Linkage Disequilibrium Method Research Articles

Extensive linkage disequilibrium in a wild bird population

Knowledge about the extent and patterns of linkage disequilibrium (LD) can provide important insights into demographic processes and strategies to identify the genetic basis of complex phenotypes in wild populations. However, data on the extent and patterns of LD from non-model vertebrate species from the wild are still scarce. We conducted so far the most extensive and detailed examination of LD in a pedigreed wild bird population using genotypes from 97 autosomal and 6 gonosomal microsatellites and a recently established linkage map of Siberian jays (Perisoreus infaustus). Analysis of syntenic marker pairs showed high levels of LD that extended over tens of centimorgans or several megabases and generally decayed as an increasing function of intermarker distance. In addition, significant LD was also very common between nonsyntenic markers. Patterns of LD varied across different linkage groups possibly because of the differences in chromosomal structure (macro-, micro-, and Z-chromosome). In particular, the level of LD was significantly lower on the Z-chromosome than on the autosomes at comparable genetic distances. In general, the high levels and extent of LD in this population are likely owing to its relatively small size, significant intrapopulation genetic structure, and occurrence of inbreeding. Whatever the cause, the long-range LD between syntenic loci suggests that LD mapping of phenotypic traits in this population using low-density markers maps is feasible. However, the frequent occurrence of LD between nonsyntenic markers suggests that the combined use of linkage and LD methods is needed to reduce the likelihood of false-positive associations between marker loci and traits of ecological and evolutionary interest.

A new method for estimating effective population sizes from a single sample of multilocus genotypes

Equations for the effective size (N(e)) of a population were derived in terms of the frequencies of a pair of offspring taken at random from the population being sibs sharing the same one or two parents. Based on these equations, a novel method (called sibship assignment method) was proposed to infer N(e) from the sibship frequencies estimated from a sibship assignment analysis, using the multilocus genotypes of a sample of offspring taken at random from a single cohort in a population. Comparative analyses of extensive simulated data and some empirical data clearly demonstrated that the sibship assignment method is much more accurate [measured by the root mean squared error, RMSE, of 1/(2N(e))] than other methods such as the heterozygote excess method, the linkage disequilibrium method, and the temporal method. The RMSE of 1/(2N(e)) from the sibship assignment method is typically a small fraction of that from other methods. The new method is also more general and flexible than other methods. It can be applied to populations with nonoverlapping generations of both diploid and haplodiploid species under random or nonrandom mating, using either codominant or dominant markers. It can also be applied to the estimation of N(e) for a subpopulation with immigration. With some modification, it could be applied to monoecious diploid populations with self-fertilization, and to populations with overlapping generations.

Genetic structure of the northwestern Russian wolf populations and gene flow between Russia and Finland

We examined the genetic diversity and structure of wolf populations in northwestern Russia. Populations in Republic of Karelia and Arkhangelsk Oblast were sampled during 1995–2000, and 43 individuals were genotyped with 10 microsatellite markers. Moreover, 118 previously genotyped wolves from the neighbouring Finnish population were used as a reference population. A relatively large amount of genetic variation was found in the Russian populations, and the Karelian wolf population tended to be slightly more polymorphic than the Arkhangelsk population. We found significant inbreeding (F = 0.094) in the Karelian, but not in the Arkhangelsk population. The effective size estimates of the Karelian wolf population based on the approximate Bayesian computation and linkage disequilibrium methods were 39.9 and 46.7 individuals, respectively. AMOVA-analysis and exact test of population differentiation suggested clear differentiation between the Karelian, Arkhangelsk and Finnish wolf populations. Indirect estimates of gene flow based on the level of population differentiation (ϕST = 0.152) and frequency of private alleles (0.029) both suggested a low level of gene flow between the populations (Nm = 1.4 and Nm = 3.7, respectively). Assignment analysis of Karelian and Finnish populations suggested an even lower number of recent migrants (less than 0.03) between populations, with a larger amount of migration from Finland to Karelia than vice versa. Our findings emphasise the role of physical obstacles and territorial behaviour in creating barriers to gene flow between populations in relatively limited geographical areas, even in large-bodied mammalian species with long-distance dispersal capabilities and an apparently continuous population structure.

Genetic diversity and effective size of the Atlantic salmon Salmo salar L. inhabiting the River Eo (Spain) following a stock collapse

Historic angling records suggest the occurrence of a drastic decline in the River Eo (Spain) Atlantic salmon population size during the past two decades, as a result of overexploitation and habitat deterioration. In recent years, the population has been apparently recovering, and the present study is aimed to report information on the level of genetic diversity and the effective size of the current population as these may have immediate consequences for its conservation. Eighty‐six salmon from two temporal groups (1998–1999 and 2004–2006), representing three generations, were genotyped using a panel of eight microsatellites. Inspite of the recent decline in census numbers and the detection of the signs of a population bottleneck, the population exhibits a high level of genetic diversity, similar to that from other populations, and almost unchanged during the period of study [average allelic richness (A) = 14·0 and 13·9, and average heterozygosity (He) = 0·843 and 0·851 in 1998–1999 and 2004–2006, respectively]. The effective population size (Ne) estimated by two different temporal methods showed a consistent value around 80 salmon, whereas the estimates from the linkage disequilibrium (LD) method provided a value around 165 individuals for either sample. The recent growing number of salmon, as indicated by fisheries records, the relatively large estimates of the ratio Ne/N (with range 0·23–0·44 for the temporal estimates and 0·31–0·59 for the LD estimates) and the high levels of diversity found suggest that the population has not been greatly affected by the historical census declines and can be expected to recover in the future.

The human pseudoautosomal regions: a review for genetic epidemiologists

Two intervals of sequence identity at the tips of X and Y chromosomes, the human pseudoautosomal regions PAR1 and PAR2, have drawn interest from researchers in human genetics, cytogenetics, and evolutionary biology. However, they have been widely ignored in linkage and association studies. The pseudoautosomal regions (PARs) pair and recombine during meiosis like autosomes, but the recombination activity in PAR1 is extremely different between sexes. In men, it exhibits the highest recombination frequencies of the genome. Conflicting genetic maps of this region have been estimated by using three-generation pedigrees, sperm typing, and by using haplotypes from single nucleotide polymorphisms. Male genetic map lengths in the literature vary, and linkage disequilibrium has not been analyzed in detail. We review existing tools like genetic and physical maps, linkage disequilibrium methods, linkage and association analysis, implemented statistical methods, and their suitability for PARs. For multipoint linkage analysis, sex specificity must be indicated twice, first using sex-specific maps, and second by considering the sex-specific pseudoautosomal inheritance pattern. Currently, microsatellite panels and single nucleotide polymorphism chips do not contain sufficient numbers of markers in PAR1 and PAR2. The number of markers in PAR1, needed in indirect association studies, should be much larger than for autosomal regions alike in size, since linkage disequilibrium is very low. For genome-wide studies, it is essential to include pseudoautosomal markers since such expensive studies cannot afford to oversee pseudoautosomal linkage or association. This drawback could be solved with a sufficient number of markers, statistical methods that are adopted for the PARs, and their integration into softwares.

Association analysis of the constructed linkage maps covering TLR2 and TLR4 with clinical mastitis in Norwegian Red cattle

Toll-like receptors (TLR) are important cell-surface molecules mediating immune responses. Previous studies have identified TLR2 and TLR4 as potential candidate genes for disease resistance. In this study, dense linkage maps comprising single nucleotide polymorphisms (SNPs) have been constructed for the chromosomal regions harbouring TLR2 and TLR4 on bovine chromosome 17 and 8. The most likely marker orders for both regions were compared with the corresponding human map positions and used to reorder bovine scaffolds available from the bovine genome sequence assembly (Btau_3.1). A combined linkage and linkage disequilibrium method was used to investigate possible associations between the TLR genes and mastitis susceptibility recorded in the Norwegian Red cattle population. The analysis did not detect any significant association between the chromosomal regions surrounding TLR2 and TLR4 and mastitis in Norwegian Red cattle.

European Mathematical Genetics Meeting, Heidelberg, Germany, 12th–13th April 2007

European Mathematical Genetics Meeting, Heidelberg, Germany, 12^th–13^th April 2007

A potential bias in the temporal method for estimatingNein admixed populations under natural selection

Indirect genetic methods are frequently used to estimate the effective population size (N(e)) or effective number of breeders (N(b)) in natural populations. Although assumptions behind these methods are often violated, there have been few attempts to evaluate how accurate these estimates really are in practice. Here we investigate the influence of natural selection following a population admixture on the temporal method for estimating N(e). Our analytical and simulation results suggest that N(e) is often underestimated in this method when subpopulations differ substantially in allele frequencies and in reproductive success. The underestimation is exacerbated when true N(e) and the fraction of the low-fitness group are large. As an empirical example, we compared N(b) estimated in natural populations of steelhead trout (Oncorhynchus mykiss) using the temporal method (N(b[temp])) with estimates based on direct demographic methods (N(b[demo])) and the linkage disequilibrium method (N(b[LD])). While N(b[LD]) was generally in close agreement with N(b[demo]), N(b[temp]) was much lower in sample sets that were dominated by nonlocal hatchery fish with low reproductive success, as predicted by the analytical results. This bias in the temporal method, which arises when genes associated with a particular group of parents are selected against in the offspring sample, has not been widely appreciated before. Such situations may be particularly common when artificial propagation or translocations are used for conservation. The linkage disequilibrium method, which requires data from only one sample, is robust to this type of bias, although it can be affected by other factors.

Genome scan to detect quantitative trait loci for economically important traits in Holstein cattle using a dense SNP map

Quantitative trait loci (QTL) are chromosome regions which are significantly associated with the expression of a phenotypic trait in a particular population. Detection of a QTL is carried out using association with a genetic marker, such as a single nucleotide polymorphism (SNP), which is in linkage disequilibrium (LD) with the QTL. The two main categories of association studies are linkage analyses (LA), which consider LD within families and linkage disequilibrium methods, which make use of LD across an entire population. The recent reduction in genotyping costs has allowed for testing individuals for a large number of SNP. This substantial increase in genotypic data has lead to denser marker distributions on the bovine genome thus potentially increasing the power of QTL detection studies. The objective of this study was to scan the bovine genome to detect QTL for 305 day lactation milk yield (MY), 305 day lactation fat yield (FY), 305 day lactation protein yield (PY), herd life (HL), somatic cell score (SCS), interval from calving to first service in cows (CTFS) and age at first service in heifers (AFS). HL is a measure of longevity measured in the number of lactations a cow stays in the herd. SCS refers to the amount of somatic cells a cow has in her milk and is an important indicator trait for mastitis. CTFS is the period from parturition to first insemination in days and AFS is the age in days at which a heifer was artificially inseminated for the first time. Fertility traits, such as CTFS and AFS, are indicators of reproductive efficiency.

Simulations Provide Support for the Common Disease–Common Variant Hypothesis

The success of mapping genes involved in complex diseases, using association or linkage disequilibrium methods, depends heavily on the number and frequency of susceptibility alleles of these genes. These methods will be economically and statistically feasible if common diseases are usually influenced by one or a few susceptibility alleles at each locus (common disease-common variant, CDCV, hypothesis), but not so if there is a high degree of allelic heterogeneity. Here, we use forward-time population simulations to investigate the impact of various genetic and demographic factors on the allelic spectra of human diseases, on the basis of two models proposed by Reich and Lander and by Pritchard. Factors considered are more complex demographies, a finite-allele mutation model, population structure and migration, and interaction between disease susceptibility loci. The conclusion is that the CDCV hypothesis holds and that the phenomenon is caused by transient effects of demography (population expansion). As a result, we devise a multilocus generalization of the Reich and Lander model and demonstrate how interaction between loci with respect to their response to selection may lead to complex effects. We discuss the implications for mapping of complex diseases.

Effect of linkage disequilibrium between markers in linkage and association analyses

Contributions to Group 17 of the Genetic Analysis Workshop 15 considered dense markers in linkage disequilibrium (LD) in the context of either linkage or association analysis. Three contributions reported on methods for modeling LD or selecting a subset of markers in linkage equilibrium to perform linkage analysis. When all markers were used without modeling LD, inflated evidence for linkage was observed when parental genotypes were missing. All methods for handling LD led to some decreased linkage evidence. Two groups performed a genome-wide association scan using either mixed models to account for known or unknown relatedness between individuals, trend tests or combination statistics. All methods failed to detect four of the eight simulated loci because of low LD in some regions. Three groups performed association analysis using simulated dense markers on chromosome 6, where a simulated HLA-DRB1 locus played a major role in disease susceptibility along with two additional loci of smaller effect. The overall conditional genotype method correctly identified both additional loci while a novel transmission disequilibrium test-statistic to combine studies with non-overlapping markers identified one HLA locus after stratifying on the parental HLA-DRB1 genotypes; LD mapping using the Malécot model mapped two loci in this region, even when using greatly reduced marker density. While LD between markers appears to be a nuisance that may cause spurious linkage results with missing parental genotypes in linkage analysis, association analysis thrives on LD, and disease genes fail to be detected in regions of low LD.

Pattern-Recognition Techniques with Haplotype Analysis in Pharmacogenomics

Single nucleotide polymorphisms (SNPs) can be used in clinical association studies to determine the contribution of genes to drug efficacy. However, it would be extremely inefficient to test all the 10 million common SNPs for an association study. Here we review haplotype analysis and pattern-recognition techniques to systematically select candidate SNPs for candidate-gene association studies in pharmacogenomics. First, we survey linkage disequilibrium methods to identify tag SNPs and explore the use of haplotypes as genetic markers that are correlated and associated with drug efficacy. Secondly, we investigate pattern-recognition algorithms and statistical analyses to assess drug efficacy based on SNPs and other factors. Finally, we study pattern-recognition approaches to evaluate the epistasis among genes and SNPs. These techniques may provide tools for clinical association studies and help find genes/SNPs involved in responses to therapeutic drugs or adverse drug reactions.

Demographic and Genetic Estimates of Effective Population and Breeding Size in the AmphibianRana temporaria

Genetic methods for estimating effective population size ( Ne) or the effective number of breeders ( Nb) have become popular, but comparisons of these estimates with demographic estimates of Ne and Nb are rare, especially in anurans. We used three genetic (linkage disequilibrium, temporal moments, Bayesian coalescent-based method) and three demographic models, the latter considering number of breeding individuals, sex ratio, reproductive skew, and other demographic data, to estimate Ne and Nb in two subarctic populations (T and P) of the common frog Rana temporaria, subject to long-term capture-recapture studies. Demographic estimates of Ne based on total population size ( Ne ([T])= 44.5-56.9; Ne ([P])= 68.8-93.7) deviated markedly from the genetic estimates obtained using the linkage disequilibrium method ( Ne ([T])= 97.1; Ne ([P])= 13.2). The demographic estimates of Nb, taking into consideration sex ratio and variance in reproductive success ( Nb ([T])= 10.1-39.7; Nb ([P])= 3.9-21.3), were higher than the genetic estimates ( Nb ([T])= 3.7-5.4; Nb ([P])= 3.5-3.9). The main factors affecting the effective size estimates were sex ratio and reproductive skew. The discrepancies between corresponding Ne and Nb estimates highlight the sensitivity of both demographic and genetic estimates on their underlying assumptions. Yet the ratios of effective or breeding effective size to the census population size were similar to those reported earlier for anurans, reinforcing the view that the discrepancy between actual and effective breeding sizes in anuran populations is typically very large.

A bias correction for estimates of effective population size based on linkage disequilibrium at unlinked gene loci*

Analysis of linkage disequilibrium (\(\hat{r}^2\)=mean squared correlation of allele frequencies at different gene loci) provides a means of estimating effective population size (N e) from a single sample, but this method has seen much less use than the temporal method (which requires at least two samples). It is shown that for realistic numbers of loci and alleles, the linkage disequilibrium method can provide precision comparable to that of the temporal method. However, computer simulations show that estimates of N e based on \(\hat{r}^2\) for unlinked, diallelic gene loci are sharply biased downwards (\(\hat{N}_{\rm e}/N <0.1\) in some cases) if sample size (S) is less than true N e. The bias is shown to arise from inaccuracies in published formula for \(E(\hat{r}^2)\) when S and/or N e are small. Empirically derived modifications to \(E(\hat{r}^2)\) for two mating systems (random mating and lifetime monogamy) effectively eliminate the bias (residual bias in \(\hat{N}_{\rm e}<5\)% in most cases). The modified method also performs well in estimating N e in non-ideal populations with skewed sex ratio or non-random variance in reproductive success. Recent population declines are not likely to seriously affect \(\hat{N}_{\rm e}\), but if N has recently increased from a bottleneck \(\hat{N}_{\rm e}\) can be biased downwards for a few generations. These results should facilitate application of the disequilibrium method for estimating contemporary N e in natural populations. However, a comprehensive assessment of performance of \(\hat{r}^2\) with highly polymorphic markers such as microsatellites is needed.

Defining haplotype blocks and tag single-nucleotide polymorphisms in the human genome.

Recent studies suggest that the genome is organized into blocks of haplotypes, and efforts to create a genome-wide haplotype map of single-nucleotide polymorphisms (SNPs) are already underway. Haplotype blocks are defined algorithmically and to date several algorithms have been proposed. However, little is known about their relative performance in real data or about the impact of allele frequencies and parameter choices on the detection of haplotype blocks and the markers that tag them. Here we present a formal comparison of two major algorithms, a linkage disequilibrium (LD)-based method and a dynamic programming algorithm (DPA), in three chromosomal regions differing in gene content and recombination rate. The two methods produced strikingly different results. DPA identified fewer and larger haplotype blocks as well as a smaller set of tag SNPs than the LD method. For both methods, the results were strongly dependent on the allele frequency. Decreasing the minor allele frequency led to an up to 3.7-fold increase in the number of haplotype blocks and tag SNPs. Definition of haploytpe blocks and tag SNPs was also sensitive to parameter changes, but the results could not be reconciled simply by parameter adjustment. These results show that two major methods for detecting haplotype blocks and tag SNPs can produce different results in the same data and that these results are sensitive to marker allele frequencies and parameter choices. More information is needed to guide the choice of method, marker allele frequencies, and parameters in the development of a haplotype map.

Multipoint linkage disequilibrium mapping for complex diseases.

Linkage disequilibrium (LD) or association studies using case-parent trios have become a common approach to locate unobserved susceptibility genes underlying complex diseases. With the availability of ever more dense marker maps, how to utilize the information carried by multiple markers simultaneously remains challenging. Recently, Liang et al. ([2001a] Am. J. Hum. Genet. 68: 937-950) proposed a multipoint LD method to estimate the location of a susceptibility gene within a framework map along with its sampling uncertainty. Two important features of this method are that 1) it uses all trios whether parents are heterozygous for a given marker or not, and 2) it provides a single test statistic for the null hypothesis of no linkage or no LD to the region, avoiding the multiple testing problem encountered when performing individual transmission disequilibrium tests (TDT) for each marker individually. In this paper, we discuss how this method can be expanded to address important issues pertaining to complex diseases in a unified fashion. These issues include, among others, gene-gene and gene-environment interactions, genetic heterogeneity, phenotypic refinement, and paternal vs. maternal transmission. We applied this method to asthmatic case-parent trios from the Collaborative Study on the Genetics of Asthma (CSGA), and found that the previous evidence for linkage and LD in a 13.6 cM region of chromosome 11 can be attributed to maternal transmission, while there was no evidence of excess paternal transmission. Furthermore, such discrepancy in preferential transmission was most evident among probands with early onset age (6 years old or younger).

Linkage disequilibrium mapping of a Verticillium dahliae resistance quantitative trait locus in tetraploid potato ( Solanum tuberosum) through a candidate gene approach.

We have used the linkage disequilibrium mapping method to test for an association between a candidate gene marker and resistance to Verticillium dahliae in tetraploid potato. A probe derived from the tomato Verticillium resistance gene ( Ve1) identified homologous sequences ( StVe1) in potato, which in a diploid population map to chromosome 9, in a position analogous to that of the tomato resistance gene. When a molecular marker closely linked (1.5 cM) to the homologues was used as a candidate gene marker on 137 tetraploid potato genotypes (mostly North American cultivars), the association between the marker and resistance was confirmed ( P<0.001). The amount of phenotypic variation in resistance explained by the allele of the STM1051 marker was greater than 10% and 25% in two subpopulations that were inferred from coancestry data matrix. Cloning of homologues from the highly resistant potato cv. Reddale indicates that the resistance quantitative trait locus (QTL) comprises at least an eleven-member family, encoding plant-specific leucine-rich repeat proteins highly similar to the tomato Ve genes. The sequence analysis shows that all homologues are uninterrupted open reading frames and thus represent putative functional resistance genes. This is the first time that the linkage disequilibrium method has been used to find an association between a resistance gene and a candidate gene marker in tetraploid potato. We have shown that it is possible to map QTL directly on already available potato cultivars, without developing a new mapping population.

Demographic and genetic estimates of effective population size (Ne) reveals genetic compensation in steelhead trout.

Estimates of effective population size (Ne) are required to predict the impacts of genetic drift and inbreeding on the evolutionary dynamics of populations. How the ratio of Ne to the number of sexually mature adults (N) varies in natural vertebrate populations has not been addressed. We examined the sensitivity of Ne/N to fluctuations of N and determined the major variables responsible for changing the ratio over a period of 17 years in a population of steelhead trout (Oncorhynchus mykiss) from Washington State. Demographic and genetic methods were used to estimate Ne. Genetic estimates of Ne were gained via temporal and linkage disequilibrium methods using data from eight microsatellite loci. DNA for genetic analysis was amplified from archived smolt scales. The Ne/N from 1977 to 1994, estimated using the temporal method, was 0.73 and the comprehensive demographic estimate of Ne/N over the same time period was 0.53. Demographic estimates of Ne indicated that variance in reproductive success had the most substantial impact on reducing Ne in this population, followed by fluctuations in population size. We found increased Ne/N ratios at low N, which we identified as genetic compensation. Combining the information from the demographic and genetic methods of estimating Ne allowed us to determine that a reduction in variance in reproductive success must be responsible for this compensation effect. Understanding genetic compensation in natural populations will be valuable for predicting the effects of changes in N (i.e. periods of high population density and bottlenecks) on the fitness and genetic variation of natural populations.

Genome-wide association study and mouse model identify interaction between RET and EDNRB pathways in Hirschsprung disease.

Genetic studies of Hirschsprung disease, a common congenital malformation, have identified eight genes with mutations that can be associated with this condition. Mutations at individual loci are, however, neither necessary nor sufficient to cause clinical disease. We conducted a genome-wide association study in 43 Mennonite family trios using 2,083 microsatellites and single-nucleotide polymorphisms and a new multipoint linkage disequilibrium method that searches for association arising from common ancestry. We identified susceptibility loci at 10q11, 13q22 and 16q23; the gene at 13q22 is EDNRB, encoding a G protein-coupled receptor (GPCR) and the gene at 10q11 is RET, encoding a receptor tyrosine kinase (RTK). Statistically significant joint transmission of RET and EDNRB alleles in affected individuals and non-complementation of aganglionosis in mouse intercrosses between Ret null and the Ednrb hypomorphic piebald allele are suggestive of epistasis between EDNRB and RET. Thus, genetic interaction between mutations in RET and EDNRB is an underlying mechanism for this complex disorder.

Population Admixture: Detection by Hardy-Weinberg Test and Its Quantitative Effects on Linkage-Disequilibrium Methods for Localizing Genes Underlying Complex Traits

In association studies searching for genes underlying complex traits, the results are often inconsistent, and population admixture has been recognized qualitatively as one major potential cause. Hardy-Weinberg equilibrium (HWE) is often employed to test for population admixture; however, its power is generally unknown. Through analytical and simulation approaches, we quantify the power of the HWE test for population admixture and the effects of population admixture on increasing the type I error rate of association studies under various scenarios of population differentiation and admixture. We found that (1) the power of the HWE test for detecting population admixture is usually small; (2) population admixture seriously elevates type I error rate for detecting genes underlying complex traits, the extent of which depends on the degrees of population differentiation and admixture; (3) HWE testing for population admixture should be performed with random samples or only with controls at the candidate genes, or the test can be performed for combined samples of cases and controls at marker loci that are not linked to the disease; (4) testing HWE for population admixture generally reduces false positive association findings of genes underlying complex traits but the effect is small; and (5) with population admixture, a linkage disequilibrium method that employs cases only is more robust and yields many fewer false positive findings than conventional case-control analyses. Therefore, unless random samples are carefully selected from one homogeneous population, admixture is always a legitimate concern for positive findings in association studies except for the analyses that deliberately control population admixture.