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.     

Measures of linkage disequilibrium among neighbouring SNPs indicate asymmetries across the house mouse hybrid zone

Theory predicts that naturally occurring hybrid zones between genetically distinct taxa can move over space and time as a result of selection and/or demographic processes, with certain types of hybrid zones being more or less likely to move. Determining whether a hybrid zone is stationary or moving has important implications for understanding evolutionary processes affecting interactions in hybrid populations. However, direct observations of hybrid zone movement are difficult to make unless the zone is moving rapidly. Here, evidence for movement in the house mouse Mus musculus domesticus × Mus musculus musculus hybrid zone is provided using measures of LD and haplotype structure among neighbouring SNP markers from across the genome. Local populations of mice across two transects in Germany and the Czech Republic were sampled, and a total of 1301 mice were genotyped at 1401 markers from the nuclear genome. Empirical measures of LD provide evidence for extinction and (re)colonization in single populations and, together with simulations, suggest hybrid zone movement because of either geography-dependent asymmetrical dispersal or selection favouring one subspecies over the other.     

Examining the effect of linkage disequilibrium on multipoint linkage analysis

Most linkage programs assume linkage equilibrium among multiple linked markers. This assumption may lead to bias for tightly linked markers where strong linkage disequilibrium (LD) exists. We used simulated data from Genetic Analysis Workshop 14 to examine the possible effect of LD on multipoint linkage analysis. Single-nucleotide polymorphism packets from a non-disease-related region that was generated with LD were used for both model-free and parametric linkage analyses. Results showed that high LD among markers can induce false-positive evidence of linkage for affected sib-pair analysis when parental data are missing. Bias can be eliminated with parental data and can be reduced when additional markers not in LD are included in the analyses.     

Associative overdominance: Evaluating the effects of inbreeding and linkage disequilibrium

Expressions are obtained for the expected phenotypic values of homozygous and heterozygous genotypes for a neutral marker locus linked to a locus segregating for a recessive deleterious gene. The phenotypic values are functions of the allele frequencies at the marker locus, the inbreeding coefficient and the degree of association of the deleterious gene with the marker alleles. The analysis is extended to more than two alleles at the marker locus. Either linkage disequilibrium or inbreeding alone can produce an apparent superiority of heterozygotes for the marker locus (unless specified otherwise, the terms ‘homozygote’ and ‘heterozygote’ will refer to the marker locus). The effect of linkage disequilibrium on the difference between the heterozygote and homozygote values can be positive (associative overdominance) or negative (associative underdominance), depending on the frequencies of the marker alleles and the degree of their association with the deleterious gene. Inbreeding has always a positive effect. In general, the expected value of a homozygote is a positive function of its allele frequency. When the various homozygous genotypes are combined into one class and the various heterozygous genotypes into another, the phenotypic difference of the two classes is a function of the evenness of the allelic frequency distribution. Inbreeding is a more likely explanation of associative overdominance if the frequency of the deleterious gene is low, but its effect on the character high. Conversely, linkage disequilibrium is more likely if the frequency is high and the effect low. The degrees of association between marker alleles and the deleterious gene can, in principle, be estimated from the observed phenotypic scores and used to calculate expected multi-locus genotype scores. This could provide the basis for statistical tests of the associative overdominance hypothesis as an explanation of observed correlations between multi-locus heterozygosity and phenotypic traits.     

The effect of linkage disequilibrium on linkage analysis of incomplete pedigrees

Dense SNP maps can be highly informative for linkage studies. But when parental genotypes are missing, multipoint linkage scores can be inflated in regions with substantial marker-marker linkage disequilibrium (LD). Such regions were observed in the Affymetrix SNP genotypes for the Genetic Analysis Workshop 14 (GAW14) Collaborative Study on the Genetics of Alcoholism (COGA) dataset, providing an opportunity to test a novel simulation strategy for studying this problem. First, an inheritance vector (with or without linkage present) is simulated for each replicate, i.e., locations of recombinations and transmission of parental chromosomes are determined for each meiosis. Then, two sets of founder haplotypes are superimposed onto the inheritance vector: one set that is inferred from the actual data and which contains the pattern of LD; and one set created by randomly selecting parental alleles based on the known allele frequencies, with no correlation (LD) between markers. Applying this strategy to a map of 176 SNPs (66 Mb of chromosome 7) for 100 replicates of 116 sibling pairs, significant inflation of multipoint linkage scores was observed in regions of high LD when parental genotypes were set to missing, with no linkage present. Similar inflation was observed in analyses of the COGA data for these affected sib pairs with parental genotypes set to missing, but not after reducing the marker map until r2 between any pair of markers was 相似文献   

The effects of genotype-dependent recombination, and transmission asymmetry, on linkage disequilibrium

A recent sperm-typing study by Jeffreys and Neumann suggested that recombination rates in different individuals at the DNA2 recombination hotspot appeared to be highly dependent on their genotype at a particular A/G SNP, FG11. Specifically, individuals who carried at least one copy of the A allele at this SNP exhibited rates of crossover considerably higher than those of individuals with no copies. Further, recombinant sperm from heterozygous individuals showed a preferential tendency to carry the G allele. We consider the effects of these phenomena on patterns of linkage disequilibrium and find them to be more subtle than might have been expected. In particular, our analysis suggests that, perhaps surprisingly, patterns of LD among chromosomes carrying the "hot" allele (in this case, A) will typically be similar to those among chromosomes carrying the "cold" allele (G).     

Simulation of marker-assisted selection utilizing linkage disequilibrium: the effects of several additional factors

Use was made of our published model and methods to investigate the effects of several additional factors on marker-assisted selection (MAS) utilizing linkage disequilibrium. The additional factors were: size of the sample used to estimate the marker quantitative trait locus (MQTL) association effects, the method used to estimate the MQTL effects, use of the average of the top MQTL estimates in selection rather than individual estimates, size of the selection population, and the crossing of duplicate selection lines to generate further linkage disequilibrium and further selection response. The average map distance between the quantitative trait loci (QTLs) and their nearest marker was 0.15 Morgans. Use of estimates of MQTL effects derived by least squares yielded smaller selection responses than estimates derived by mixed-model methods. Selection responses were also reduced by using a smaller sample for estimating the associations because MQTL effects were less well estimated. This applied to selection on the MQTL effects themselves and to selection combining the MQTL with phenotypic information. Thus, poorly estimated MQTL effects added noise to the system and reduced selection response in combined selection. Using the average of the top MQTL estimates, rather than individual estimates, also reduced selection response. New linkage disequilibrium, generated by crossing two lines selected from the same population, did not lead to additional selection response in the cross line. These results show limitations to MAS using linkage disequilibrium until close linkages of markers and QTLs are available.     

Bias of allele-sharing linkage statistics in the presence of intermarker linkage disequilibrium

Current genome-wide linkage-mapping single-nucleotide polymorphism (SNP) panels with densities of 0.3 cM are likely to have increased intermarker linkage disequilibrium (LD) compared to 5-cM microsatellite panels. The resulting difference in haplotype frequencies versus that predicted may affect multipoint linkage analysis with ungenotyped founders; a common haplotype may be assumed to be rare, leading to inflation of identical-by-descent (IBD) allele-sharing estimates and evidence for linkage. Using data simulated for the Genetic Analysis Workshop 14, we assessed bias in allele-sharing measures and nonparametric linkage (NPL all) and Kong and Cox LOD (KC-LOD) scores in a targeted analysis of regions with and without LD and with and without genes. Using over 100 replicates, we found that if founders were not genotyped, multipoint IBD estimates and delta parameters were modestly inflated and NPL all and KC-LOD scores were biased upwards in the region with LD and no gene; rather than centering on the null, the mean NPL all and KC-LOD scores were 0.51 +/- 0.91 and 0.19 +/- 0.38, respectively. Reduction of LD by dropping markers reduced this upward bias. These trends were not seen in the non-LD region with no gene. In regions with genes (with and without LD), a slight loss in power with dropping markers was suggested. These results indicate that LD should be considered in dense scans; removal of markers in LD may reduce false-positive results although information may also be lost. Methods to address LD in a high-throughput manner are needed for efficient, robust genomic scans with dense SNPs.     

Utilizing linkage disequilibrium information from Indian Genome Variation Database for mapping mutations: SCA12 case study

Stratification in heterogeneous populations poses an enormous challenge in linkage disequilibrium (LD) based identification of causal loci using surrogate markers. In this study, we demonstrate the enormous potential of endogamous Indian populations for mapping mutations in candidate genes using minimal SNPs, mainly due to larger regions of LD. We show this by a case study of the PPP2R2B gene (∼400 kb) that harbours a CAG repeat, expansion of which has been implicated in spinocerebellar ataxia type 12 (SCA12). Using LD information derived from Indian Genome Variation database (IGVdb) on populations which share similar ethnic and linguistic backgrounds as the SCA12 study population, we could map the causal loci using a minimal set of three SNPs, without the generation of additional basal data from the ethnically matched population. We could also demonstrate transferability of tagSNPs from a related HapMap population for mapping the mutation. Composition first described in Hum. Genet. 2005, 118, 1–11     

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.     

Contrasting effects of selection on sequence diversity and linkage disequilibrium at two phytoene synthase loci

We investigated the effects of human selection for yellow endosperm color, representing increased carotenoid content, on two maize genes, the Y1 phytoene synthase and PSY2, a putative second phytoene synthase. Multiple polymorphic sites were identified at Y1 and PSY2 in 75 white and yellow maize inbred lines. Many polymorphic sites showed strong association with the endosperm color phenotype at Y1, but no detectable association was found at PSY2. Nucleotide diversity was equivalent for whites and yellows at PSY2 but was 19-fold less in yellows than in whites at Y1, consistent with the white ancestral state of the gene. The strong sequence haplotype conservation within yellows at Y1 and a significant, negative Tajima's D both verified positive selection for yellow endosperm. We propose that two independent gain-of-function events associated with insertions into the promoter of the Y1 gene and upregulation of expression in endosperm have been incorporated into yellow maize.     

Assessing the effects of rare alleles and linkage disequilibrium on estimates of genetic diversity in the chicken populations

Phenotypic diversity in poultry has been mainly driven by artificial selection and genetic drift. These led to the adaptation to the environment and the development of specific phenotypic traits of chickens in response to their economic use. This study evaluated genetic diversity within and between Russian breeds and populations using Illumina Chicken 60 K SNP iSelect BeadChip by analysing genetic differences between populations with Hudson's fixation index (F_ST statistic) and heterozygosity. We estimated the effect of rare alleles and linkage disequilibrium (LD) on these measurements. To assess the effect of LD on the genetic diversity population, we carried out the LD-based pruning (LD < 0.5 and LD < 0.1) for seven chicken populations combined (I) or separately (II). LD pruning was specific for different dataset groups. Because of the noticeably large sample size in the Russian White RG population, pruning was substantial for Dataset I, and F_ST values were only positive when LD < 0.1 pruning was applied. For Dataset II, the LD pruning results were confirmed by examining heterozygosity and alleles' frequency distribution. LD between single nucleotide polymorphisms was consistent across the seven chicken populations, except the Russian White RG population with the smallest r² values and the largest effective population size. Our findings suggest to study variability in each population LD pruning has to be carried separately not after merging to avoid bias in estimates.     

Contribution of genetic effects to genetic variance components with epistasis and linkage disequilibrium

Background

Cockerham genetic models are commonly used in quantitative trait loci (QTL) analysis with a special feature of partitioning genotypic variances into various genetic variance components, while the F_∞ genetic models are widely used in genetic association studies. Over years, there have been some confusion about the relationship between these two type of models. A link between the additive, dominance and epistatic effects in an F_∞ model and the additive, dominance and epistatic variance components in a Cockerham model has not been well established, especially when there are multiple QTL in presence of epistasis and linkage disequilibrium (LD).

Results

In this paper, we further explore the differences and links between the F_∞ and Cockerham models. First, we show that the Cockerham type models are allelic based models with a special modification to correct a confounding problem. Several important moment functions, which are useful for partition of variance components in Cockerham models, are also derived. Next, we discuss properties of the F_∞ models in partition of genotypic variances. Its difference from that of the Cockerham models is addressed. Finally, for a two-locus biallelic QTL model with epistasis and LD between the loci, we present detailed formulas for calculation of the genetic variance components in terms of the additive, dominant and epistatic effects in an F_∞ model. A new way of linking the Cockerham and F_∞ model parameters through their coding variables of genotypes is also proposed, which is especially useful when reduced F_∞ models are applied.

Conclusion

The Cockerham type models are allele-based models with a focus on partition of genotypic variances into various genetic variance components, which are contributed by allelic effects and their interactions. By contrast, the F_∞ regression models are genotype-based models focusing on modeling and testing of within-locus genotypic effects and locus-by-locus genotypic interactions. When there is no need to distinguish the paternal and maternal allelic effects, these two types of models are transferable. Transformation between an F_∞ model's parameters and its corresponding Cockerham model's parameters can be established through a relationship between their coding variables of genotypes. Genetic variance components in terms of the additive, dominance and epistatic genetic effects in an F_∞ model can then be calculated by translating formulas derived for the Cockerham models.

     

Haplotype diversity and the block structure of linkage disequilibrium

Several recent studies indicate that patterns of linkage disequilibrium in the human genome cannot be reconciled with a uniform distribution of recombination events, but crossovers appear to be localized in short hot-spots that separate longer stretches of DNA. Markers within these low-recombination blocks show increased levels of linkage disequilibrium and very low haplotype diversity. This could simplify study of the genetic basis of complex diseases if causal variants are common.     

Estimation of the rate and effects of deleterious genomic mutations in finite populations with linkage disequilibrium

Under several assumptions such as infinite population size with unlinked loci at linkage equilibrium (LD) under mutation-selection (M-S) balance, the rate (U), and the average effects (dominance and selection coefficients h and s) of deleterious genomic mutations (DGM) can be estimated by the Deng-Lynch method in some natural populations. However, all natural populations are finite in size and many of them are not large enough to be considered as approximately infinite. In the absence of an analytical estimation approach to characterize DGM in finite populations, we test the robustness and applicability of the Deng-Lynch method in finite populations with computer simulations. The results indicate that the estimation obtained by the Deng-Lynch method in finite populations with LD is generally robust when population size is greater than 400. With constant mutation effects, in outcrossing populations, the estimates U and ? are unbiased or only slightly upwardly biased, and ? is unbiased for most cases. In highly selfing populations, U and ? are upwardly biased, U is no more than 1.5U and ? is less than 1.1 h, and ? is either unbiased or slightly downwardly biased. With variable mutation effects, U ranges from 0.56 to 0.72U, and s ranges from 1.4 to 1.8s. Generally speaking, with the same finite population size, the estimation in outcrossing populations is better than in highly selfing populations. Given that even the order of the magnitude of the parameters of DMG (U in particular) is controversial, our investigation here may provide a basis for using the Deng-Lynch method to characterize DGM in finite populations of size greater than 400 in the presence of LD.     

The transmission/disequilibrium test for linkage on the X chromosome

The transmission/disequilibrium test (TDT), which detects linkage between a marker and disease loci in the presence of linkage disequilibrium, was introduced by Spielman et al. The original TDT requires families in which the genotypes are known for both parents and for at least one affected offspring, and this limits its applicability to diseases with late onset. The sib-TDT, or S-TDT, which utilizes families with affected and unaffected siblings, was introduced as an alternative method, by Spielman and Ewens, and the TDT and S-TDT can be combined in an overall test (i.e., a combined-TDT, or C-TDT). The TDT statistics described so far are for autosomal chromosomes. We have extended these TDT methods to test for linkage between X-linked markers and diseases that affect either males only or both sexes. For diseases of late onset, when parental genotypes are often unavailable, the X-linkage C-TDT may allow for more power than is provided by the X-linkage TDT alone.     

Risks of fetal cystic fibrosis based on linkage disequilibrium data

Summary First-trimester prenatal diagnosis of cystic fibrosis depends on tissues being available from a previous affected child for determination of the phase relationship of DNA markers. If no such tissues are available, it is possible to estimate the risks of a couple producing an affected child from the distribution of haplotypes showing linkage disequilibrium with the cystic fibrosis gene. We have calculated all the fetal risk subsets from the various parental haplotype combinations for the restriction fragment length polymorphisms identified by the KM. 19/PstI and XV-2c/TaqI systems. We conclude that only in a limited number of parental combinations are the fetal risks sufficiently high or sufficiently low to be used in prenatal diagnosis.     

Impact of polymorphic transposable elements on linkage disequilibrium along chromosomes

Recombination and selection drive the extent of linkage disequilibrium (LD) among loci and therefore affect the reshuffling of adaptive genetic variation. However, it is poorly known to what extent the enrichment of transposable elements (TEs) in recombinationally‐inert regions reflects their inefficient removal by purifying selection and whether the presence of polymorphic TEs can modify the local recombination rate. In this study, we investigate how TEs and recombination interact at fine scale along chromosomes and possibly support linked selection in natural populations. Whole‐genome sequencing data of 304 individuals from nearby alpine populations of Arabis alpina were used to show that the density of polymorphic TEs is specifically correlated with local LD along chromosomes. Consistent with TEs modifying recombination, the characterization of 28 such LD blocks of up to 5.5 Mb in length revealed strong evidence of selective sweeps at a few loci through either site frequency spectrum or haplotype structure. A majority of these blocks were enriched in genes related to ecologically relevant functions such as responses to cold, salt stress or photoperiodism. In particular, the S‐locus (i.e., supergene responsible for strict outcrossing) was identified in a LD block with high levels of polymorphic TEs and evidence of selection. Another such LD block was enriched in cold‐responding genes and presented evidence of adaptive loci related to photoperiodism and flowering being increasingly linked by polymorphic TEs. These results are consistent with the hypothesis that TEs modify recombination landscapes and thus interact with selection in driving blocks of linked adaptive loci in natural populations.