Genetic analysis of diet-induced hypercholesterolemia in exogenously hypercholesterolemic rats

The exogenously hypercholesterolemic (ExHC) rat is an established strain that exhibits a polygenic syndrome of hypercholesterolemia after feeding on a cholesterol-containing diet, and the extent of this differs between male and female rats in the strain. The present study was performed to determine the genetic background of diet-induced hypercholesterolemia in ExHC rats. We used quantitative trait locus (QTL) analyses of the F2 progeny derived from ExHC and Brown-Norway rats. Rats were fed a diet containing 1% cholesterol, and a genome-wide scan was then performed. Significant QTLs for serum total cholesterol levels were revealed on chromosomes 5 and 14 in the vicinity of markers D5Rat95 and D14Rat43, having maximum logarithm of the odds scores of 6.0 and 5.8, respectively. A suggestive QTL for the trait was also detected on chromosome 3 at D3Rat140. In particular, the QTL on chromosome 5 was specific for female rats. These loci were novel QTLs for post-dietary serum total cholesterol levels. In addition, cross-mating analysis in F1 generations suggested that the responsiveness to dietary cholesterol in ExHC rats is partly attributable to X-linked inheritance. Identifying such genetic factors may be useful in predicting the risks associated with diet-induced hypercholesterolemia in humans.     

The Design of Inheritance Studies

In a study of the inheritance of a quantitative trait in the general population, data are collected from the three-generational nuclear families of many index cases. The question arises as to the optimal choice of family members to maximise the power of testing a hypothesis of polygenic and environmental effects against an alternative of environmental effects only. The method chosen is to minimise the asymptotic variance of the ratio of polygenic to environmental variance, for fixed total variance and the environmental correlations between family members. Using Taylor expansions in the region where the ratio is close to zero, an approximate expression for the variance of the ratio is obtained. This expression can then be evaluated for all possible structures of a three-generational nuclear family of a given size.     

Semiparametric variance components models for genetic studies with longitudinal phenotypes

In a family-based genetic study such as the Framingham Heart Study (FHS), longitudinal trait measurements are recorded on subjects collected from families. Observations on subjects from the same family are correlated due to shared genetic composition or environmental factors such as diet. The data have a 3-level structure with measurements nested in subjects and subjects nested in families. We propose a semiparametric variance components model to describe phenotype observed at a time point as the sum of a nonparametric population mean function, a nonparametric random quantitative trait locus (QTL) effect, a shared environmental effect, a residual random polygenic effect and measurement error. One feature of the model is that we do not assume a parametric functional form of the age-dependent QTL effect, and we use penalized spline-based method to fit the model. We obtain nonparametric estimation of the QTL heritability defined as the ratio of the QTL variance to the total phenotypic variance. We use simulation studies to investigate performance of the proposed methods and apply these methods to the FHS systolic blood pressure data to estimate age-specific QTL effect at 62cM on chromosome 17.     

A model for sibling effects in man.

A model is developed to specify the environmental effect of one sibling on another for a polygenic trait. Such effects are detectable in priniciple and the approach is illustrated with twin data relating to psychoticism. The relationship between the model and those employed in the treatment of kin selection is indicated.     

Power and Predictive Accuracy of Polygenic Risk Scores

Polygenic scores have recently been used to summarise genetic effects among an ensemble of markers that do not individually achieve significance in a large-scale association study. Markers are selected using an initial training sample and used to construct a score in an independent replication sample by forming the weighted sum of associated alleles within each subject. Association between a trait and this composite score implies that a genetic signal is present among the selected markers, and the score can then be used for prediction of individual trait values. This approach has been used to obtain evidence of a genetic effect when no single markers are significant, to establish a common genetic basis for related disorders, and to construct risk prediction models. In some cases, however, the desired association or prediction has not been achieved. Here, the power and predictive accuracy of a polygenic score are derived from a quantitative genetics model as a function of the sizes of the two samples, explained genetic variance, selection thresholds for including a marker in the score, and methods for weighting effect sizes in the score. Expressions are derived for quantitative and discrete traits, the latter allowing for case/control sampling. A novel approach to estimating the variance explained by a marker panel is also proposed. It is shown that published studies with significant association of polygenic scores have been well powered, whereas those with negative results can be explained by low sample size. It is also shown that useful levels of prediction may only be approached when predictors are estimated from very large samples, up to an order of magnitude greater than currently available. Therefore, polygenic scores currently have more utility for association testing than predicting complex traits, but prediction will become more feasible as sample sizes continue to grow.     

Multivariate mixed inheritance models for QTL detection on porcine chromosome 6

A series of multivariate mixed-inheritance models is fitted to the data from an outbred-line pig cross commercially used in Norway. Each model accommodates information on polygenic (co)variances between F2 individuals and their F1 parents across the five traits through incorporation of a random animal effect. Considered traits relate to meat quality and are chosen following up the results from a previous evaluation, in which a putative quantitative trait locus (QTL) was identified on chromosome six that affects the amount of intramuscular fat (IMF), meat percentage, meat tenderness and smell intensity (Grindflek et al., 2001). An additional trait included in the model, based on results of other studies, is the backfat thickness. The analysed material comprises data scored for 305 F2 individuals, whereas marker information is available for F1 and F2 generations. Based on the results of the multivariate analysis with the mixed-inheritance model, it was possible to conclude that the evidence for QTLs for meat percentage, meat tenderness and smell intensity in the study of Grindflek et al. (2001) do not represent separate QTLs, but is caused by the fact that the applied pre-adjustment of trait values for polygenic effects failed properly to remove the polygenic variation. The QTL effect on IMF on chromosome six was confirmed.     

A nonparametric and a parametric version of a test for the detection of the presence of a major gene applicable on data for the complete nuclear family

Summary Nonparametric and parametric tests are suggested for detecting the presence of a major gene for a quantitative trait. The model for the determination of the quantitative trait is an additive one with polygenic, family environment, and individual environment components. The power functions with respect to the major gene effect have been calculated by simulation, and the tests have therefore been compared with each other. The tests have been applied to nuclear family data on human obesity, and the results compared with those obtained using other methods on the same data.This work was done while the author was a visitor at the Istituto di Genetica Biochemica ed Evoluzionistica, CNR, Pavia     

Modeling effect of homo- or heterozygosity on animal growth intensity

A model has been developed that describes the dependence of a quantitative selective trait on the animal homo- and heterozygosity for the genes that control the biochemical reaction rate (isoenzyme systems). The model includes any cases of gene control of a quantitative trait and is applicable to real, genetically heterogeneous populations. The results of testing the model show that it can be used for identifying the genes involved in additive polygenic determination of quantitative commercially valuable traits.     

A powerful and robust method for mapping quantitative trait loci in general pedigrees

The variance-components model is the method of choice for mapping quantitative trait loci in general human pedigrees. This model assumes normally distributed trait values and includes a major gene effect, random polygenic and environmental effects, and covariate effects. Violation of the normality assumption has detrimental effects on the type I error and power. One possible way of achieving normality is to transform trait values. The true transformation is unknown in practice, and different transformations may yield conflicting results. In addition, the commonly used transformations are ineffective in dealing with outlying trait values. We propose a novel extension of the variance-components model that allows the true transformation function to be completely unspecified. We present efficient likelihood-based procedures to estimate variance components and to test for genetic linkage. Simulation studies demonstrated that the new method is as powerful as the existing variance-components methods when the normality assumption holds; when the normality assumption fails, the new method still provides accurate control of type I error and is substantially more powerful than the existing methods. We performed a genomewide scan of monoamine oxidase B for the Collaborative Study on the Genetics of Alcoholism. In that study, the results that are based on the existing variance-components method changed dramatically when three outlying trait values were excluded from the analysis, whereas our method yielded essentially the same answers with or without those three outliers. The computer program that implements the new method is freely available.     

Using the mixed model for interval mapping of quantitative trait loci in outbred line crosses

Interval mapping by simple regression is a powerful method for the detection of quantitative trait loci (QTLs) in line crosses such as F2 populations. Due to the ease of computation of the regression approach, relatively complex models with multiple fixed effects, interactions between QTLs or between QTLs and fixed effects can easily be accommodated. However, polygenic effects, which are not targeted in QTL analysis, cannot be treated as random effects in a least squares analysis. In a cross between true inbred lines this is of no consequence, as the polygenic effect contributes just to the residual variance. In a cross between outbred lines, however, if a trait has high polygenic heritability, the additive polygenic effect has a large influence on variation in the population. Here we extend the fixed model for the regression interval mapping method to a mixed model using an animal model. This makes it possible to use not only the observations from progeny (e.g. F2), but also those from the parents (F1) to evaluate QTLs and polygenic effects. We show how the animal model using parental observations can be applied to an outbred cross and so increase the power and accuracy of QTL analysis. Three estimation methods, i.e. regression and an animal model either with or without parental observations, are applied to simulated data. The animal model using parental observations is shown to have advantages in estimating QTL position and additive genotypic value, especially when the polygenic heritability is large and the number of progeny per parent is small.     

A Bayesian multilocus association method: allowing for higher-order interaction in association studies

For most common diseases with heritable components, not a single or a few single-nucleotide polymorphisms (SNPs) explain most of the variance for these disorders. Instead, much of the variance may be caused by interactions (epistasis) among multiple SNPs or interactions with environmental conditions. We present a new powerful statistical model for analyzing and interpreting genomic data that influence multifactorial phenotypic traits with a complex and likely polygenic inheritance. The new method is based on Markov chain Monte Carlo (MCMC) and allows for identification of sets of SNPs and environmental factors that when combined increase disease risk or change the distribution of a quantitative trait. Using simulations, we show that the MCMC method can detect disease association when multiple, interacting SNPs are present in the data. When applying the method on real large-scale data from a Danish population-based cohort, multiple interactions are identified that severely affect serum triglyceride levels in the study individuals. The method is designed for quantitative traits but can also be applied on qualitative traits. It is computationally feasible even for a large number of possible interactions and differs fundamentally from most previous approaches by entertaining nonlinear interactions and by directly addressing the multiple-testing problem.     

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.     

Bayesian mapping of quantitative trait loci for complex binary traits

A complex binary trait is a character that has a dichotomous expression but with a polygenic genetic background. Mapping quantitative trait loci (QTL) for such traits is difficult because of the discrete nature and the reduced variation in the phenotypic distribution. Bayesian statistics are proved to be a powerful tool for solving complicated genetic problems, such as multiple QTL with nonadditive effects, and have been successfully applied to QTL mapping for continuous traits. In this study, we show that Bayesian statistics are particularly useful for mapping QTL for complex binary traits. We model the binary trait under the classical threshold model of quantitative genetics. The Bayesian mapping statistics are developed on the basis of the idea of data augmentation. This treatment allows an easy way to generate the value of a hypothetical underlying variable (called the liability) and a threshold, which in turn allow the use of existing Bayesian statistics. The reversible jump Markov chain Monte Carlo algorithm is used to simulate the posterior samples of all unknowns, including the number of QTL, the locations and effects of identified QTL, genotypes of each individual at both the QTL and markers, and eventually the liability of each individual. The Bayesian mapping ends with an estimation of the joint posterior distribution of the number of QTL and the locations and effects of the identified QTL. Utilities of the method are demonstrated using a simulated outbred full-sib family. A computer program written in FORTRAN language is freely available on request.     

Complex genetic architecture revealed by analysis of high-density lipoprotein cholesterol in chromosome substitution strains and F2 crosses

Intercrosses between inbred lines provide a traditional approach to analysis of polygenic inheritance in model organisms. Chromosome substitution strains (CSSs) have been developed as an alternative to accelerate the pace of gene identification in quantitative trait mapping. We compared a classical intercross and three CSS intercrosses to examine the genetic architecture underlying plasma high-density lipoprotein cholesterol (HDL) levels in the C57BL/6J (B) and A/J (A) mouse strains. The B x A intercross revealed significant quantitative trait loci (QTL) for HDL on chromosomes 1, 4, 8, 15, 17, 18, and 19. A CSS survey revealed that many have significantly different HDL levels compared to the background strain B, including chromosomes with no significant QTL in the intercross and, in some cases (CSS-1, CSS-17), effects that are opposite to those observed in the B x A intercross population. Intercrosses between B and three CSSs (CSS-3, CSS-11, and CSS-8) revealed significant QTL but with some unexpected differences from the B x A intercross. Our inability to predict the results of CSS intercrosses suggests that additional complexity will be revealed by further crosses and that the CSS mapping strategy should be viewed as a complement to, rather than a replacement for, classical intercross mapping.     

An Approximate Model of Polygenic Inheritance

The finite polygenic model approximates polygenic inheritance by postulating that a quantitative trait is determined by n independent, additive loci. The 3(n) possible genotypes for each person in this model limit its applicability. CANNINGS, THOMPSON, and SKOLNICK suggested a simplified, nongenetic version of the model involving only 2n + 1 genotypes per person. This article shows that this hypergeometric polygenic model also approximates polygenic inheritance well. In particular, for noninbred pedigrees, trait means, variances, covariances, and marginal distributions match those of the ordinary finite polygenic model. Furthermore as n -> &, the trait values within a pedigree collectively tend toward multivariate normality. The implications of these results for likelihood evaluation under the polygenic threshold and mixed models of inheritance are discussed. Finally, a simple numerical example illustrates the application of the hypergeometric polygenic model to risk prediction under the polygenic threshold model.     

An EM algorithm for mapping quantitative resistance loci

Many disease resistance traits in plants have a polygenic background and the disease phenotypes are modified by environmental factors. As a consequence, the phenotypic values usually show a quantitative variation. The phenotypes of such disease traits, however, are often measured in discrete but ordered categories. These traits are called ordinal traits. In terms of disease resistance, they are called quantitative resistance traits, as opposed to qualitative resistance traits, and are controlled by the quantitative resistance loci (QRL). Classical quantitative trait locus mapping methods are not optimal for ordinal trait analysis because the assumption of normal distribution is violated. Methods for mapping binary trait loci are not suitable either because there are more than two categories in ordinal traits. We developed a maximum likelihood method to map these QRL. The method is implemented via a multicycle expectation-conditional-maximization (ECM) algorithm under the threshold model, where we can estimate both the QRL effects and the thresholds that link the disease liability and the categorical phenotype. The method is verified in simulated data under various combinations of the parameters. An SAS program is available to implement the multicycle ECM algorithm. The program can be downloaded from our website at www.statgen.ucr.edu.     

Complex segregation analysis of dental morphological variants

A set of 20 morphological variants of the dental crowns and four characteristics of the jaws are tested for probable mode of inheritance using the complex segregation analysis method of Morton et al. (Am. J. Hum. Genet. 23:602-611, 1971). Models tested include three two-allele single-locus models (dominant, codominant, and recessive) and a model employing the polychotomized normal distribution of liability (an additive polygenic model), with transmissibility estimated via maximum likelihood. Most of the traits studied are observed using ordinal scales with several grades, and many are tested using more than one dichotomy of their scale. These multiple analyses allow for an examination of such factors as trait incidence on the results of the statistical analysis. The results of the analysis yield propositions of major genes for 13 of the 24 traits examined. Two traits give good evidence of being polygenic in origin. The remaining nine characters present methodological problems that do not allow for a definite conclusion on their mode of inheritance at this time. The ability to test varying levels of transmissibility in the polygenic model allows for an estimation of the percentage of trait variance determined by familial factors. Estimates of transmissibility for all characters examined range from 0 to 1, with a mean of 0.36. These findings may suggest a large environmental role in the development of dental crown morphology. However, the possibility exists that difficulties in the ability to classify the expression of certain traits consistently result in overestimates of the environmental influences on the development of those characters.     

Inheritance of total serum IgE (basal levels) in man.

Since allergic individuals with atopic allergy tend to have higher total serum IgE levels than do nonallergic subjects, family studies of total serum IgE levels are necessary in delineating the genetic and environmental factors involved in the expression of allergic disease. However, previous studies do not agree as to the genetic basis of total IgE production. To try to resolve this conflict, a total of 278 individuals from 42 nuclear families ascertained for large family size (at least four children) were studied. The families were not selected for the presence of allergic disease. Segregation analysis showed that the mixed model of recessive inheritance of high levels was most appropriate for these data--with approximately 36% of the total phenotypic variation in log[IgE] attributable to genetic factors, equally divided between a Mendelian component and a more general polygenic component. Thus, these data suggest some role for Mendelian control of basal IgE levels, but there is significant familial aggregation in IgE levels over and above that due to a Mendelian factor.     

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.     

Sex-specific and sex-independent quantitative trait loci for facets of the metabolic syndrome in WOKW rats

WOKW rats develop a complete metabolic syndrome closely resembling human disease. Since genetic studies using male (WOKW x DA)F2 progeny showed that several independent genetic factors were involved, a polygenic basis for the syndrome in WOKW was assumed. However, because the metabolic syndrome in human clearly demonstrates sex differences, we have extended our study to include both male and female (WOKW x DA)F2 progeny in a genome-wide scan. Male- or female-specific quantitative trait loci (QTLs) were mapped for body weight, body mass index, adiposity index and serum insulin on chromosomes 1 and 5, serum triglycerides on chromosomes 4, 7, 11, and 16, serum total and high density lipoprotein cholesterol on chromosomes 3, 4, 5, 10, and 17, and serum leptin on chromosomes 8 and 16 as well as blood glucose and glucose tolerance (AUC) on chromosomes 3, 4 and 17. QTLs for both, males and females were only found for body weight on chromosome 1 and for serum total cholesterol on chromosome 3 and 10. These findings clearly demonstrate that there are sex-specific and sex-independent QTLs for facets of the metabolic syndrome in WOKW rats.