Heterogeneity in Rates of Recombination across the Mouse Genome

If loci are randomly distributed on a physical map, the density of markers on a genetic map will be inversely proportional to recombination rate. First proposed by MARY LYON, we have used this idea to estimate recombination rates from the Drosophila melanogaster linkage map. These results were compared with results of two other studies that estimated regional recombination rates in D. melanogaster using both physical and genetic maps. The three methods were largely concordant in identifying large-scale genomic patterns of recombination. The marker density method was then applied to the Mus musculus microsatellite linkage map. The distribution of microsatellites provided evidence for heterogeneity in recombination rates. Centromeric regions for several mouse chromosomes had significantly greater numbers of markers than expected, suggesting that recombination rates were lower in these regions. In contrast, most telomeric regions contained significantly fewer markers than expected. This indicates that recombination rates are elevated at the telomeres of many mouse chromosomes and is consistent with a comparison of the genetic and cytogenetic maps in these regions. The density of markers on a genetic map may provide a generally useful way to estimate regional recombination rates in species for which genetic, but not physical, maps are available.     

Linkage disequilibrium patterns across a recombination gradient in African Drosophila melanogaster

Previous multilocus surveys of nucleotide polymorphism have documented a genome-wide excess of intralocus linkage disequilibrium (LD) in Drosophila melanogaster and D. simulans relative to expectations based on estimated mutation and recombination rates and observed levels of diversity. These studies examined patterns of variation from predominantly non-African populations that are thought to have recently expanded their ranges from central Africa. Here, we analyze polymorphism data from a Zimbabwean population of D. melanogaster, which is likely to be closer to the standard population model assumptions of a large population with constant size. Unlike previous studies, we find that levels of LD are roughly compatible with expectations based on estimated rates of crossing over. Further, a detailed examination of genes in different recombination environments suggests that markers near the telomere of the X chromosome show considerably less linkage disequilibrium than predicted by rates of crossing over, suggesting appreciable levels of exchange due to gene conversion. Assuming that these populations are near mutation-drift equilibrium, our results are most consistent with a model that posits heterogeneity in levels of exchange due to gene conversion across the X chromosome, with gene conversion being a minor determinant of LD levels in regions of high crossing over. Alternatively, if levels of exchange due to gene conversion are not negligible in regions of high crossing over, our results suggest a marked departure from mutation-drift equilibrium (i.e., toward an excess of LD) in this Zimbabwean population. Our results also have implications for the dynamics of weakly selected mutations in regions of reduced crossing over.     

Equilibrium processes cannot explain high levels of short- and medium-range linkage disequilibrium in the domesticated grass Sorghum bicolor

Patterns of linkage disequilibrium (LD) are of interest because they provide evidence of both equilibrium (e.g., mating system or long-term population structure) and nonequilibrium (e.g., demographic or selective) processes, as well as because of their importance in strategies for identifying the genetic basis of complex phenotypes. We report patterns of short and medium range (up to 100 kb) LD in six unlinked genomic regions in the partially selfing domesticated grass, Sorghum bicolor. The extent of allelic associations in S. bicolor, as assessed by pairwise measures of LD, is higher than in maize but lower than in Arabidopsis, in qualitative agreement with expectations based on mating system. Quantitative analyses of the population recombination parameter, rho, however, based on empirical estimates of rates of recombination, mutation, and self-pollination, show that LD is more extensive than expected under a neutral equilibrium model. The disparity between rho and the population mutation parameter, , is similar to that observed in other species whose population history appears to be complex. From a practical standpoint, these results suggest that S. bicolor is well suited for association studies using reasonable numbers of markers, since LD typically extends at least several kilobases but has largely decayed by 15 kb.     

Demography,recombination hotspot intensity,and the block structure of linkage disequilibrium

BACKGROUND: Effective gene mapping based on genetic association data will require detailed knowledge of patterns of linkage disequilibrium (LD) in human populations. It has been recently suggested that linkage disequilibrium in humans may be organized in a block-like structure, with islands of high LD separated by regions of rapid breakdown of LD due to recombination hotspots. The experimental data to date, however, are limited, and fundamental questions remain about the implications of recombination rate heterogeneity. Here, we use computer simulations to evaluate how such heterogeneity influences patterns of LD, and we develop formal criteria to assess whether the patterns are functionally block like in the context of association mapping.RESULTS: Our analyses suggest that, even in models of extreme recombination rate heterogeneity, some human populations will have a functionally block-like structure to the pattern of LD, but others will not, depending on their precise demographic histories. In fact, for many models, we find that, following an LD-generating event, populations may move through discrete phases that can be functionally described as pre-block, block, and post-block. An analysis of observed and expected patterns of LD surrounding hotspots within the MHC Class II region confirms these theoretical expectations.CONCLUSIONS: Even if highly punctuated patterns of recombination are the rule, patterns of LD are still likely to show differences among populations and among genomic regions that are of practical importance in the design of genetic association studies. The notion that the average extent of LD is a useful concept for the design of association studies must be abandoned in light of the experimental and theoretical evidence.     

Linkage Disequilibrium in Humans: Models and Data

In this review, we describe recent empirical and theoretical work on the extent of linkage disequilibrium (LD) in the human genome, comparing the predictions of simple population-genetic models to available data. Several studies report significant LD over distances longer than those predicted by standard models, whereas some data from short, intergenic regions show less LD than would be expected. The apparent discrepancies between theory and data present a challenge-both to modelers and to human geneticists-to identify which important features are missing from our understanding of the biological processes that give rise to LD. Salient features may include demographic complications such as recent admixture, as well as genetic factors such as local variation in recombination rates, gene conversion, and the potential segregation of inversions. We also outline some implications that the emerging patterns of LD have for association-mapping strategies. In particular, we discuss what marker densities might be necessary for genomewide association scans.     

GOLDsurfer: three dimensional display of linkage disequilibrium

GOLDsurfer is a java-based analysis and graphics program for three-dimensional plotting of linkage disequilibrium (LD). Simultaneous presentation of LD measures, including recombination rate estimates and disease association statistics, helps to clarify LD patterns and facilitates interpretations based on multiple indices of local genetic data.     

Test for interaction between two unlinked loci

Despite the growing consensus on the importance of testing gene-gene interactions in genetic studies of complex diseases, the effect of gene-gene interactions has often been defined as a deviance from genetic additive effects, which is essentially treated as a residual term in genetic analysis and leads to low power in detecting the presence of interacting effects. To what extent the definition of gene-gene interaction at population level reflects the genes' biochemical or physiological interaction remains a mystery. In this article, we introduce a novel definition and a new measure of gene-gene interaction between two unlinked loci (or genes). We developed a general theory for studying linkage disequilibrium (LD) patterns in disease population under two-locus disease models. The properties of using the LD measure in a disease population as a function of the measure of gene-gene interaction between two unlinked loci were also investigated. We examined how interaction between two loci creates LD in a disease population and showed that the mathematical formulation of the new definition for gene-gene interaction between two loci was similar to that of the LD between two loci. This finding motived us to develop an LD-based statistic to detect gene-gene interaction between two unlinked loci. The null distribution and type I error rates of the LD-based statistic for testing gene-gene interaction were validated using extensive simulation studies. We found that the new test statistic was more powerful than the traditional logistic regression under three two-locus disease models and demonstrated that the power of the test statistic depends on the measure of gene-gene interaction. We also investigated the impact of using tagging SNPs for testing interaction on the power to detect interaction between two unlinked loci. Finally, to evaluate the performance of our new method, we applied the LD-based statistic to two published data sets. Our results showed that the P values of the LD-based statistic were smaller than those obtained by other approaches, including logistic regression models.     

Linkage disequilibrium-based quality control for large-scale genetic studies

Quality control (QC) is a critical step in large-scale studies of genetic variation. While, on average, high-throughput single nucleotide polymorphism (SNP) genotyping assays are now very accurate, the errors that remain tend to cluster into a small percentage of "problem" SNPs, which exhibit unusually high error rates. Because most large-scale studies of genetic variation are searching for phenomena that are rare (e.g., SNPs associated with a phenotype), even this small percentage of problem SNPs can cause important practical problems. Here we describe and illustrate how patterns of linkage disequilibrium (LD) can be used to improve QC in large-scale, population-based studies. This approach has the advantage over existing filters (e.g., HWE or call rate) that it can actually reduce genotyping error rates by automatically correcting some genotyping errors. Applying this LD-based QC procedure to data from The International HapMap Project, we identify over 1,500 SNPs that likely have high error rates in the CHB and JPT samples and estimate corrected genotypes. Our method is implemented in the software package fastPHASE, available from the Stephens Lab website (http://stephenslab.uchicago.edu/software.html).     

Selection at linked sites in the partial selfer Caenorhabditis elegans

Natural selection can produce a correlation between local recombination rates and levels of neutral DNA polymorphism as a consequence of genetic hitchhiking and background selection. Theory suggests that selection at linked sites should affect patterns of neutral variation in partially selfing populations more dramatically than in outcrossing populations. However, empirical investigations of selection at linked sites have focused primarily on outcrossing species. To assess the potential role of selection as a determinant of neutral polymorphism in the context of partial self-fertilization, we conducted a multivariate analysis of single-nucleotide polymorphism (SNP) density throughout the genome of the nematode Caenorhabditis elegans. We based the analysis on a published SNP data set and partitioned the genome into windows to calculate SNP densities, recombination rates, and gene densities across all six chromosomes. Our analyses identify a strong, positive correlation between recombination rate and neutral polymorphism (as estimated by noncoding SNP density) across the genome of C. elegans. Furthermore, we find that levels of neutral polymorphism are lower in gene-dense regions than in gene-poor regions in some analyses. Analyses incorporating local estimates of divergence between C. elegans and C. briggsae indicate that a mutational explanation alone is unlikely to explain the observed patterns. Consequently, we interpret these findings as evidence that natural selection shapes genome-wide patterns of neutral polymorphism in C. elegans. Our study provides the first demonstration of such an effect in a partially selfing animal. Explicit models of genetic hitchhiking and background selection can each adequately describe the relationship between recombination rate and SNP density, but only when they incorporate selfing rate. Clarification of the relative roles of genetic hitchhiking and background selection in C. elegans awaits the development of specific theoretical predictions that account for partial self-fertilization and biased sex ratios.     

Disentangling linkage disequilibrium and linkage from dense single-nucleotide polymorphism trio data

Parent-offspring trios are widely collected for disease gene-mapping studies and are being extensively genotyped as part of the International HapMap Project. With dense maps of markers on trios, the effects of LD and linkage can be separated, allowing estimation of recombination rates in a model-free setting. Here we define a model-free multipoint method on the basis of dense sequence polymorphism data from parent-offspring trios to estimate intermarker recombination rates. We use simulations to show that this method has up to 92% power to detect recombination hotspots of intensity 25 times background over a region of size 10 kb typed at density 1 marker per 2.5 kb and almost 100% power to detect large hotspots of intensity >125 times background over regions of size 10 kb typed with just 1 marker per 5 kb (alpha = 0.05). We found strong agreement at megabase scales between estimates from our method applied to HapMap trio data and estimates from the genetic map. At finer scales, using Centre d'Etude du Polymorphisme Humain (CEPH) pedigree data across a 10-Mb region of chromosome 20, a comparison of population recombination rate estimates obtained from our method with estimates obtained using a coalescent-based approximate-likelihood method implemented in PHASE 2.0 shows detection of the same coldspots and most hotspots: The Spearman rank correlation between the estimates from our method and those from PHASE is 0.58 (p < 2.2(-16)).     

Distinguishing recombination and intragenic gene conversion by linkage disequilibrium patterns

Deterministic theory suggests that reciprocal recombination and intragenic, interallelic conversion have different effects on the linkage disequilibrium between a pair of genetic markers. Under a model of reciprocal recombination, the decay rate of linkage disequilibrium depends on the distance between the two markers, while under conversion the decay rate is independent of this distance, provided that conversion tracts are short. A population genetic three-locus model provides a function Q of two-locus linkage disequilibria. Viewed as a random variable, Q is the basis for a test of the relative impact of conversion and recombination. This test requires haplotype frequency data of a sufficiently variable three-locus system. One of the few examples currently available is data from the Human Leukocyte Antigen (HLA) class I genes of three Amerindian populations. We find that conversion may have played a dominant role in shaping haplotype patterns over short stretches of DNA, whereas reciprocal recombination may have played a greater role over longer stretches of DNA. However, in order to draw firm conclusions more independent data are necessary.     

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.     

Extensive linkage disequilibrium and parallel adaptive divergence across threespine stickleback genomes

Population genomic studies are beginning to provide a more comprehensive view of dynamic genome-scale processes in evolution. Patterns of genomic architecture, such as genomic islands of increased divergence, may be important for adaptive population differentiation and speciation. We used next-generation sequencing data to examine the patterns of local and long-distance linkage disequilibrium (LD) across oceanic and freshwater populations of threespine stickleback, a useful model for studies of evolution and speciation. We looked for associations between LD and signatures of divergent selection, and assessed the role of recombination rate variation in generating LD patterns. As predicted under the traditional biogeographic model of unidirectional gene flow from ancestral oceanic to derived freshwater stickleback populations, we found extensive local and long-distance LD in fresh water. Surprisingly, oceanic populations showed similar patterns of elevated LD, notably between large genomic regions previously implicated in adaptation to fresh water. These results support an alternative biogeographic model for the stickleback radiation, one of a metapopulation with appreciable bi-directional gene flow combined with strong divergent selection between oceanic and freshwater populations. As predicted by theory, these processes can maintain LD within and among genomic islands of divergence. These findings suggest that the genomic architecture in oceanic stickleback populations may provide a mechanism for the rapid re-assembly and evolution of multi-locus genotypes in newly colonized freshwater habitats, and may help explain genetic mapping of parallel phenotypic variation to similar loci across independent freshwater populations.     

Human recombination rates are increased around accelerated conserved regions--evidence for continued selection?

MOTIVATION: We hypothesized that recombination rates might be increased at genetic loci that are subject to more intense selection. Here, we test this hypothesis by using a recently published set of accelerated conserved regions and fine-scale recombination rate estimates provided by the HapMap project. RESULTS: We observed that fine-scale recombination rates are increased around conserved noncoding regions that show accelerated evolution in human or chimp, as compared to noncoding regions showing accelerated evolution in mouse and those being conserved between human and fugu. Recombination rates around hominid accelerated conserved regions (ACRs) are furthermore increased as compared to exonic regions. On the other hand, GC-content is reduced around ACRs, excluding a major confounding influence of GC-content on the observed variation in recombination rate. Conclusion: Our observations indicate that selection intensity could be an important determinant of local recombination rate variation and that continued positive selection might act at many ACR loci. Alternatively, a confounding factor needs to be found that causes a congruent signal in recombination rate estimates based on human polymorphism data and in the comparative genomic data. Researchers who consider the explanation involving selection as more likely may expect more common functional sequence variants at ACRs in genetic association studies.     

Variation in recombination rate across the genome: evidence and implications

Recent data from humans and other species provide convincing evidence of variation in recombination rate in different genomic regions. Comparison of physical and genetic maps reveals variation on a scale of megabases, with substantial differences between sexes. Recombination is often suppressed near centromeres and elevated near telomeres, but neither of these observations is true for all chromosomes. In humans, patterns of linkage disequilibrium and experimental measures of recombination from sperm-typing reveal dramatic hotspots of recombination on a scale of kilobases. Genome-wide variation in the amount of crossing-over may be due to variation in the density of hotspots, the intensity of hotspots, or both. Theoretical models of selection and linkage predict that genetic variation will be reduced in regions of low recombination, and this prediction is supported by data from several species. Heterogeneity in rates of crossing-over provides both an opportunity and a challenge for identifying disease genes: as associations occur in blocks, genomic regions containing disease loci may be identified with relatively few markers, yet identifying the causal mutations is unlikely to be achieved through associations alone.     

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.     

Recombination and Gene Flux Caused by Gene Conversion and Crossing over in Inversion Heterokaryotypes

A theoretical analysis of the effects of inversions on recombination and gene flux between arrangements caused by gene conversion and crossing over was carried out. Two different mathematical models of recombination were used: the Poisson model (without interference) and the Counting model (with interference). The main results are as follows. (1) Recombination and gene flux are highly site-dependent both inside and outside the inverted regions. (2) Crossing over overwhelms gene conversion as a cause of gene flux in large inversions, while conversion becomes relatively significant in short inversions and in regions around the breakpoints. (3) Under the Counting model the recombination rate between two markers depends strongly on the position of the markers along the inverted segment. Two equally spaced markers in the central part of the inverted segment have less recombination than if they are in a more extreme position. (4) Inversions affect recombination rates in the uninverted regions of the chromosome. Recombination increases in the distal segment and decreases in the proximal segment. These results provide an explanation for a number of observations reported in the literature. Because inversions are ubiquitous in the evolutionary history of many Drosophila species, the effects of inversions on recombination are expected to influence DNA variation patterns.     

Population genomics in bacteria: a case study of Staphylococcus aureus

We analyzed the genome-wide pattern of single nucleotide polymorphisms (SNPs) in a sample with 12 strains of Staphylococcus aureus. Population structure of S. aureus seems to be complex, and the 12 strains were divided into five groups, named A, B, C, D, and E. We conducted a detailed analysis of the topologies of gene genealogies across the genomes and observed a high rate and frequency of tree-shape switching, indicating extensive homologous recombination. Most of the detected recombination occurred in the ancestral population of A, B, and C, whereas there are a number of small regions that exhibit evidence for homologous recombination with a distinct related species. As such regions would contain a number of novel mutations, it is suggested that homologous recombination would play a crucial role to maintain genetic variation within species. In the A-B-C ancestral population, we found multiple lines of evidence that the coalescent pattern is very similar to what is expected in a panmictic population, suggesting that this population is suitable to apply the standard population genetic theories. Our analysis showed that homologous recombination caused a dramatic decay in linkage disequilibrium (LD) and there is almost no LD between SNPs with distance more than 10 kb. Coalescent simulations demonstrated that a high rate of homologous recombination-a relative rate of 0.6 to the mutation rate with an average tract length of about 10 kb-is required to produce patterns similar to those observed in the S. aureus genomes. Our results call for more research into the evolutionary role of homologous recombination in bacterial populations.