marker locus. Based on this joint survival function, we derive score tests for genetic association. The proposed methods utilize the phenotype data of all the sibs and have the advantages of family-based designs which can avoid the potential spurious association caused by population admixture. In addition, the methods can account for variable age of onset or age at censoring and possible covariate effects, and therefore provide important tools for modelling disease heterogeneity. Simulation studies and application to the data sets from the 12th Genetic Analysis Workshop indicate that the proposed methods have correct type 1 error rates and increased power over other existing methods for testing allelic association.     

Biases and reconciliation in estimates of linkage disequilibrium in the human genome

Genetic association studies of common disease often rely on linkage disequilibrium (LD) along the human genome and in the population under study. Although understanding the characteristics of this correlation has been the focus of many large-scale surveys (culminating in genomewide haplotype maps), the results of different studies have yielded wide-ranging estimates. Since understanding these differences (and whether they can be reconciled) has important implications for whole-genome association studies, in this article we dissect biases in these estimations that are due to known aspects of study design and analytic methodology. In particular, we document in the empirical data that the long-known complicating effects of allele frequency, marker density, and sample size largely reconcile all large-scale surveys. Two exceptions are an underappraisal of redundancy among single-nucleotide polymorphisms (SNPs) when evaluation is limited to short regions (as in candidate-gene resequencing studies) and an inflation in the extent of LD in HapMap phase I, which is likely due to oversampling of specific haplotypes in the creation of the public SNP map. Understanding these factors can guide the understanding of empirical LD surveys and has implications for genetic association studies.     

Linkage disequilibrium for different scales and applications

Assessing the patterns of linkage disequilibrium (LD) has become an important issue in both evolutionary biology and medical genetics since the rapid accumulation of densely spaced DNA sequence variation data in several organisms. LD deals with the correlation of genetic variation at two or more loci or sites in the genome within a given population. There are a variety of LD measures which range from traditional pairwise LD measures such as D' or r2 to entropy-based multi-locus measures or haplotype-specific approaches. Understanding the evolutionary forces (in particular recombination) that generate the observed variation of LD patterns across genomic regions is addressed by model-based LD analysis. Marker type and its allelic composition also influence the observed LD pattern, microsatellites having a greater power to detect LD in population isolates than SNPs. This review aims to explain basic LD measures and their application properties.     

The impact of genetic relationship information on genome-assisted breeding values

The success of genomic selection depends on the potential to predict genome-assisted breeding values (GEBVs) with high accuracy over several generations without additional phenotyping after estimating marker effects. Results from both simulations and practical applications have to be evaluated for this potential, which requires linkage disequilibrium (LD) between markers and QTL. This study shows that markers can capture genetic relationships among genotyped animals, thereby affecting accuracies of GEBVs. Strategies to validate the accuracy of GEBVs due to LD are given. Simulations were used to show that accuracies of GEBVs obtained by fixed regression-least squares (FR-LS), random regression-best linear unbiased prediction (RR-BLUP), and Bayes-B are nonzero even without LD. When LD was present, accuracies decrease rapidly in generations after estimation due to the decay of genetic relationships. However, there is a persistent accuracy due to LD, which can be estimated by modeling the decay of genetic relationships and the decay of LD. The impact of genetic relationships was greatest for RR-BLUP. The accuracy of GEBVs can result entirely from genetic relationships captured by markers, and to validate the potential of genomic selection, several generations have to be analyzed to estimate the accuracy due to LD. The method of choice was Bayes-B; FR-LS should be investigated further, whereas RR-BLUP cannot be recommended.     

Inferring coancestry in population samples in the presence of linkage disequilibrium

In both pedigree linkage studies and in population-based association studies there has been much interest in the use of modern dense genetic marker data to infer segments of gene identity by descent (ibd) among individuals not known to be related, to increase power and resolution in localizing genes affecting complex traits. In this article, we present a hidden Markov model (HMM) for ibd among a set of chromosomes and describe methods and software for inference of ibd among the four chromosomes of pairs of individuals, using either phased (haplotypic) or unphased (genotypic) data. The model allows for missing data and typing error, but does not model linkage disequilibrium (LD), because fitting an accurate LD model requires large samples from well-studied populations. However, LD remains a major confounding factor, since LD is itself a reflection of coancestry at the population level. To study the impact of LD, we have developed a novel simulation approach to generate realistic dense marker data for the same set of markers but at varying levels of LD. Using this approach, we present results of a study of the impact of LD on the sensitivity and specificity of our HMM model in estimating segments of ibd among sets of four chromosomes and between genotype pairs. We show that, despite not incorporating LD, our model has been quite successful in detecting segments as small as 10(6) bp (1 Mpb); we present also comparisons with fastIBD which uses an LD model in estimating ibd.     

Assessment of the functionality of genome‐wide canine SNP arrays and implications for canine disease association studies

Domestic dogs share a wide range of important disease conditions with humans, including cancers, diabetes and epilepsy. Many of these conditions have similar or identical underlying pathologies to their human counterparts and thus dogs represent physiologically relevant natural models of human disorders. Comparative genomic approaches whereby disease genes can be identified in dog diseases and then mapped onto the human genome are now recognized as a valid method and are increasing in popularity. The majority of dog breeds have been created over the past few hundred years and, as a consequence, the dog genome is characterized by extensive linkage disequilibrium (LD), extending usually from hundreds of kilobases to several megabases within a breed, rather than tens of kilobases observed in the human genome. Genome‐wide canine SNP arrays have been developed, and increasing success of using these arrays to map disease loci in dogs is emerging. No equivalent of the human HapMap currently exists for different canine breeds, and the LD structure for such breeds is far less understood than for humans. This study is a dedicated large‐scale assessment of the functionalities (LD and SNP tagging performance) of canine genome‐wide SNP arrays in multiple domestic dog breeds. We have used genotype data from 18 breeds as well as wolves and coyotes genotyped by the Illumina 22K canine SNP array and Affymetrix 50K canine SNP array. As expected, high tagging performance was observed with most of the breeds using both Illumina and Affymetrix arrays when multi‐marker tagging was applied. In contrast, however, large differences in population structure, LD coverage and pairwise tagging performance were found between breeds, suggesting that study designs should be carefully assessed for individual breeds before undertaking genome‐wide association studies (GWAS).     

Human QTL linkage mapping

Human quantitative trait locus (QTL) linkage mapping, although based on classical statistical genetic methods that have been around for many years, has been employed for genome-wide screening for only the last 10–15 years. In this time, there have been many success stories, ranging from QTLs that have been replicated in independent studies to those for which one or more genes underlying the linkage peak have been identified to a few with specific functional variants that have been confirmed in in vitro laboratory assays. Despite these successes, there is a general perception that linkage approaches do not work for complex traits, possibly because many human QTL linkage studies have been limited in sample size and have not employed the family configurations that maximize the power to detect linkage. We predict that human QTL linkage studies will continue to be productive for the next several years, particularly in combination with RNA expression level traits that are showing evidence of regulatory QTLs of large effect sizes and in combination with high-density genome-wide SNP panels. These SNP panels are being used to identify QTLs previously localized by linkage and linkage results are being used to place informative priors on genome-wide association studies.     

Randomly distributed crossovers may generate block-like patterns of linkage disequilibrium: an act of genetic drift

There is considerable interest in identifying and characterizing block-like patterns of linkage disequilibrium (LD; haplotype blocks) in the human genome as these may facilitate the identification of complex disease genes via genome-wide association studies. Although recombination hot-spots have been suggested as the primary mechanism to explain the block-like pattern of LD, other forces, such as genetic drift, may also be important. To this end, we have studied the effect of various recombination models on patterns of LD by using extensive simulations. As expected, haplotype blocks were observed under a model allowing recombination hot-spots. However, we also observed similar block-like patterns in the models where recombination crossovers are randomly and uniformly distributed, and we demonstrate that these blocks are generated by genetic drift. We caution that genetic drift may be an alternative mechanism (in addition to recombination hot-spots) that can lead to block-like patterns of LD. Our findings highlight the necessity of characterizing haplotype blocks in world-wide populations.     

Population demographic history can cause the appearance of recombination hotspots

Although the prevailing view among geneticists suggests that recombination hotspots exist ubiquitously across the human genome, there is only limited experimental evidence from a few genomic regions to support the generality of this claim. A small number of true recombination hotspots are well supported experimentally, but the vast majority of hotspots have been identified on the basis of population genetic inferences from the patterns of linkage disequilibrium (LD) seen in the human population. These inferences are made assuming a particular model of human history, and one of the assumptions of that model is that the effective population size of humans has remained constant throughout our history. Our results show that relaxation of the constant population size assumption can create LD and variation patterns that are qualitatively and quantitatively similar to human populations without any need to invoke localized hotspots of recombination. In other words, apparent recombination hotspots could be an artifact of variable population size over time. Several lines of evidence suggest that the vast majority of hotspots identified on the basis of LD information are unlikely to have elevated recombination rates.