Disequilibrium mapping of a quantitative-trait locus in an expanding population.

Linkage disequilibrium (LD) mapping can be successful if there is strong nonrandom association between marker alleles and an allele affecting a trait of interest. The principles of LD mapping of dichotomous traits are well understood, but less is known about LD mapping of a quantitative-trait locus (QTL). It is shown in this report that selective genotyping can increase the power to detect and map a rare allele of large effect at a QTL. Two statistical tests of the association between an allele and a quantitative character are proposed. These tests are approximately independent, so information from them can be combined. Analytic theory is developed to show that these two tests are effective in detecting the presence of a low-frequency allele with a relatively large effect on the character when the QTL is either already a candidate locus or closely linked to a marker locus that is in strong LD with the QTL. The latter situation is expected in a rapidly growing population in which the allele of large effect was present initially in one copy. Therefore, the proposed tests are useful under the same conditions as those for successful LD mapping of a dichotomous trait or disease. Simulations show that, for detection of the presence of a QTL, these tests are more powerful than a simple t-test. The tests also provide a basis for defining a measure of association, gamma, between a low-frequency allele at a putative QTL and a low-frequency allele at a marker locus.     

A fast expectation-maximum algorithm for fine-scale QTL mapping

The recent technology of the single-nucleotide-polymorphism (SNP) array makes it possible to genotype millions of SNP markers on genome, which in turn requires to develop fast and efficient method for fine-scale quantitative trait loci (QTL) mapping. The single-marker association (SMA) is the simplest method for fine-scale QTL mapping, but it usually shows many false-positive signals and has low QTL-detection power. Compared with SMA, the haplotype-based method of Meuwissen and Goddard who assume QTL effect to be random and estimate variance components (VC) with identity-by-descent (IBD) matrices that inferred from unknown historic population is more powerful for fine-scale QTL mapping; furthermore, their method also tends to show continuous QTL-detection profile to diminish many false-positive signals. However, as we know, the variance component estimation is usually very time consuming and difficult to converge. Thus, an extremely fast EMF (Expectation-Maximization algorithm under Fixed effect model) is proposed in this research, which assumes a biallelic QTL and uses an expectation-maximization (EM) algorithm to solve model effects. The results of simulation experiments showed that (1) EMF was computationally much faster than VC method; (2) EMF and VC performed similarly in QTL detection power and parameter estimations, and both outperformed the paired-marker analysis and SMA. However, the power of EMF would be lower than that of VC if the QTL was multiallelic.     

GeneRecon--a coalescent based tool for fine-scale association mapping

SUMMARY: GeneRecon is a tool for fine-scale association mapping using a coalescence model. GeneRecon takes as input case-control data from phased or unphased SNP and microsatellite genotypes. The posterior distribution of disease locus position is obtained by Metropolis-Hastings sampling in the state space of genealogies. Input format, search strategy and the sampled statistics can be configured through the Guile Scheme programming language embedded in GeneRecon, making GeneRecon highly configurable. AVAILABILITY: The source code for GeneRecon, written in C++ and Scheme, is available under the GNU General Public License (GPL) at http://www.birc.au.dk/~mailund/GeneRecon CONTACT: mailund@birc.au.dk.     

A coalescent model of ancestry for a rare allele

In disequilibrium mapping from data on a rare allele, interest may focus on the ancestry of a random sample of current descendants of a mutation. The mutation is assumed to have been introduced into the population as a single copy a known time ago and to have reached a given copy number within the population. Theory has been developed to describe the ancestral distribution under arbitrary patterns of population expansion. Further results permit convenient realization of the ancestry for a random sample of copies of a rare allele within populations of constant size or within populations growing or shrinking at constant exponential rate. In this article, we present an efficient approximate method for realizing coalescence times under more general patterns of population growth. We also apply diagnostics, checking the age of the mutation. In the course of the derivation, some additional insight is gained into the dynamics of the descendants of the mutation.     

Multiple local maxima for likelihoods of phylogenetic trees: a simulation study.

Steel demonstrated that the maximum-likelihood function for a phylogenetic tree may have multiple local maxima. If this phenomenon were general, it would compromise the applicability of maximum likelihood as an optimality criterion for phylogenetic trees. In several simulation studies reported on in this paper, the true tree, and other trees of very high likelihood, rarely had multiple maxima. Our results thus provide reassurance that the value of maximum likelihood as a tree selection criterion is not compromised by the presence of multiple local maxima--the best estimates of the true tree are not likely to have them. This result holds true even when an incorrect nucleotide substitution model is used for tree selection.     

Bayesian fine-scale mapping of disease loci, by hidden Markov models

We present a new multilocus method for the fine-scale mapping of genes contributing to human diseases. The method is designed for use with multiple biallelic markers-in particular, single-nucleotide polymorphisms for which high-density genetic maps will soon be available. We model disease-marker association in a candidate region via a hidden Markov process and allow for correlation between linked marker loci. Using Markov-chain-Monte Carlo simulation methods, we obtain posterior distributions of model parameter estimates including disease-gene location and the age of the disease-predisposing mutation. In addition, we allow for heterogeneity in recombination rates, across the candidate region, to account for recombination hot and cold spots. We also obtain, for the ancestral marker haplotype, a posterior distribution that is unique to our method and that, unlike maximum-likelihood estimation, can properly account for uncertainty. We apply the method to data for cystic fibrosis and Huntington disease, for which mutations in disease genes have already been identified. The new method performs well compared with existing multi-locus mapping methods.     

Little loss of information due to unknown phase for fine-scale linkage-disequilibrium mapping with single-nucleotide-polymorphism genotype data

We present the results of a simulation study that indicate that true haplotypes at multiple, tightly linked loci often provide little extra information for linkage-disequilibrium fine mapping, compared with the information provided by corresponding genotypes, provided that an appropriate statistical analysis method is used. In contrast, a two-stage approach to analyzing genotype data, in which haplotypes are inferred and then analyzed as if they were true haplotypes, can lead to a substantial loss of information. The study uses our COLDMAP software for fine mapping, which implements a Markov chain-Monte Carlo algorithm that is based on the shattered coalescent model of genetic heterogeneity at a disease locus. We applied COLDMAP to 100 replicate data sets simulated under each of 18 disease models. Each data set consists of haplotype pairs (diplotypes) for 20 SNPs typed at equal 50-kb intervals in a 950-kb candidate region that includes a single disease locus located at random. The data sets were analyzed in three formats: (1). as true haplotypes; (2). as haplotypes inferred from genotypes using an expectation-maximization algorithm; and (3). as unphased genotypes. On average, true haplotypes gave a 6% gain in efficiency compared with the unphased genotypes, whereas inferring haplotypes from genotypes led to a 20% loss of efficiency, where efficiency is defined in terms of root mean integrated square error of the location of the disease locus. Furthermore, treating inferred haplotypes as if they were true haplotypes leads to considerable overconfidence in estimates, with nominal 50% credibility intervals achieving, on average, only 19% coverage. We conclude that (1). given appropriate statistical analyses, the costs of directly measuring haplotypes will rarely be justified by a gain in the efficiency of fine mapping and that (2). a two-stage approach of inferring haplotypes followed by a haplotype-based analysis can be very inefficient for fine mapping, compared with an analysis based directly on the genotypes.     

DOGSET: pre-designed primer sets for fine-scale mapping and DNA sequence interrogation in the dog

DOGSET is an online resource that provides access to primer sequences that have been computationally mined from the reference genome using heuristic algorithms. The electronic repository includes PCR primers corresponding to 32 135 markers for genetic mapping and 334 657 sequence-tagged gene elements for targeted re-sequencing and mutation discovery. A customized report that tailors primer design to wet bench protocols can be exported for a region of interest by specifying genome coordinates in a graphical user interface.     

Assessment of linkage disequilibrium by the decay of haplotype sharing, with application to fine-scale genetic mapping.

Linkage disequilibrium (LD) is of great interest for gene mapping and the study of population history. We propose a multilocus model for LD, based on the decay of haplotype sharing (DHS). The DHS model is most appropriate when the LD in which one is interested is due to the introduction of a variant on an ancestral haplotype, with recombinations in succeeding generations resulting in preservation of only a small region of the ancestral haplotype around the variant. This is generally the scenario of interest for gene mapping by LD. The DHS parameter is a measure of LD that can be interpreted as the expected genetic distance to which the ancestral haplotype is preserved, or, equivalently, 1/(time in generations to the ancestral haplotype). The method allows for multiple origins of alleles and for mutations, and it takes into account missing observations and ambiguities in haplotype determination, via a hidden Markov model. Whereas most commonly used measures of LD apply to pairs of loci, the DHS measure is designed for application to the densely mapped haplotype data that are increasingly available. The DHS method explicitly models the dependence among multiple tightly linked loci on a chromosome. When the assumptions about population structure are sufficiently tractable, the estimate of LD is obtained by maximum likelihood. For more-complicated models of population history, we find means and covariances based on the model and solve a quasi-score estimating equation. Simulations show that this approach works extremely well both for estimation of LD and for fine mapping. We apply the DHS method to published data sets for cystic fibrosis and progressive myoclonus epilepsy.     

Genetic analysis and molecular mapping of a pale flower allele at the W4 locus in soybean.

In soybean (Glycine max (L.) Merr.), the w4-mutable line that harbors the w4-m allele was identified in 1983. It was proposed that this line contained an autonomous transposable element at the W4 locus, which is a major locus controlling the biosynthesis of anthocyanin. The w4-m allele can revert to the W4 allele that produces the wild-type phenotype, or sometimes to other alleles that produce intermediate phenotypes. Mutant plants that produce pale flowers were identified among the progeny of a single germinal revertant event from the w4-mutable line. Through genetic analysis, we established that the pale-flower mutation was conditioned by a new allele (w4-p) at the W4 locus. The w4-p allele is dominant to the w4 allele but recessive to the W4 allele, and the w1 allele has an epistatic effect on the w4-p allele. The pale-mutant line (w4-pw4-p) was designated as Genetic Type Collection number T369. An F2 mapping population derived from the cross of Minsoy (W4W4) x T369 (w4-pw4-p) was used to map the W4/w4-p locus, using simple sequence repeat (SSR) markers. The W4 locus was located at one end of molecular linkage group D2, 2.3 cM from the SSR marker Satt386 and close to the nearby telomere.     

The genetic architecture of selection response. Inferences from fine-scale mapping of bristle number quantitative trait loci in Drosophila melanogaster.

Quantitative trait loci (QTL) affecting responses and correlated responses to selection for abdominal and sternopleural bristle number have been mapped with high resolution to the X and third chromosomes. Advanced intercross recombinant isogenic chromosomes were constructed from high and low selection lines in an unselected inbred background, and QTL were detected using composite interval mapping and high density transposable element marker maps. We mapped a total of 26 bristle number QTL with large effects, which were in or immediately adjacent to intervals previously inferred to contain bristle number QTL on these chromosomes. The QTL contributing to response to selection for high bristle number were not the same as those contributing to response to selection for low bristle number, suggesting that distributions of allelic effects per locus may be asymmetrical. Correlated responses were more often attributable to loose linkage than pleiotropy or close linkage. Bristle number QTL mapping to the same locations have been inferred in studies with different parental strains. Of the 26 QTL, 20 mapped to locations consistent with candidate genes affecting peripheral nervous system development and/or bristle number. This facilitates determining the molecular basis of quantitative variation and allele frequencies by associating molecular variation at the candidate genes with phenotypic variation in bristle number in samples of alleles from nature.     

A rare haplotype of the RET proto-oncogene is a risk-modifying allele in hirschsprung disease

Hirschsprung disease (HSCR) is a common genetic disorder characterized by intestinal obstruction secondary to enteric aganglionosis. HSCR demonstrates a complex pattern of inheritance, with the RET proto-oncogene acting as a major gene and with several additional susceptibility loci related to the Ret-signaling pathway or to other developmental programs of neural crest cells. To test how the HSCR phenotype may be affected by the presence of genetic variants, we investigated the role of a single-nucleotide polymorphism (SNP), 2508C-->T (S836S), in exon 14 of the RET gene, characterized by low frequency among patients with HSCR and overrepresentation in individuals affected by sporadic medullary thyroid carcinoma. Typing of several different markers across the RET gene demonstrated that a whole conserved haplotype displayed anomalous distribution and nonrandom segregation in families with HSCR. We provide genetic evidence about a protective role of this low-penetrant haplotype in the pathogenesis of HSCR and demonstrate a possible functional effect linked to RET messenger RNA expression.     

Pedigree analysis for the rare RHD DVa allele: serological and molecular studies

Until now, worldwide more than 80 different alleles producing weak D phenotypes have been identified. Here we identified rare RHD DVa alleles in Chinese individuals associated with weak expression of D antigen and an RHD phenotype resembling DVI. Multi-monoclonal anti-D antibodies were used to identify the RHD phenotyping for rare RHD DVa. RHD genotyping was used to confirm the presence of RHD exons and identify RHD, RHCE hybrids and exon deficiencies. Sanger sequencing was used to identify nucleotide polymorphisms in RHD exons. Pedigree analysis demonstrated RHD DVa allele alterations of 667 T>G, 676 G>C, 697 G>C, 712 G>A, 733 G>C, 744 C>T and 1227 G>A, which means the proband''s alleles were RHD DVa-3 [also called RHD-CE(5)-D] and 1227 G>A. The results also demonstrated RHD DVa and the original RHD Va allele without 1227 G>A. The study suggests that RHD phenotyping is a superior strategy for the molecular analysis of RHD variant in Chinese subjects, and for understanding related polymorphisms and mutations.     

Practical use of modified maximum likelihoods for stratified data

Stratified data arise in several settings, such as longitudinal studies or multicenter clinical trials. Between-strata heterogeneity is usually addressed by random effects models, but an alternative approach is given by fixed effects models, which treat the incidental nuisance parameters as fixed unknown quantities. This approach presents several advantages, like computational simplicity and robustness to confounding by strata. However, maximum likelihood estimates of the parameter of interest are typically affected by incidental parameter bias. A remedy to this is given by the elimination of stratum-specific parameters by exact or approximate conditioning. The latter solution is afforded by the modified profile likelihood, which is the method applied in this paper. The aim is to demonstrate how the theory of modified profile likelihoods provides convenient solutions to various inferential problems in this setting. Specific procedures are available for different kinds of response variables, and they are useful both for inferential purposes and as a diagnostic method for validating random effects models. Some examples with real data illustrate these points.     

Minisatellite allele diversification: the origin of rare alleles at the HRAS1 locus.

Three genetic markers within the promoter-exon 1 region of the HRAS1 locus have been employed to investigate lineage relationships among alleles of the highly polymorphic variable tandem repeat (VTR) immediately downstream of the HRAS1 gene. These markers were in absolute linkage disequilibrium with the HRAS1 VTR, allowing the assignment of unique upstream haplotypes to each of the four common VTR alleles. Analysis of 17 rare alleles revealed a stratification of allele fragment size and upstream haplotype in which each rare VTR allele possessed the markers characteristic of the common allele nearest in size. Therefore, hyperallelism emanated from the four common alleles in a defined fashion, the size of a rare allele specifying its origin. As discussed below, this result implies that unequal crossing-over between homologues is unlikely to be the predominant mechanism for generating new VTR alleles at this minisatellite locus.