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.     

Recombination disequilibrium in ideal and natural populations

Following Hardy-Weinberg disequilibrium (HWD) occurring at a single locus and linkage disequilibrium (LD) between two loci in generations, we here proposed the third genetic disequilibrium in a population: recombination disequilibrium (RD). RD is a measurement of crossover interference among multiple loci in a random mating population. In natural populations besides recombination interference, RD may also be due to selection, mutation, gene conversion, drift and/or migration. Therefore, similarly to LD, RD will also reflect the history of natural selection and mutation. In breeding populations, RD purely results from recombination interference and hence can be used to build or evaluate and correct a linkage map. Practical examples from F₂, testcross and human populations indeed demonstrate that RD is useful for measuring recombination interference between two short intervals and evaluating linkage maps. As with LD, RD will be important for studying genetic mapping, association of haplotypes with disease, plant breading and population history.     

Linkage analysis of "necessary" disease loci versus "susceptibility" loci.

The association of some diseases with specific alleles of certain genetic markers has been difficult to explain. Several explanations have been proposed for the phenomenon of association, e.g. the existence of multiple, interacting genes (epistasis) or a disease locus in linkage disequilibrium with the marker locus. One might suppose that when marker data from families with associated diseases are analyzed for linkage, the existence of the association would assure that linkage will be found, and found at a tight recombination fraction. In fact, however, linkage analyses of some diseases associated with HLA, as well as diseases associated with alleles at other loci located throughout the genome, show significant evidence against linkage, and others show loose linkage, to the puzzlement of many researchers. In part, the puzzlement arises because linkage analysis is ideal for looking for loci that are necessary, even if not sufficient, for disease expression but may be much less useful for finding loci that are neither necessary nor sufficient for disease expression (so-called susceptibility loci). This work explores what happens when one looks for linkage to susceptibility loci. A susceptibility locus in this case means that the allele increases risk but is neither necessary nor sufficient for disease expression. It might be either an allele at the marker locus itself that is increasing susceptibility or an allele at a locus in linkage disequilibrium with the marker. This work uses computer simulation to examine how linkage analyses behave when confronted with data from such a model.(ABSTRACT TRUNCATED AT 250 WORDS)     

Linkage disequilibrium under recurrent bottlenecks

To model deviations from selectively neutral genetic variation caused by different forms of selection, it is necessary to first understand patterns of neutral variation. Best understood is neutral genetic variation at a single locus. But, as is well known, additional insights can be gained by investigating multiple loci. The resulting patterns reflect the degree of association (linkage) between loci and provide information about the underlying multilocus gene genealogies. The statistical properties of two-locus gene genealogies have been intensively studied for populations of constant size, as well as for simple demographic histories such as exponential population growth and single bottlenecks. By contrast, the combined effect of recombination and sustained demographic fluctuations is poorly understood. Addressing this issue, we study a two-locus Wright-Fisher model of a population subject to recurrent bottlenecks. We derive coalescent approximations for the covariance of the times to the most recent common ancestor at two loci in samples of two chromosomes. This covariance reflects the degree of association and thus linkage disequilibrium between these loci. We find, first, that an effective population-size approximation describes the numerically observed association between two loci provided that recombination occurs either much faster or much more slowly than the population-size fluctuations. Second, when recombination occurs frequently between but rarely within bottlenecks, we observe that the association of gene histories becomes independent of physical distance over a certain range of distances. Third, we show that in this case, a commonly used measure of linkage disequilibrium, σ(2)(d) (closely related to r(2)), fails to capture the long-range association between two loci. The reason is that constituent terms, each reflecting the long-range association, cancel. Fourth, we analyze a limiting case in which the long-range association can be described in terms of a Xi coalescent allowing for simultaneous multiple mergers of ancestral lines.     

Analytical results concerning linkage disequilibrium in models with genetic transformation and conjugation

Expressions are obtained for the expected levels of linkage disequilibrium under three different equilibrium neutral models that make different assumptions about how recombination takes place. A transformation model is considered in which exchange events involve only one locus at a time. Two conjugation models are considered one with a linear genome and one with a circular genome. In the conjugation models large blocks of genes can be transferred with each conjugation. Consistent with published simulation results, it is found that if the transformation rate per locus is more than twenty times the mutation rate per locus, then the levels of linkage disequilibrium are quite low. If the number of loci being sampled is greater than 10, conjugation with a circular genome can be considerably more effective than transformation in reducing linkage disequilibrium. When recombination rates are high, expected linkage disequilibrium is shown to be proportional to the inverse of the transformation rate (or conjugation rate.)     

Association studies under general disease models

There is great expectation that the levels of association found between genetic markers and disease status will play a role in the location of disease genes. This expectation follows from regarding association as being proportional to linkage disequilibrium and therefore inversely related to recombination value. For disease genes with more than two alleles, the association measure is instead a weighted average of linkage disequilibria, with the weights depending on allele frequencies and genotype susceptibilities at the disease loci. There is no longer a simple relationship, even in expectation, with recombination. We adopt a general framework to examine association mapping methods which helps to clarify the nature of case-control and transmission/disequilibrium-type tests and reveals the relationship between measures of association and coefficients of linkage disequilibrium. In particular, we can show the consequences of additive and nonadditive effects at the trait locus on the behavior of these tests. These concepts have a natural extension to marker haplotypes. The association of two-locus marker haplotypes with disease phenotype depends on a weighted average of three-locus disequilibria (two markers with each disease locus). It is likely that these two-marker analyses will provide additional information in association mapping studies.     

A cladistic analysis of phenotypic associations with haplotypes inferred from restriction endonuclease mapping. I. Basic theory and an analysis of alcohol dehydrogenase activity in Drosophila

Because some genes have been cloned that have a known biochemical or physiological function, genetic variation can be measured in a population at loci that may directly influence a phenotype of interest. With this measured genotype approach, specific alleles or haplotypes in the probed DNA region can be assigned phenotypic effects. In this paper we address several problems encountered in implementing the measured genotype approach with restriction site data. A number of analytical problems arise in part as a consequence of the linkage disequilibrium that is commonly encountered when dealing with small DNA regions: 1) different restriction site polymorphisms are not statistically independent, 2) the sites being measured are not likely to be the direct cause of the associated phenotypic effects, 3) haplotype classes may be phenotypically heterogeneous, and 4) the sites that are most strongly associated with phenotypic effects are not necessarily the most closely linked to the actual genetic cause of the effects. When recombination and gene conversion are rare, the primary cause of linkage disequilibrium is history (mutational origin, genetic drift, hitchhiking, etc.). We deal with historical association directly by producing a cladogram that partially reconstructs the evolutionary history of the present-day haplotype variability. The cladogram defines a nested analysis of variance that simultaneously detects phenotypic effects, localizes the effects within the cladogram, and identifies haplotypes that are potentially heterogeneous in their phenotypic associations. The power of this approach is illustrated by an analysis of the associations between alcohol dehydrogenase (ADH) activity and restriction site variability in a 13-kb fragment surrounding the ADH locus in Drosophila melanogaster.     

Mapping genes for common diseases: the case for genetic (LD) maps

We examine the current effort to develop a haplotype map of the human genome and suggest an alternative approach which represents linkage disequilibrium patterns in the form of a metric LD map. LD maps have some of the useful properties of genetic linkage maps but have a much higher resolution which is optimal for SNP-based association mapping of common diseases. The studies that have been undertaken to date suggest that LD and recombination maps show some close similarities because of abundant, narrow, recombination hot spots. These hot spots are co-localised in all populations but, unlike linkage maps, LD maps differ in scale for different populations because of differences in population history. The prospects for developing optimized panels of SNPs and the use of linkage disequilibrium maps in disease gene localisation are assessed in the light of recent evidence.     

The deviation from linkage equilibrium with multiple loci varying in a stepping-stone cline

The balance between the creation of associations between alleles at different loci by immigration and the convergence to linkage equilibrium due to the recombination process is studied in a theoretical model. The geographical structure of the model is a stepping-stone chain of populations linking two genetically constant source populations. The model assumes an arbitrary number of autosomal loci and considers genetic variation (two alleles at each locus) that is not subject to natural selection. The gene frequencies at each locus will then show a linear cline through the stepping-stone chain of populations. The deviation from linkage equilibrium through the stepping-stone cline is characterized by an equation for linear measures that provide the linkage disequilibrium measures for a given set of loci in terms of the gene frequencies and the linkage disequilibria in the source populations and in terms of the linkage disequilibrium measures through the cline for lower numbers of loci. Numerical examples of this iterative solution are given, and it is shown that the build-up of the higher order Bennett-disequilibria through the cline is considerably more pronounced than the build-up of two-locus disequilibria.     

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.     

Contrasting genetic structure in Plasmodium vivax populations from Asia and South America

Populations of Plasmodium falciparum show striking differences in linkage disequilibrium, population differentiation and diversity, but only fragmentary data exists on the genetic structure of Plasmodium vivax. We genotyped nine tandem repeat loci bearing 2-8 bp motifs from 345 P. vivax infections collected from three Asian countries and from five locations in Colombia. We observed 9-37 alleles per locus and high diversity (He=0.72-0.79, mean=0.75) in all countries. Numbers of multiple clone infections varied considerably: these were rare in Colombia and India, but > 60% of isolates carried multiple alleles in at least one locus in Thailand and Laos. However, only one or two of the nine loci show >1 allele in many samples, suggesting that mutation within infections may result in overestimation of true multiple carriage rates. Identical nine-locus genotypes were frequently found in Colombian populations, contributing to strong linkage disequilibrium. These identical genotypes were strongly clustered in time, consistent with epidemic transmission of clones and subsequent breakdown of allelic associations, suggesting high rates of inbreeding and low effective recombination rates in this country. In contrast, identical genotypes were rare and loci were randomly associated in all three Asian populations, consistent with higher rates of outcrossing and recombination. We observed low but significant differentiation between different Asian countries (standardized FST = 0.13-0.45). In comparison, we see greater differentiation between collection locations within Colombia (standardized FST = 0.4-0.7), and strong differentiation between continents (standardized FST = 0.48-0.79). The observed heterogeneity in multiple clone carriage rates, linkage disequilibrium and population differentiation are similar in some, but not all, respects to those observed in P. falciparum, and have important implications for the design of association mapping studies, and interpretation of P. vivax epidemiology.     

林木全同胞群体的多位点连锁分析

多位点连锁分析是构建人类以及动植物的遗传连锁图谱的关键步骤之一。但是由于林木遗传背景的复杂性,多位点连锁分析在林木的全同胞群体中还没有得到应用．本文将多位点连锁分析应用到林木的F1代全同胞群体中．对于全同胞群体的任意分离比的两个位点,给出了在不同的连锁相下从一个位点到另一个位点的转移概率矩阵．对于给定的一列标记位点,考虑了不同分离比位点以及两位点间的连锁相信息,采用隐马尔可夫链模型计算极大似然函数和相邻位点间的重组率．本文的方法有助于构建完整的高密度的林木遗传连锁图谱．     

SimPed: a simulation program to generate haplotype and genotype data for pedigree structures

With the widespread availability of SNP genotype data, there is great interest in analyzing pedigree haplotype data. Intermarker linkage disequilibrium for microsatellite markers is usually low due to their physical distance; however, for dense maps of SNP markers, there can be strong linkage disequilibrium between marker loci. Linkage analysis (parametric and nonparametric) and family-based association studies are currently being carried out using dense maps of SNP marker loci. Monte Carlo methods are often used for both linkage and association studies; however, to date there are no programs available which can generate haplotype and/or genotype data consisting of a large number of loci for pedigree structures. SimPed is a program that quickly generates haplotype and/or genotype data for pedigrees of virtually any size and complexity. Marker data either in linkage disequilibrium or equilibrium can be generated for greater than 20,000 diallelic or multiallelic marker loci. Haplotypes and/or genotypes are generated for pedigree structures using specified genetic map distances and haplotype and/or allele frequencies. The simulated data generated by SimPed is useful for a variety of purposes, including evaluating methods that estimate haplotype frequencies for pedigree data, evaluating type I error due to intermarker linkage disequilibrium and estimating empirical p values for linkage and family-based association studies.     

Linkage disequilibria between pairs of loci within a highly polymorphic region of chromosome 2Q.

A recently described region on chromosome 2q contains seven restriction fragment length polymorphisms (RFLPs) revealed by single-copy probes isolated from a 20-kilobase (kb) segment of a single cosmid insert. Analysis of six of these loci demonstrates modest amounts of linkage disequilibrium. This reflects the presence of a substantial number of different haplotypes in this chromosome region and indicates that the region could be used as one highly polymorphic locus. No consistent relationship is found between the amount of linkage disequilibrium and the physical distance between pairs of loci. For seven of the 10 pairs of diallelic loci studied, the observed disequilibrium can be attributed primarily to the absence of the minor haplotype from the population. These results suggest that, for small regions of the genome, factors such as mutation, genetic drift, and population admixture may have effects that outweight those of recombination. In addition, results are reviewed which show that estimates of linkage disequilibrium coefficients for tightly linked loci are very imprecise. Thus, the inference of gene order from linkage disequilibrium values must be regarded with caution.     

Towards linkage analysis with markers in linkage disequilibrium by graphical modelling

We review recent developments of MCMC integration methods for computations on graphical models for two applications in statistical genetics: modelling allelic association and pedigree based linkage analysis. We discuss and illustrate estimation of graphical models from haploid and diploid genotypes, and the importance of MCMC updating schemes beyond what is strictly necessary for irreducibility. We then outline an approach combining these methods to compute linkage statistics when alleles at the marker loci are in linkage disequilibrium. Other extensions suitable for analysis of SNP genotype data in pedigrees are also discussed and programs that implement these methods, and which are available from the author's web site, are described. We conclude with a discussion of how this still experimental approach might be further developed.     

Uncoupling the roles of HLA-DRB1 and HLA-DRB5 genes in multiple sclerosis

Genetic susceptibility to multiple sclerosis (MS) is associated with the MHC located on chromosome 6p21. This signal maps primarily to a 1-Mb region encompassing the HLA class II loci, and it segregates often with the HLA-DQB1*0602, -DQA1*0102, -DRB1*1501, -DRB5*0101 haplotype. However, the identification of the true predisposing gene or genes within the susceptibility haplotype has been handicapped by the strong linkage disequilibrium across the locus. African Americans have greater MHC haplotypic diversity and distinct patterns of linkage disequilibrium, which make this population particularly informative for fine mapping efforts. The purpose of this study was to establish the telomeric boundary of the HLA class II region affecting susceptibility to MS by assessing genetic association with the neighboring HLA-DRB5 gene as well as seven telomeric single nucleotide polymorphisms in a large, well-characterized African American dataset. Rare DRB5*null individuals were previously described in African populations. Although significant associations with both HLA-DRB1 and HLA-DRB5 loci were present, HLA-DRB1*1503 was associated with MS in the absence of HLA-DRB5, providing evidence for HLA-DRB1 as the primary susceptibility gene. Interestingly, the HLA-DRB5*null subjects appear to be at increased risk for developing secondary progressive MS. Thus, HLA-DRB5 attenuates MS severity, a finding consistent with HLA-DRB5's proposed role as a modifier in experimental autoimmune encephalomyelitis. Additionally, conditional haplotype analysis revealed a susceptibility signal at the class III AGER locus independent of DRB1. The data underscore the power of the African American MS dataset to identify disease genes by association in a region of high linkage disequilibrium.     

Linkage mapping of a polymorphic plumage locus associated with intermorph incompatibility in the Gouldian finch (Erythrura gouldiae)

Colour polymorphism is known to facilitate speciation but the genetic basis of animal pigmentation and how colour polymorphisms contribute to speciation is poorly understood. Restricted recombination may promote linkage disequilibrium between the colour locus and incompatibility genes. Genomic rearrangement and the position of relevant loci within a chromosome are important factors that influence the frequency of recombination. Therefore, it is important to know the position of the colour locus, gene order and recombination landscape of the chromosome to understand the mechanism that generates incompatibilities between morphs. Recent studies showed remarkable pre- and postzygotic incompatibilities between sympatric colour morphs of the Gouldian finch (Erythrura gouldiae), in which head feather colour is genetically determined by a single sex-linked locus, Red. We constructed a genetic map for the Z chromosome of the Gouldian finch (male-specific map distance=131 cM), using 618 captive-bred birds and 34 microsatellite markers, to investigate the extent of inter- and intraspecific genomic rearrangements and variation in recombination rate within the Z chromosome. We refined the location of the Red locus to a ~7.2-cM interval in a region with a moderate recombination rate but outside the least-recombining, putative centromeric region. There was no evidence of chromosome-wide genomic rearrangements between the chromosomes carrying the red or black alleles with the current marker resolution. This work will contribute to identifying the causal gene, which will in turn enable alternative explanations for the association between incompatibility and colouration, such as fine-scale linkage disequilibrium, genomic rearrangements and pleiotropy, to be tested.     

Use of restriction fragment length polymorphisms for genetic counseling: Population genetic considerations

Two-locus population genetic models are analyzed to evaluate the utility of restriction fragment length polymorphisms for purposes of genetic counseling. It is shown that the linkage disequilibrium between a neutral marker and a tightly linked overdominant mutant will increase rapidly as the mutant moves to its polymorphic equilibrium. The linkage disequilibrium decays for deleterious recessive mutants. Two measures involving the linkage disequilibrium are investigated to determine how much information the transmission of the neutral marker provides about the transmission of the selected gene. In certain kinds of matings, where the parental two-locus genotypes and linkage phases are known, it is possible to determine whether or not a progeny is homozygous for the selected gene on the basis of the fetal genotype at the marker locus. A quantity of primary interest is the fraction of matings between individuals heterozygous for the selected gene in which exact diagnosis can be made in this way. The expected proportion of such matings, taken over all two-locus matings involving heterozygotes at the selected locus, is calculated as a function of the gene frequencies at the two loci and the linkage disequilibrium between them. This expected value is maximized when the linkage disequilibrium is at its maximum in absolute value. Fewer than half of all matings are informative if the linkage disequilibrium is small in magnitude or if the gene frequencies at the two loci are quite different. Consideration is also given to various conditional measures of association that may be useful when the parental two-locus genotypes are unknown. The results suggest that the utility of tightly linked neutral marker genes in predicting the transmission of a selected gene is generally less when selection acts against a recessive gene than for overdominant selection.     

Utility and efficiency of linked marker genes for genetic counseling. III. Proportion of informative families under linkage disequilibrium.

A marker locus closely linked to a disease locus is often useful for genetic counseling provided that a counselee is heterozygous at both disease and marker loci. Furthermore, the linkage phase of these genes in the counselee must be known. When the linkage between the disease and marker loci is very close, one often finds linkage disequilibrium between the loci. To evaluate the effect of such nonrandom associations on the utility of linked marker genes for genetic counseling, the proportion of informative families is studied for X-linked recessive and autosomal dominant diseases. This proportion is higher for X-linked genes than for autosomal genes, if other factors are the same. In general, codominant markers are more useful than dominant markers. Also, under appropriate conditions, the proportion of informative families is higher when linkage disequilibrium is present. The results obtained in this paper are useful for evaluating the utility of polymorphic restriction endonuclease cleavage sites as markers in genetic counseling.