The genetic dissection of complex traits in a founder population.

We estimated broad heritabilities (H(2)) and narrow heritabilities (h(2)) and conducted genomewide screens, using a novel association-based mapping approach for 20 quantitative trait loci (QTLs) among the Hutterites, a founder population that practices a communal lifestyle. Heritability estimates ranged from.21 for diastolic blood pressure (DBP) to.99 for whole-blood serotonin levels. Using a multipoint method to detect association under a recessive model we found evidence of major QTLs for six traits: low-density lipoprotein (LDL), triglycerides, lipoprotein (a) (Lp[a]), systolic blood pressure (SBP), serum cortisol, and whole-blood serotonin. Second major QTLs for Lp(a) and for cortisol were identified using a single-point method to detect association under a general two-allele model. The heritabilities for these six traits ranged from.37 for triglycerides to.99 for serotonin, and three traits (LDL, SBP, and serotonin) had significant dominance variances (i.e., H(2) > h(2)). Surprisingly, there was little correlation between measures of heritability and the strength of association on a genomewide screen (P>.50), suggesting that heritability estimates per se do not identify phenotypes that are influenced by genes with major effects. The present study demonstrates the feasibility of genomewide association studies for QTL mapping. However, even in this young founder population that has extensive linkage disequilibrium, map densities <<5 cM may be required to detect all major QTLs.

Broad and narrow heritabilities of quantitative traits in a founder population.

Estimation of the components of variance for a quantitative trait allows one to evaluate both the degree to which genetics influences the trait and the trait's underlying genetic architecture. For particular traits, the estimates also may have implications for discriminating between potential models of selection and for choosing an appropriate model for linkage analysis. Using a recently developed method, we estimate the additive and dominance components of variance--or, equivalently, the narrow and broad sense heritabilities--of several traits in the Hutterites, a founder population with extensive genealogical records. As a result of inbreeding and because Hutterite individuals are typically related through multiple lines of descent, we expect that power to detect dominance variance will be increased relative to that in outbred studies. Furthermore, the communal lifestyle of the Hutterites allows us to evaluate the genetic influences in a relatively homogeneous environment. Four phenotypes had a significant dominance variance, resulting in a relatively high broad heritability. We estimated the narrow and broad heritabilities as being, respectively,.36 and.96 for LDL,.51 and 1.0 for serotonin levels, and.45 and.76 for fat free mass (FFM). There was no significant additive component for systolic blood pressure (SBP), resulting in a narrow heritability of 0 and a broad heritability of.45. There were several traits for which we found no significant dominance component, resulting in equal broad and narrow heritability estimates. These traits and their heritabilities are as follows: HDL,.63; triglycerides,.37; diastolic blood pressure,.21; immunoglobulin E,.63; lipoprotein(a),.77; and body-mass index,.54. The large difference between broad and narrow heritabilities for LDL, serotonin, FFM, and SBP are indicative of strong dominance effects in these phenotypes. To our knowledge, this is the first study to report an estimate of heritability for serotonin and to detect a dominance variance for LDL, FFM, and SBP.

Detection of mis-specified relationships in inbred and outbred pedigrees.

Genome screen data collected for linkage analysis can be used to detect pedigree errors. We have developed methods applicable to a broad range of relationships. We discuss applications of our methods to data on asthma, in which we detect a number of likely mis-specified relative pairs. We propose a graphical method for error detection in complex inbred pedigrees, with application to the Hutterites.

Estimation of variance components of quantitative traits in inbred populations.

Use of variance-component estimation for mapping of quantitative-trait loci in humans is a subject of great current interest. When only trait values, not genotypic information, are considered, variance-component estimation can also be used to estimate heritability of a quantitative trait. Inbred pedigrees present special challenges for variance-component estimation. First, there are more variance components to be estimated in the inbred case, even for a relatively simple model including additive, dominance, and environmental effects. Second, more identity coefficients need to be calculated from an inbred pedigree in order to perform the estimation, and these are computationally more difficult to obtain in the inbred than in the outbred case. As a result, inbreeding effects have generally been ignored in practice. We describe here the calculation of identity coefficients and estimation of variance components of quantitative traits in large inbred pedigrees, using the example of HDL in the Hutterites. We use a multivariate normal model for the genetic effects, extending the central-limit theorem of Lange to allow for both inbreeding and dominance under the assumptions of our variance-component model. We use simulated examples to give an indication of under what conditions one has the power to detect the additional variance components and to examine their impact on variance-component estimation. We discuss the implications for mapping and heritability estimation by use of variance components in inbred populations.

Statistical tests for detection of misspecified relationships by use of genome-screen data.

Misspecified relationships can have serious consequences for linkage studies, resulting in either reduced power or false-positive evidence for linkage. If some individuals in the pedigree are untyped, then Mendelian errors may not be observed. Previous approaches to detection of misspecified relationships by use of genotype data were developed for sib and half-sib pairs. We extend the likelihood calculations of Göring and Ott and Boehnke and Cox to more-general relative pairs, for which identity-by-descent (IBD) status is no longer a Markov chain, and we propose a likelihood-ratio test. We also extend the identity-by-state (IBS)-based test of Ehm and Wagner to nonsib relative pairs. The likelihood-ratio test has high power, but its drawbacks include the need to construct and apply a separate Markov chain for each possible alternative relationship and the need for simulation to assess significance. The IBS-based test is simpler but has lower power. We propose two new test statistics-conditional expected IBD (EIBD) and adjusted IBS (AIBS)-designed to retain the simplicity of IBS while increasing power by taking into account chance sharing. In simulations, the power of EIBD is generally close to that of the likelihood-ratio test. The power of AIBS is higher than that of IBS, in all cases considered. We suggest a strategy of initial screening by use of EIBD and AIBS, followed by application of the likelihood-ratio test to only a subset of relative pairs, identified by use of EIBD and AIBS. We apply the methods to a Genetic Analysis Workshop 11 data set from the Collaborative Study on the Genetics of Alcoholism.

Meiotic segregation analysis of RB1 alleles in retinoblastoma pedigrees by use of single-sperm typing.

In hereditary retinoblastoma, different epidemiological studies have indicated a preferential paternal transmission of mutant retinoblastoma alleles to offspring, suggesting the occurrence of a meiotic drive. To investigate this mechanism, we analyzed sperm samples from six individuals from five unrelated families affected with hereditary retinoblastoma. Single-sperm typing techniques were performed for each sample by study of two informative short tandem repeats located either in or close to the retinoblastoma gene (RB1). The segregation probability of mutant RB1 alleles in sperm samples was assessed by use of the SPERMSEG program, which includes experimental parameters, recombination fractions between the markers, and segregation parameters. A total of 2,952 single sperm from the six donors were analyzed. We detected a significant segregation distortion in the data as a whole (P=.0099) and a significant heterogeneity in the segregation rate across donors (.0092). Further analysis shows that this result can be explained by segregation distortion in favor of the normal allele in one donor only and that it does not provide evidence of a significant segregation distortion in the other donors. The segregation distortion favoring the mutant RB1 allele does not seem to occur during spermatogenesis, and, thus, meiotic drive may result either from various mechanisms, including a fertilization advantage or a better mobility in sperm bearing a mutant RB1 gene, or from the existence of a defectively imprinted gene located on the human X chromosome.

French Machado-Joseph disease patients do not exhibit gametic segregation distortion: a sperm typing analysis.

Segregation distortion has been reported to occur in a number of the trinucleotide repeat disorders. On the basis of a sperm typing study performed in patients of Japanese descent with Machado-Joseph disease (MJD), it was reported that disease alleles are preferentially transmitted during meiosis. We performed a sperm typing study of five MJD patients of French descent and analysis of the pooled data shows a ratio of mutant to normal alleles of 379:436 (46.5:53.5%), which does not support meiotic segregation distortion. To confirm these results, sperm typing analysis was also performed using a polymorphic marker, D14S1050, closely linked to the MJD1 gene. Among 910 sperm analyzed, the allele linked to the disease chromosome was detected in 50.3% of the samples and the allele linked to the normal chromosome was found in 49.6% of the sperm. The difference in frequency of these two alleles is not significant ( P = 0.8423). Likelihood-based analysis of segregation distortion in the single sperm data using the SPERMSEG program also showed no support for segregation distortion at the gamete level in this patient population. The previous report on the Japanese patients also suggested that disease allele stability may be influenced by a trans effect of an intragenic polymorphism (987 G/C) in the wild-type allele. All of the French patients were heterozygous for this polymorphism. However, analysis of the variance in repeat number in sperm from the French MJD patients overlapped significantly with the variance in repeat number observed in the C/C homozygous Japanese patients.

Assessment of linkage disequilibrium by the decay of haplotype sharing, with application to fine-scale genetic mapping.

Linkage disequilibrium (LD) is of great interest for gene mapping and the study of population history. We propose a multilocus model for LD, based on the decay of haplotype sharing (DHS). The DHS model is most appropriate when the LD in which one is interested is due to the introduction of a variant on an ancestral haplotype, with recombinations in succeeding generations resulting in preservation of only a small region of the ancestral haplotype around the variant. This is generally the scenario of interest for gene mapping by LD. The DHS parameter is a measure of LD that can be interpreted as the expected genetic distance to which the ancestral haplotype is preserved, or, equivalently, 1/(time in generations to the ancestral haplotype). The method allows for multiple origins of alleles and for mutations, and it takes into account missing observations and ambiguities in haplotype determination, via a hidden Markov model. Whereas most commonly used measures of LD apply to pairs of loci, the DHS measure is designed for application to the densely mapped haplotype data that are increasingly available. The DHS method explicitly models the dependence among multiple tightly linked loci on a chromosome. When the assumptions about population structure are sufficiently tractable, the estimate of LD is obtained by maximum likelihood. For more-complicated models of population history, we find means and covariances based on the model and solve a quasi-score estimating equation. Simulations show that this approach works extremely well both for estimation of LD and for fine mapping. We apply the DHS method to published data sets for cystic fibrosis and progressive myoclonus epilepsy.

Optimal allele-sharing statistics for genetic mapping using affected relatives.

The choice of allele-sharing statistics can have a great impact on the power of robust affected relative methods. Similarly, when allele-sharing statistics from several pedigrees are combined, the weight applied to each pedigree's statistic can affect power. Here we describe the direct connection between the affected relative methods and traditional parametric linkage analysis, and we use this connection to give explicit formulae for the optimal sharing statistics and weights, applicable to all pedigree types. One surprising consequence is that under any single gene model, the value of the optimal allele-sharing statistic does not depend on whether observed sharing is between more closely or more distantly related affected relatives. This result also holds for any multigene model with loci unlinked, additivity between loci, and all loci having small effect. For specific classes of two-allele models, we give the most powerful statistics and optimal weights for arbitrary pedigrees. When the effect size is small, these also extend to multigene models with additivity between loci. We propose a useful new statistic, S(rob dom), which performs well for dominant and additive models with varying phenocopy rates and varying predisposing allele frequency. We find that the statistic S(_#alleles), performs well for recessive models with varying phenocopy rates and varying redisposing allele frequency. We also find that for models with large deviation from null sharing, the correspondence between allele-sharing statistics and the models for which they are optimal may also depend on which method is used to test for linkage.

Analysis of meiotic segregation, using single-sperm typing: meiotic drive at the myotonic dystrophy locus.

Meiotic drive at the myotonic dystrophy (DM) locus has recently been suggested as being responsible for maintaining the frequency, in the human population, of DM chromosomes capable of expansion to the disease state. In order to test this hypothesis, we have studied samples of single sperm from three individuals heterozygous at the DM locus, each with one allele larger and one allele smaller than 19 CTG repeats. To guard against the possible problem of differential PCR amplification rates based on the lengths of the alleles, the sperm were also typed at another closely linked marker whose allele size was unrelated to the allele size at the DM locus. Using statistical models specifically designed to study single-sperm segregation data, we find no evidence of meiotic segregation distortion. The upper limit of the two-sided 95% confidence interval for the estimate of the common segregation probability for the three donors is at or below .515 for all models considered, and no statistically significant difference from .5 is detected in any of the models. This suggests that any greater amount of segregation distortion at the myotonic dystrophy locus must result from events following sperm ejaculation. The mathematical models developed make it possible to study segregation distortion with high resolution by using sperm-typing data from any locus.

Modeling interference in genetic recombination.

In analyzing genetic linkage data it is common to assume that the locations of crossovers along a chromosome follow a Poisson process, whereas it has long been known that this assumption does not fit the data. In many organisms it appears that the presence of a crossover inhibits the formation of another nearby, a phenomenon known as "interference." We discuss several point process models for recombination that incorporate position interference but assume no chromatid interference. Using stochastic simulation, we are able to fit the models to a multilocus Drosophila dataset by the method of maximum likelihood. We find that some biologically inspired point process models incorporating one or two additional parameters provide a dramatically better fit to the data than the usual "no-interference" Poisson model.

Statistical analysis of crossover interference using the chi-square model.

The chi-square model (also known as the gamma model with integer shape parameter) for the occurrence of crossovers along a chromosome was first proposed in the 1940's as a description of interference that was mathematically tractable but without biological basis. Recently, the chi-square model has been reintroduced into the literature from a biological perspective. It arises as a result of certain hypothesized constraints on the resolution of randomly distributed crossover intermediates. In this paper under the assumption of no chromatid interference, the probability for any single spore or tetrad joint recombination pattern is derived under the chi-square model. The method of maximum likelihood is then used to estimate the chi-square parameter m and genetic distances among marker loci. We discuss how to interpret the goodness-of-fit statistics appropriately when there are some recombination classes that have only a small number of observations. Finally, comparisons are made between the chi-square model and some other tractable models in the literature.

Statistical analysis of chromatid interference.

The nonrandom occurrence of crossovers along a single strand during meiosis can be caused by either chromatid interference, crossover interference or both. Although crossover interference has been consistently observed in almost all organisms since the time of the first linkage studies, chromatid interference has not been as thoroughly discussed in the literature, and the evidence provided for it is inconsistent. In this paper with virtually no restrictions on the nature of crossover interference, we describe the constraints that follow from the assumption of no chromatid interference for single spore data. These constraints are necessary consequences of the assumption of no chromatid interference, but their satisfaction is not sufficient to guarantee no chromatid interference. Models can be constructed in which chromatid interference clearly exists but is not detectable with single spore data. We then extend our analysis to cover tetrad data, which permits more powerful tests of no chromatid interference. We note that the traditional test of no chromatid interference based on tetrad data does not make full use of the information provided by the data, and we offer a statistical procedure for testing the no chromatid interference constraints that does make full use of the data. The procedure is then applied to data from several organisms. Although no strong evidence of chromatid interference is found, we do observe an excess of two-strand double recombinations, i.e., negative chromatid interference.

Atypical regions in large genomic DNA sequences.

Large genomic DNA sequences contain regions with distinctive patterns of sequence organization. We describe a method using logarithms of probabilities based on seventh-order Markov chains to rapidly identify genomic sequences that do not resemble models of genome organization built from compilations of octanucleotide usage. Data bases have been constructed from Escherichia coli and Saccharomyces cerevisiae DNA sequences of > 1000 nt and human sequences of > 10,000 nt. Atypical genes and clusters of genes have been located in bacteriophage, yeast, and primate DNA sequences. We consider criteria for statistical significance of the results, offer possible explanations for the observed variation in genome organization, and give additional applications of these methods in DNA sequence analysis.

Robustness of the no-interference model for ordering genetic markers.

Under the assumption of no chromatid interference, we derive constraints on the probabilities of the different recombination patterns among m + 1 genetic loci. An application of these constraints is a proof that the ordering of the loci that maximizes the likelihood under the assumption of no interference is, in fact, a consistent estimator of the true order even when there is interference.