Linkage disequilibrium in wild mice

Crosses between laboratory strains of mice provide a powerful way of detecting quantitative trait loci for complex traits related to human disease. Hundreds of these loci have been detected, but only a small number of the underlying causative genes have been identified. The main difficulty is the extensive linkage disequilibrium (LD) in intercross progeny and the slow process of fine-scale mapping by traditional methods. Recently, new approaches have been introduced, such as association studies with inbred lines and multigenerational crosses. These approaches are very useful for interval reduction, but generally do not provide single-gene resolution because of strong LD extending over one to several megabases. Here, we investigate the genetic structure of a natural population of mice in Arizona to determine its suitability for fine-scale LD mapping and association studies. There are three main findings: (1) Arizona mice have a high level of genetic variation, which includes a large fraction of the sequence variation present in classical strains of laboratory mice; (2) they show clear evidence of local inbreeding but appear to lack stable population structure across the study area; and (3) LD decays with distance at a rate similar to human populations, which is considerably more rapid than in laboratory populations of mice. Strong associations in Arizona mice are limited primarily to markers less than 100 kb apart, which provides the possibility of fine-scale association mapping at the level of one or a few genes. Although other considerations, such as sample size requirements and marker discovery, are serious issues in the implementation of association studies, the genetic variation and LD results indicate that wild mice could provide a useful tool for identifying genes that cause variation in complex traits.     

一个基于熵的对疾病基因精细定位的指数

针对人类疾病基因的精细定位,本文利用稠密的标记位点,通过比较标记的熵和条件熵,给出了一个基于熵的指数。该指数可以度量标记基因和性状位点间连锁不平衡(LD)程度。该指数的特性是它不依赖于标记基因的频率。同时它对应疾病易感位点(DSL)精细定位的哈迪-温伯格不平衡(HWD)指数。通过计算机模拟,文章调查了不同遗传参数下该指数的性质。模拟结果表明该指数用作疾病易感位点精细定位是有效的。     

Fine-scale mapping of disease susceptibility locus with Bayesian partition model

The causal relationship between genes and diseases has been investigated with the development of DNA sequence. Polymorphisms incorporated in the HapMap Project have enabled fine mapping with linkage disequilibrium (LD) and prior clustering of the haplotypes on the basis of a similarity measure has often been performed in an attempt to capture coalescent events because they can reduce the amount of computation. However an inappropriate choice of similarity measure can lead to wrong conclusions and we propose a new haplotype-based clustering algorithm for fine-scale mapping by using a Bayesian partition model. To handle phase-unknown genotypes, we propose a new algorithm based on a Metropolized Gibbs sampler and it is implemented in C++. Our simulation studies found that the proposed method improves the accuracy of the estimator for the disease susceptibility locus. We illustrated the practical implication of the new analysis method by an application to fine-scale mapping of CYP2D6 in drug metabolism.     

植物基因组中的连锁不平衡

在植物基因组学研究领域, 连锁不平衡(linkage disequilibrium, LD)分析是近年来的一个研究亮点和热点。基于LD的作图方法不仅是新基因发掘的有效途径, 而且也是联系结构基因组学和表型组学的一座桥梁。自2001年基于LD的作图方法在植物中的成功运用至今, 已有大量关于植物基因组中LD结构及LD作图的研究报道。文章系统介绍了LD的基本理论及其在LD作图、单倍型多样性分析、单倍型标签SNP的开发和群体遗传学等研究中的应用, 并就近年来关于LD与群体结构、基因转换和上位效应及G×E互作等方面的研究热点和发展趋势进行了探讨。当前, 世界各国基因争夺大战日趋激烈。中国是基因资源大国, 但还不是基因大国。植物基因组中LD研究热潮的兴起及LD研究的进一步深入, 必将大大推动植物基因组学的快速发展, 特别是加速从作物种质资源中发掘新基因的进程。     

一种有效的复杂疾病基因定位的检测法

连锁不平衡（LD）应用于某些复杂疾病基因的定位,近年来发展了许多LD定位方法,除TDT外,大多数LD定位方法须先假定无人群混和,人群混合可增大在疾病基因定位时犯Ⅰ类错误的机率,产生无效结果。此方法利用LD来检测标记位点和疾病敏感位点（DSL）的连锁（有连锁不平衡）相关（有连锁）。分析时采用不相关样本,已知其父母基因型和至少父母之一为杂合子,再将随机样本依基因型不同分类,然后对来自不同类的数据应用有力的统计方法进行单独和联合分析。此LD定位法不仅适用于患病和正常个体,而且有效消除据父母基因分类的样本定位时人群混合的影响,分析结果和模拟结果也表明此方法解决了在检测标记位点和疾病敏感位点之间的连锁和相关时人群混和的问题,但与TDT比,此法在检测的位点为DSL时丙能有效和充分地利用矫正数据,检测位点不是DSL时,此法和TDT法可相互补充更有效地检测连锁的DSL。     

Population structure and linkage disequilibrium unravelled in tetraploid potato

Association mapping is considered to be an important alternative strategy for the identification of quantitative trait loci (QTL) as compared to traditional QTL mapping. A necessary prerequisite for association analysis to succeed is detailed information regarding hidden population structure and the extent of linkage disequilibrium. A collection of 430 tetraploid potato cultivars, comprising two association panels, has been analysed with 41 AFLP^® and 53 SSR primer combinations yielding 3364 AFLP fragments and 653 microsatellite alleles, respectively. Polymorphism information content values and detected number of alleles for the SSRs studied illustrate that commercial potato germplasm seems to be equally diverse as Latin American landrace material. Genome-wide linkage disequilibrium (LD)—reported for the first time for tetraploid potato—was observed up to approximately 5 cM using r ² higher than 0.1 as a criterion for significant LD. Within-group LD, however, stretched on average twice as far when compared to overall LD. A Bayesian approach, a distance-based hierarchical clustering approach as well as principal coordinate analysis were adopted to enquire into population structure. Groups differing in year of market release and market segment (starch, processing industry and fresh consumption) were repeatedly detected. The observation of LD up to 5 cM is promising because the required marker density is not likely to disable the possibilities for association mapping research in tetraploid potato. Population structure appeared to be weak, but strong enough to demand careful modelling of genetic relationships in subsequent marker-trait association analyses. There seems to be a good chance that linkage-based marker-trait associations can be identified at moderate marker densities.     

Modeling linkage disequilibrium and identifying recombination hotspots using single-nucleotide polymorphism data

We introduce a new statistical model for patterns of linkage disequilibrium (LD) among multiple SNPs in a population sample. The model overcomes limitations of existing approaches to understanding, summarizing, and interpreting LD by (i) relating patterns of LD directly to the underlying recombination process; (ii) considering all loci simultaneously, rather than pairwise; (iii) avoiding the assumption that LD necessarily has a "block-like" structure; and (iv) being computationally tractable for huge genomic regions (up to complete chromosomes). We examine in detail one natural application of the model: estimation of underlying recombination rates from population data. Using simulation, we show that in the case where recombination is assumed constant across the region of interest, recombination rate estimates based on our model are competitive with the very best of current available methods. More importantly, we demonstrate, on real and simulated data, the potential of the model to help identify and quantify fine-scale variation in recombination rate from population data. We also outline how the model could be useful in other contexts, such as in the development of more efficient haplotype-based methods for LD mapping.     

Genetic diversity and population structure of a diverse set of rice germplasm for association mapping

Germplasm diversity is the mainstay for crop improvement and genetic dissection of complex traits. Understanding genetic diversity, population structure, and the level and distribution of linkage disequilibrium (LD) in target populations is of great importance and a prerequisite for association mapping. In this study, 100 genome-wide simple sequence repeat (SSR) markers were used to assess genetic diversity, population structure, and LD of 416 rice accessions including landraces, cultivars and breeding lines collected mostly in China. A model-based population structure analysis divided the rice materials into seven subpopulations. 63% of the SSR pairs in these accessions were in LD, which was mostly due to an overall population structure, since the number of locus pairs in LD was reduced sharply within each subpopulation, with the SSR pairs in LD ranging from 5.9 to 22.9%. Among those SSR pairs showing significant LD, the intrachromosomal LD had an average of 25–50 cM in different subpopulations. Analysis of the phenotypic diversity of 25 traits showed that the population structure accounted for an average of 22.4% of phenotypic variation. An example association mapping for starch quality traits using both the candidate gene mapping and genome-wide mapping strategies based on the estimated population structure was conducted. Candidate gene mapping confirmed that the Wx and starch synthase IIa (SSIIa) genes could be identified as strongly associated with apparent amylose content (AAC) and pasting temperature (PT), respectively. More importantly, we revealed that the Wx gene was also strongly associated with PT. In addition to the major genes, we found five and seven SSRs were associated with AAC and PT, respectively, some of which have not been detected in previous linkage mapping studies. The results suggested that the population may be useful for the genome-wide marker–trait association mapping. This new association population has the potential to identify quantitative trait loci (QTL) with small effects, which will aid in dissecting complex traits and in exploiting the rich diversity present in rice germplasm.     

一个基于熵的精细定位数量性状位点的指数

针对数量性状位点的精细定位,本文采用群体的极端样本,利用稠密的标记位点,通过比较标记的熵和条件熵,给出了一个基于熵的指数。该指数是标记基因和性状位点间连锁不平衡系数的函数,它不依赖于标记基因的频率。该指数对应我们之前提出的数量性状位点精细定位的哈迪-温伯格不平衡(HWD)指数,但在精细定位数量性状位点时,本文提出的指数的效能要高于哈迪-温伯格不平衡(HWD)指数。通过计算机模拟,文章调查了不同遗传参数下该指数的性质。模拟结果表明该指数用作精细定位是有效的。     

Multipoint identity-by-descent prediction using dense markers to map quantitative trait loci and estimate effective population size

A novel multipoint method, based on an approximate coalescence approach, to analyze multiple linked markers is presented. Unlike other approximate coalescence methods, it considers all markers simultaneously but only two haplotypes at a time. We demonstrate the use of this method for linkage disequilibrium (LD) mapping of QTL and estimation of effective population size. The method estimates identity-by-descent (IBD) probabilities between pairs of marker haplotypes. Both LD and combined linkage and LD mapping rely on such IBD probabilities. The method is approximate in that it considers only the information on a pair of haplotypes, whereas a full modeling of the coalescence process would simultaneously consider all haplotypes. However, full coalescence modeling is computationally feasible only for few linked markers. Using simulations of the coalescence process, the method is shown to give almost unbiased estimates of the effective population size. Compared to direct marker and haplotype association analyses, IBD-based QTL mapping showed clearly a higher power to detect a QTL and a more realistic confidence interval for its position. The modeling of LD could be extended to estimate other LD-related parameters such as recombination rates.     

Combined linkage disequilibrium and linkage mapping: Bayesian multilocus approach

Quantitative trait loci (QTL) affecting the phenotype of interest can be detected using linkage analysis (LA), linkage disequilibrium (LD) mapping or a combination of both (LDLA). The LA approach uses information from recombination events within the observed pedigree and LD mapping from the historical recombinations within the unobserved pedigree. We propose the Bayesian variable selection approach for combined LDLA analysis for single-nucleotide polymorphism (SNP) data. The novel approach uses both sources of information simultaneously as is commonly done in plant and animal genetics, but it makes fewer assumptions about population demography than previous LDLA methods. This differs from approaches in human genetics, where LDLA methods use LA information conditional on LD information or the other way round. We argue that the multilocus LDLA model is more powerful for the detection of phenotype–genotype associations than single-locus LDLA analysis. To illustrate the performance of the Bayesian multilocus LDLA method, we analyzed simulation replicates based on real SNP genotype data from small three-generational CEPH families and compared the results with commonly used quantitative transmission disequilibrium test (QTDT). This paper is intended to be conceptual in the sense that it is not meant to be a practical method for analyzing high-density SNP data, which is more common. Our aim was to test whether this approach can function in principle.     

Multilocus association mapping using variable-length Markov chains

I propose a new method for association-based gene mapping that makes powerful use of multilocus data, is computationally efficient, and is straightforward to apply over large genomic regions. The approach is based on the fitting of variable-length Markov chain models, which automatically adapt to the degree of linkage disequilibrium (LD) between markers to create a parsimonious model for the LD structure. Edges of the fitted graph are tested for association with trait status. This approach can be thought of as haplotype testing with sophisticated windowing that accounts for extent of LD to reduce degrees of freedom and number of tests while maximizing information. I present analyses of two published data sets that show that this approach can have better power than single-marker tests or sliding-window haplotypic tests.     

Prospects for whole genome linkage disequilibrium mapping in domestic dog breeds

Linkage disequilibrium (LD) mapping is commonly used as a fine mapping tool in human genome mapping and has been used with some success for initial disease gene isolation in certain isolated inbred human populations. An understanding of the population history of domestic dog breeds suggests that LD mapping could be routinely utilized in this species for initial genome-wide scans. Such an approach offers significant advantages over traditional linkage analysis. Here, we demonstrate, using canine copper toxicosis in the Bedlington terrier as the model, that LD mapping could be reasonably expected to be a useful strategy in low-resolution, genome-wide scans in pure-bred dogs. Significant LD was demonstrated over distances up to 33.3 cM. It is very unlikely, for a number of reasons discussed, that this result could be extrapolated to the rest of the genome. It is, however, consistent with the expectation given the population structure of canine breeds and, in this breed at least, with the hypothesis that it may be possible to utilize LD in a genome-wide scan. In this study, LD mapping confirmed the location of the copper toxicosis in Bedlington terrier gene (CT-BT) and was able to do so in a population that was refractory to traditional linkage analysis.     

Coverage and characteristics of the Affymetrix GeneChip Human Mapping 100K SNP set

Improvements in technology have made it possible to conduct genome-wide association mapping at costs within reach of academic investigators, and experiments are currently being conducted with a variety of high-throughput platforms. To provide an appropriate context for interpreting results of such studies, we summarize here results of an investigation of one of the first of these technologies to be publicly available, the Affymetrix GeneChip Human Mapping 100K set of single nucleotide polymorphisms (SNPs). In a systematic analysis of the pattern and distribution of SNPs in the Mapping 100K set, we find that SNPs in this set are undersampled from coding regions (both nonsynonymous and synonymous) and oversampled from regions outside genes, relative to SNPs in the overall HapMap database. In addition, we utilize a novel multilocus linkage disequilibrium (LD) coefficient based on information content (analogous to the information content scores commonly used for linkage mapping) that is equivalent to the familiar measure r² in the special case of two loci. Using this approach, we are able to summarize for any subset of markers, such as the Affymetrix Mapping 100K set, the information available for association mapping in that subset, relative to the information available in the full set of markers included in the HapMap, and highlight circumstances in which this multilocus measure of LD provides substantial additional insight about the haplotype structure in a region over pairwise measures of LD.     

The Textile Plot: A New Linkage Disequilibrium Display of Multiple-Single Nucleotide Polymorphism Genotype Data

Linkage disequilibrium (LD) is a major concern in many genetic studies because of the markedly increased density of SNP (Single Nucleotide Polymorphism) genotype markers. This dramatic increase in the number of SNPs may cause problems in statistical analyses, such as by introducing multiple comparisons in hypothesis testing and colinearity in logistic regression models, because of the presence of complex LD structures. Inferences must be made about the underlying genetic variation through the LD structure before applying statistical models to the data. Therefore, we introduced the textile plot to provide a visualization of LD to improve the analysis of the genetic variation present in multiple-SNP genotype data. The plot can accentuate LD by displaying specific geometrical shapes, and allowing for the underlying haplotype structure to be inferred without any haplotype-phasing algorithms. Application of this technique to simulated and real data sets illustrated the potential usefulness of the textile plot as an aid to the interpretation of LD in multiple-SNP genotype data. The initial results of LD mapping and haplotype analyses of disease genes are encouraging, indicating that the textile plot may be useful in disease association studies.     

Patterns of linkage disequilibrium in the human genome

Particular alleles at neighbouring loci tend to be co-inherited. For tightly linked loci, this might lead to associations between alleles in the population a property known as linkage disequilibrium (LD). LD has recently become the focus of intense study in the hope that it might facilitate the mapping of complex disease loci through whole-genome association studies. This approach depends crucially on the patterns of LD in the human genome. In this review, we draw on empirical studies in humans and Drosophila, as well as simulation studies, to assess the current state of knowledge about patterns of LD, and consider the implications for the use of LD as a mapping tool.     

Linkage disequilibrium mapping via cladistic analysis of single-nucleotide polymorphism haplotypes

We present a novel approach to disease-gene mapping via cladistic analysis of single-nucleotide polymorphism (SNP) haplotypes obtained from large-scale, population-based association studies, applicable to whole-genome screens, candidate-gene studies, or fine-scale mapping. Clades of haplotypes are tested for association with disease, exploiting the expected similarity of chromosomes with recent shared ancestry in the region flanking the disease gene. The method is developed in a logistic-regression framework and can easily incorporate covariates such as environmental risk factors or additional unlinked loci to allow for population structure. To evaluate the power of this approach to detect disease-marker association, we have developed a simulation algorithm to generate high-density SNP data with short-range linkage disequilibrium based on empirical patterns of haplotype diversity. The results of the simulation study highlight substantial gains in power over single-locus tests for a wide range of disease models, despite overcorrection for multiple testing.     

Linkage disequilibrium in domestic sheep

The last decade has seen a dramatic increase in the number of livestock QTL mapping studies. The next challenge awaiting livestock geneticists is to determine the actual genes responsible for variation of economically important traits. With the advent of high density single nucleotide polymorphism (SNP) maps, it may be possible to fine map genes by exploiting linkage disequilibrium between genes of interest and adjacent markers. However, the extent of linkage disequilibrium (LD) is generally unknown for livestock populations. In this article microsatellite genotype data are used to assess the extent of LD in two populations of domestic sheep. High levels of LD were found to extend for tens of centimorgans and declined as a function of marker distance. However, LD was also frequently observed between unlinked markers. The prospects for LD mapping in livestock appear encouraging provided that type I error can be minimized. Properties of the multiallelic LD coefficient D' were also explored. D' was found to be significantly related to marker heterozygosity, although the relationship did not appear to unduly influence the overall conclusions. Of potentially greater concern was the observation that D' may be skewed when rare alleles are present. It is recommended that the statistical significance of LD is used in conjunction with coefficients such as D' to determine the true extent of LD.     

Linkage disequilibrium and inference of ancestral recombination in 538 single-nucleotide polymorphism clusters across the human genome

The prospect of using linkage disequilibrium (LD) for fine-scale mapping in humans has attracted considerable attention, and, during the validation of a set of single-nucleotide polymorphisms (SNPs) for linkage analysis, a set of data for 4,833 SNPs in 538 clusters was produced that provides a rich picture of local attributes of LD across the genome. LD estimates may be biased depending on the means by which SNPs are first identified, and a particular problem of ascertainment bias arises when SNPs identified in small heterogeneous panels are subsequently typed in larger population samples. Understanding and correcting ascertainment bias is essential for a useful quantitative assessment of the landscape of LD across the human genome. Heterogeneity in the population recombination rate, rho=4Nr, along the genome reflects how variable the density of markers will have to be for optimal coverage. We find that ascertainment-corrected rho varies along the genome by more than two orders of magnitude, implying great differences in the recombinational history of different portions of our genome. The distribution of rho is unimodal, and we show that this is compatible with a wide range of mixtures of hotspots in a background of variable recombination rate. Although rho is significantly correlated across the three population samples, some regions of the genome exhibit population-specific spikes or troughs in rho that are too large to be explained by sampling. This result is consistent with differences in the genealogical depth of local genomic regions, a finding that has direct bearing on the design and utility of LD mapping and on the National Institutes of Health HapMap project.     

Assessing the performance of the haplotype block model of linkage disequilibrium

Several recent studies have suggested that linkage disequilibrium (LD) in the human genome has a fundamentally "blocklike" structure. However, thus far there has been little formal assessment of how well the haplotype block model captures the underlying structure of LD. Here we propose quantitative criteria for assessing how blocklike LD is and apply these criteria to both real and simulated data. Analyses of several large data sets indicate that real data show a partial fit to the haplotype block model; some regions conform quite well, whereas others do not. Some improvement could be obtained by genotyping higher marker densities but not by increasing the number of samples. Nonetheless, although the real data are only moderately blocklike, our simulations indicate that, under a model of uniform recombination, the structure of LD would actually fit the block model much less well. Simulations of a model in which much of the recombination occurs in narrow hotspots provide a much better fit to the observed patterns of LD, suggesting that there is extensive fine-scale variation in recombination rates across the human genome.