A score test for the linkage analysis of qualitative and quantitative traits based on identity by descent data from sib-pairs

We propose a general likelihood-based approach to the linkage analysis of qualitative and quantitative traits using identity by descent (IBD) data from sib-pairs. We consider the likelihood of IBD data conditional on phenotypes and test the null hypothesis of no linkage between a marker locus and a gene influencing the trait using a score test in the recombination fraction theta between the two loci. This method unifies the linkage analysis of qualitative and quantitative traits into a single inferential framework, yielding a simple and intuitive test statistic. Conditioning on phenotypes avoids unrealistic random sampling assumptions and allows sib-pairs from differing ascertainment mechanisms to be incorporated into a single likelihood analysis. In particular, it allows the selection of sib-pairs based on their trait values and the analysis of only those pairs having the most informative phenotypes. The score test is based on the full likelihood, i.e. the likelihood based on all phenotype data rather than just differences of sib-pair phenotypes. Considering only phenotype differences, as in Haseman and Elston (1972) and Kruglyak and Lander (1995), may result in important losses in power. The linkage score test is derived under general genetic models for the trait, which may include multiple unlinked genes. Population genetic assumptions, such as random mating or linkage equilibrium at the trait loci, are not required. This score test is thus particularly promising for the analysis of complex human traits. The score statistic readily extends to accommodate incomplete IBD data at the test locus, by using the hidden Markov model implemented in the programs MAPMAKER/SIBS and GENEHUNTER (Kruglyak and Lander, 1995; Kruglyak et al., 1996). Preliminary simulation studies indicate that the linkage score test generally matches or outperforms the Haseman-Elston test, the largest gains in power being for selected samples of sib-pairs with extreme phenotypes.     

Joint Multipoint Linkage Analysis of Multivariate Qualitative and Quantitative Traits. I. Likelihood Formulation and Simulation Results

We describe a variance-components method for multipoint linkage analysis that allows joint consideration of a discrete trait and a correlated continuous biological marker (e.g., a disease precursor or associated risk factor) in pedigrees of arbitrary size and complexity. The continuous trait is assumed to be multivariate normally distributed within pedigrees, and the discrete trait is modeled by a threshold process acting on an underlying multivariate normal liability distribution. The liability is allowed to be correlated with the quantitative trait, and the liability and quantitative phenotype may each include covariate effects. Bivariate discrete-continuous observations will be common, but the method easily accommodates qualitative and quantitative phenotypes that are themselves multivariate. Formal likelihood-based tests are described for coincident linkage (i.e., linkage of the traits to distinct quantitative-trait loci [QTLs] that happen to be linked) and pleiotropy (i.e., the same QTL influences both discrete-trait status and the correlated continuous phenotype). The properties of the method are demonstrated by use of simulated data from Genetic Analysis Workshop 10. In a companion paper, the method is applied to data from the Collaborative Study on the Genetics of Alcoholism, in a bivariate linkage analysis of alcoholism diagnoses and P300 amplitude of event-related brain potentials.     

Genome-wide association: a promising start to a long race

A recent study by Cheung et al. demonstrates how to identify expression quantitative trait loci (eQTLs) underlying gene expression phenotypes through a combination of genome-wide linkage analysis and subsequent fine mapping or by genome-wide association (GWA) analysis. This study emphasizes the complexity of human traits, highlighting the challenges faced by investigators--in particular, insufficient linkage disequilibrium between the trait and marker variant, genetic heterogeneity and correcting for multiple testing will all adversely impact the power to detect loci by association. These issues must be considered carefully if the GWA approach is to succeed in mapping complex phenotypes.     

Joint mapping of quantitative trait Loci for multiple binary characters

Joint mapping for multiple quantitative traits has shed new light on genetic mapping by pinpointing pleiotropic effects and close linkage. Joint mapping also can improve statistical power of QTL detection. However, such a joint mapping procedure has not been available for discrete traits. Most disease resistance traits are measured as one or more discrete characters. These discrete characters are often correlated. Joint mapping for multiple binary disease traits may provide an opportunity to explore pleiotropic effects and increase the statistical power of detecting disease loci. We develop a maximum-likelihood method for mapping multiple binary traits. We postulate a set of multivariate normal disease liabilities, each contributing to the phenotypic variance of one disease trait. The underlying liabilities are linked to the binary phenotypes through some underlying thresholds. The new method actually maps loci for the variation of multivariate normal liabilities. As a result, we are able to take advantage of existing methods of joint mapping for quantitative traits. We treat the multivariate liabilities as missing values so that an expectation-maximization (EM) algorithm can be applied here. We also extend the method to joint mapping for both discrete and continuous traits. Efficiency of the method is demonstrated using simulated data. We also apply the new method to a set of real data and detect several loci responsible for blast resistance in rice.     

SAMPLE SIZE ESTIMATION FOR GENE ACTION ANALYSIS BY USING ORTHOGONAL CONTRAST

IIntroductionTheuseofrestrlctlonfragmentlengthpolymorphism（RFLP）markershasgreatlyslmpllfledthegeneticanalysisofquantitativetraits,providingareliableandextensiveframeworkofquantltatlvemarkerstowhichquantltatlyetyaitIOCI（QTL）clnhilinked［‘］．TodetectthelinkagebetwwenRFLPmarkersandPhenotyPlcvariationsoh－served,generallinearmodelofanalysisofvariance（ANOVA）hasbeenextensivelyusedL‘zJ．ByusingF、populations,thecompletegeneticInformation,thatIs,thethreegenotypesofageneticfact…     

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.     

Mapping Mendelian Factors Underlying Quantitative Traits Using RFLP Linkage Maps

The advent of complete genetic linkage maps consisting of codominant DNA markers [typically restriction fragment length polymorphisms (RFLPs)] has stimulated interest in the systematic genetic dissection of discrete Mendelian factors underlying quantitative traits in experimental organisms. We describe here a set of analytical methods that modify and extend the classical theory for mapping such quantitative trait loci (QTLs). These include: (i) a method of identifying promising crosses for QTL mapping by exploiting a classical formula of SEWALL WRIGHT; (ii) a method (interval mapping) for exploiting the full power of RFLP linkage maps by adapting the approach of LOD score analysis used in human genetics, to obtain accurate estimates of the genetic location and phenotypic effect of QTLs; and (iii) a method (selective genotyping) that allows a substantial reduction in the number of progeny that need to be scored with the DNA markers. In addition to the exposition of the methods, explicit graphs are provided that allow experimental geneticists to estimate, in any particular case, the number of progeny required to map QTLs underlying a quantitative trait.     

The extent and distribution of linkage disequilibrium in a multi-hierarchic outbred canine pedigree

A canine integrated linkage-radiation map has been recently constructed by using microsatellite markers. This map, with a good coverage of the canine genome, allows for a genome-wide search for the extent and distribution of linkage disequilibrium derived from linkage and evolutionary forces. In this study, we genotyped an outbred pedigree between Labrador retriever and Greyhound breeds with a set of microsatellite markers (240) from the canine linkage map. Linkage disequilibrium was measured between all syntenic and nonsyntenic marker pairs. Analysis of syntenic pairs revealed a significant correlation (–0.229, P < 0.001) between linkage disequilibrium and genetic distance (log transformed). Significant linkage disequilibria were observed more frequently between syntenic pairs spaced <40 cM than those paced >40 cM. There is a clear trend for linkage disequilibrium to decline with marker distance. From our results, a genome-wide screen with markers at low to moderate density (1–2 per 10 cM) should take full advantage of linkage disequilibrium for quantitative trait locus mapping in dogs. This study supports the appropriateness of linkage disequilibrium analysis to detect and map quantitative trait loci underlying complex traits in dogs.     

豌豆种质表型性状SSR标记关联分析

关联分析是以连锁不平衡原理为基础,鉴定某一群体内表型性状与遗传标记或候选基因间关系的遗传分析方法。本研究利用59个多态性SSR标记,对192份豌豆种质进行全基因组扫描,以分析SSR位点遗传多样性,寻找其连锁不平衡位点;采用TASSEL软件的一般线性模型,利用59个SSR标记对19个形态性状进行关联分析。结果显示SSR位点间有较高的多态性和一定程度的连锁不平衡,共检测出32个SSR标记位点与14个表形性状相关联,一些SSR标记与2个或多个形态性状相关联。     

Genetic diversity, structure and marker-trait associations in a collection of Italian tomato (Solanum lycopersicum L.) landraces

The study of phenotypic and genetic diversity in landrace collections is important for germplasm conservation. In addition, the characterisation of very diversified materials with molecular markers offers a unique opportunity to define significant marker-trait associations of biological and agronomic interest. Here, 50 tomato landraces (mainly collected in central Italy), nine vintage and modern cultivars, and two wild outgroups were grown at two locations in central Italy and characterised for 15 morpho-physiological traits and 29 simple sequence repeat (SSR) loci. The markers were selected to include a group of loci in regions harbouring reported quantitative trait loci (QTLs) that affect fruit size and/or shape (Q-SSRs) and a group of markers that have not been mapped or shown to have a priori known linkage (NQ-SSRs). As revealed by univariate and multivariate analyses of morphological data, the landraces grouped according to vegetative and reproductive traits, with emphasis on fruit size, shape and final destination of the product. Compared to the low molecular polymorphism reported in tomato modern cultivars, our data reveal a high level of molecular diversity in landraces. Such diversity has allowed the inference of the existence of a genetic structure that was factored into the association analysis. As the proportion of significant associations is higher between the Q-SSR subset of markers and the subset of traits related to fruit size and shape than for all of the other combinations, we conclude that this approach is valid for establishing true-positive marker-trait relationships in tomato. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Joint Multipoint Linkage Analysis of Multivariate Qualitative and Quantitative Traits. II. Alcoholism and Event-Related Potentials

The availability of robust quantitative biological markers that are correlated with qualitative psychiatric phenotypes can potentially improve the power of linkage methods to detect quantitative-trait loci influencing psychiatric disorders. We apply a variance-component method for joint multipoint linkage analysis of multivariate discrete and continuous traits to the extended pedigree data from the Collaborative Study on the Genetics of Alcoholism, in a bivariate analysis of qualitative alcoholism phenotypes and quantitative event-related potentials. Joint consideration of the DSM-IV diagnosis of alcoholism and the amplitude of the P300 component of the Cz event-related potential significantly increases the evidence for linkage of these traits to a chromosome 4 region near the class I alcohol dehydrogenase locus ADH3. A likelihood-ratio test for complete pleiotropy is significant, suggesting that the same quantitative-trait locus influences both risk of alcoholism and the amplitude of the P300 component.     

Accounting for epistasis in linkage analysis of general pedigrees

Complex traits are generally believed to be influenced by multiple loci. Identification of loci involved in complex traits is more difficult for interacting than for additive loci. Here we describe an extension of the program lm_twoqtl in the package MORGAN to handle two quantitative trait loci (QTLs) with gene-gene interaction. We investigate whether parametric linkage analysis that accounts for such epistasis improves prospects for linkage detection and accuracy of localization of QTLs. Through use of simulated data we show that analysis that accounts for epistasis provides higher lod scores and better localization than does analysis without epistasis. In addition, we demonstrate that the difference between lod scores in the presence vs. absence of use of an interaction model in analysis is greater in extended than in nuclear pedigrees.     

Approaches to mapping genetically correlated complex traits

Our Markov chain Monte Carlo (MCMC) methods were used in linkage analyses of the Framingham Heart Study data using all available pedigrees. Our goal was to detect and map loci associated with covariate-adjusted traits log triglyceride (lnTG) and high-density lipoprotein cholesterol (HDL) using multipoint LOD score analysis, Bayesian oligogenic linkage analysis and identity-by-descent (IBD) scoring methods. Each method used all marker data for all markers on a chromosome. Bayesian linkage analysis detected a linkage signal on chromosome 7 for lnTG and HDL, corroborating previously published results. However, these results were not replicated in a classical linkage analysis of the data or by using IBD scoring methods.We conclude that Bayesian linkage analysis provides a powerful paradigm for mapping trait loci but interpretation of the Bayesian linkage signals is subjective. In the absence of a LOD score method accommodating genetically complex traits and linkage heterogeneity, validation of these signals remains elusive.     

Relaxed significance criteria for linkage analysis

Linkage analysis involves performing significance tests at many loci located throughout the genome. Traditional criteria for declaring a linkage statistically significant have been formulated with the goal of controlling the rate at which any single false positive occurs, called the genomewise error rate (GWER). As complex traits have become the focus of linkage analysis, it is increasingly common to expect that a number of loci are truly linked to the trait. This is especially true in mapping quantitative trait loci (QTL), where sometimes dozens of QTL may exist. Therefore, alternatives to the strict goal of preventing any single false positive have recently been explored, such as the false discovery rate (FDR) criterion. Here, we characterize some of the challenges that arise when defining relaxed significance criteria that allow for at least one false positive linkage to occur. In particular, we show that the FDR suffers from several problems when applied to linkage analysis of a single trait. We therefore conclude that the general applicability of FDR for declaring significant linkages in the analysis of a single trait is dubious. Instead, we propose a significance criterion that is more relaxed than the traditional GWER, but does not appear to suffer from the problems of the FDR. A generalized version of the GWER is proposed, called GWERk, that allows one to provide a more liberal balance between true positives and false positives at no additional cost in computation or assumptions.     

Use of the robust sib-pair method to screen for single-locus, multiple-locus, and pleiotropic effects: application to traits related to hypertension.

Robust sib-pair linkage analysis can be used as a screening tool in the search for the potential involvement of single-loci, multiple-loci, and pleiotropic effects of single loci underlying phenotypic variation. Four large families were each ascertained through one adult white male with essential hypertension. The robust sib-pair method was used to screen these families for evidence of linkage between 39 quantitative traits related to hypertension and 25 genetic marker loci. All traits were analyzed on the untransformed, square-root and log-transformed scales. Among other findings, there is a suggestion of linkage between the 6-phosphogluconate dehydrogenase locus on chromosome 1p36 and mean fifth-phase diastolic blood pressure. There may also be linkage between the following markers and traits: the adenylate kinase-1 marker and/or the Lewis blood group marker and the traits height, weight, and biacromial breadth; the glyoxylase I marker and the traits upper-arm circumference and suprailiac skinfold thickness; the ABO blood group and adenylate kinase-1 markers on chromosome 9q34 and the third component of complement marker on chromosome 19p13 and dopamine-beta-hydroxylase; and the P1 blood group and the traits weight and 1-h postload serum glucose level.     

Genetic linkage map of a wheat×spelt cross

 We constructed a genetic map of a cross between the Swiss winter wheat (Triticum aestivum L.) variety Forno and the Swiss winter spelt (Triticum spelta L.) variety Oberkulmer. For the linkage analysis,176 polymorphic RFLP probes and nine microsatellites were tested on 204 F₅ recombinant inbred lines (RILs) of Forno×Oberkulmer revealing 242 segregating marker loci. Thirty five percent of these loci showed significant (P>0.05) deviation from a 1 : 1 segregation, and the percentage of Forno alleles ranged from 21% to 83% for individual marker loci. Linkage analysis was performed with the program MAPMAKER using the Haldane mapping function. Using a LOD threshold of 10, we obtained 37 linkage groups. After finding the best order of marker loci within linkage groups by multi-point analysis we assembled the linkage groups into 23 larger units by lowering the LOD threshold. All except one of the 23 new linkage groups could be assigned to physical chromosomes or chromosome arms according to hybridisation patterns of nulli-tetrasomic lines of Chinese Spring and published wheat maps. This resulted in a genetic map comprising 230 marker loci and spanning 2469 cM. Since the analysed population is segregating for a wide range of agronomically important traits, this genetic map is an ideal basis for the identification of quantitative trait loci (QTLs) for these traits. Received: 3 August 1998 / Accepted: 28 November 1998     

Analyses of quantitative trait loci associated with resistance to shape Sclerotinia sclerotiorum in sunflowers (shape Helianthus annuus L.) using molecular markers

Restriction fragment length polymorphism and isoenzyme markers were used to investigate quantitative trait loci involved in sunflower resistance to mycelial extension of Sclerotinia sclerotiorum on leaves and capitula. Seed weight, oil content and flowering data were also evaluated. Four quantitative trait loci were demonstrated for leaf resistance and two for capitulum resistance. One of these zones appears involved in resistance to both types of S. sclerotiorum attack while the others appear specific for resistance of one part of the plant. Two quantitative trait loci were detected for seed weight, three for oil content and three for flowering date. Individual quantitative trait loci explained 9% to 48% of the phenotypic variability, confirming the polygenic basis of the quantitative traits studied. Overall, the quantitative trait loci explain 60% of the genetic variation for leaf resistance and 38% for capitulum resistance to S. sclerotiorum. One linkage group is particularly interesting since it includes quantitative trait loci for all the five quantitative traits measured. Hypotheses for linkage versus pleiotropy and consequences of all the results in resistance breeding are discussed.     

Physical linkage and mate preference generate linkage disequilibrium for behavioral isolation in two parapatric crickets

Behavioral isolation is a potent barrier to gene flow and a source of striking diversity in the animal kingdom. However, it remains unclear if the linkage disequilibrium (LD) between sex‐specific traits required for behavioral isolation results mostly from physical linkage between signal and preference loci or from directional mate preferences. Here, we test this in the field crickets Gryllus rubens and G. texensis. These closely related species diverged with gene flow and have strongly differentiated songs and preference functions for the mate calling song rhythm. We map quantitative trait loci for signal and preference traits (pQTL) as well as for gene expression associated with these traits (eQTL). We find strong, positive genetic covariance between song traits and between song and preference. Our results show that this is in part explained by incomplete physical linkage: although both linked pQTL and eQTL couple male and female traits, major effect loci for different traits were never on the same chromosome. We suggest that the finely tuned, highly divergent preference functions are likely an additional source of LD between male and female traits in this system. Furthermore, pleiotropy of gene expression presents an underappreciated mechanism to link sexually dimorphic phenotypes.     

The Contribution of Quantitative Trait Loci and Neutral Marker Loci to the Genetic Variances and Covariances among Quantitative Traits in Random Mating Populations

Using Cockerham's approach of orthogonal scales, we develop genetic models for the effect of an arbitrary number of multiallelic quantitative trait loci (QTLs) or neutral marker loci (NMLs) upon any number of quantitative traits. These models allow the unbiased estimation of the contributions of a set of marker loci to the additive and dominance variances and covariances among traits in a random mating population. The method has been applied to an analysis of allozyme and quantitative data from the European oyster. The contribution of a set of marker loci may either be real, when the markers are actually QTLs, or apparent, when they are NMLs that are in linkage disequilibrium with hidden QTLs. Our results show that the additive and dominance variances contributed by a set of NMLs are always minimum estimates of the corresponding variances contributed by the associated QTLs. In contrast, the apparent contribution of the NMLs to the additive and dominance covariances between two traits may be larger than, equal to or lower than the actual contributions of the QTLs. We also derive an expression for the expected variance explained by the correlation between a quantitative trait and multilocus heterozygosity. This correlation explains only a part of the genetic variance contributed by the markers, i.e., in general, a combination of additive and dominance variances and, thus, provides only very limited information relative to the method supplied here.