Accurate haplotype inference for multiple linked single-nucleotide polymorphisms using sibship data

Sibships are commonly used in genetic dissection of complex diseases, particularly for late-onset diseases. Haplotype-based association studies have been advocated as powerful tools for fine mapping and positional cloning of complex disease genes. Existing methods for haplotype inference using data from relatives were originally developed for pedigree data. In this study, we proposed a new statistical method for haplotype inference for multiple tightly linked single-nucleotide polymorphisms (SNPs), which is tailored for extensively accumulated sibship data. This new method was implemented via an expectation-maximization (EM) algorithm without the usual assumption of linkage equilibrium among markers. Our EM algorithm does not incur extra computational burden for haplotype inference using sibship data when compared with using unrelated parental data. Furthermore, its computational efficiency is not affected by increasing sibship size. We examined the robustness and statistical performance of our new method in simulated data created from an empirical haplotype data set of human growth hormone gene 1. The utility of our method was illustrated with an application to the analyses of haplotypes of three candidate genes for osteoporosis.     

Transmission/disequilibrium test based on haplotype sharing for tightly linked markers

Studies using haplotypes of multiple tightly linked markers are more informative than those using a single marker. However, studies based on multimarker haplotypes have some difficulties. First, if we consider each haplotype as an allele and use the conventional single-marker transmission/disequilibrium test (TDT), then the rapid increase in the degrees of freedom with an increasing number of markers means that the statistical power of the conventional tests will be low. Second, the parental haplotypes cannot always be unambiguously reconstructed. In the present article, we propose a haplotype-sharing TDT (HS-TDT) for linkage or association between a disease-susceptibility locus and a chromosome region in which several tightly linked markers have been typed. This method is applicable to both quantitative traits and qualitative traits. It is applicable to any size of nuclear family, with or without ambiguous phase information, and it is applicable to any number of alleles at each of the markers. The degrees of freedom (in a broad sense) of the test increase linearly as the number of markers considered increases but do not increase as the number of alleles at the markers increases. Our simulation results show that the HS-TDT has the correct type I error rate in structured populations and that, in most cases, the power of HS-TDT is higher than the power of the existing single-marker TDTs and haplotype-based TDTs.     

Comparison of strategies to detect epistasis from eQTL data

Genome-wide association studies have been instrumental in identifying genetic variants associated with complex traits such as human disease or gene expression phenotypes. It has been proposed that extending existing analysis methods by considering interactions between pairs of loci may uncover additional genetic effects. However, the large number of possible two-marker tests presents significant computational and statistical challenges. Although several strategies to detect epistasis effects have been proposed and tested for specific phenotypes, so far there has been no systematic attempt to compare their performance using real data. We made use of thousands of gene expression traits from linkage and eQTL studies, to compare the performance of different strategies. We found that using information from marginal associations between markers and phenotypes to detect epistatic effects yielded a lower false discovery rate (FDR) than a strategy solely using biological annotation in yeast, whereas results from human data were inconclusive. For future studies whose aim is to discover epistatic effects, we recommend incorporating information about marginal associations between SNPs and phenotypes instead of relying solely on biological annotation. Improved methods to discover epistatic effects will result in a more complete understanding of complex genetic effects.     

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.     

Handling marker-marker linkage disequilibrium: pedigree analysis with clustered markers

Single-nucleotide polymorphisms (SNPs) are rapidly replacing microsatellites as the markers of choice for genetic linkage studies and many other studies of human pedigrees. Here, we describe an efficient approach for modeling linkage disequilibrium (LD) between markers during multipoint analysis of human pedigrees. Using a gene-counting algorithm suitable for pedigree data, our approach enables rapid estimation of allele and haplotype frequencies within clusters of tightly linked markers. In addition, with the use of a hidden Markov model, our approach allows for multipoint pedigree analysis with large numbers of SNP markers organized into clusters of markers in LD. Simulation results show that our approach resolves previously described biases in multipoint linkage analysis with SNPs that are in LD. An updated version of the freely available Merlin software package uses the approach described here to perform many common pedigree analyses, including haplotyping and haplotype frequency estimation, parametric and nonparametric multipoint linkage analysis of discrete traits, variance-components and regression-based analysis of quantitative traits, calculation of identity-by-descent or kinship coefficients, and case selection for follow-up association studies. To illustrate the possibilities, we examine a data set that provides evidence of linkage of psoriasis to chromosome 17.     

Optimising the identification of causal variants across varying genetic architectures in crops

Association studies use statistical links between genetic markers and the phenotype variation across many individuals to identify genes controlling variation in the target phenotype. However, this approach, particularly conducted on a genome‐wide scale (GWAS), has limited power to identify the genes responsible for variation in traits controlled by complex genetic architectures. In this study, we employ real‐world genotype datasets from four crop species with distinct minor allele frequency distributions, population structures and linkage disequilibrium patterns. We demonstrate that different GWAS statistical approaches provide favourable trade‐offs between power and accuracy for traits controlled by different types of genetic architectures. FarmCPU provides the most favourable outcomes for moderately complex traits while a Bayesian approach adopted from genomic prediction provides the most favourable outcomes for extremely complex traits. We assert that by estimating the complexity of genetic architectures for target traits and selecting an appropriate statistical approach for the degree of complexity detected, researchers can substantially improve the ability to dissect the genetic factors controlling complex traits such as flowering time, plant height and yield component.     

An algorithm for molecular dissection of tumor progression

The volumetric growth of tumor cells as a function of time is most often likely to be a complex trait, controlled by the combined influences of multiple genes and environmental influences. Genetic mapping has proven to be a powerful tool for detecting and identifying specific genes affecting complex traits, i.e., quantitative trait loci (QTL), based on polymorphic markers. In this article, we present a novel statistical model for genetic mapping of QTL governing tumor growth trajectories in humans. In principle, this model is a combination of functional mapping proposed to map function-valued traits and linkage disequilibrium mapping designed to provide high resolution mapping of QTL by making use of recombination events created at a historic time. We implement an EM-simplex hybrid algorithm for parameter estimation, in which a closed-form solution for the EM algorithm is derived to estimate the population genetic parameters of QTL including the allele frequencies and the coefficient of linkage disequilibrium, and the simplex algorithm incorporated to estimate the curve parameters describing the dynamic changes of cancer cells for different QTL genotypes. Extensive simulations are performed to investigate the statistical properties of our model. Through a number of hypothesis tests, our model allows for cutting-edge studies aimed to decipher the genetic mechanisms underlying cancer growth, development and differentiation. The implications of our model in gene therapy for cancer research are discussed.     

Statistical Estimation of Correlated Genome Associations to a Quantitative Trait Network

Many complex disease syndromes, such as asthma, consist of a large number of highly related, rather than independent, clinical or molecular phenotypes. This raises a new technical challenge in identifying genetic variations associated simultaneously with correlated traits. In this study, we propose a new statistical framework called graph-guided fused lasso (GFlasso) to directly and effectively incorporate the correlation structure of multiple quantitative traits such as clinical metrics and gene expressions in association analysis. Our approach represents correlation information explicitly among the quantitative traits as a quantitative trait network (QTN) and then leverages this network to encode structured regularization functions in a multivariate regression model over the genotypes and traits. The result is that the genetic markers that jointly influence subgroups of highly correlated traits can be detected jointly with high sensitivity and specificity. While most of the traditional methods examined each phenotype independently and combined the results afterwards, our approach analyzes all of the traits jointly in a single statistical framework. This allows our method to borrow information across correlated phenotypes to discover the genetic markers that perturb a subset of the correlated traits synergistically. Using simulated datasets based on the HapMap consortium and an asthma dataset, we compared the performance of our method with other methods based on single-marker analysis and regression-based methods that do not use any of the relational information in the traits. We found that our method showed an increased power in detecting causal variants affecting correlated traits. Our results showed that, when correlation patterns among traits in a QTN are considered explicitly and directly during a structured multivariate genome association analysis using our proposed methods, the power of detecting true causal SNPs with possibly pleiotropic effects increased significantly without compromising performance on non-pleiotropic SNPs.     

Special issues on advances in quantitative genetics: introduction

Adaptation is commonly a multidimensional problem, with changes in multiple traits required to match a complex environment. This is epitomized by balanced polymorphisms in which multiple phenotypes co-exist and are maintained in a population by a balance of selective forces. Consideration of such polymorphisms led to the concept of the supergene, where alternative phenotypes in a balanced polymorphism segregate as if controlled by a single genetic locus, resulting from tight genetic linkage between multiple functional loci. Recently, the molecular basis for several supergenes has been resolved. Thus, major chromosomal inversions have been shown to be associated with polymorphisms in butterflies, ants and birds, offering a mechanism for localised reduction in recombination. In several examples of plant self-incompatibility, the functional role of multiple elements within the supergene architecture has been demonstrated, conclusively showing that balanced polymorphism can be maintained at multiple coadapted and tightly linked elements. Despite recent criticism, we argue that the supergene concept remains relevant and is more testable than ever with modern molecular methods.     

Applications of DNA genetic markers to the study of plant growth and development

DNA genetic markers, such as restriction fragment length polymorphisms (RFLPs) and random amplified polymorphic DNA markers (RAPDs), are powerful tools for studying the genetics of plant growth and development. DNA markers are defined sequences of DNA that can be used in traditional linkage mapping. Using DNA marker technology, scientists can uncover relationships between cloned cDNA sequences and classically characterized genes. DNA markers make it possible to dissect the contributions of multiple genetic loci underlying complex developmental processes. Moreover, changes in genome organization that occur during development or in response to environmental signals can be monitored using RFLP technology. In the future, it may be possible to clone any gene based solely on its map position. This will involve the use of tightly linked DNA markers as entry points for chromosome walking, in which a series of overlapping genomic clones reaching from the tightly linked DNA marker to the gene of interest are identified.     

Two-trait-locus linkage analysis: a powerful strategy for mapping complex genetic traits.

Recent advances in molecular biology have provided geneticists with ever-increasing numbers of highly polymorphic genetic markers that have made possible linkage mapping of loci responsible for many human diseases. However, nearly all diseases mapped to date follow clear Mendelian, single-locus segregation patterns. In contrast, many common familial diseases such as diabetes, psoriasis, several forms of cancer, and schizophrenia are familial and appear to have a genetic component but do not exhibit simple Mendelian transmission. More complex models are required to explain the genetics of these important diseases. In this paper, we explore two-trait-locus, two-marker-locus linkage analysis in which two trait loci are mapped simultaneously to separate genetic markers. We compare the utility of this approach to standard one-trait-locus, one-marker-locus linkage analysis with and without allowance for heterogeneity. We also compare the utility of the two-trait-locus, two-marker-locus analysis to two-trait-locus, one-marker-locus linkage analysis. For common diseases, pedigrees are often bilineal, with disease genes entering via two or more unrelated pedigree members. Since such pedigrees often are avoided in linkage studies, we also investigate the relative information content of unilineal and bilineal pedigrees. For the dominant-or-recessive and threshold models that we consider, we find that two-trait-locus, two-marker-locus linkage analysis can provide substantially more linkage information, as measured by expected maximum lod score, than standard one-trait-locus, one-marker-locus methods, even allowing for heterogeneity, while, for a dominant-or-dominant generating model, one-locus models that allow for heterogeneity extract essentially as much information as the two-trait-locus methods. For these three models, we also find that bilineal pedigrees provide sufficient linkage information to warrant their inclusion in such studies. We also discuss strategies for assessing the significance of the two linkages assumed in two-trait-locus, two-marker-locus models.     

Use of multivariate linkage analysis for dissection of a complex cognitive trait

Replication of linkage results for complex traits has been exceedingly difficult, owing in part to the inability to measure the precise underlying phenotype, small sample sizes, genetic heterogeneity, and statistical methods employed in analysis. Often, in any particular study, multiple correlated traits have been collected, yet these have been analyzed independently or, at most, in bivariate analyses. Theoretical arguments suggest that full multivariate analysis of all available traits should offer more power to detect linkage; however, this has not yet been evaluated on a genomewide scale. Here, we conduct multivariate genomewide analyses of quantitative-trait loci that influence reading- and language-related measures in families affected with developmental dyslexia. The results of these analyses are substantially clearer than those of previous univariate analyses of the same data set, helping to resolve a number of key issues. These outcomes highlight the relevance of multivariate analysis for complex disorders for dissection of linkage results in correlated traits. The approach employed here may aid positional cloning of susceptibility genes in a wide spectrum of complex traits.     

A haplotype-based algorithm for multilocus linkage disequilibrium mapping of quantitative trait loci with epistasis

For tightly linked loci, cosegregation may lead to nonrandom associations between alleles in a population. Because of its evolutionary relationship with linkage, this phenomenon is called linkage disequilibrium. Today, linkage disequilibrium-based mapping has become a major focus of recent genome research into mapping complex traits. In this article, we present a new statistical method for mapping quantitative trait loci (QTL) of additive, dominant, and epistatic effects in equilibrium natural populations. Our method is based on haplotype analysis of multilocus linkage disequilibrium and exhibits two significant advantages over current disequilibrium mapping methods. First, we have derived closed-form solutions for estimating the marker-QTL haplotype frequencies within the maximum-likelihood framework implemented by the EM algorithm. The allele frequencies of putative QTL and their linkage disequilibria with the markers are estimated by solving a system of regular equations. This procedure has significantly improved the computational efficiency and the precision of parameter estimation. Second, our method can detect marker-QTL disequilibria of different orders and QTL epistatic interactions of various kinds on the basis of a multilocus analysis. This can not only enhance the precision of parameter estimation, but also make it possible to perform whole-genome association studies. We carried out extensive simulation studies to examine the robustness and statistical performance of our method. The application of the new method was validated using a case study from humans, in which we successfully detected significant QTL affecting human body heights. Finally, we discuss the implications of our method for genome projects and its extension to a broader circumstance. The computer program for the method proposed in this article is available at the webpage http://www.ifasstat.ufl.edu/genome/~LD.     

On a Randomization Procedure in Linkage Analysis

Although much theoretical work has been undertaken to derive thresholds for statistical significance in genetic linkage studies, real data are often complicated by many factors, such as missing individuals or uninformative markers, which make the validity of these theoretical results questionable. Many simulation-based methods have been proposed in the literature to determine empirically the statistical significance of the observed test statistics. However, these methods either are not generally applicable to complex pedigree structures or are too time-consuming. In this article, we propose a computationally efficient simulation procedure that is applicable to arbitrary pedigree structures. This procedure can be combined with statistical tests, to assess the statistical significance for genetic linkage between a locus and a qualitative or quantitative trait. Furthermore, the genomewide significance level can be appropriately controlled when many linked markers are studied in a genomewide scan. Simulated data and a diabetes data set are analyzed to demonstrate the usefulness of this novel simulation method.     

Systematic detection of epistatic interactions based on allele pair frequencies

Epistatic genetic interactions are key for understanding the genetic contribution to complex traits. Epistasis is always defined with respect to some trait such as growth rate or fitness. Whereas most existing epistasis screens explicitly test for a trait, it is also possible to implicitly test for fitness traits by searching for the over- or under-representation of allele pairs in a given population. Such analysis of imbalanced allele pair frequencies of distant loci has not been exploited yet on a genome-wide scale, mostly due to statistical difficulties such as the multiple testing problem. We propose a new approach called Imbalanced Allele Pair frequencies (ImAP) for inferring epistatic interactions that is exclusively based on DNA sequence information. Our approach is based on genome-wide SNP data sampled from a population with known family structure. We make use of genotype information of parent-child trios and inspect 3×3 contingency tables for detecting pairs of alleles from different genomic positions that are over- or under-represented in the population. We also developed a simulation setup which mimics the pedigree structure by simultaneously assuming independence of the markers. When applied to mouse SNP data, our method detected 168 imbalanced allele pairs, which is substantially more than in simulations assuming no interactions. We could validate a significant number of the interactions with external data, and we found that interacting loci are enriched for genes involved in developmental processes.     

Multilocus linkage analysis of affected sib pairs

OBJECTIVE: The conventional affected sib pair methods evaluate the linkage information at a locus by considering only marginal information. We describe a multilocus linkage method that uses both the marginal information and information derived from the possible interactions among several disease loci, thereby increasing the significance of loci with modest effects. METHODS: Our method is based on a statistic that quantifies the linkage information contained in a set of markers. By a marker selection-reduction process, we screen a set of polymorphisms and select a few that seem linked to disease. RESULTS: We test our approach on genome scan data for inflammatory bowel disease (InfBD) and on simulated data. On real data we detect 6 of the 8 known InfBD loci; on simulated data we obtain improvements in power of up to 40% compared to a conventional single-locus method. CONCLUSION: Our extensive simulations and the results on real data show that our method is in general more powerful than single-locus methods in detecting disease loci responsible for complex traits. A further advantage of our approach is that it can be extended to make use of both the linkage and the linkage disequilibrium between disease loci and nearby markers.     

Multivariate segregation analysis for quantitative traits in line crosses

Segregation analysis is a method of detecting major genes for quantitative traits without using marker information. It serves as an important tool in helping investigators to plan further studies such as quantitative trait loci mapping or more sophisticated genomic analyses. However, current methods of segregation analysis for a single trait typically have low statistical power. We propose a multivariate segregation analysis (MSA) that takes advantage of the correlation structure of multiple quantitative traits to detect major genes. This method not only increases the statistical power, but allows dissection of the genetic architecture underlying the trait complex. In MSA the observed phenotypes of multiple correlated traits are fitted to a multivariate Gaussian mixture model. Model parameters are estimated under the maximum likelihood framework via the expectation-maximization algorithm. The presence of major genes is tested using likelihood ratio test statistics. Pleiotropy is distinguished from close linkage by comparing three possible models using the Bayesian information criterion. Two simulation experiments were performed based on the F(2) mating design. In the first, the statistical properties of MSA under varying heritabilities and sample sizes were investigated and the results compared with those obtained from single-trait analysis. In the second simulation the efficacy of MSA in separating pleiotropy from close linkage was demonstrated. Finally, the new method was applied to real data and detected a major gene responsible for both plant height and tiller number in rice.     

Analysis of genome-wide linkage disequilibrium in the highly polyploid sugarcane

Linkage disequilibrium (LD) in crops, established by domestication and early breeding, can be a valuable basis for mapping the genome. We undertook an assessment of LD in sugarcane (Saccharum spp), characterized by one of the most complex crop genomes, with its high ploidy level (>or=8) and chromosome number (>100) as well as its interspecific origin. Using AFLP markers, we surveyed 1,537 polymorphisms among 72 modern sugarcane cultivars. We exploited information from available genetic maps to determine a relevant statistical threshold that discriminates marker associations due to linkage from other associations. LD is very common among closely linked markers and steadily decreases within a 0-30 cM window. Many instances of linked markers cannot be recognized due to the confounding effect of polyploidy. However, LD within a sample of cultivars appears as efficient as linkage analysis within a controlled progeny in terms of assigning markers to cosegregation groups. Saturating the genome coverage remains a challenge, but applying LD-based mapping within breeding programs will considerably speed up the localization of genes controlling important traits by making use of phenotypic information produced in the course of selection.