A multipoint linkage map of the distal short arm of the human X chromosome.

The distal portion of the short arm of the human X chromosome (Xp) exhibits many unique and interesting features. Distal Xp contains the pseudoautosomal region, a number of disease loci, and several cell-surface markers. Several genes in this area have also been observed to escape X-chromosomal inactivation. The characterization of new polymorphic loci in this region has permitted the construction of a refined multipoint linkage map extending 15 cM from the Xp telomere. This interval is known to contain the loci for the diseases X-linked ichthyosis, chondrodysplasia punctata, and Kallmann syndrome, as well as the cell-surface markers Xg and 12E7. This region also contains the junction between the pseudoautosomal region and strictly X-linked sequences. The locus MIC2 has been demonstrated by linkage analysis to be indistinguishable from the pseudoautosomal junction. The steroid sulfatase locus has been mapped to an interval adjacent to the DXS278 locus and 6 cM from the pseudoautosomal junction. The polymorphic locus (STS) DXS278 was shown to be informative in all families studied, and linkage analysis reveals that the locus represents a low-copy repeat with at least one copy distal to the STS gene. The generation of a multipoint linkage map of distal Xp will be useful in the genetic dissection of many of the unique features of this region.     

Linkage analysis in the presence of errors I: complex-valued recombination fractions and complex phenotypes

Linkage is a phenomenon that correlates the genotypes of loci, rather than the phenotypes of one locus to the genotypes of another. It is therefore necessary to convert the observed trait phenotypes into trait-locus genotypes, which can then be analyzed for coinheritance with marker-locus genotypes. However, if the mode of inheritance of the trait is not known accurately, this conversion can often result in errors in the inferred trait-locus genotypes, which, in turn, can lead to the misclassification of the recombination status of meioses. As a result, the recombination fraction can be overestimated in two-point analysis, and false exclusions of the true trait locus can occur in multipoint analysis. We propose a method that increases the robustness of multipoint analysis to errors in the mode of inheritance assumptions of the trait, by explicitly allowing for misclassification of trait-locus genotypes. To this end, the definition of the recombination fraction is extended to the complex plane, as Theta=straight theta+straightepsiloni; theta is the recombination fraction between actual ("real") genotypes of marker and trait loci, and straightepsilon is the probability of apparent but false ("imaginary") recombinations between the actual and inferred trait-locus genotypes. "Complex" multipoint LOD scores are proven to be stochastically equivalent to conventional two-point LOD scores. The greater robustness to modeling errors normally associated with two-point analysis can thus be extended to multiple two-point analysis and multipoint analysis. The use of complex-valued recombination fractions also allows the stochastic equivalence of "model-based" and "model-free" methods to be extended to multipoint analysis.     

A framework for detecting and characterizing genetic background-dependent imprinting effects

Genomic imprinting, where the effects of alleles depend on their parent-of-origin, can be an important component of the genetic architecture of complex traits. Although there has been a rapidly increasing number of studies of genetic architecture that have examined imprinting effects, none have examined whether imprinting effects depend on genetic background. Such effects are critical for the evolution of genomic imprinting because they allow the imprinting state of a locus to evolve as a function of genetic background. Here we develop a two-locus model of epistasis that includes epistatic interactions involving imprinting effects and apply this model to scan the mouse genome for loci that modulate the imprinting effects of quantitative trait loci (QTL). The inclusion of imprinting leads to nine orthogonal forms of epistasis, five of which do not appear in the usual two-locus decomposition of epistasis. Each form represents a change in the imprinting status of one locus across different classes of genotypes at the other locus. Our genome scan identified two different locus pairs that show complex patterns of epistasis, where the imprinting effect at one locus changes across genetic backgrounds at the other locus. Thus, our model provides a framework for the detection of genetic background-dependent imprinting effects that should provide insights into the background dependence and evolution of genomic imprinting. Our application of the model to a genome scan supports this assertion by identifying pairs of loci that show reciprocal changes in their imprinting status as the background provided by the other locus changes.     

Comparison of a multipoint identity-by-descent method with parametric multipoint linkage analysis for mapping quantitative traits.

We previously developed a method of partitioning genetic variance of a quantitative trait to loci in specific chromosomal regions. In this paper, we compare this method--multipoint IBD (identical by descent) method (MIM)--with parametric multipoint linkage analysis (MLINK). A simulation study was performed comparing the methods for the major-locus, mixed, and two-locus models. The criterion for comparisons between MIM and MLINK was the average lod score from multiple replicates of simulated data sets. The effect of gene frequency, dominance, model misspecification, marker spacing, and informativeness are also considered in a smaller set of simulations. Within the context of the models examined, the MIM approach was found to be comparable in power with parametric multipoint linkage analysis when (a) parental data are unknown, (b) the effect of the major locus is small and there is additional genetic variation, or (c) the parameters of the major-locus model are misspecified. The performance of the MIM method relative to MLINK was markedly lower when the allele frequency at the trait locus was .2 versus .5, particularly for the case when parental data were assumed to be known. Dominance at the trait major locus, as well as marker spacing and heterozygosity, did not appear to have a large effect on the ELOD comparisons.     

Exact multipoint quantitative-trait linkage analysis in pedigrees by variance components

Methods based on variance components are powerful tools for linkage analysis of quantitative traits, because they allow simultaneous consideration of all pedigree members. The central idea is to identify loci making a significant contribution to the population variance of a trait, by use of allele-sharing probabilities derived from genotyped marker loci. The technique is only as powerful as the methods used to infer these probabilities, but, to date, no implementation has made full use of the inheritance information in mapping data. Here we present a new implementation that uses an exact multipoint algorithm to extract the full probability distribution of allele sharing at every point in a mapped region. At each locus in the region, the program fits a model that partitions total phenotypic variance into components due to environmental factors, a major gene at the locus, and other unlinked genes. Numerical methods are used to derive maximum-likelihood estimates of the variance components, under the assumption of multivariate normality. A likelihood-ratio test is then applied to detect any significant effect of the hypothesized major gene. Simulations show the method to have greater power than does traditional sib-pair analysis. The method is freely available in a new release of the software package GENEHUNTER.     

ASP – a simulation-based power calculator for genetic linkage studies of qualitative traits, using sib-pairs

An easy-to-use, simulation-based power calculator (ASP) for linkage analysis using sib-pair designs (concordant or discordant) has been developed and made publicly available via the Internet. The program employs a diallelic model for the trait locus, at which parental/offspring genotypes are simulated, assuming Hardy-Weinberg equilibrium in the parental generation. Genotypes at a linked multiallelic marker locus are simulated conditional upon the inheritance pattern at the trait locus, allowing for recombination. Marker genotypes are tested for non-Mendelian identity-by-descent sharing, using both an unrestricted and a restricted likelihood ratio test, the latter representing an extension of the "mean test" from fully to partially informative families. The power of user-defined datasets is estimated by the number of simulations giving significant results at varying type I error levels.     

Multipoint linkage analysis and heterogeneity testing in 20 X-linked retinitis pigmentosa families

Using multipoint linkage analysis in 20 families segregating for X-linked retinitis pigmentosa (XLRP), the lod scores on a map of eight RFLP loci were obtained. Our results indicate that under the hypothesis of homogeneity the maximal multipoint lod score supports one disease locus located slightly distal to OTC at Xp21.1. Heterogeneity testing for two XLRP loci suggested that a second XLRP locus may be located 8.5 cM proximal to DXS28 at Xp21.3. Further heterogeneity testing for three disease loci failed to detect a third XLRP locus proximal to DXS7 in any of our 20 XLRP families.     

A Random Model Approach to Interval Mapping of Quantitative Trait Loci

Mapping quantitative trait loci in outbred populations is important because many populations of organisms are noninbred. Unfortunately, information about the genetic architecture of the trait may not be available in outbred populations. Thus, the allelic effects of genes can not be estimated with ease. In addition, under linkage equilibrium, marker genotypes provide no information about the genotype of a QTL (our terminology for a single quantitative trait locus is QTL while multiple loci are referred to as QTLs). To circumvent this problem, an interval mapping procedure based on a random model approach is described. Under a random model, instead of estimating the effects, segregating variances of QTLs are estimated by a maximum likelihood method. Estimation of the variance component of a QTL depends on the proportion of genes identical-by-descent (IBD) shared by relatives at the locus, which is predicted by the IBD of two markers flanking the QTL. The marker IBD shared by two relatives are inferred from the observed marker genotypes. The procedure offers an advantage over the regression interval mapping in terms of high power and small estimation errors and provides flexibility for large sibships, irregular pedigree relationships and incorporation of common environmental and fixed effects.     

Linkage analysis in the presence of errors II: marker-locus genotyping errors modeled with hypercomplex recombination fractions

It is well known that genotyping errors lead to loss of power in gene-mapping studies and underestimation of the strength of correlations between trait- and marker-locus genotypes. In two-point linkage analysis, these errors can be absorbed in an inflated recombination-fraction estimate, leaving the test statistic quite robust. In multipoint analysis, however, genotyping errors can easily result in false exclusion of the true location of a disease-predisposing gene. In a companion article, we described a "complex-valued" extension of the recombination fraction to accommodate errors in the assignment of trait-locus genotypes, leading to a multipoint LOD score with the same robustness to errors in trait-locus genotypes that is seen with the conventional two-point LOD score. Here, a further extension of this model to "hypercomplex-valued" recombination fractions (hereafter referred to as "hypercomplex recombination fractions") is presented, to handle random and systematic sources of marker-locus genotyping errors. This leads to a multipoint method (either "model-based" or "model-free") with the same robustness to marker-locus genotyping errors that is seen with conventional two-point analysis but with the advantage that multiple marker loci can be used jointly to increase meiotic informativeness. The cost of this increased robustness is a decrease in fine-scale resolution of the estimated map location of the trait locus, in comparison with traditional multipoint analysis. This probability model further leads to algorithms for the estimation of the lower bounds for the error rates for genomewide and locus-specific genotyping, based on the null-hypothesis distribution of the LOD-score statistic in the presence of such errors. It is argued that those genome scans in which the LOD score is 0 for >50% of the genome are likely to be characterized by high rates of genotyping errors in general.     

An improved formulation of marker heterozygosity in recurrent selection and backcross schemes

This report presents a theoretical formulation for predicting heterozygosity of a putative marker locus linked to two quantitative trait loci (QTL) in a recurrent selection and backcross (RSB) scheme. Since the heterozygosity at any given marker locus maintained in such a breeding programme reflects its map location relative to QTL, the present study develops the theoretical analysis of the QTL mapping method that recently appeared in the literature. The formulae take into account selection, recombination and finite population size during the multiple-generation breeding scheme. The single-marker and two-QTL model was compared numerically with the model involving two linked marker loci and two QTL. Without recombination interference, the two models predict the same expected heterozygosity at the linked marker loci, indicating that the model is valid for predicting marker heterozygosity maintained at any loci in an RSB breeding scheme. The formulation is demonstrated numerically for several RSB schemes and its implications in developing a likelihood-based statistical framework for modeling the RSB experiments are discussed.     

DNA-marking of quantitative traits in corn

Methods of ISSR- and RAPD-analyses were used for marking quantitative trait loci (QTLs) determining the development of some morphological and biological traits in maize. Specificity of marker locus alleles was established for certain levels of polygenic trait phenotype manifestation. Criteria of marker locus informativity are discussed. A possibility of marker-assisted selection for valuable genotypes with desired for breeding trait values was demonstrated.     

Calculation of multipoint likelihoods using flanking marker data: a simulation study

The calculation of multipoint likelihoods is computationally challenging, with the exact calculation of multipoint probabilities only possible on small pedigrees with many markers or large pedigrees with few markers. This paper explores the utility of calculating multipoint likelihoods using data on markers flanking a hypothesized position of the trait locus. The calculation of such likelihoods is often feasible, even on large pedigrees with missing data and complex structures. Performance characteristics of the flanking marker procedure are assessed through the calculation of multipoint heterogeneity LOD scores on data simulated for Genetic Analysis Workshop 14 (GAW14). Analysis is restricted to data on the Aipotu population on chromosomes 1, 3, and 4, where chromosomes 1 and 3 are known to contain disease loci. The flanking marker procedure performs well, even when missing data and genotyping errors are introduced.     

A simple method for detection of imprinting effects based on case-parents trios

Using data from families in which marker genotypes are known for the father, the mother and the affected offspring, a simple statistic for testing for imprinting effects is developed. The statistic considers whether the expected number of families in which the father carries more copies of a particular marker allele than the mother is equal to the expected number of families in which the mother carries more copies of the allele than the father. The proposed parent-of-origin effects test statistic (POET) is shown to be normally distributed and can be employed to test for imprinting in situations where the marker locus need not be a disease susceptibility locus and where the female and male recombination fractions are sex-specific. A simulation study is conducted to characterize the power of the POET and other properties, and its results show that it is appropriate to employ the POET.     

Using molecular markers to map multiple quantitative trait loci: models for backcross,recombinant inbred,and doubled haploid progeny

Summary To maximize parameter estimation efficiency and statistical power and to estimate epistasis, the parameters of multiple quantitative trait loci (QTLs) must be simultaneously estimated. If multiple QTL affect a trait, then estimates of means of QTL genotypes from individual locus models are statistically biased. In this paper, I describe methods for estimating means of QTL genotypes and recombination frequencies between marker and quantitative trait loci using multilocus backcross, doubled haploid, recombinant inbred, and testcross progeny models. Expected values of marker genotype means were defined using no double or multiple crossover frequencies and flanking markers for linked and unlinked quantitative trait loci. The expected values for a particular model comprise a system of nonlinear equations that can be solved using an interative algorithm, e.g., the Gauss-Newton algorithm. The solutions are maximum likelihood estimates when the errors are normally distributed. A linear model for estimating the parameters of unlinked quantitative trait loci was found by transforming the nonlinear model. Recombination frequency estimators were defined using this linear model. Certain means of linked QTLs are less efficiently estimated than means of unlinked QTLs.     

Performance of Markov chain-Monte Carlo approaches for mapping genes in oligogenic models with an unknown number of loci

Markov chain-Monte Carlo (MCMC) techniques for multipoint mapping of quantitative trait loci have been developed on nuclear-family and extended-pedigree data. These methods are based on repeated sampling-peeling and gene dropping of genotype vectors and random sampling of each of the model parameters from their full conditional distributions, given phenotypes, markers, and other model parameters. We further refine such approaches by improving the efficiency of the marker haplotype-updating algorithm and by adopting a new proposal for adding loci. Incorporating these refinements, we have performed an extensive simulation study on simulated nuclear-family data, varying the number of trait loci, family size, displacement, and other segregation parameters. Our simulation studies show that our MCMC algorithm identifies the locations of the true trait loci and estimates their segregation parameters well-provided that the total number of sibship pairs in the pedigree data is reasonably large, heritability of each individual trait locus is not too low, and the loci are not too close together. Our MCMC algorithm was shown to be significantly more efficient than LOKI (Heath 1997) in our simulation study using nuclear-family data.     

An interstitial deletion in Xp22.3 in a family with X-linked recessive chondrodysplasia punctata and short stature

Summary In a four-generation family, chondrodysplasia punctata was found in a boy and one of his maternal uncles. These two patients also have short stature, as do all female members of the family. DNA molecular analysis of the pseudoautosomal and Xp22.3-specific loci revealed the presence of an interstitial deletion that cosegregates with the phenotypic abnormalities. The proximal breakpoint of this deletion was located distal to the DXS31 locus and the distal breakpoint in the pseudoautosomal region between DXYS59 and DXYS17. This maps the recessive X-linked form of chondrodysplasia punctata between the proximal boundary of the pseudoautosomal region and DXS31, and an Xp gene controlling growth between DXYS59 and DXS31.     

On the detection of imprinted quantitative trait loci in line crosses: effect of linkage disequilibrium

Imprinted quantitative trait loci (QTL) are commonly reported in studies using line-cross designs, especially in livestock species. It was previously shown that such parent-of-origin effects might result from the nonfixation of QTL alleles in one or both parental lines, rather than from genuine molecular parental imprinting. We herein demonstrate that if linkage disequilibrium exists between marker loci and nonfixed QTL, spurious detection of pseudo-imprinting is increased by an additional 40–80% in scenarios mimicking typical livestock situations. This is due to the fact that imprinting can be tested only in F₂ offspring whose sire and dam have distinct marker genotypes. In the case of linkage disequilibrium between markers and QTL, such parents have a higher chance to have distinct QTL genotypes as well, thus resulting in distinct padumnal and madumnal allele substitution effects, i.e., QTL pseudo-imprinting.     

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.     

Y-linkage and pseudoautosomal linkage.

Presently existing computer program allow for an autosomal or an X-linked mode of inheritance of loci to be analyzed for genetic linkage. They do not, however, specifically allow for more general sex-linked modes of inheritance. This study proposes methods that permit the carrying out of linkage analyses of loci following a Y-linked or a pseudoautosomal mode of inheritance.