Estimation of multilocus linkage disequilibria in diploid populations with dominant markers

Analysis of population structure and organization with DNA-based markers can provide important information regarding the history and evolution of a species. Linkage disequilibrium (LD) analysis based on allelic associations between different loci is emerging as a viable tool to unravel the genetic basis of population differentiation. In this article, we derive the EM algorithm to obtain the maximum-likelihood estimates of the linkage disequilibria between dominant markers, to study the patterns of genetic diversity for a diploid species. The algorithm was expanded to estimate and test linkage disequilibria of different orders among three dominant markers and can be technically extended to manipulate an arbitrary number of dominant markers. The feasibility of the proposed algorithm is validated by an example of population genetic studies of hickory trees, native to southeastern China, using dominant random amplified polymorphic DNA markers. Extensive simulation studies were performed to investigate the statistical properties of this algorithm. The precision of the estimates of linkage disequilibrium between dominant markers was compared with that between codominant markers. Results from simulation studies suggest that three-locus LD analysis displays increased power of LD detection relative to two-locus LD analysis. This algorithm is useful for studying the pattern and amount of genetic variation within and among populations.     

A haplotype-based algorithm for multilocus linkage disequilibrium mapping of quantitative trait loci with epistasis

For tightly linked loci, cosegregation may lead to nonrandom associations between alleles in a population. Because of its evolutionary relationship with linkage, this phenomenon is called linkage disequilibrium. Today, linkage disequilibrium-based mapping has become a major focus of recent genome research into mapping complex traits. In this article, we present a new statistical method for mapping quantitative trait loci (QTL) of additive, dominant, and epistatic effects in equilibrium natural populations. Our method is based on haplotype analysis of multilocus linkage disequilibrium and exhibits two significant advantages over current disequilibrium mapping methods. First, we have derived closed-form solutions for estimating the marker-QTL haplotype frequencies within the maximum-likelihood framework implemented by the EM algorithm. The allele frequencies of putative QTL and their linkage disequilibria with the markers are estimated by solving a system of regular equations. This procedure has significantly improved the computational efficiency and the precision of parameter estimation. Second, our method can detect marker-QTL disequilibria of different orders and QTL epistatic interactions of various kinds on the basis of a multilocus analysis. This can not only enhance the precision of parameter estimation, but also make it possible to perform whole-genome association studies. We carried out extensive simulation studies to examine the robustness and statistical performance of our method. The application of the new method was validated using a case study from humans, in which we successfully detected significant QTL affecting human body heights. Finally, we discuss the implications of our method for genome projects and its extension to a broader circumstance. The computer program for the method proposed in this article is available at the webpage http://www.ifasstat.ufl.edu/genome/~LD.     

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.     

The power to detect linkage disequilibrium with quantitative traits in selected samples

Results from power studies for linkage detection have led to many ongoing and planned collections of phenotypically extreme nuclear families. Given the great expense of collecting these families and the imminent availability of a dense diallelic marker map, the families are likely to be used in allelic-association as well as linkage studies. However, optimal selection strategies for linkage may not be equally powerful for association. We examine the power to detect linkage disequilibrium for quantitative traits after phenotypic selection. The results encompass six selection strategies that are in widespread use, including single selection (two designs), affected sib pairs, concordant and discordant pairs, and the extreme-concordant and -discordant design. Selection of sibships on the basis of one extreme proband with high or low trait scores provides as much power as discordant sib pairs but requires the screening and phenotyping of substantially fewer initial families from which to select. Analysis of the role of allele frequencies within each selection design indicates that common trait alleles generally offer the most power, but similarities between the marker- and trait-allele frequencies are much more important than the trait-locus frequency alone. Some of the most widespread selection designs, such as single selection, yield power gains only when both the marker and quantitative trait loci (QTL) are relatively rare in the population. In contrast, discordant pairs and the extreme-proband design provide power for the broadest range of QTL-marker-allele frequency differences. Overall, proband selection from either tail provides the best balance of power, robustness, and simplicity of ascertainment for family-based association analysis.     

On different approximations to multilocus identity-by-descent calculations and the resulting power of variance component-based linkage analysis

An empirical comparison between three different methods for estimation of pair-wise identity-by-descent (IBD) sharing at marker loci was conducted in order to quantify the resulting differences in power and localization precision in variance components-based linkage analysis. On the examined simulated, error-free data set, it was found that an increase in accuracy of allele sharing calculation resulted in an increase in power to detect linkage. Linkage analysis based on approximate multi-marker IBD matrices computed by a Markov chain Monte Carlo approach was much more powerful than linkage analysis based on exact single-marker IBD probabilities. A "multiple two-point" approximation to true "multipoint" IBD computation was found to be roughly intermediate in power. Both multi-marker approaches were similar to each other in accuracy of localization of the quantitative trait locus and far superior to the single-marker approach. The overall conclusions of this study with respect to power are expected to also hold for different data structures and situations, even though the degree of superiority of one approach over another depends on the specific circumstances. It should be kept in mind, however, that an increase in computational accuracy is expected to go hand in hand with a decrease in robustness to various sources of errors.     

Optimum spacing of genetic markers for determining linkage between marker loci and quantitative trait loci

The cost of experiments aimed at determining linkage between marker loci and quantitative trait loci (QTL) was investigated as a function of marker spacing and number of individuals scored. It was found that for a variety of experimental designs, fairly wide marker spacings (ca. 50 cM) are optimum or close to optimum for initial studies of marker-QTL linkage, in the sense of minimizing overall cost of the experiment. Thus, even when large numbers of more or less evenly spaced markers are available, it will not always be cost effective to make full utilization of this capacity. This is particularly true when costs of rearing and trait evaluation per individual scored are low, as when marker data are obtained on individuals raised and evaluated for quantitative traits as part of existing programs. When costs of rearing and trait evaluation per individual scored are high, however, as in human family data collection carried out primarily for subsequent marker — QTL analyses, or when plants or animals are raised specifically for purposes of marker — QTL linkage experiments, optimum spacing may be rather narrow. It is noteworthy that when marginal costs of additional markers or individuals are constant, total resources allocated to a given experiment will determine total number of individuals sampled, but not the optimal marker spacing.     

Combined linkage and association mapping of quantitative trait loci by multiple markers

Using multiple diallelic markers, variance component models are proposed for high-resolution combined linkage and association mapping of quantitative trait loci (QTL) based on nuclear families. The objective is to build a model that may fully use marker information for fine association mapping of QTL in the presence of prior linkage. The measures of linkage disequilibrium and the genetic effects are incorporated in the mean coefficients and are decomposed into orthogonal additive and dominance effects. The linkage information is modeled in variance-covariance matrices. Hence, the proposed methods model both association and linkage in a unified model. On the basis of marker information, a multipoint interval mapping method is provided to estimate the proportion of allele sharing identical by descent (IBD) and the probability of sharing two alleles IBD at a putative QTL for a sib-pair. To test the association between the trait locus and the markers, both likelihood-ratio tests and F-tests can be constructed on the basis of the proposed models. In addition, analytical formulas of noncentrality parameter approximations of the F-test statistics are provided. Type I error rates of the proposed test statistics are calculated to show their robustness. After comparing with the association between-family and association within-family (AbAw) approach by Abecasis and Fulker et al., it is found that the method proposed in this article is more powerful and advantageous based on simulation study and power calculation. By power and sample size comparison, it is shown that models that use more markers may have higher power than models that use fewer markers. The multiple-marker analysis can be more advantageous and has higher power in fine mapping QTL. As an application, the Genetic Analysis Workshop 12 German asthma data are analyzed using the proposed methods.     

Investigation of altering single-nucleotide polymorphism density on the power to detect trait loci and frequency of false positive in nonparametric linkage analyses of qualitative traits

Genome-wide linkage analysis using microsatellite markers has been successful in the identification of numerous Mendelian and complex disease loci. The recent availability of high-density single-nucleotide polymorphism (SNP) maps provides a potentially more powerful option. Using the simulated and Collaborative Study on the Genetics of Alcoholism (COGA) datasets from the Genetics Analysis Workshop 14 (GAW14), we examined how altering the density of SNP marker sets impacted the overall information content, the power to detect trait loci, and the number of false positive results. For the simulated data we used SNP maps with density of 0.3 cM, 1 cM, 2 cM, and 3 cM. For the COGA data we combined the marker sets from Illumina and Affymetrix to create a map with average density of 0.25 cM and then, using a sub-sample of these markers, created maps with density of 0.3 cM, 0.6 cM, 1 cM, 2 cM, and 3 cM. For each marker set, multipoint linkage analysis using MERLIN was performed for both dominant and recessive traits derived from marker loci. Our results showed that information content increased with increased map density. For the homogeneous, completely penetrant traits we created, there was only a modest difference in ability to detect trait loci. Additionally, as map density increased there was only a slight increase in the number of false positive results when there was linkage disequilibrium (LD) between markers. The presence of LD between markers may have led to an increased number of false positive regions but no clear relationship between regions of high LD and locations of false positive linkage signals was observed.     

Examination of X chromosome markers in Rett syndrome: exclusion mapping with a novel variation on multilocus linkage analysis.

Rett syndrome is a neurologic disorder characterized by early normal development followed by regression, acquired deceleration of head growth, autism, ataxia, and stereotypic hand movements. The exclusive occurrence of the syndrome in females and the occurrence of a few familial cases with inheritance through maternal lines suggest that this disorder is most likely secondary to a mutation on the X chromosome. To address this hypothesis and to identify candidate regions for the Rett syndrome gene locus, genotypic analysis was performed in two families with maternally related affected half-sisters by using 63 DNA markers from the X chromosome. Maternal and paternal X chromosomes from the affected sisters were separated in somatic cell hybrids and were examined for concordance/discordance of maternal alleles at the tested loci. Thirty-six markers were informative in at least one of the two families, and 25 markers were informative in both families. Twenty loci were excluded as candidates for the Rett syndrome gene, on the basis of discordance for maternal alleles in the half-sisters. Nineteen of the loci studied were chosen for multipoint linkage analysis because they have been previously genetically mapped using a large number of meioses from reference families. Using the exclusion criterion of a lod score less than -2, we were able to exclude the region between the Duchenne muscular dystrophy locus and the DXS456 locus. This region extends from Xp21.2 to Xq21-q23. The use of the multipoint linkage analysis approach outlined in this study should allow the exclusion of additional regions of the X chromosome as new markers are analyzed. This in turn will result in a defined region of the X chromosome that should be searched for candidate sequences for the Rett syndrome gene in both familial and sporadic cases.     

Comparison of the power and accuracy of biallelic and microsatellite markers in population-based gene-mapping methods.

Because of their great abundance and amenability to fully automated genotyping, single-nucleotide polymorphisms (SNPs) and simple insertion/deletion are emerging as a new generation of markers for positional cloning. Although the efficiency and cost associated with the markers are important in the mapping of human disease genes, the power to detect the linkage between the marker and the disease locus, as well as the accuracy of the estimation of the map location of the disease gene, dictate the selection of the markers. Both the power and the accuracy depend not only on the type of the markers but also on other factors, such as the age of the disease mutation, the magnitude of the genetic effect, the marker-allele distribution in the population, mutation rates of marker loci, the frequency of the disease allele, the recombination fraction, and the methods for mapping the human disease genes. In this article, we develop a mathematical framework and the analytical formulas for calculation of the power and the accuracy and investigate the impact that the aforementioned factors have on the power and the accuracy, by using two population-based gene-mapping methods-likelihood-based linkage-disequilibrium mapping and the transmission/disequilibrium test, for both biallelic SNPs and microsatellites. These studies provide not only guidance in selection of the markers and in the design of the sample scheme for positional cloning but also insight into the biological bases of the mapping of human disease genes.     

Effect of two- and three-locus linkage disequilibrium on the power to detect marker/phenotype associations

There has been much recent interest in describing the patterns of linkage disequilibrium (LD) along a chromosome. Most empirical studies that have examined this issue have concentrated on LD between collections of pairs of markers and have not considered the joint effect of a group of markers beyond these pairwise connections. Here, we examine many different patterns of LD defined by both pairwise and joint multilocus LD terms. The LD patterns we considered were chosen in part by examining those seen in real data. We examine how changes in these patterns affect the power to detect association when performing single-marker and haplotype-based case-control tests, including a novel haplotype test based on contrasting LD between affected and unaffected individuals. Through our studies we find that differences in power between single-marker tests and haplotype-based tests in general do not appear to be large. Where moderate to high levels of multilocus LD exist, haplotype tests tend to be more powerful. Single-marker tests tend to prevail when pairwise LD is high. For moderate pairwise values and weak multilocus LD, either testing strategy may come out ahead, although it is also quite likely that neither has much power.     

PKU locus: Genetic linkage with human amylase (Amy) loci and assignment to linkage group I

Summary The linked alpha-amylase loci Amy 1 and Amy 2 were evaluated for their linkage relationship to the PKU locus using data collected from two (one Czech and one Polish) groups of families. The five sibships informative for Amy 1: PKU give a score of 1.505 at =0.00 and the eight sibships informative for Amy 2: PKU give a score of 2.709 at =0.00. Due to the tandem position of Amy 1 and Amy 2 loci, these data could be combined, and linkage between Amy and PKU loci established with a score 4.214 at =0.00. The practical significance of the linkage, especially for identifying PKU allele carriers, is emphasized.     

Linkage disequilibrium analysis of biallelic DNA markers, human quantitative trait loci, and threshold-defined case and control subjects

Linkage disequilibrium (LD) mapping has been applied to many simple, monogenic, overtly Mendelian human traits, with great success. However, extensions and applications of LD mapping approaches to more complex human quantitative traits have not been straightforward. In this article, we consider the analysis of biallelic DNA marker loci and human quantitative trait loci in settings that involve sampling individuals from opposite ends of the trait distribution. The purpose of this sampling strategy is to enrich samples for individuals likely to possess (and not possess) trait-influencing alleles. Simple statistical models for detecting LD between a trait-influencing allele and neighboring marker alleles are derived that make use of this sampling scheme. The power of the proposed method is investigated analytically for some hypothetical gene-effect scenarios. Our studies indicate that LD mapping of loci influencing human quantitative trait variation should be possible in certain settings. Finally, we consider possible extensions of the proposed methods, as well as areas for further consideration and improvement.     

Characterization and linkage mapping often sheep microsatellite markers derived from a sheep x hamster cell hybrid

A cosmid library has been constructed from a sheep x hamster cell hybrid containing sheep chromosome t₁, rob (6;24). Clones containing sheep DNA were identified by hybridizing to a total sheep genomic DNA probe. Small fragments (<500 bp) containing (AC)_n microsatellites were subcloned and sequenced. Ten microsatellite markers were characterized and six were mapped back to chromosomes 6 and 24. The remaining microsatellites mapped to chromosome 26, which was shown to be present in a small proportion of cells of the cell line.     

A simulation study on the performance of differentiation-based methods to detect selected loci using linked neutral markers

We investigated the performance of two of the most popular differentiation-based methods to detect loci under selection (dfdist/fdist and bayescan) in order to ascertain the average chromosome map distance between the detected outlier markers and the nearest loci under selection. We used a model of neutral markers genetically linked to selected loci (QTL) controlling a quantitative trait subject to divergent selection in two subpopulations connected by migration. The results are not particularly encouraging because for chromosome lengths above 0.5 morgan, at least 30% of outliers detected were positioned in chromosomes where QTL were absent, clearly denoting false positives. Outliers linked to QTL were on average closer to the nearest QTL than randomly chosen markers, but the methods showed a substantial uncertainty about the genetic association between markers and selected loci, as this association could be shown significantly only in a moderate number of replicates for most scenarios. At equal conditions, bayescan seemed to perform somewhat more efficiently than dfdist/fdist, with little difference between results for dominant and codominant markers.     

Toxoplasma gondii: genotyping of strains from Brazilian AIDS patients with cerebral toxoplasmosis by multilocus PCR-RFLP markers

This study investigated the genetic characteristics of the Toxoplasma gondii strains isolated from 87 patients with cerebral toxoplasmosis and AIDS, treated in Sao Paulo State, Brazil. The laboratorial diagnosis of cerebral toxoplasmosis was based on positive serological exams and PCR of blood and/or cerebrospinal fluid. Four markers (5'-SAG2, 3'-SAG2, SAG3 and GRA6) were chosen to analyze the samples. Each having clear resolution to distinguish the three clonal lineages after PCR amplified targets were treated with restriction enzyme digestion (PCR-RFLP). The genotyping provided the following results: 40 patients (46%) were infected with strains classified as type I; 4 (4%), as type III; 13 (15%) were infected with polymorphic strains (unusual genotype); 6 patients with type I or II alleles; and 15 (17%) patients had strains not classified for any marker. PCR-RFLP, also classified 9 (11%) clinical isolates as type II, which is uncommon in South America. However, the sequencing of the nested-PCR products (of SAG3 marker) of type II and polymorphic isolates (of 5'-SAG2, SAG3 and GRA6 markers) showed a nucleotide polymorphism compared with the archetypal clonal genotypes (types I, II and III) and these isolates were considered as polymorphic strains. The markers used here were inappropriate to distinguish the most isolates considered as polymorphic strains. These data confirm other studies showing the high rate of genetic polymorphism in T. gondii strains isolated in Brazil.     

Macroinvertebrates associated with submerged macrophytes: sample size and power to detect effects

When planning and conducting ecological experiments, it is important to consider how many samples are necessary to detect differences among treatments with acceptably high statistical power. An analysis of statistical power is especially important when studying epiphytic macroinvertebrate colonization of submerged plants because they exhibit large plant-to-plant variability. Despite this variability, many studies have suggested that epiphytic macroinvertebrates preferentially colonize plants based on plant architecture type (broad versus dissected leaves). In this study, we calculated the power and number of samples necessary to detect differences in epiphytic macroinvertebrate abundance (numbers and biomass) among five species and two architecture types of macrophytes in a lake in MI, U.S.A. Using power analysis, we found that we had very high power to detect the differences present between macroinvertebrate abundance by architecture type and by macrophyte species (power = 1.000 and 0.994; effect sizes = 0.872 and 0.646, respectively. However, to detect very small differences between the two architecture types and the five plant species, we determined that many more samples were necessary to achieve similar statistical power (effect size = 0.1–0.3, number of samples = 60–527 and 36–310, respectively; power = 0.9). Our results suggest that macroinvertebrate abundance does in fact vary predictably with plant architecture. Dissected-leaf plants harbored higher abundances of macroinvertebrates than broad-leaf plants (ANOVA, density p = 0.001, biomass p < 0.001). This knowledge should allow us to better design future studies of epiphytic macroinvertebrates.     

Bayesian analysis of linkage between genetic markers and quantitative trait loci. I. Prior knowledge

Summary Prior information on gene effects at individual quantitative trait loci (QTL) and on recombination rates between marker loci and QTL is derived. The prior distribution of QTL gene effects is assumed to be exponential with major effects less likely than minor ones. The prior probability of linkage between a marker and another single locus is a function of the number and length of chromosomes, and of the map function relating recombination rate to genetic distance among loci. The prior probability of linkage between a marker locus and a quantitative trait depends additionally on the number of detectable QTL, which may be determined from total additive genetic variance and minimum detectable QTL effect. The use of this prior information should improve linkage tests and estimates of QTL effects.