A new strategy for estimating recombination fractions between dominant markers from an F2 population

Although most high-density linkage maps have been constructed from codominant markers such as single-nucleotide polymorphisms (SNPs) and microsatellites due to their high linkage information, dominant markers can be expected to be even more significant as proteomic technique becomes widely applicable to generate protein polymorphism data from large samples. However, for dominant markers, two possible linkage phases between a pair of markers complicate the estimation of recombination fractions between markers and consequently the construction of linkage maps. The low linkage information of the repulsion phase and high linkage information of coupling phase have led geneticists to construct two separate but related linkage maps. To circumvent this problem, we proposed a new method for estimating the recombination fraction between markers, which greatly improves the accuracy of estimation through distinction between the coupling phase and the repulsion phase of the linked loci. The results obtained from both real and simulated F2 dominant marker data indicate that the recombination fractions estimated by the new method contain a large amount of linkage information for constructing a complete linkage map. In addition, the new method is also applicable to data with mixed types of markers (dominant and codominant) with unknown linkage phase.     

Modeling linkage disequilibrium in natural populations: the example of the Soay sheep population of St. Kilda, Scotland

The use of linkage disequilibrium to localize the genes underlying quantitative traits has received considerable attention in the livestock genetics community over the past few years. This has resulted in the investigation of linkage disequilibrium structures of several domestic livestock populations to assess their potential use in fine-mapping efforts. However, the linkage disequilibrium structure of free-living populations has been less well investigated. As the direct evaluation of linkage disequilibrium can be both time consuming and expensive the use of simulations that include as many aspects of population history as possible is advocated as an alternative. A simulation of the linkage disequilibrium structure of the Soay sheep population of St. Kilda, Scotland, is provided as an example. The simulated population showed significant decline of linkage disequilibrium with genetic distance and low levels of background linkage disequilibrium, indicating that the Soay sheep population is a viable resource for linkage disequilibrium fine mapping of quantitative trait loci.     

Power comparison of parametric and nonparametric linkage tests in small pedigrees

When the mode of inheritance of a disease is unknown, the LOD-score method of linkage analysis must take into account uncertainties in model parameters. We have previously proposed a parametric linkage test called "MFLOD," which does not require specification of disease model parameters. In the present study, we introduce two new model-free parametric linkage tests, known as "MLOD" and "MALOD." These tests are defined, respectively, as the LOD score and the admixture LOD score, maximized (subject to the same constraints as MFLOD) over disease-model parameters. We compared the power of these three parametric linkage tests and that of two nonparametric linkage tests, NPLall and NPLpairs, which are implemented in GENEHUNTER. With the use of small pedigrees and a fully informative marker, we found the powers of MLOD, NPLall, and NPLpairs to be almost equivalent to each other and not far below that of a LOD-score analysis performed under the assumption the correct genetic parameters. Thus, linkage analysis is not much hindered by uncertain mode of inheritance. The results also suggest that both parametric and nonparametric methods are suitable for linkage analysis of complex disorders in small pedigrees. However, whether these results apply to large pedigrees remains to be answered.     

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)     

Incorrect specification of marker allele frequencies: effects on linkage analysis.

Most current linkage analyses make use of highly polymorphic DNA markers. Assigning correct allele frequencies for these markers may be extremely difficult in particular study populations. Designation of erroneous frequencies may result in false-positive evidence for linkage, as well as in failure to correctly exclude linkage. These effects are most pronounced in small pedigrees with key individuals unavailable for typing. The power to correctly detect true linkage does not appear to be greatly affected by inaccurate allele frequencies. Before linkage analyses are performed for specific pedigrees, it is recommended that simulation analyses be performed, followed by uncertainty and sensitivity analyses.     

Genome-wide linkage scan of prostate cancer Gleason score and confirmation of chromosome 19q

Despite evidence that prostate cancer has a genetic etiology, it has been extremely difficult to confirm genetic linkage results across studies, emphasizing the large extent of genetic heterogeneity associated with this disease. Because prostate cancer is common—approximately one in six men will be diagnosed with prostate cancer in their life—genetic linkage studies are likely plagued by phenocopies (i.e., men with prostate cancer due to environmental or lifestyle factors), weakly penetrant alleles, or a combination of both, making it difficult to replicate linkage findings. One way to account for heterogeneous causes is to use clinical information that is related to the aggressiveness of disease as an endpoint for linkage analyses. Gleason grade is a measure of prostate tumor differentiation, with higher grades associated with more aggressive disease. This semi-quantitative score has been used as a quantitative trait for linkage analysis in several prior studies. Our aim was to determine if prior linkage reports of Gleason grade to specific loci could be replicated, and to ascertain if new regions of linkage could be found. Gleason scores were available for 391 affected sib pairs from 183 hereditary prostate cancer pedigrees as part of the PROGRESS study. Analyzing Gleason score as a quantitative trait, and using microsatellite markers, suggestive evidence for linkage (P-value ≤ 0.001) was found on chromosomes 19q and 5q, with P-values ≤ 0.01 observed on chromosomes 3q, 7q, and 16q. Our results confirm reports of Gleason score linkage to chromosome 19q and suggest new loci for further investigation.     

Assessing whether an allele can account in part for a linkage signal: the Genotype-IBD Sharing Test (GIST)

To fine map genes, investigators often test for disease-marker association in chromosomal regions with evidence for linkage. Given a marker allele tentatively associated with disease, one would ask if this allele, or one in linkage disequilibrium (LD) with it, could account in part for the observed linkage signal. This question can be addressed by determining if families selected on the basis of the presence of the tentatively associated allele show stronger evidence of linkage as measured by increased allele sharing identical by descent (IBD) by affected family members. However, common selection strategies can be biased for or against linkage in the marker region, even given no disease-marker association. We define unbiased selection schemes and extend the definition to allow weighted selection on the basis of all genotyped family members. For affected-sibship data, we describe three genotype-based weight variables, corresponding to dominant, recessive, and additive models. We then introduce a test for association of a family weight variable with excess IBD sharing. This test allows us to determine if the linkage signal in a region can be attributed in part to the presence of a marker allele, either because of direct involvement in disease etiology or because of LD with a predisposing genetic variant. For samples of 500 affected sib pairs, the tests are powerful in detection of genotype-IBD sharing association, even for disease models with sib relative risk as low as lambda S=1.1, or when evidence for linkage is absent because of sampling variation. This makes our method a new tool for detecting linkage as well as association, especially in regions harboring a candidate gene. We have implemented these methods in the software package GIST (Genotype-IBD Sharing Test).     

Comparison of microsatellites, single-nucleotide polymorphisms (SNPs) and composite markers derived from SNPs in linkage analysis

There is growing evidence that a map of dense single-nucleotide polymorphisms (SNPs) can outperform a map of sparse microsatellites for linkage analysis. There is also argument as to whether a clustered SNP map can outperform an evenly spaced SNP map. Using Genetic Analysis Workshop 14 simulated data, we compared for linkage analysis microsatellites, SNPs, and composite markers derived from SNPs. We encoded the composite markers in a two-step approach, in which the maximum identity length contrast method was employed to allow for recombination between loci. A SNP map 2.3 times as dense as a microsatellite map (approximately 2.9 cM compared to approximately 6.7 cM apart) provided slightly less information content (approximately 0.83 compared to approximately 0.89). Most inheritance information could be extracted when the SNPs were spaced < 1 cM apart. Comparing the linkage results on using SNPs or composite markers derived from them based on both 3 cM and 0.3 cM resolution maps, we showed that the inter-SNP distance should be kept small (< 1 cM), and that for multipoint linkage analysis the original markers and the derived composite markers had similar power; but for single point linkage analysis the resulting composite markers lead to more power. Considering all factors, such as information content, flexibility of analysis method, map errors, and genotyping errors, a map of clustered SNPs can be an efficient design for a genome-wide linkage scan.     

Linkage disequilibrium inflates type I error rates in multipoint linkage analysis when parental genotypes are missing

OBJECTIVES: Describe the inflation in nonparametric multipoint LOD scores due to inter-marker linkage disequilibrium (LD) across many markers with varied allele frequencies. METHOD: Using simulated two-generation families with and without parents, we conducted nonparametric multipoint linkage analysis with 2 to 10 markers with minor allele frequencies (MAF) of 0.5 and 0.1. RESULTS: Misspecification of population haplotype frequencies by assuming linkage equilibrium caused inflated multipoint LOD scores due to inter-marker LD when parental genotypes were not included. Inflation increased as more markers in LD were included and decreased as markers in equilibrium were added. When marker allele frequencies were unequal, the r2 measure of LD was a better predictor of inflation than D'. CONCLUSION: This observation strongly supports the evaluation of LD in multipoint linkage analyses, and further suggests that unaccounted for LD may be suspected when two-point and multipoint linkage analyses show a marked disparity in regions with elevated r2 measures of LD. Given the increasing popularity of high-density genome-wide SNP screens, inter-marker LD should be a concern in future linkage studies.     

Hereditary spastic paraplegia: LOD-score considerations for confirmation of linkage in a heterogeneous trait.

Hereditary spastic paraplegia (HSP) is a degenerative disorder of the motor system, defined by progressive weakness and spasticity of the lower limbs. HSP may be inherited as an autosomal dominant (AD), autosomal recessive, or an X-linked trait. AD HSP is genetically heterogeneous, and three loci have been identified so far: SPG3 maps to chromosome 14q, SPG4 to 2p, and SPG4a to 15q. We have undertaken linkage analysis with 21 uncomplicated AD families to the three AD HSP loci. We report significant linkage for three of our families to the SPG4 locus and exclude several families by multipoint linkage. We used linkage information from several different research teams to evaluate the statistical probability of linkage to the SPG4 locus for uncomplicated AD HSP families and established the critical LOD-score value necessary for confirmation of linkage to the SPG4 locus from Bayesian statistics. In addition, we calculated the empirical P-values for the LOD scores obtained with all families with computer simulation methods. Power to detect significant linkage, as well as type I error probabilities, were evaluated. This combined analytical approach permitted conclusive linkage analyses on small to medium-size families, under the restrictions of genetic heterogeneity.     

The effectiveness of pseudomagic traits in promoting divergence and enhancing local adaptation*

“Magic traits,” in which the same trait is both under divergent ecological selection and forms the basis of assortative mating, have been sought after due to their supposed unique ability to promote divergence with gene flow. Here, we ask how unique magic traits are, by exploring whether a tightly linked complex of a locus under divergent selection and a locus that acts as a mating cue can mimic a magic trait in its divergence. We find that these “pseudomagic traits” can be very effective in promoting divergence; with tight linkage they are essentially as effective as a magic trait and with loose linkage, and even no linkage, divergence can still be enhanced. Distinguishing between magic and pseudomagic traits in empirical cases may thus not be important when inferring their role in divergence. The ability of divergence in the mating trait to drive divergence in the ecological trait by lowering the effective migration rate, which occurs somewhat even without linkage, is particularly striking; magic traits are typically considered to have the other direction of causality. Our results thus suggest that divergence in a mating trait can at least modestly increase local adaption by allowing more ecological divergence, particularly with tighter linkage.     

成人型多囊肾病的遗传研究

３＇ＨＶＲ是成人型多囊肾病基因诊断中最常用的探针。我们分析了５１个无亲缘关系健康学生和３个成人多囊肾病家系的３＇ＨＶＲ－ＰｖｕＩＩ ＲＦＬＰ,所得多态信息用计算机软件ＬＩＮＫ－ＡＧＥ和ＨＯＭＯＧ进行连锁分析和同质性检验,其中１个家系致病基因位点与３＇ＨＶＲ不连锁,因而判定为ｎｏｎ ＰＫＤ１。剩下的两个家系中１个有明显的重组,但还不能判定为ｎｏｎ ＰＫＤ１,另１个与３＇ＨＶＲ连锁,属于ＰＫＤ１。成人     

Detection of linkage for heterogeneous disorders by using multipoint linkage analysis.

We have compared the efficiency of the lod score test which assumes heterogeneity (lod2) to the standard lod score test which assumes homogeneity (lod1) when three-point linkage analysis is used in successive map intervals. If it is assumed that a gene located midway between two linked marker loci is responsible for a proportion of disease cases, then the lod1 test loses power relative to the lod2 test, as the proportion of linked families decreases, as the flanking markers are more closely linked, and as more map intervals are tested. Moreover, when multipoint analysis is used, linkage for a disease gene is more likely to be incorrectly excluded from a complete and dense linkage map if true genetic heterogeneity is ignored. We thus conclude that, in general, the lod2 linkage test is more efficient for detecting a true linkage when a complete genetic marker map is screened for a heterogeneous disorder.     

Comparison off genetic distance and order off DNA markers in five populations of rice.

A group of about 300 evenly distributed DNA markers from a high density RFLP linkage map of rice constructed using an F2 population derived from a japonica variety, Nipponbare, and an indica variety, Kasalath, were used to evaluate gene order and genetic distance in four other rice mapping populations. The purpose of this study was to determine the degree to which information gained from the high density linkage map could be applied to other mapping populations, particularly with regard to its utility in bridging quantitative traits and molecular and physical mapping information. The mapping populations consisted of two F2 populations derived from Dao Ren Qiao/Fl-1084 and Kinandangputi/Fl-1007, recombinant inbred lines from Asominori/IR24, and a backcross population from Sasanishiki/Habataki//Sasanishiki. All DNA markers commonly mapped in the four populations showed the same linkage groups as in the Nipponbare/Kasalath linkage map with conserved linkage order. The genetic distance between markers among the different populations did not vary to a significant level in any of the 12 chromosomes. The differences in some markers could be attributed to the size of the population used in the construction of the linkage maps. Furthermore, the conservation of linkage order found in the distal region of chromosomes 11 and 12 was also confirmed in the RFLP maps based on the four populations of rice. These suggest that any major genetic information from the Nipponbare/Kasalath map can be expected to be approximately the same in other crosses or populations. This high density RFLP linkage map, which is being utilized in constructing a physical map of rice, can be very useful in interpreting genome structure with great accuracy in other populations. Key words : linkage map, japonica, indica, gene order, genetic distance.     

High-resolution joint linkage disequilibrium and linkage mapping of quantitative trait loci based on sibship data

This paper proposes variance component models for high resolution joint linkage disequilibrium (LD) and linkage mapping of quantitative trait loci (QTL) based on sibship data; this can include population data if independent individuals are treated as single sibships. One application of these models is late onset complex disease gene mapping, when parental data are not available. The models simultaneously incorporate both LD and linkage information. The LD information is contained in mean coefficients of sibship data. The linkage information is contained in the variance-covariance matrices of trait values for sibships with at least two siblings. We derive formulas for calculating the probability of sharing two trait alleles identical by descent (IBD) for sibpairs in interval mapping of QTL; this is the coefficient of dominant variance of the trait covariance of sibpairs on major QTL. To investigate the performance of the formulas, we calculate the numerical values via the formulas and get satisfactory approximations. We compare the power and sample sizes for both LD and linkage mapping. By simulation and theoretical analysis, we compare the results with those of Fulker and Abecasis "AbAw" approach. It is well known that the resolution of linkage analysis can be low for complex disease gene mapping. LD mapping, on the other hand, can increase mapping precision and is useful in high resolution mapping. Linkage analysis is less sensitive to population subdivisions and admixtures. The level of LD is sensitive to population stratification which may easily lead to spurious association. Performing a joint analysis of LD and linkage mapping can help to overcome the limits of both approaches. Moreover, the advantages of the two complementary strategies can be utilized maximally. In practice, linkage analysis may be performed using pedigree data to identify suggestive linkage between markers and trait loci based on a sparse marker map. In the presence of linkage, joint LD and linkage mapping can be carried out to do fine gene mapping based on a dense genetic map using both pedigree and population data. Population and pedigree data of any type can be combined to perform a joint analysis of high resolution LD and linkage mapping of QTL by generalizing the method.     

The posterior probability of linkage allowing for linkage disequilibrium and a new estimate of disequilibrium between a trait and a marker

The posterior probability of linkage (PPL) statistic has been developed as a method for the rigorous accumulation of evidence for or against linkage allowing for both intra- and inter-sample heterogeneity. To date, the method has assumed linkage equilibrium between alleles at the trait locus and the marker locus. We now generalize the PPL to allow for linkage disequilibrium (LD), by incorporating variable phase probabilities into the underlying linkage likelihood. This enables us to recover the marginal posterior density of the recombination fraction, integrating out nuisance parameters of the trait model, including the locus heterogeneity (admixture) parameter, as well as a vector of LD parameters. The marginal posterior density can then be updated across data subsets or new data as they become available, while allowing parameters of the trait model to vary between data sets. The method applies immediately to general pedigree structures and to markers with multiple alleles. In the case of SNPs, the likelihood is parameterized in terms of the standard single LD parameter D'; and it therefore affords a mechanism for estimation of D' between the marker and the trait, again, without fixing the parameters of the trait model and allowing for updating across data sets. It is even possible to allow for a different associated allele in different populations, while accumulating information regarding the strength of LD. While a computationally efficient implementation for multi-allelic markers is still in progress, we have implemented a version of this new LD-PPL for SNPs and evaluated its performance in nuclear families. Our simulations show that LD-PPLs tend to be larger than PPLs (stronger evidence in favor of linkage/LD) with increased LD level, under a variety of generating models; while in the absence of linkage and LD, LD-PPLs tend to be smaller than PPLs (stronger evidence against linkage). The estimate of D' also behaves well even in relatively small, heterogeneous samples.     

Construction of a composite sorghum genome map and comparison with sugarcane, a related complex polyploid

 A sorghum composite linkage map was constructed with two recombinant inbred line populations using heterologous probes already mapped on maize and sugarcane. This map includes 199 loci revealed by 188 probes and distributed on 13 linkage groups. A comparison based on 84 common probes was performed between the sorghum composite map and a map of a sugarcane (Saccharum spp.) cultivar being developed and presently comprising 10 tentative linkage groups. A straight synteny was observed for 2 pairs of linkage groups; in two cases, 1 sorghum linkage group corresponded to 2 or 3 sugarcane linkage groups, respectively; in two cases 1 sugarcane link- age group corresponded to 2 separate sorghum linkage groups; for 2 sorghum linkage groups, no complete correspondance was found in the sugarcane genome. In most cases loci appeared to be colinear between homoeologous chromosomal segments in sorghum and sugarcane. These results are discussed in relation to published data on sorghum genomic maps, with specific reference to the genetic organization of sugarcane cultivars, and they, illustrate how investigations on relatively simple diploid genomes as sorghum will facilitate the mapping of related polyploid species such as sugarcane. Received: 12 August 1996 / Accepted: 30 August 1996     

Joint modeling of linkage and association: identifying SNPs responsible for a linkage signal

Once genetic linkage has been identified for a complex disease, the next step is often association analysis, in which single-nucleotide polymorphisms (SNPs) within the linkage region are genotyped and tested for association with the disease. If a SNP shows evidence of association, it is useful to know whether the linkage result can be explained, in part or in full, by the candidate SNP. We propose a novel approach that quantifies the degree of linkage disequilibrium (LD) between the candidate SNP and the putative disease locus through joint modeling of linkage and association. We describe a simple likelihood of the marker data conditional on the trait data for a sample of affected sib pairs, with disease penetrances and disease-SNP haplotype frequencies as parameters. We estimate model parameters by maximum likelihood and propose two likelihood-ratio tests to characterize the relationship of the candidate SNP and the disease locus. The first test assesses whether the candidate SNP and the disease locus are in linkage equilibrium so that the SNP plays no causal role in the linkage signal. The second test assesses whether the candidate SNP and the disease locus are in complete LD so that the SNP or a marker in complete LD with it may account fully for the linkage signal. Our method also yields a genetic model that includes parameter estimates for disease-SNP haplotype frequencies and the degree of disease-SNP LD. Our method provides a new tool for detecting linkage and association and can be extended to study designs that include unaffected family members.     

Regression models for linkage heterogeneity applied to familial prostate cancer

Linkage heterogeneity frequently occurs for complex genetic diseases, and statistical methods must account for it to avoid severe loss in power to discover susceptibility genes. A common method to allow for only a fraction of linked pedigrees is to fit a mixture likelihood and then to test for linkage homogeneity, given linkage (admixture test), or to test for linkage while allowing for heterogeneity, using the heterogeneity LOD (HLOD) score. Furthermore, features of the families, such as mean age at diagnosis, may help to discriminate families that demonstrate linkage from those that do not. Pedigree features are often used to create homogeneous subsets, and LOD or HLOD scores are then computed within the subsets. However, this practice introduces several problems, including reduced power (which results from multiple testing and small sample sizes within subsets) and difficulty in interpretation of results. To address some of these limitations, we present a regression-based extension of the mixture likelihood for which pedigree features are used as covariates that determine the probability that a family is the linked type. Some advantages of this approach are that multiple covariates can be used (including quantitative covariates), covariates can be adjusted for each other, and interactions among covariates can be assessed. This new regression method is applied to linkage data for familial prostate cancer and provides new insights into the understanding of prostate cancer linkage heterogeneity.