Likelihood-based disequilibrium mapping for two-marker haplotype data

We report a theory that gives the sampling distribution of two-marker haplotypes that are linked to a rare disease mutation. The sampling distribution is generated with successive Monte Carlo realizations of the coalescence of the disease mutation having recombination and marker mutation events placed along the lineage. Given a sample of mutation-bearing, two-marker haplotypes, the maximum likelihood estimate of the location of the disease mutation can be calculated from the generated sampling distribution, provided that one knows enough about the population history in order to model it. The two-marker likelihood method is compared to a single-marker likelihood and a composite likelihood. The two-marker maximum likelihood gives smaller confidence intervals for the location of the disease locus than a comparable single-marker maximum likelihood. The composite likelihood can give biased results and the bias increases as the extent of linkage disequilibrium on mutation-bearing chromosomes decreases. Haplotype configurations exist for which the composite likelihood will fail to place the disease locus in the correct marker interval.     

Isolation of a marker linked to the Charcot-Marie-Tooth disease type IA gene by differential Alu-PCR of human chromosome 17-retaining hybrids.

We report the isolation of a new marker (S6.1) from band p11.2 of human chromosome 17 by differential Alu-polymerase chain reaction (Alu-PCR) of both a monochromosomal hybrid retaining a single human chromosome 17 and a hybrid retaining a del(17)(p11.2p11.2) in addition to other human chromosomes. The method is based on the preferential PCR amplification of human DNA in rodent/human hybrids when primers specific to the human Alu repeat element are used. MspI and SstI RFLPs associated with S6.1 were identified and used in linkage analysis of both a previously reported and a newly identified French-Acadian kindred segregating autosomal dominant Charcot-Marie-Tooth disease (CMT). A cumulative peak lod score of 3.41 at a peak recombination fraction of .12 indicates that this marker is linked to the CMT 1A locus but is at a distance from the disease gene. Thus, the marker S6.1 will be useful in further delineating the candidate region for the CMT gene when its location with respect to pA10-41 and 1516, two other markers from 17p11.2 which have previously demonstrated close linkage to the CMT locus, has been determined.     

Testing for association between disease and linked marker loci: a log-linear-model analysis.

One approach frequently used for identifying genetic factors involved in the process of a complex disease is the comparison of patients and controls for a number of genetic markers near a candidate gene. The analysis of such association studies raises some specific problems because of the fact that genotypic and not gametic data are generally available. We present a log-linear-model analysis providing a valid method for analyzing such studies. When studying the association of disease with one marker locus, the log-linear model allows one to test for the difference between allelic frequencies among affected and unaffected individuals, Hardy-Weinberg (H-W) equilibrium in both groups, and interaction between the association of alleles at the marker locus and disease. This interaction provides information about the dominance of the disease susceptibility locus, with dominance defined using the epidemiological notion of odds ratio. The degree of dominance measured at the marker locus depends on the strength of linkage disequilibrium between the marker locus and the disease locus. When studying the association of disease with several linked markers, the model becomes rapidly complex and uninterpretable unless it is assumed that affected and unaffected populations are in H-W equilibrium at each locus. This hypothesis must be tested before going ahead in the analysis. If it is not rejected, the log-linear model offers a stepwise method of identification of the parameters causing the difference between populations. This model can be extended to any number of loci, alleles, or populations.     

Coalescent-based association mapping and fine mapping of complex trait loci

We outline a general coalescent framework for using genotype data in linkage disequilibrium-based mapping studies. Our approach unifies two main goals of gene mapping that have generally been treated separately in the past: detecting association (i.e., significance testing) and estimating the location of the causative variation. To tackle the problem, we separate the inference into two stages. First, we use Markov chain Monte Carlo to sample from the posterior distribution of coalescent genealogies of all the sampled chromosomes without regard to phenotype. Then, averaging across genealogies, we estimate the likelihood of the phenotype data under various models for mutation and penetrance at an unobserved disease locus. The essential signal that these models look for is that in the presence of disease susceptibility variants in a region, there is nonrandom clustering of the chromosomes on the tree according to phenotype. The extent of nonrandom clustering is captured by the likelihood and can be used to construct significance tests or Bayesian posterior distributions for location. A novelty of our framework is that it can naturally accommodate quantitative data. We describe applications of the method to simulated data and to data from a Mendelian locus (CFTR, responsible for cystic fibrosis) and from a proposed complex trait locus (calpain-10, implicated in type 2 diabetes).     

An improved formulation of marker heterozygosity in recurrent selection and backcross schemes

This report presents a theoretical formulation for predicting heterozygosity of a putative marker locus linked to two quantitative trait loci (QTL) in a recurrent selection and backcross (RSB) scheme. Since the heterozygosity at any given marker locus maintained in such a breeding programme reflects its map location relative to QTL, the present study develops the theoretical analysis of the QTL mapping method that recently appeared in the literature. The formulae take into account selection, recombination and finite population size during the multiple-generation breeding scheme. The single-marker and two-QTL model was compared numerically with the model involving two linked marker loci and two QTL. Without recombination interference, the two models predict the same expected heterozygosity at the linked marker loci, indicating that the model is valid for predicting marker heterozygosity maintained at any loci in an RSB breeding scheme. The formulation is demonstrated numerically for several RSB schemes and its implications in developing a likelihood-based statistical framework for modeling the RSB experiments are discussed.     

A test of transmission/disequilibrium for quantitative traits in pedigree data, by multiple regression.

The transmission/disequilibrium (TD) test (TDT), proposed, by Spielman et al., for binary traits is a powerful method for detection of linkage between a marker locus and a disease locus, in the presence of allelic association. As a test for linkage disequilibrium, the TDT makes the assumption that any allelic association present is due to linkage. Allison proposed a series of TD-type tests for quantitative traits and calculated their power, assuming that the marker locus is the disease locus. All these tests assume that the observations are independent, and therefore they are applicable, as a test for linkage, only for nuclear-family data. In this report, we propose a regression-based TD-type test for linkage between a marker locus and a quantitative trait locus, using information on the parent-to-offspring transmission status of the associated allele at the marker locus. This method does not require independence of observations, thus allowing for analysis of pedigree data as well, and allows adjustment for covariates. We investigate the statistical power and validity of the test by simulating markers at various recombination fractions from the disease locus.     

In silico analysis of disease-association mapping strategies using the coalescent process and incorporating ascertainment and selection

We present a new method for simulating samples of marker haplotypes, genotypes, or diplotypes in case-control studies in which the markers are linked to a disease locus in any specified region of the genome. The method allows realistic features to be incorporated into the simulations, including selection acting on disease alleles, sample ascertainment of disease chromosomes and polymorphic markers, a genetic dominance model of disease expression that allows incomplete penetrance and phenocopies, and an accurate genetic map of recombination rates and hotspots for recombination in the human genome (or, alternatively, an improved method for simulating the distribution of hotspots). The new method uses an approach that combines simulation of the coalescent process for the sampled chromosomes with a diffusion process used to model the evolution of the disease-mutation frequency over time. Examples illustrate how the method may be used to study the expected power of a marker-disease association study.     

Multipoint linkage-disequilibrium-mapping approach based on the case-parent trio design

In the present study we propose a multipoint approach, for the mapping of genes, that is based on the case-parent trio design. We first derive an expression for the expected preferential-allele-transmission statistics for transmission, from either parent to an affected child, for an arbitrary location within a chromosomal region demarcated by several genetic markers. No assumption about genetic mechanism is needed in this derivation, beyond the assumption that no more than one disease gene lies in the region framed by the markers. When one builds on this representation, the way in which one may maximize the genetic information from multiple markers becomes obvious. This proposed method differs from the popular transmission/disequilibrium test (TDT) approach for fine mapping, in the following ways: First, in contrast with the TDT approach, all markers contribute information, regardless of whether the parents are heterozygous at any one marker, and incomplete trio data can be utilized in our approach. Second, rather than performing the TDT at each marker separately, we propose a single test statistic that follows a chi(2) distribution with 1 df, under the null hypothesis of no linkage or linkage disequilibrium to the region. Third, in the presence of linkage evidence, we offer a means to estimate the location of the disease locus along with its sampling uncertainty. We illustrate the proposed method with data from a family study of asthma, conducted in Barbados.     

Estimating linkage disequilibrium between a polymorphic marker locus and a trait locus in natural populations.

Positional cloning of gene(s) underlying a complex trait requires a high-resolution linkage map between the trait locus and genetic marker loci. Recent research has shown that this may be achieved through appropriately modeling and screening linkage disequilibrium between the candidate marker locus and the major trait locus. A quantitative genetics model was developed in the present study to estimate the coefficient of linkage disequilibrium between a polymorphic genetic marker locus and a locus underlying a quantitative trait as well as the relevant genetic parameters using the sample from randomly mating populations. Asymptotic covariances of the maximum-likelihood estimates of the parameters were formulated. Convergence of the EM-based statistical algorithm for calculating the maximum-likelihood estimates was confirmed and its utility to analyze practical data was exploited by use of extensive Monte-Carlo simulations. Appropriateness of calculating the asymptotic covariance matrix in the present model was investigated for three different approaches. Numerical analyses based on simulation data indicated that accurate estimation of the genetic parameters may be achieved if a sample size of 500 is used and if segregation at the trait locus explains not less than a quarter of phenotypic variation of the trait, but the study reveals difficulties in predicting the asymptotic variances of these maximum-likelihood estimates. A comparison was made between the statistical powers of the maximum-likelihood analysis and the previously proposed regression analysis for detecting the disequilibrium.     

High-Resolution Multipoint Linkage-Disequilibrium Mapping in the Context of a Human Genome Sequence

A new method is presented for fine-scale linkage disequilibrium (LD) mapping of a disease mutation; it uses multiple linked single-nucleotide polymorphisms, restriction-fragment-length polymorphisms, or microsatellite markers and incorporates information from an annotated human genome sequence (HGS) and from a human mutation database. The method takes account of population demographic effects, using Markov chain Monte Carlo methods to integrate over the unknown gene genealogy and gene coalescence times. Information about the relative frequency of disease mutations in exons, introns, and other regions, from mutational databases, as well as assumptions about the completeness of the gene annotation, are used with an annotated HGS, to generate a prior probability that a mutation lies at any particular position in a specified region of the genome. This information is updated with information about mutation location, from LD at a set of linked markers in the region, to generate the posterior probability density of the mutation location. The performance of the method is evaluated by simulation and by analysis of a data set for diastrophic dysplasia (DTD) in Finland. The DTD disease gene has been positionally cloned, so the actual location of the mutation is known and can be compared with the position predicted by our method. For the DTD data, the addition of information from an HGS results in disease-gene localization at a resolution that is much higher than that which would be possible by LD mapping alone. In this case, the gene would be found by sequencing a region < or =7 kb in size.     

Extent and distribution of linkage disequilibrium in three genomic regions

The positional cloning of genes underlying common complex diseases relies on the identification of linkage disequilibrium (LD) between genetic markers and disease. We have examined 127 polymorphisms in three genomic regions in a sample of 575 chromosomes from unrelated individuals of British ancestry. To establish phase, 800 individuals were genotyped in 160 families. The fine structure of LD was found to be highly irregular. Forty-five percent of the variation in disequilibrium measures could be explained by physical distance. Additional factors, such as allele frequency, type of polymorphism, and genomic location, explained <5% of the variation. Nevertheless, disequilibrium was occasionally detectable at 500 kb and was present for over one-half of marker pairs separated by <50 kb. Although these findings are encouraging for the prospects of a genomewide LD map, they suggest caution in interpreting localization due to allelic association.     

Genealogies and weak purifying selection

The assumption that selection alters the genealogical tree of a sample of alleles from a population relative to the neutral expectation underlies several "tests of neutrality." Two recent papers have studied the effect of purifying selection; their suggestive but incomplete results indicate that, in the single site case, the shape of a gene genealogy for a locus may differ only from the neutral expectation. We verify this finding for weak selection using the "ancestral selection graph." We consider a wider range of models, including both a four-allele single-site model and an infinite-sites model. Our results confirm the previous claim for the symmetric-mutation single site model. We emphasize, however, that a neutral-seeming genealogy is consistent with detectable effects of selection on the distribution of allele frequences within the sample. With selection operating, the information about a sample cannot be reduced to the genealogy. As a result, a distinction needs to be made between the selected sites themselves, for which the genealogy offers insufficient information, and linked neutral variation. This distinction seems to have been overlooked in previous papers, yet it has significant implications for the interpretation of data on DNA sequence variation. In particular, it predicts that under purifying selection, the frequency spectrum of neutral mutations will not reflect the skew toward rare polymorphisms at replacement sites even if there is no recombination between them. We caution, however, that the effect of weak selection on the genealogy is specific to the model; a (more realistic) model of multiple linked sites could lead to a more distorted genealogy than is observed for a single site.     

A composite-conditional-likelihood approach for gene mapping based on linkage disequilibrium in windows of marker loci

A composite-conditional-likelihood (CCL) approach is proposed to map the position of a trait-influencing mutation (TIM) using the ancestral recombination graph (ARG) and importance sampling to reconstruct the genealogy of DNA sequences with respect to windows of marker loci and predict the linkage disequilibrium pattern observed in a sample of cases and controls. The method is designed to fine-map the location of a disease mutation, not as an association study. The CCL function proposed for the position of the TIM is a weighted product of conditional likelihood functions for windows of a given number of marker loci that encompass the TIM locus, given the sample configuration at the marker loci in those windows. A rare recessive allele is assumed for the TIM and single nucleotide polymorphisms (SNPs) are considered as markers. The method is applied to a range of simulated data sets. Not only do the CCL profiles converge more rapidly with smaller window sizes as the number of simulated histories of the sampled sequences increases, but the maximum-likelihood estimates for the position of the TIM remain as satisfactory, while requiring significantly less computing time. The simulations also suggest that non-random samples, more precisely, a non-proportional number of controls versus the number of cases, has little effect on the estimation procedure as well as sample size and marker density beyond some threshold values. Moreover, when compared with some other recent methods under the same assumptions, the CCL approach proves to be competitive.     

A train of thoughts on gene mapping

Complex traits, by definition, are the pheonotypic outcome from multiple interacting genes. The traditional analysis of association studies on complex traits is to test one locus at a time, but a better approach is to analyze all markers simultaneously. We previously proposed a two-stage approach, first selecting the influential markers and then modeling main and interaction effects of these markers. Here we introduce alternative approaches to marker selection and discuss issues regarding analytical tools for disease gene mapping, marker selection, and statistical modeling.     

Efficient mining of haplotype patterns for linkage disequilibrium mapping

Effective identification of disease-causing gene locations can have significant impact on patient management decisions that will ultimately increase survival rates and improve the overall quality of health care. Linkage disequilibrium mapping is the process of finding disease gene locations through comparisons of haplotype frequencies between disease chromosomes and normal chromosomes. This work presents a new method for linkage disequilibrium mapping. The main advantage of the proposed algorithm, called LinkageTracker, is its consistency in producing good predictive accuracy under different conditions, including extreme conditions where the occurrence of disease samples with the mutation of interest is very low and there is presence of error or noise. We compared our method with some leading methods in linkage disequilibrium mapping such as HapMiner, Blade, GeneRecon, and Haplotype Pattern Mining (HPM). Experimental results show that for a substantial class of problems, our method has good predictive accuracy while taking reasonably short processing time. Furthermore, LinkageTracker does not require any population ancestry information about the disease and the genealogy of the haplotypes. Therefore, it is useful for linkage disequilibrium mapping when the users do not have such information about their datasets.     

A radiation hybrid mapping panel for the rhesus macaque

The genomes of nonhuman primates have recently become highly visible candidates for full genome analysis, as they provide powerful models of human disease and a better understanding of the evolution of the human genome. We describe the creation of a 5000 rad radiation hybrid (RH) mapping panel for the rhesus macaque. Duplicate genotypes of 84 microsatellite and coding gene sequence tagged sites from six macaque chromosomes produced an estimated whole genome retention frequency of 0.33. To test the mapping ability of the panel, we constructed RH maps for macaque chromosomes 7 and 9 and compared them to orthologous locus orders in existing human and baboon maps derived from different methodologies. Concordant marker order between all three species maps suggests that the current panel represents a powerful mapping resource for generating high-density comparative maps of the rhesus macaque and other species genomes.     

Polymorphic Chromosomes Bearing the Tox2 Locus in Cochliobolus carbonum Behave as Homologs during Meiosis

The HTS1 gene in the Tox2 locus of the fungal pathogen Cochliobolus carbonum race 1 is required for synthesis of a host-selective phytotoxin and for increased virulence on susceptible genotypes of maize. The locus is present in race 1 isolates but absent from isolates of the other races, which do not produce the toxin. By pulsed-field gel electrophoresis and Southern analysis with HTS1 sequences and chromosome-specific markers, the HTS1 gene was detected on a 4-Mb chromosome in one group of isolates and on a 2.3-Mb chromosome in another group, which lacked the 4-Mb chromosome. A chromosome-specific marker from C. heterostrophus hybridized to a 2.3-Mb chromosome in non-toxin-producing isolates and in toxin-producing isolates, including those with a 4-Mb chromosome. A marker from C. carbonum hybridized to the 4-Mb chromosome, but in isolates lacking the 4-Mb chromosome, this marker hybridized to a smaller, 2.0-Mb chromosome. Thus, the Tox2 locus is on different chromosomes in different groups of race 1 isolates. Single ascospore progeny from crosses between isolates having HTS1 on different chromosomes were analyzed for toxin-producing ability, virulence, and the presence and chromosomal location of HTS1. All progeny produced HC toxin in culture, incited race 1-type lesions on susceptible maize genotypes, and contained HTS1 sequences, as determined by PCR amplification with gene-specific primers. Analysis of the chromosomal complements of several progeny indicated that they all had only one Tox2-containing chromosome. Thus, despite their differences in size, these chromosomes behave as homologs during meiosis and may have arisen by a translocation.     

A comparison between methods for linkage disequilibrium fine mapping of quantitative trait loci

We present a maximum likelihood method for mapping quantitative trait loci that uses linkage disequilibrium information from single and multiple markers. We made paired comparisons between analyses using a single marker, two markers and six markers. We also compared the method to single marker regression analysis under several scenarios using simulated data. In general, our method outperformed regression (smaller mean square error and confidence intervals of location estimate) for quantitative trait loci with dominance effects. In addition, the method provides estimates of the frequency and additive and dominance effects of the quantitative trait locus.     

Haplotype Analysis of Hemochromatosis: Evaluation of Different Linkage-Disequilibrium Approaches and Evolution of Disease Chromosomes

We applied several types of linkage-disequilibrium calculations to analyze the hereditary hemochromatosis (hh) locus. Twenty-four polymorphic markers in the major histocompatibility complex (MHC) class I region were used to haplotype hh and normal chromosomes. A total of 169 hh and 161 normal chromosomes were analyzed. Disequilibrium values were found to be high over an unusually large region beginning 150 kb centro-meric of HLA-A and extending nearly 5 Mb telomeric of it. Recombination in this region was −28% of the expected value. This low level of recombination contributes to the unusually broad region of linkage disequilibrium found with hh. The strongest disequilibrium was found at locus HLA-H (d = .84) and at locus D6S2239 (d = .85), a marker −10 kb telomeric to HLA-H. All disequilibrium methods employed in this study found peak disequilibrium at HLA-H or D6S2239. The cys282tyr mutation in HLA-H, a candidate gene for hh, was found in 85% of disease chromosomes. A haplotype phylogeny for hh chromosomes was constructed and suggests that the mutation associated with the most common haplotype occurred relatively recently. The age of the hh mutation was estimated to be −60-70 generations. Disequilibrium was maintained over a greater distance for hh-carrying chromosomes, consistent with a recent mutation for hh. Our data provide a reasonable explanation for previous difficulties in localizing the hh locus and provide an evolutionary history for disease chromosomes.