Using Object Oriented Bayesian Networks to Model Linkage, Linkage Disequilibrium and Mutations between STR Markers

In a number of applications there is a need to determine the most likely pedigree for a group of persons based on genetic markers. Adequate models are needed to reach this goal. The markers used to perform the statistical calculations can be linked and there may also be linkage disequilibrium (LD) in the population. The purpose of this paper is to present a graphical Bayesian Network framework to deal with such data. Potential LD is normally ignored and it is important to verify that the resulting calculations are not biased. Even if linkage does not influence results for regular paternity cases, it may have substantial impact on likelihood ratios involving other, more extended pedigrees. Models for LD influence likelihoods for all pedigrees to some degree and an initial estimate of the impact of ignoring LD and/or linkage is desirable, going beyond mere rules of thumb based on marker distance. Furthermore, we show how one can readily include a mutation model in the Bayesian Network; extending other programs or formulas to include such models may require considerable amounts of work and will in many case not be practical. As an example, we consider the two STR markers vWa and D12S391. We estimate probabilities for population haplotypes to account for LD using a method based on data from trios, while an estimate for the degree of linkage is taken from the literature. The results show that accounting for haplotype frequencies is unnecessary in most cases for this specific pair of markers. When doing calculations on regular paternity cases, the markers can be considered statistically independent. In more complex cases of disputed relatedness, for instance cases involving siblings or so-called deficient cases, or when small differences in the LR matter, independence should not be assumed. (The networks are freely available at http://arken.umb.no/~dakl/BayesianNetworks.)     

Comparison of Linkage Disequilibrium in Elite European Maize Inbred Lines using AFLP and SSR Markers

Application of association mapping to plant breeding populations has the potential to revolutionize plant genetics. The main objectives of this study were to (i) investigate the extent and genomic distribution of linkage disequilibrium (LD) between pairs of amplified fragment length polymorphism (AFLP) markers, (ii) compare these results with those obtained with simple sequence repeat (SSR) markers, and (iii) compare the usefulness of AFLP and SSR markers for genomewide association mapping in plant breeding populations. We examined LD in a cross-section of 72 European elite inbred lines genotyped with 452 AFLP and 93 SSR markers. LD was significant (p < 0.05) for about 15% of the AFLP marker pairs and for about 49% of the SSR marker pairs in each of the two germplasm groups, flint and dent. In both germplasm groups the ratio of linked to unlinked loci pairs in LD was higher for AFLPs than for SSRs. The observation of LD due to linkage for both marker types suggested that genome-wide association mapping should be possible using either AFLPs or SSRs. The results of our study indicated that SSRs should be favored over AFLPs but the opposite applies to populations with a long history of recombination.     

Simulating Linkage Disequilibrium Structures in a Human Population for SNP Association Studies

Existing simulation methods usually simulate linkage disequilibrium (LD) structures starting with an initial population that is randomly generated according to specified allele frequencies. These at random based methods might be unstable because the LD level of the initial population is generally extremely low. This study presents a new algorithm, SIMLD, to simulate genome populations with real LD structures. SIMLD begins from an initial population with possibly the highest LD level, and then the LD decays to fit the desired level through processes of mating and recombination over generations. SIMLD can produce case-control samples according to various disease models. Using empirical SNP marker information from three populations of HapMap data, we implement the proposed algorithm and demonstrate a set of experimental results.     

Linkage Disequilibrium and Genetic Variances under Mutation-Selection Balance

I determine the contribution of linkage disequilibrium to genetic variances using results for two loci and for induced or marginal systems. The analysis allows epistasis and dominance, but assumes that mutation is weak relative to selection. The linkage disequilibrium component of genetic variance is shown to be unimportant for unlinked loci if the gametic mutation rate divided by the harmonic mean of the pairwise recombination rates is much less than one. For tightly linked loci, linkage disequilibrium is unimportant if the gametic mutation rate divided by the (induced) per locus selection is much less than one.     

微卫星标记对资源猪群的遗传分析和连锁图谱构建

在猪数量性状位点的定位研究中,标记的使用和图谱的构建是很重要的。本研究从猪的第4、6、7、8和13染色体上选取39个微卫星标记,在来源于约克夏和梅山214头猪组成的资源群中,分析了遗传特征并构建了图谱。研究表明,平均等位基因数、平均观察杂合度(Ho)和平均多态信息含量(PIC)在F1和F2代中分别为:3.2,0.528,0.463和3.2,0.496,0.447。结果表明大多数微卫星标记位点表现为中高度杂合性。在资源群体中,平均有信息减数分裂数是217.4(44-316),而各染色体上两性平均图谱的长度分别是:172.3cM(SSC4),168.7cM(SSC6),191.7cM(SSC7),197.3cM(SSC8),178.3cM(SSC13)。与USDA-MARC的参考图谱相比,标记位点的顺序相同,但长度均较长。雌雄两性图谱相比,第4和第6染色体上雌性图谱长于雄性图谱;而在另外3条染色体上,则雄性图谱长于雌性图谱。结果显示了标记位点在资源猪群的遗传特征和遗传关系,其连锁图谱可用于今后的QTL定位。     

Ataxia with Vitamin E Deficiency: Refinement of Genetic Localization and Analysis of Linkage Disequilibrium by Using New Markers in 14 Families

Ataxia with vitamin E deficiency (AVED) is an autosomal recessive disease characterized clinically by neurological symptoms with often striking resemblance to those of Friedreich ataxia. This disorder has been reported previously as familial isolated vitamin E deficiency. We have mapped recently the AVED locus to a 5-cM confidence interval on chromosome 8q by homozygosity mapping in six Mediterranean families. We have now analyzed six new and two previously described families and demonstrate genetic homogeneity despite important clinical variability and wide geographic origins. Analysis of nine new tightly linked microsatellite markers, including four characterized in this study, revealed a predominant but not unique mutation in northern African populations, where this condition is more frequent. Haplotype analysis but also classical recombinations allowed us to refine the AVED position to a 1-cM interval. A YAC contig over this interval was constructed from marker STSs and YAC fingerprint data, in order to facilitate the search of the AVED gene.     

RAPD和SSR两种标记构建的中国对虾遗传连锁图谱

利用RAPD和SSR分子标记结合拟测交策略,对中国对虾(Fenneropenaeuschinensis)“黄海1号”雌虾与野生雄虾作为亲本进行单对杂交产生的F1代,采用RAPD和SSR两种分子标记技术初步构建了中国对虾雌、雄遗传连锁图谱。对460个RAPD引物和44对SSR引物进行筛选,共选出61个RAPD引物和20对SSR引物,用于对父母本和82个F1个体进行遗传分析。共得到母本分离标记146个(RAPD标记128个,微卫星标记18个)和父本分离标记127个(RAPD标记109个,微卫星标记18个)。雌性图谱包括8个连锁群、9个三联体和14个连锁对,标记间平均间隔为11·28cM,图谱共覆盖1173cM,覆盖率为59·36%;雄性图谱包括10个连锁群、12个三联体和7个连锁对,标记间平均间隔为12·05cM,图谱共覆盖1144·6cM,覆盖率为62·01%。中国对虾遗传图谱的构建为其分子标记辅助育种、比较基因组作图及数量性状位点的定位与克隆奠定了基础。     

Genetic Diversity, Population Structure and Linkage Disequilibrium in Elite Chinese Winter Wheat Investigated with SSR Markers

To ascertain genetic diversity, population structure and linkage disequilibrium (LD) among a representative collection of Chinese winter wheat cultivars and lines, 90 winter wheat accessions were analyzed with 269 SSR markers distributed throughout the wheat genome. A total of 1,358 alleles were detected, with 2 to 10 alleles per locus and a mean genetic richness of 5.05. The average genetic diversity index was 0.60, with values ranging from 0.05 to 0.86. Of the three genomes of wheat, ANOVA revealed that the B genome had the highest genetic diversity (0.63) and the D genome the lowest (0.56); significant differences were observed between these two genomes (P<0.01). The 90 Chinese winter wheat accessions could be divided into three subgroups based on STRUCTURE, UPGMA cluster and principal coordinate analyses. The population structure derived from STRUCTURE clustering was positively correlated to some extent with geographic eco-type. LD analysis revealed that there was a shorter LD decay distance in Chinese winter wheat compared with other wheat germplasm collections. The maximum LD decay distance, estimated by curvilinear regression, was 17.4 cM (r(2)>0.1), with a whole genome LD decay distance of approximately 2.2 cM (r(2)>0.1, P<0.001). Evidence from genetic diversity analyses suggest that wheat germplasm from other countries should be introduced into Chinese winter wheat and distant hybridization should be adopted to create new wheat germplasm with increased genetic diversity. The results of this study should provide valuable information for future association mapping using this Chinese winter wheat collection.     

The Admixture Linkage Disequilibrium and Genetic Linkage Inference on the Gradual Admixture Population

Through the theoretical analysis of the admixture linkage disequilibrium (ALD) in the gradual admixture (GA) model, in which admixture occurs in every generation, the ALD is found to be proportional to the difference in marker allele frequencies, p₁-p₂, between two subpopulations. Based on this property, we can employ a strict monotonic function (Δ_ker=Δ/(p₁-p₂), where Δ denotes the linkage disequilibrium (LD)) of the recombination fraction between the marker locus and the disease locus to infer the true genetic linkage. We construct a quasi likelihood ratio test (LRT) for the case-only data utilizing the information of unlinked markers in the human genome. The simulation results show that our tests can be used to fine map a disease locus. The effects of parameter values in the ALD mapping are also discussed.     

渐近混合群体的混合连锁不平衡及其遗传连锁推断

在渐近混合模型中,混合现象发生在每一世代,通过对其混合连锁不平衡的理论分析,发现混合连锁不平衡与两个子群体间的基因频率差成正比。基于这一点,构造了一个对重组率严格单调的函数（△ker=△／（p1-p2）,其中△代表连锁不平衡）,进而据此推断标记基因座与疾病基因座的遗传连锁。应用人类基因组上不连锁的标记基因提供的连锁不平衡信息,基于病人组数据构造了一个准似然比统计量。模拟结果显示,此检验可用于精确的基因定位。文章亦讨论了参数对检验的影响。     

Genome-Wide Estimation of Linkage Disequilibrium from Population-Level High-Throughput Sequencing Data

Rapidly improving sequencing technologies provide unprecedented opportunities for analyzing genome-wide patterns of polymorphisms. In particular, they have great potential for linkage-disequilibrium analyses on both global and local genetic scales, which will substantially improve our ability to derive evolutionary inferences. However, there are some difficulties with analyzing high-throughput sequencing data, including high error rates associated with base reads and complications from the random sampling of sequenced chromosomes in diploid organisms. To overcome these difficulties, we developed a maximum-likelihood estimator of linkage disequilibrium for use with error-prone sampling data. Computer simulations indicate that the estimator is nearly unbiased with a sampling variance at high coverage asymptotically approaching the value expected when all relevant information is accurately estimated. The estimator does not require phasing of haplotypes and enables the estimation of linkage disequilibrium even when all individual reads cover just single polymorphic sites.     

Inferring Admixture Histories of Human Populations Using Linkage Disequilibrium

Long-range migrations and the resulting admixtures between populations have been important forces shaping human genetic diversity. Most existing methods for detecting and reconstructing historical admixture events are based on allele frequency divergences or patterns of ancestry segments in chromosomes of admixed individuals. An emerging new approach harnesses the exponential decay of admixture-induced linkage disequilibrium (LD) as a function of genetic distance. Here, we comprehensively develop LD-based inference into a versatile tool for investigating admixture. We present a new weighted LD statistic that can be used to infer mixture proportions as well as dates with fewer constraints on reference populations than previous methods. We define an LD-based three-population test for admixture and identify scenarios in which it can detect admixture events that previous formal tests cannot. We further show that we can uncover phylogenetic relationships among populations by comparing weighted LD curves obtained using a suite of references. Finally, we describe several improvements to the computation and fitting of weighted LD curves that greatly increase the robustness and speed of the calculations. We implement all of these advances in a software package, ALDER, which we validate in simulations and apply to test for admixture among all populations from the Human Genome Diversity Project (HGDP), highlighting insights into the admixture history of Central African Pygmies, Sardinians, and Japanese.     

Construction of Genetic Linkage Maps and Comparative Genome Analysis of Catfish Using Gene-Associated Markers

A genetic linkage map of the channel catfish genome (N = 29) was constructed using EST-based microsatellite and single nucleotide polymorphism (SNP) markers in an interspecific reference family. A total of 413 microsatellites and 125 SNP markers were polymorphic in the reference family. Linkage analysis using JoinMap 4.0 allowed mapping of 331 markers (259 microsatellites and 72 SNPs) to 29 linkage groups. Each linkage group contained 3–18 markers. The largest linkage group contained 18 markers and spanned 131.2 cM, while the smallest linkage group contained 14 markers and spanned only 7.9 cM. The linkage map covered a genetic distance of 1811 cM with an average marker interval of 6.0 cM. Sex-specific maps were also constructed; the recombination rate for females was 1.6 times higher than that for males. Putative conserved syntenies between catfish and zebrafish, medaka, and Tetraodon were established, but the overall levels of genome rearrangements were high among the teleost genomes. This study represents a first-generation linkage map constructed by using EST-derived microsatellites and SNPs, laying a framework for large-scale comparative genome analysis in catfish. The conserved syntenies identified here between the catfish and the three model fish species should facilitate structural genome analysis and evolutionary studies, but more importantly should facilitate functional inference of catfish genes. Given that determination of gene functions is difficult in nonmodel species such as catfish, functional genome analysis will have to rely heavily on the establishment of orthologies from model species.     

新疆石榴种质资源遗传多样性的SRAP分析

采用SRAP分子标记技术,对21份新疆石榴品种的遗传多样性与亲缘关系进行分析。从36对引物组合中筛选出16对扩增条带清晰、多态性高的引物组合分析供试材料,共检测出271个位点,其中194个为多态性位点,多态性比率达71.59%,平均每对引物组合产生16.94个位点和12.13个多态性位点。21份石榴样品间的相似性系数为0.63~0.89,平均为0.77。UPGMA聚类结果显示,在相似性系数为0.776时,21份材料可被分为5个类群。新疆石榴品种间平均观察等位基因数(Na)、有效等位基因数(Ne)、Neis基因多样性指数(H)及Shannons信息指数(I)分别为1.712 2、1.352 8、0.199 9及0.310 5。研究表明,新疆喀什地区石榴品种的遗传多样性最为丰富;SRAP聚类结果与石榴的表型特征存在一致性,且SRAP分子标记技术是研究石榴遗传多样性简单而有效的手段。     

LDx: Estimation of Linkage Disequilibrium from High-Throughput Pooled Resequencing Data

High-throughput pooled resequencing offers significant potential for whole genome population sequencing. However, its main drawback is the loss of haplotype information. In order to regain some of this information, we present LDx, a computational tool for estimating linkage disequilibrium (LD) from pooled resequencing data. LDx uses an approximate maximum likelihood approach to estimate LD (r²) between pairs of SNPs that can be observed within and among single reads. LDx also reports r² estimates derived solely from observed genotype counts. We demonstrate that the LDx estimates are highly correlated with r² estimated from individually resequenced strains. We discuss the performance of LDx using more stringent quality conditions and infer via simulation the degree to which performance can improve based on read depth. Finally we demonstrate two possible uses of LDx with real and simulated pooled resequencing data. First, we use LDx to infer genomewide patterns of decay of LD with physical distance in D. melanogaster population resequencing data. Second, we demonstrate that r² estimates from LDx are capable of distinguishing alternative demographic models representing plausible demographic histories of D. melanogaster.     

Exploring the Genetic Characteristics of Two Recombinant Inbred Line Populations via High-Density SNP Markers in Maize

Understanding genetic characteristics can reveal the genetic diversity in maize and be used to explore evolutionary mechanisms and gene cloning. A high-density linkage map was constructed to determine recombination rates (RRs), segregation distortion regions (SDRs), and recombinant blocks (RBs) in two recombinant inbred line populations (RILs) (B73/By804 and Zong3/87-1) generated by the single seed descent method. Population B73/By804 containing 174 lines were genotyped with 198 simple sequence repeats (SSRs) markers while population Zong3/87-1 comprised of 175 lines, were genotyped with 210 SSR markers along with 1536 single nucleotide polymorphism (SNP) markers for each population, spanning 1526.7 cM and 1996.2 cM in the B73/By804 and Zong3/87-1 populations, respectively. The total variance of the RR in the whole genome was nearly 100 fold, and the maximum average was 10.43–11.50 cM/Mb while the minimum was 0.08–0.10 cM/Mb in the two populations. The average number of RB was 44 and 37 in the Zong3/87-1 and B73/By804 populations, respectively, whereas 28 SDRs were observed in both populations. We investigated 11 traits in Zong3/87-1 and 10 traits in B73/By804. Quantitative trait locus (QTLs) mapping of SNP+SSR with SNP and SSR marker sets were compared to showed the impact of different density markers on QTL mapping and resolution. The confidence interval of QTL Pa19 (FatB gene controlling palmitic acid content) was reduced from 3.5 Mb to 1.72 Mb, and the QTL Oil6 (DGAT1-2 gene controlling oil concentration) was significantly reduced from 10.8 Mb to 1.62 Mb. Thus, the use of high-density markers considerably improved QTL mapping resolution. The genetic information resulting from this study will support forthcoming efforts to understand recombination events, SDRs, and variations among different germplasm. Furthermore, this study will facilitate gene cloning and understanding of the fundamental sources of total variation and RR in maize, which is the most widely cultivated cereal crop.     

Fine-Scale Genetic Mapping Based on Linkage Disequilibrium: Theory and Applications

Linkage-disequilibrium mapping (LDM) recently has been hailed as a powerful statistical method for fine-scale mapping of disease genes. After reviewing its historical background and methodological development, we present a general, mathematical, and conceptually coherent framework for LDM that incorporates multilocus and multiallelic markers and mutational processes at the marker and disease loci. With this framework, we address several issues relevant to fine-scale mapping and propose some efficient computational methods for LDM. We implement various LDM methods that incorporate population growth, recurrent mutation, and marker mutations, on the basis of a general framework. We demonstrate these methods by applying them to published data on cystic fibrosis, Huntington disease, Friedreich ataxia, and progressive myoclonus epilepsy. Since the genes responsible for these diseases all have been cloned, we can evaluate the performance of our methods and can compare ours with that of other methods. Using the proposed methods, we successfully and accurately predicted the locations of genes responsible for these diseases, on the basis of published data only.     

Massive Sorghum Collection Genotyped with SSR Markers to Enhance Use of Global Genetic Resources

Large ex situ collections require approaches for sampling manageable amounts of germplasm for in-depth characterization and use. We present here a large diversity survey in sorghum with 3367 accessions and 41 reference nuclear SSR markers. Of 19 alleles on average per locus, the largest numbers of alleles were concentrated in central and eastern Africa. Cultivated sorghum appeared structured according to geographic regions and race within region. A total of 13 groups of variable size were distinguished. The peripheral groups in western Africa, southern Africa and eastern Asia were the most homogeneous and clearly differentiated. Except for Kafir, there was little correspondence between races and marker-based groups. Bicolor, Caudatum, Durra and Guinea types were each dispersed in three groups or more. Races should therefore better be referred to as morphotypes. Wild and weedy accessions were very diverse and scattered among cultivated samples, reinforcing the idea that large gene-flow exists between the different compartments. Our study provides an entry to global sorghum germplasm collections. Our reference marker kit can serve to aggregate additional studies and enhance international collaboration. We propose a core reference set in order to facilitate integrated phenotyping experiments towards refined functional understanding of sorghum diversity.     

Genetic Linkage Maps of Eucalyptus Grandis and Eucalyptus Urophylla Using a Pseudo-Testcross: Mapping Strategy and Rapd Markers

We have used a ``two-way pseudo-testcross' mapping strategy in combination with the random amplified polymorhic DNA (RAPD) assay to construct two moderate density genetic linkage maps for species of Eucalyptus. In the cross between two heterozygous individuals many single-dose RAPD markers will be heterozygous in one parent, null in the other and therefore segregate 1:1 in their F(1) progeny following a testcross configuration. Meiosis and gametic segregation in each individual can be directly and efficiently analyzed using RAPD markers. We screened 305 primers of arbitrary sequence, and selected 151 to amplify a total of 558 markers. These markers were grouped at LOD 5.0, θ = 0.25, resulting in the maternal Eucalyptus grandis map having a total of 240 markers into 14 linkage groups (1552 cM) and the paternal Eucalyptus urophylla map with 251 markers in 11 linkage groups (1101 cM) (n = 11 in Eucalyptus). Framework maps ordered with a likelihood support >/=1000:1 were assembled covering 95% of the estimated genome size in both individuals. Characterization of genome complexity of a sample of 48 mapped random amplified polymorphic DNA (RAPD) markers indicate that 53% amplify from low copy regions. These are the first reported high coverage linkage maps for any species of Eucalyptus and among the first for any hardwood tree species. We propose the combined use of RAPD markers and the pseudo-testcross configuration as a general strategy for the construction of single individual genetic linkage maps in outbred forest trees as well as in any highly heterozygous sexually reproducing living organism. A survey of the occurrence of RAPD markers in different individuals suggests that the pseudo-testcross/RAPD mapping strategy should also be efficient at the intraspecific level and increasingly so with crosses of genetically divergent individuals. The ability to quickly construct single-tree genetic linkage maps in any forest species opens the way for a shift from the paradigm of a species index map to the heterodox proposal of constructing several maps for individual trees of a population, therefore mitigating the problem of linkage equilibrium between marker and trait loci for the application of marker assisted strategies in tree breeding.