Simple, robust linkage tests for affected sibs

Parametric-linkage analysis applied to large pedigrees with many affected individuals has helped in the identification of highly penetrant genes; but, for diseases lacking a clear Mendelian inheritance pattern or caused by several genes of low to moderate penetrance, a more robust strategy is nonparametric analysis applied to small sets of affected relatives, such as affected sib pairs. Here we show that the robustness of affected-sib-pair tests is related to the shape of the constraint set for the sibs' identity-by-descent (IBD) probabilities. We also derive a set of constraints for the IBD probabilities of affected sib triples and use common features of the shapes of the two constrain sets to introduce new nonparametric tests (called "minmax" tests) that are more robust than those in current use. Asymptotic-power computations support the robustness of the proposed minmax tests.     

Nonparametric simulation-based statistics for detecting linkage in general pedigrees

We present here four nonparametric statistics for linkage analysis that test whether pairs of affected relatives share marker alleles more often than expected. These statistics are based on simulating the null distribution of a given statistic conditional on the unaffecteds' marker genotypes. Each statistic uses a different measure of marker sharing: the SimAPM statistic uses the simulation-based affected-pedigree-member measure based on identity-by-state (IBS) sharing. The SimKIN (kinship) measure is 1.0 for identity-by-descent (IBD) sharing, 0.0 for no IBD status sharing, and the kinship coefficient when the IBD status is ambiguous. The simulation-based IBD (SimIBD) statistic uses a recursive algorithm to determine the probability of two affecteds sharing a specific allele IBD. The SimISO statistic is identical to SimIBD, except that it also measures marker similarity between unaffected pairs. We evaluated our statistics on data simulated under different two-locus disease models, comparing our results to those obtained with several other nonparametric statistics. Use of IBD information produces dramatic increases in power over the SimAPM method, which uses only IBS information. The power of our best statistic in most cases meets or exceeds the power of the other nonparametric statistics. Furthermore, our statistics perform comparisons between all affected relative pairs within general pedigrees and are not restricted to sib pairs or nuclear families.     

Sib-pair collection strategies for complex diseases

When planning an affected sib pair collection for use in a genomewide search for complex trait loci, researchers must ask: (a) Which family structures will yield the most informative pairs? and (b) Should recruitment extend beyond the index sib pair? The optimal collection strategy will depend on the trait's genetic architecture, but this is rarely known for non-Mendelian diseases. In the present report, we study the consequences of collecting only those sib pairs arising from pedigrees with a precisely specified structure as opposed to a strategy that collects all affected sib pairs at random (i.e., blind to the affection status of first-degree relatives). The former approach turns out to be risky because the power of specific pedigree structures can vary dramatically even among models producing identical observable parameters (such as population prevalence and sibling recurrence rate). In contrast, the latter approach typically involves only a modest loss of power as compared with the optimal (but unknowable) design. Further, we compare the strategy of collecting all affected sib pairs at random with the alternative of imposing some modest limitations on family structure (e.g., presence of at least one unaffected sib or parent). The latter approach generally provides some increase in power but entails additional effort to contact and phenotype relatives: the overall merit of imposing such requirements needs to be evaluated in the context of the specific disease to be studied and of the clinical and analytical resources available. In addition, these findings suggest that a further explanation for failure to replicate positive complex trait linkages lies in differences in ascertainment strategy between data sets.     

Computation of the full likelihood function for estimating variance at a quantitative trait locus

The proportion of alleles identical by descent (IBD) determines the genetic covariance between relatives, and thus is crucial in estimating genetic variances of quantitative trait loci (QTL). However, IBD proportions at QTL are unobservable and must be inferred from marker information. The conventional method of QTL variance analysis maximizes the likelihood function by replacing the missing IBDs by their conditional expectations (the expectation method), while in fact the full likelihood function should take into account the conditional distribution of IBDs (the distribution method). The distribution method for families of more than two sibs has not been obvious because there are n(n - 1)/2 IBD variables in a family of size n, forming an n x n symmetrical matrix. In this paper, I use four binary variables, where each indicates the event that an allele from one of the four grandparents has passed to the individual. The IBD proportion between any two sibs is then expressed as a function of the indicators. Subsequently, the joint distribution of the IBD matrix is derived from the distribution of the indicator variables. Given the joint distribution of the unknown IBDs, a method to compute the full likelihood function is developed for families of arbitrary sizes.     

Density estimation by mixture models with smoothing priors

In the statistical approach for self-organizing maps (SOMs), learning is regarded as an estimation algorithm for a gaussian mixture model with a gaussian smoothing prior on the centroid parameters. The values of the hyperparameters and the topological structure are selected on the basis of a statistical principle. However, since the component selection probabilities are fixed to a common value, the centroids concentrate on areas with high data density. This deforms a coordinate system on an extracted manifold and makes smoothness evaluation for the manifold inaccurate. In this article, we study an extended SOM model whose component selection probabilities are variable. To stabilize the estimation, a smoothing prior on the component selection probabilities is introduced. An estimation algorithm for the parameters and the hyperparameters based on empirical Bayesian inference is obtained. The performance of density estimation by the new model and the SOM model is compared via simulation experiments.     

Characterization of deleterious mutations in outcrossing populations

Deng and Lynch recently proposed estimating the rate and effects of deleterious genomic mutations from changes in the mean and genetic variance of fitness upon selfing/outcrossing in outcrossing/highly selfing populations. The utility of our original estimation approach is limited in outcrossing populations, since selfing may not always be feasible. Here we extend the approach to any form of inbreeding in outcrossing populations. By simulations, the statistical properties of the estimation under a common form of inbreeding (sib mating) are investigated under a range of biologically plausible situations. The efficiencies of different degrees of inbreeding and two different experimental designs of estimation are also investigated. We found that estimation using the total genetic variation in the inbred generation is generally more efficient than employing the genetic variation among the mean of inbred families, and that higher degree of inbreeding employed in experiments yields higher power for estimation. The simulation results of the magnitude and direction of estimation bias under variable or epistatic mutation effects may provide a basis for accurate inferences of deleterious mutations. Simulations accounting for environmental variance of fitness suggest that, under full-sib mating, our extension can achieve reasonably well an estimation with sample sizes of only approximately 2000-3000.     

Estimation of effects of quantitative trait loci in large complex pedigrees

A method was derived to estimate effects of quantitative trait loci (QTL) using incomplete genotype information in large outbreeding populations with complex pedigrees. The method accounts for background genes by estimating polygenic effects. The basic equations used are very similar to the usual linear mixed model equations for polygenic models, and segregation analysis was used to estimate the probabilities of the QTL genotypes for each animal. Method R was used to estimate the polygenic heritability simultaneously with the QTL effects. Also, initial allele frequencies were estimated. The method was tested in a simulated data set of 10,000 animals evenly distributed over 10 generations, where 0, 400 or 10,000 animals were genotyped for a candidate gene. In the absence of selection, the bias of the QTL estimates was < 2%. Selection biased the estimate of the Aa genotype slightly, when zero animals were genotyped. Estimates of the polygenic heritability were 0.251 and 0.257, in absence and presence of selection, respectively, while the simulated value was 0.25. Although not tested in this study, marker information could be accommodated by adjusting the transmission probabilities of the genotypes from parent to offspring according to the marker information. This renders a QTL mapping study in large multi-generation pedigrees possible.     

Least squares interval mapping of quantitative trait loci under the infinitesimal genetic model in outbred populations

Genetic marker and phenotypic data for a quantitative trait were simulated on 20 paternal half-sib families with 100 progeny to investigate properties of within-family-regression interval mapping of a postulated single quantitative trait locus (QTL) in a marker interval under the infinitesimal genetic model, which has been the basis of the application of quantitative genetics to genetic improvement programs, and to investigate use of the infinitesimal model as null hypothesis in testing for presence of a major QTL. Genetic effects on the marked chromosome were generated based on a major gene model, which simulated a central biallelic QTL, or based on 101 biallelic QTL of equal effect, which approximated the infinitesimal model. The marked chromosome contained 0, 3.3%, 13.3%, or 33.3% of genetic variance and heritability was 0.25 or 0.70. Under the polygenic model with 3.3% of genetic variance on the marked chromosome, which corresponds to the infinitesimal model for the bovine, significant QTL effects were found for individual families. Correlations between estimates of QTL effects and true chromosome substitution effects were 0.29 and 0.47 for heritabilities of 0.25 and 0.70 but up to 0.85 with 33.3% of polygenic variance on the marked chromosome. These results illustrate the potential of marker-assisted selection even under the infinitesimal genetic model. Power of tests for presence of QTL was substantially reduced when the polygenic model with 3.3% of genetic variance on the chromosome was used as a null hypothesis. The ability to determine whether genetic variance on a chromosome was contributed by a single QTL of major effect or a large number of QTL with minor effects, corresponding to the infinitesimal model, was limited.     

Linkage of circulating eosinophils to markers on chromosome 5q

Although peripheral blood eosinophilia is strongly associated with the risk of developing asthma, genetic determinants of eosinophilia have not been extensively studied. We used sib-pair analysis to assess linkage of circulating eosinophils (as a percent of total white blood cells [WBC]) to nine markers located in chromosome 5q31-33. The study was divided into two phases. Of 246 sib pairs available for the first phase, 35 were classified as low concordant (LC) (both sibs had <= 2% circulating eosinophils), 18 were defined as high concordant (HC) (both sibs had 5% or more circulating eosinophils), and 26 were defined as discordant (one sib had <= 2% and the other sib had 5% or more circulating eosinophils). Significant evidence for linkage among low concordant sib pairs was found for several markers in the region under study, with a peak for marker D5S500 (proportion of alleles shared identical by descent [ibd] = 0.68 +/- 0.05 [mean +/- SE], p = 0.0004). A cross-validating study was done in which an additional 19 sib pairs that were low concordant for circulating eosinophils were studied. Evidence for linkage was also observed in this subset. Results were independent of current wheezing, total serum IgE levels, and other potential confounders. A multipoint analysis done for all low-concordant sib pairs available showed that the maximal logarithm of the odds favoring genetic linkage (LOD) score (2.4, p = 0.0004) was observed in correspondence with marker D5S658. We conclude that a locus or loci may be present in chromosome 5q31-33 that controls for circulating eosinophils as a proportion of total WBC.     

Testing natural selection vs. genetic drift in phenotypic evolution using quantitative trait locus data

Evolutionary biologists have long sought a way to determine whether a phenotypic difference between two taxa was caused by natural selection or random genetic drift. Here I argue that data from quantitative trait locus (QTL) analyses can be used to test the null hypothesis of neutral phenotypic evolution. I propose a sign test that compares the observed number of plus and minus alleles in the "high line" with that expected under neutrality, conditioning on the known phenotypic difference between the taxa. Rejection of the null hypothesis implies a role for directional natural selection. This test is applicable to any character in any organism in which QTL analysis can be performed.     

Extreme discordant sib pairs for mapping quantitative trait loci in humans

Analysis of differences between siblings (sib pair analysis) is a standard method of genetic linkage analysis for mapping quantitative trait loci, such as those contributing to hypertension and obesity, in humans. In traditional designs, pairs are selected at random or with one sib having an extreme trait value. The majority of such pairs provide little power to detect linkage; only pairs that are concordant for high values, low values, or extremely discordant pairs (for example, one in the top 10 percent and the other in the bottom 10 percent of the distribution) provide substantial power. Focus on discordant pairs can reduce the amount of genotyping necessary over conventional designs by 10- to 40-fold.     

Surgical treatment of primary malignant chest wall tumours

Our objective was to infer the genetic model for the quantitative traits using a variety of methods developed in our group. Only a single data set was analyzed in any one analysis, although some comparison between data sets was made. In addition, the simulated model was not known during the course of the analysis. Basic modeling and segregation analyses for the five quantitative traits was followed by several simple genome scans to indicate areas of interest. A Markov chain Monte Carlo (MCMC) multipoint quantitative trait locus (QTL) mapping approach was then used to estimate the posterior probabilities of linkage of QTL to each chromosome simultaneously with trait model parameters, and to further localize the genes. Comparisons between the nuclear family and pedigree data sets indicated a greater power for QTL detection and mapping with the pedigree data sets. Even with the pedigree data, however, precise localization of the QTL did not appear to be possible using single replicate data sets. Two of the three genes with effects on trait Q1 were detected by the MCMC method.     

Genetic response from marker assisted selection in an outbred population for differing marker bracket sizes and with two identified quantitative trait loci

Effect of flanking quantitative trait loci (QTL)-marker bracket size on genetic response to marker assisted selection in an outbred population was studied by simulation of a nucleus breeding scheme. In addition, genetic response with marker assisted selection (MAS) from two quantitative trait loci on the same and different chromosome(s) was investigated. QTL that explained either 5% or 10% of phenotypic variance were simulated. A polygenic component was simulated in addition to the quantitative trait loci. In total, 35% of the phenotypic variance was due to genetic factors. The trait was measured on females only. Having smaller marker brackets flanking the QTL increased the genetic response from MAS selection. This was due to the greater ability to trace the QTL transmission from one generation to the next with the smaller flanking QTL-marker bracket, which increased the accuracy of estimation of the QTL allelic effects. Greater negative covariance between effects at both QTL was observed when two QTL were located on the same chromosome compared to different chromosomes. Genetic response with MAS was greater when the QTL were on the same chromosome in the early generations and greater when they were on different chromosomes in the later generations of MAS.     

A quantitative-trait locus on chromosome 6p influences different aspects of developmental dyslexia

Recent application of nonparametric-linkage analysis to reading disability has implicated a putative quantitative-trait locus (QTL) on the short arm of chromosome 6. In the present study, we use QTL methods to evaluate linkage to the 6p25-21.3 region in a sample of 181 sib pairs from 82 nuclear families that were selected on the basis of a dyslexic proband. We have assessed linkage directly for several quantitative measures that should correlate with different components of the phenotype, rather than using a single composite measure or employing categorical definitions of subtypes. Our measures include the traditional IQ/reading discrepancy score, as well as tests of word recognition, irregular-word reading, and nonword reading. Pointwise analysis by means of sib-pair trait differences suggests the presence, in 6p21.3, of a QTL influencing multiple components of dyslexia, in particular the reading of irregular words (P=.0016) and nonwords (P=.0024). A complementary statistical approach involving estimation of variance components supports these findings (irregular words, P=.007; nonwords, P=.0004). Multipoint analyses place the QTL within the D6S422-D6S291 interval, with a peak around markers D6S276 and D6S105 consistently identified by approaches based on trait differences (irregular words, P=.00035; nonwords, P=.0035) and variance components (irregular words, P=.007; nonwords, P=.0038). Our findings indicate that the QTL affects both phonological and orthographic skills and is not specific to phoneme awareness, as has been previously suggested. Further studies will be necessary to obtain a more precise localization of this QTL, which may lead to the isolation of one of the genes involved in developmental dyslexia.     

Multiple-trait mapping of quantitative trait loci after selective genotyping using logistic regression

Experiments to map QTL usually measure several traits, and not uncommonly genotype only those animals that are extreme for some trait(s). Analysis of selectively genotyped, multiple-trait data presents special problems, and most simple methods lead to biased estimates of the QTL effects. The use of logistic regression to estimate QTL effects is described, where the genotype is treated as the dependent variable and the phenotype as the independent variable. In this way selection on phenotype does not bias the results. If normally distributed errors are assumed, the logistic-regression analysis is almost equivalent to a maximum-likelihood analysis, but can be carried out with standard statistical packages. Analysis of a simulated half-sib experiment shows that logistic regression can estimate the effect and position of a QTL without bias and confirms the increased power achieved by multiple-trait analysis.     

Advances in statistical methods to map quantitative trait loci in outbred populations

Statistical methods to map quantitative trait loci (QTL) in outbred populations are reviewed, extensions and applications to human and plant genetic data are indicated, and areas for further research are identified. Simple and computationally inexpensive methods include (multiple) linear regression of phenotype on marker genotypes and regression of squared phenotypic differences among relative pairs on estimated proportions of identity-by-descent at a locus. These methods are less suited for genetic parameter estimation in outbred populations but allow the determination of test statistic distributions via simulation or data permutation; however, further inferences including confidence intervals of QTL location require the use of Monte Carlo or bootstrap sampling techniques. A method which is intermediate in computational requirements is residual maximum likelihood (REML) with a covariance matrix of random QTL effects conditional on information from multiple linked markers. Testing for the number of QTLs on a chromosome is difficult in a classical framework. The computationally most demanding methods are maximum likelihood and Bayesian analysis, which take account of the distribution of multilocus marker-QTL genotypes on a pedigree and permit investigators to fit different models of variation at the QTL. The Bayesian analysis includes the number of QTLs on a chromosome as an unknown.     

Gain in efficiency from using generalized least squares in the Haseman-Elston test

Techniques that test for linkage between a marker and a trait locus based on the regression methods proposed by Haseman and Elston [1972] involve testing a null hypothesis of no linkage by examination of the regression coefficient. Modified Haseman-Elston methods accomplish this using ordinary least squares (OLS), weighted least squares (WLS), in which weights are reciprocals of estimated variances, and generalized estimating equations (GEE). Methods implementing the WLS and GEE currently use a diagonal covariance matrix, thus incorrectly treating the squared trait differences of two sib pairs within a family as uncorrelated. Correctly specifying the correlations between sib pairs in a family yields the best linear unbiased estimator of the regression coefficient [Scheffe, 1959]. This estimator will be referred to as the generalized least squares (GLS) estimator. We determined the null variance of the GLS estimator and the null variance of the WLS/OLS estimator. The correct null variance of the WLS/OLS estimate of the Haseman-Elston (H-E) regression coefficient may be either larger or smaller than the variance of the WLS/OLS estimate calculated assuming that the squared sib-pair differences are uncorrelated. For a fully informative marker locus, the gain in efficiency using GLS rather than WLS/OLS under the null hypothesis is approximately 11% in a large multifamily study with three siblings per family and 25% for families with four siblings each.     

Continuity and change in children's social maladjustment: A developmental behavior genetic study.

Two developmental models were used to study genetic and environmental mechanisms underlying continuity and change in children's maladjustment. The transmission model assumed that successive levels of functioning were causally linked and that earlier experiences or prior genetic influences affected later maladjustment. The liability model related continuity in problem behavior to stable underlying environmental or genetic factors. The analyses pertained on average to 436 pairs of full siblings, 119 pairs of half siblings, and 122 pairs of cousins for whom maternal ratings of problem behaviors were available at ages 4–6, 6–8, and 8–10. Nonshared environmental influences appeared to be most important for changes in children's problem behaviors and did not have significant effects on age-to-age continuity. To represent the genetic and shared environmental mechanisms underlying stability in problem behavior, the authors preffered liability models without time specific effects. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Genome screening using extremely discordant and extremely concordant sib pairs

We applied extreme sib-pair methods in two ways to the GAW10 Problem 2A data sets to detect susceptible quantitative trait loci using extremely discordant sib pairs only, and combining them with the available extremely concordant sib pairs as suggested by the authors elsewhere. Ten successive original replicates were combined into one sampling pool so as to get the necessary number of extreme sib pairs. A total of 100 replicates were used to produce 10 such data sets for both initial detection and confirmations. Strong signals were found with markers D5G15 for Q1, D8G27-28 for Q4, and D9G7-9 for Q5.     

Are genetic factors important in the aetiology of leukoaraiosis? Results from a memory clinic population

Although cumulative evidence suggests that a genetic predisposition plays a major role in development of systemic lupus erythematosus (SLE) and/or lupus nephritis (LN), the susceptibility genes are mostly unknown. The difficulty in identifying susceptibility genes is due in part to multiple genes with variable genetic effects and the diverse genetic backgrounds of human populations. In human SLE, genes of early components of complements as well as many polymorphic genes (including the MHC class II and class III, FcgammaR, mannose-binding protein, IL-6, Bcl-2, and IL-10 genes) have been associated with SLE or LN by population-based case-control or within-case studies. The contribution of some of these disease-associated genes to the presence or absence of clinical manifestations has been further tested in mice with targeted disruption of the specific candidate gene. In addition to SLE susceptibility genes, there may be a separate set of nephropathy susceptibility genes predisposing to LN as suggested by the familial clustering of end-stage renal disease in African-Americans with LN. The availability of densely mapped genetic markers spanning the entire genome has enabled the identification of chromosomal regions linked to disease susceptibility genes without prior knowledge of the gene function. Our group has used known murine lupus susceptibility loci as a guide, and conducted linkage analysis of genetic markers located within a specific, possibly syntenic human chromosomal region. Evidence for linkage of a chromosome 1q41-42 region was observed in SLE-affected sib pairs from multiple ethnic groups. More recently, several groups have reported results of genome scans of SLE-affected sib pairs or pedigrees. These exciting recent developments in delineating the genetic basis of SLE or LN are summarized in this review.