TDT statistics for mapping quantitative trait loci

The original transmission disequilibrium test (TDT), was introduced to test for linkage between a marker and a disease-susceptibility locus (Spielman et al . 1993). Allison (1997) extended the TDT procedure to quantitative traits. Allison's test, however, is restrictive in that it requires family trios consisting of one heterozygous parent, one homozygous parent and one child, and considers only the situation where the marker locus is analogous to the quantitative trait locus itself. In this paper, we propose, investigate and apply a general TDT for quantitative traits that permits more than one child per family, does not require only one parent to be heterozygous, and allows for the fact that the various alleles at the marker and trait loci may be at varying degree of linkage disequilibrium. We also show that this TDT for quantitative traits is still a valid test of linkage in the presence of population substructure. To provide guidelines for study design, we develop analytic formulae for calculation of the power of the TDT for mapping quantitative trait loci and investigate the impact of various factors on the power. Power calculations show that the proposed TDT for quantitative traits is more powerful than Allison's basic test statistic and the extreme discordant sib pair linkage method. The proposed TDT statistic for quantitative traits is applied to systolic blood pressure variation in the Rochester Family Heart Study using an extremely discordant sibling pair design.     

Pedigree linkage disequilibrium mapping of quantitative trait loci

In this paper, we propose to use pedigrees of any size and any types of relatives in joint high-resolution linkage disequilibrium (LD) and linkage mapping of quantitative trait loci (QTL) by variance component models. Two or multiple markers can be simultaneously used in modeling association with the trait locus, instead of using one marker a time in the analysis. The proposed method can provide a unified result by using two or multiple markers in the modeling. This may avoid the complications of different results obtained from the separate analysis of marker by marker. The models simultaneously incorporate both linkage and LD information. The measures of LD are modeled by mean coefficients, and linkage information is modeled by variance-covariance matrix. Using analytical formulas to calculate the regression coefficients, the genetic effects are shown to be decomposed into additive and dominance components. The noncentrality parameter approximations of test statistics of LD are provided to make power calculations. Power and type I error rates are explored to investigate the merit of the proposed method by both the analytical formulas and simulations. Comparing with the association between-family and association within-family ('AbAw') approach of Fulker and Abecasis et al, it is evident that the method proposed in this article is more powerful. The method is applied to investigate the relation between polymorphisms in the angiotensin 1-converting enzyme (ACE) genes and circulating ACE levels, with a better result than that of the 'AbAw' approach. Moreover, two markers I/D and 4656(CT)3/2 can fully interpret association with the trait locus at a 0.01 significance level, which provides a unique result for the ACE data.     

Using advanced intercross lines for high-resolution mapping of HDL cholesterol quantitative trait loci

Mapping quantitative trait loci (QTLs) with high resolution facilitates identification and positional cloning of the underlying genes. The novel approach of advanced intercross lines (AILs) generates many more recombination events and thus can potentially narrow QTLs significantly more than do conventional backcrosses and F2 intercrosses. In this study, we carried out QTL analyses in (C57BL/6J x NZB/BlNJ) x C57BL/6J backcross progeny fed either chow or an atherogenic diet to detect QTLs that regulate high-density lipoprotein cholesterol (HDL)concentrations, and in (C57BL/6J x NZB/BlNJ) F11 AIL progeny to confirm and narrow those QTLs. QTLs for HDL concentrations were found on chromosomes 1, 5, and 16. AIL not only narrowed the QTLs significantly more than did a conventional backcross but also resolved a chromosome 5 QTL identified in the backcross into two QTLs, the peaks of both being outside the backcross QTL region. We tested 27 candidate genes and found significant mRNA expression differences for 12 (Nr1i3, Apoa2, Sap, Tgfb2, Fgfbp1, Prom, Ppargc1, Tcf1, Ncor2, Srb1, App, and Ifnar). Some of these underlay the same QTL, indicating that expression differences are common and not sufficient to identify QTL genes. All the major HDL QTLs in our study had homologous counterparts in humans, implying that their underlying genes regulate HDL in humans.     

Strategy for mapping quantitative trait loci (QTL) by using human metapopulations

Aim

To present a novel strategy for mapping quantitative trait loci (QTL), using human metapopulations. The strategy is based on the expectation that in geographic clusters of small and distinct human isolates, a combination of founder effect and genetic drift can dramatically increase population frequency of rare QTL variants with large effect. In such cases, the distribution of QT measurements in an “affected” isolate is expected to deviate from that observed in neighboring isolates.

Methods

We tested this hypothesis in 9 villages from a larger Croatian isolate resource, where 7 Mendelian disorders have been previously reported. The values of 10 physiological and biochemical QTs were measured in a random sample of 1001 individuals (100 inhabitants of each of 9 villages and 101 immigrant controls).

Results

Significant over- or under- representation of individuals from specific villages in extreme ends of standardized QT measurement distribution was found 10 times more frequently than expected by chance. The large majority of such clusters of individuals with extreme QT values (34/36, 94.4%) originated from the 6 villages with the most pronounced geographic isolation and endogamy.

Conclusion

Early epidemiological assessment supports the feasibility of the proposed strategy. Clusters of individuals with extreme QT values responsible for over-representation of single villages can usually be linked to a larger pedigree and may be useful for further QTL mapping, using linkage analysis.The common feature of Mendelian diseases is that their characteristic phenotype is caused by a rare mutation in a single gene in the genome. Therefore, the segregation of affected individuals in families follows simple Mendelian predictions (1). The catalogue of known Mendelian diseases is regularly published, with some 8000 diseases or syndromes listed and new ones continually added to this number (2). The last decade saw great successes in identifying genetic variants underlying several thousands of these diseases (3-5). This success was facilitated by the fact that causal genetic mutation is both necessary and sufficient for the development of the disease, which is the key property of Mendelian diseases. This ensures good correlation between disease phenotypes and underlying genotypes (high “penetrance” and “detectance,” ie, the probabilities of observing the disease phenotype given the disease genotype, and vice versa), which is an important requirement for the success of gene mapping using pedigree-based approach (6,7).Most Mendelian diseases usually present at an early age and with a number of clinically apparent phenotypic changes. Such a spectrum of phenotypes, initially described as a distinct clinical syndrome, reflects the multiple roles the affected gene products have in human development and metabolism. As the human genome harbors some 25 000 predicted genes and an unknown number of conserved functional elements and regulatory regions, perhaps many more than 8000 Mendelian diseases should be expected. Many genes, however, may interact with each other within common biochemical pathways, thus limiting the number of possible phenotypic outcomes of their mutations. However, the diagnosis of Mendelian diseases is typically based on noticing visually apparent disease phenotypes.These phenotypes all have in common that they represent measurable human biological quantitative traits. Some of them (eg, blood pressure, body mass index, cholesterol levels, and blood glucose) have recently been identified by the World Health Organization as the main contributors to disease burden in developed countries (8). An understanding of their genetic regulation is therefore of great current interest (9,10). The genes underlying human quantitative traits (QT) may actually be easier to detect than those predisposing common complex diseases, as quantitative traits represent just a fraction of the many recognized risk factors underlying common complex diseases of late onset (11). In this paper, we present and test a novel strategy for finding very rare genetic variants with large effect on QTs in human populations, ie, genes underlying "invisible Mendelian diseases." The proposed approach relies on specific population genetic properties of geographically clustered and isolated human populations, often referred to as metapopulations, which allow for increased frequency of large effect genetic variants underlying quantitative trait distributions that would have extremely small frequencies in large outbred populations.Croatia has 15 Adriatic Sea islands with a population greater than 1000. The villages on the islands have unique population histories and have preserved their isolation from other villages and outside world through many centuries. The history, demography, and genetic structure of these villages have been investigated for more than 50 years. The research, mainly carried out by the Institute for Anthropological Research in Zagreb, Croatia, resulted in over 100 publications in international journals (12-14). On some of the islands, monogenic (Mendelian) diseases and rare genetic variants were found in unexpectedly high frequencies (15-27).

Table 1

Overview of the evidence of extremely rare mutations present in unusually high frequencies in specific Croatian island isolates

Further characterization and high-resolution mapping of quantitative trait loci for ethanol-induced locomotor activity

Differential sensitivity to the stimulant effects of ethanol on locomotor activity is determined in part by genetic differences. Among inbred strains of mice, moderate doses of ethanol (1-2 g/kg) stimulate locomotor activity in some strains, e.g., the DBA/2J (D2), but only mildly affect activity in other strains, e.g., C57BL/6J (B6) (Crabbe et al., 1982, 1983; Crabbe, 1986; Dudek and Phillips, 1990; Dudek et al., 1991; Dudek and Tritto, 1994). Quantitative trait loci (QTL) for the acute ethanol (1.5 g/kg) locomotor response has been identified in the BXD recombinant inbred (RI) series (N = 25 strains), a C57BL/6J × DBA/2J (B6D2) F₂ intercross (N = 1800), and heterogeneous stock (HS) mice (N = 550). QTLs detected (p < .01) in the RI series were found on chromosomes 1, 2, and 6 and these QTLs were expressed in a time-dependent fashion. The QTLs on chromosomes 1 and 2 were confirmed in the F₂ intercross at p < 10^–7 or better. HS mice from G₃₂ to G₃₅ were used to fine-map the chromosome 2 QTL. Compared to the consensus map, the genetic map in the HS animals was expanded 10- to 15-fold. Over the region flanked by D2Mit94 to D2Mit304, three separate QTLs were detected in the HS animals. The data obtained confirm the usefulness of HS mice for the fine-mapping of QTLs to a resolution of 2 cM or less.     

Linkage mapping of quantitative trait loci in humans: an overview

In this article, we provide an overview of the different statistical procedures that have been developed for linkage mapping of quantitative trait loci. We outline the model assumptions, the data requirements and the underlying tests for linkage for the different methods.     

High resolution mapping of quantitative trait loci by linkage disequilibrium analysis

Two methods, linkage analysis and linkage disequilibrium (LD) mapping or association study, are usually utilised for mapping quantitative trait loci (QTL). Linkage mapping is appropriate for low resolution mapping to localise trait loci to broad chromosome regions within a few cM (<10 cM), and is based on family data. Linkage disequilibrium mapping, on the other hand, is useful in high resolution or fine mapping, and is based on both population and family data. Using only one marker, one may carry out single-point linkage analysis and linkage disequilibrium mapping. Using two or more markers, it is possible to flank the QTL by multipoint analysis. The development and thus availability of dense marker maps, such as single nucleotide polymorphisms (SNP) in human genome, presents a tremendous opportunity for multipoint fine mapping. In this article, we propose a regression approach of mapping QTL by linkage disequilibrium mapping based on population data. Assuming that two marker loci flank one quantitative trait locus, a two-point linear regression is proposed to analyse population data. We derive analytical formulas of parameter estimations, and non-centrality parameters of appropriate tests of genetic effects and linkage disequilibrium coefficients. The merit of the method is shown by the power calculation and comparison. The two-point regression model can capture much more linkage and linkage disequilibrium information than that derived when only one marker is used. For a complex disease with heritability h(2)> or =0.15, a study with sample size of 250 can provide high power for QTL detection under moderate linkage disequilibria.     

Linkage mapping of quantitative trait loci in humans: an overview

In this article, we provide an overview of the different statistical procedures that have been developed for linkage mapping of quantitative trait loci. We outline the model assumptions, the data requirements and the underlying tests for linkage for the different methods.     

Combined high resolution linkage and association mapping of quantitative trait loci

In this paper, we investigate variance component models of both linkage analysis and high resolution linkage disequilibrium (LD) mapping for quantitative trait loci (QTL). The models are based on both family pedigree and population data. We consider likelihoods which utilize flanking marker information, and carry out an analysis of model building and parameter estimations. The likelihoods jointly include recombination fractions, LD coefficients, the average allele substitution effect and allele dominant effect as parameters. Hence, the model simultaneously takes care of the linkage, LD or association and the effects of the putative trait locus. The models clearly demonstrate that linkage analysis and LD mapping are complementary, not exclusive, methods for QTL mapping. By power calculations and comparisons, we show the advantages of the proposed method: (1) population data can provide information for LD mapping, and family pedigree data can provide information for both linkage analysis and LD mapping; (2) using family pedigree data and a sparse marker map, one may investigate the prior suggestive linkage between trait locus and markers to obtain low resolution of the trait loci, because linkage analysis can locate a broad candidate region; (3) with the prior knowledge of suggestive linkage from linkage analysis, both population and family pedigree data can be used simultaneously in high resolution LD mapping based on a dense marker map, since LD mapping can increase the resolution for candidate regions; (4) models of high resolution LD mappings using two flanking markers have higher power than that of models of using only one marker in the analysis; (5) excluding the dominant variance from the analysis when it does exist would lose power; (6) by performing linkage interval mappings, one may get higher power than by using only one marker in the analysis.     

Parameters of quantitative trait loci

Most traits of medical relevance follow quantitative inheritance patterns. The genetic dissection of quantitative traits poses special challenges for geneticists mainly because of low penetrance and gene-gene and gene-environment interactions. Emerging genome resources and technologies are enabling systematic investigation of the genetic architecture of quantitative traits in more efficient ways. This article summarizes the current state of medical quantitative trait locus (QTL) mapping-describing the methods, limitations, and achievements in the detection and characterization of QTLs.     

Preweanling sensorial and motor development in laboratory mice: quantitative trait loci mapping

Chromosomal mapping of genes linked with 19 measures of sensorial, motor, and body weight development were investigated. Chromosomal mapping is the first step towards gene identification. When a genomic region is shown to be linked to a trait, it is possible to select a reduced number of candidate genes that have been previously mapped on this region. The involvement of every gene can be individually tested either by molecular (transgenesis, homologous recombination) or traditional methods (congenicity). Mapping was performed using 389 males and females from two inbred strains of laboratory mice C57BL/6By and NZB/BlNJ, their reciprocal F1s and F2s. Thirty-six Quantitative Trait Loci (QTL) were mapped, 12 reached the 3.13 lod score, being thus considered as confirmed. These QTL were tentatively labeled: Cliff Drop Aversion (Cliff Qtl), Geotaxia (Geot Qtl), Vertical Clinging (VertCling Qtl), Bar Holding with the 4 paws (BH4P Qtl), Age at Eyelid Opening (Aeyo Qtl), Visual Placing (Vispl Qtl), Startle Response (Start Qtl1, Start Qtl2), Body Weight at Day 10 in Males pooled with Females (Bwefmd10 Qtl), and Body Weight at Day 30 in males (Bwemd30 Qtl). For the majority of the developmental measures, the QTL that were mapped contributed little to the phenotypic variance, even when mitochondrial DNA contribution was included: Righting Response (12.7%), Cliff Drop Aversion (10%), Crossed Extensor Response (18.1%), Geotaxia (16.2%), Bar Holding Response for 10 s (12.1%), Bar Holding Response with 4 paws (8.1%), Vertical Clinging (9.3%), Vertical Climbing (5%), Startle Response (21.2%), Eyelid Opening (14.6%), Visual Placing (22%), Body Weight at Day 10 (27%), Body Weight at Day 15 in Females (52.5%), Body Weight at Day 15 in Males (17%), Body Weight at Day 30 in Females (42%), and Body Weight at Day 30 in Males (48%). A factorial analysis of the correlations between the measures of development did not provide evidence of a general factor. A general genetic factor of development was also rejected because few common genetic correlates were discovered for the 19 measures of development (Body Weight at Days 15 and 30 in Females on Chromosome 2, Eyelid Opening and Body Weight at Day 10 on Chromosome 5 and mitochondrial genome for five measures). Co-identification of genes, the function of which were previously known thanks to newly discovered QTL, should help to explain the function of QTL. Present data help to highlight candidate regions including several genes that could be candidates for the QTL function. Large confidence intervals were obtained as usual from the F2 intercrossed population. More stringent methods are suggested for more efficient co-identification.     

Evaluation of a restricted likelihood ratio test for mapping quantitative trait loci with extreme discordant sib pairs

Risch and Zhang recently proposed to use extreme discordant sib pairs for mapping quantitative trait loci. Here, it is shown that the set of genetically possible distributions of the number of marker alleles in such sib-pairs is described by two inequalities. Thus, a likelihood ratio test analogous to Holmans's possible triangle test for affected sib pairs can be defined. The performance of this test is compared to the mean test considered by Risch and Zhang. For most of the genetic models considered, the mean test is slightly more powerful than the restricted likelihood ratio test. However, for models with a rare recessive gene (or equivalently a common dominant gene), the restricted likelihood ratio test is much more powerful.     

Mapping quantitative trait loci for behavioral traits in the mouse

After many years of studying various behavioral characters in the mouse, it is clear that most are heritable and are specified by complexes of genes or quantitative trait loci (QTLs). In order to attain a more complete understanding of the genetic causes of individual differences in behavior, the mechanism of action of these QTLs must be elucidated. The most straightforward approach to determining the mechanism of action of a particular QTL is to identify and molecularly clone the gene; this can be done by positional cloning, which depends on precise knowledge of the genetic map position. As the genetic data base for the mouse genome continues to develop, such strategies will become increasingly easy to perform. Here we suggest a multistage strategy for QTL mapping using recombinant-inbred strains of mice: (1) characterize genomic DNA from parental strains originally used to generate the RI strains; (2) characterize the RI strains for a quantitative character and for DNA markers that differ in the parental strains; and (3) assess the quantitative character in F₂ mice derived from crosses between the parental strains, then determine the genotypes of extreme F₂ mice for markers that account for at least 5% of the additive genetic variance. Data from these F₂ crosses can be used to test hypotheses from the analysis of RI strains, i.e., that a QTL maps to a particular region. Using data from the mouse genome data base, this strategy should allow the molecular identification of the gene based on a candidate-gene approach. We illustrate the approach with examples from our work in mapping QTLs specifying neural sensitivity to the anesthetic effects of ethanol.This work was supported by grants from the National Institutes of Health (R01-AG08332, R01-AG10248, and K04-AG00369), by a gift from the Glenn Foundation for Medical Research, from ADAMHA (P05 AA-03527), by a training grant from the NIMH (MH-16880) to support P.D.M., and by BRSG Grant RR-07013 to the University of Colorado.     

Multivariate multipoint linkage analysis of quantitative trait loci

Resolution of the genetic components of complex disorders may require simultaneous analysis of the contribution of individual quantitative trait loci (QTLs) to multiple variables. A likelihood approach is used to illustrate how the complexities of multivariate data may be resolved with multipoint linkage analysis. Sibling pair data were simulated from a model in which two QTLs and trait-specific polygenic effects explained all the sibling resemblance within and between five variables. Multipoint linkage analysis was used to obtain individual pair probabilities of having zero, one, or two alleles identical by descent, and these probabilities were applied in a weighted maximum-likelihood fit function. The results were compared with those obtained using conventional linear structural equation modeling to estimate the contribution of latent genetic factors to the genetic covariance in the multiple measures. Both analyses were conducted using the Mx package. Relatively poor agreement was found between genetic factors defined in purely statistical terms by varimax rotation of the first two factors of the genetic covariance matrix and the structure obtained by fitting a model jointly to the phenotypic and the multipoint linkage data.     

Sex-exclusive quantitative trait loci influences in alcohol-related phenotypes

During the past half century, researchers have identified and examined sex differences in alcohol-related phenotypes, focusing more recently on understanding of the mechanisms underlying these differences. In general, the genetic contributions influencing these differences are not consistent with an interpretation of sex linkage and must, therefore, reflect some form of sex limitation in which allelic differences at particular autosomal loci have different consequences in males and females. Significant sex differences in measures of alcohol consumption in mice have been demonstrated in previous work in our laboratory. To investigate these differences further, we explore the limiting case of sex-exclusive effects using data from (BXD) recombinant inbred (RI) strains of mice and from an intercross derived from the same progenitors, C57BL/6J (B) and DBA/2J (D). By the use of two statistical approaches (examination of residual scores as a sex-exclusive phenotypic value for the RI strains and multivariate regression on sex and genotype in the F(2)) we have identified and confirmed female-exclusive markers for alcohol acceptance on chromosomes 9 and 12 and one marker for alcohol preference on chromosome 2. Am. J. Med. Genet. (Neuropsychiatr. Genet.) 88:647-652, 1999.