Multilocus genetics and the coevolution of quantitative traits

We develop and analyze an explicit multilocus genetic model of coevolution. We assume that interactions between two species (mutualists, competitors, or victim and exploiter) are mediated by a pair of additive quantitative traits that are also subject to direct stabilizing selection toward intermediate optima. Using a weak-selection approximation, we derive analytical results for a symmetric case with equal locus effects and no mutation, and we complement these results by numerical simulations of more general cases. We show that mutualistic and competitive interactions always result in coevolution toward a stable equilibrium with no more than one polymorphic locus per species. Victim-exploiter interactions can lead to different dynamic regimes including evolution toward stable equilibria, cycles, and chaos. At equilibrium, the victim is often characterized by a very large genetic variance, whereas the exploiter is polymorphic in no more than one locus. Compared to related one-locus or quantitative genetic models, the multilocus model exhibits two major new properties. First, the equilibrium structure is considerably more complex. We derive detailed conditions for the existence and stability of various classes of equilibria and demonstrate the possibility of multiple simultaneously stable states. Second, the genetic variances change dynamically, which in turn significantly affects the dynamics of the mean trait values. In particular, the dynamics tend to be destabilized by an increase in the number of loci.     

Bivariate association analysis for quantitative traits using generalized estimation equation

Quantitative traits often underlie risk for complex diseases. Many studies collect multiple correlated quantitative phenotypes and perform univariate analyses on each of them respectively. However, this strategy may not be powerful and has limitations to detect plei- otropic genes that may underlie correlated quantitative traits. In addition, testing multiple traits individually will exacerbate perplexing problem of multiple testing. In this study, generalized estimating equation 2 （GEE2） is applied to association mapping of two correlated quantitative traits. We suppose that a quantitative trait locus is located in a chromosome region that exerts pleiotropic effects on multiple quantitative traits. In that region, multiple SNPs are genotyped. Genotypes of these SNPs and the two quantitative traits affected by a causal SNP were simulated under various parameter values： residual correlation coefficient between two traits, causal SNP heritability, minor allele frequency of the causal SNP, extent of linkage disequilibrium with the causal SNP, and the test sample size. By power ana- lytical analyses, it is showed that the bivariate method is generally more powerful than the univariate method. This method is robust and yields false-positive rates close to the pre-set nominal significance level. Our real data analyses attested to the usefulness of the method.     

Combined linkage and association sib-pair analysis for quantitative traits.

An extension to current maximum-likelihood variance-components procedures for mapping quantitative-trait loci in sib pairs that allows a simultaneous test of allelic association is proposed. The method involves modeling of the allelic means for a test of association, with simultaneous modeling of the sib-pair covariance structure for a test of linkage. By partitioning of the mean effect of a locus into between- and within-sibship components, the method controls for spurious associations due to population stratification and admixture. The power and efficacy of the method are illustrated through simulation of various models of both real and spurious association.     

Imputation-based analysis of association studies: candidate regions and quantitative traits

We introduce a new framework for the analysis of association studies, designed to allow untyped variants to be more effectively and directly tested for association with a phenotype. The idea is to combine knowledge on patterns of correlation among SNPs (e.g., from the International HapMap project or resequencing data in a candidate region of interest) with genotype data at tag SNPs collected on a phenotyped study sample, to estimate ("impute") unmeasured genotypes, and then assess association between the phenotype and these estimated genotypes. Compared with standard single-SNP tests, this approach results in increased power to detect association, even in cases in which the causal variant is typed, with the greatest gain occurring when multiple causal variants are present. It also provides more interpretable explanations for observed associations, including assessing, for each SNP, the strength of the evidence that it (rather than another correlated SNP) is causal. Although we focus on association studies with quantitative phenotype and a relatively restricted region (e.g., a candidate gene), the framework is applicable and computationally practical for whole genome association studies. Methods described here are implemented in a software package, Bim-Bam, available from the Stephens Lab website http://stephenslab.uchicago.edu/software.html.     

Enhanced efficiency of quantitative trait loci mapping analysis based on multivariate complexes of quantitative traits

An approach to increase the efficiency of mapping quantitative trait loci (QTL) was proposed earlier by the authors on the basis of bivariate analysis of correlated traits. The power of QTL detection using the log-likelihood ratio (LOD scores) grows proportionally to the broad sense heritability. We found that this relationship holds also for correlated traits, so that an increased bivariate heritability implicates a higher LOD score, higher detection power, and better mapping resolution. However, the increased number of parameters to be estimated complicates the application of this approach when a large number of traits are considered simultaneously. Here we present a multivariate generalization of our previous two-trait QTL analysis. The proposed multivariate analogue of QTL contribution to the broad-sense heritability based on interval-specific calculation of eigenvalues and eigenvectors of the residual covariance matrix allows prediction of the expected QTL detection power and mapping resolution for any subset of the initial multivariate trait complex. Permutation technique allows chromosome-wise testing of significance for the whole trait complex and the significance of the contribution of individual traits owing to: (a) their correlation with other traits, (b) dependence on the chromosome in question, and (c) both a and b. An example of application of the proposed method on a real data set of 11 traits from an experiment performed on an F(2)/F(3) mapping population of tetraploid wheat (Triticum durum x T. dicoccoides) is provided.     

Joint tests of linkage and association for quantitative traits

In this paper we describe various study designs and analytic techniques for testing the joint hypothesis that a genetic marker is both linked to and associated with a quantitative phenotype. Issues of power and sampling are addressed. The distinction between methods that explicitly examine association and those that infer association by examining the distribution of allelic transmissions from a heterozygous parent is examined. Extensions to multivariate, multiallelic, and multilocus situations are addressed. Recent approaches that combine variance-components-based linkage analyses with joint tests of linkage in the presence of association for disentanglement of the linkage and association and the application of such methods to fine mapping are discussed. Finally, new classes of joint tests of linkage and association that do not require samples of related individuals are described.     

Hypothesis testing for the genetic background of quantitative traits

The testing of Bayesian point null hypotheses on variance component models have resulted in a tough assignment for which no clear and generally accepted method exists. In this work we present what we believe is a succeeding approach to such a task. It is based on a simple reparameterization of the model in terms of the total variance and the proportion of the additive genetic variance with respect to it, as well as on the explicit inclusion on the prior probability of a discrete component at origin. The reparameterization was used to bypass an arbitrariness related to the impropriety of uninformative priors onto unbounded variables while the discrete component was necessary to overcome the zero probability assigned to sets of null measure by the usual continuous variable models. The method was tested against computer simulations with appealing results.     

Estimation and testing of parent-of-origin effects for quantitative traits

Recent progress in developing family-based association methods has extended their use to the analysis of quantitative traits in the offspring and to the estimation, for dichotomous traits, of the relative contribution of genetic and environmental mechanisms for parent-of-origin effects. However, many traits of interest are not naturally measured on a binary scale yet are suspected or known to be influenced by imprinted genes, and there is consequent interest in seeking evidence for parent-of-origin effects at these loci. Here we show how simple linear models can be used to estimate these parent-of-origin effects for a broad class of phenotypes; in particular, normally distributed quantitative traits are easily dealt with.     

Haplotype-sharing analysis for alcohol dependence based on quantitative traits and the Mantel statistic

Haplotype-based methods have become increasingly popular in the last decade because shared lengths in haplotypes can be used for disease localization. In this contribution, we propose a novel linkage-based haplotype-sharing approach for quantitative traits based on the class of Mantel statistics which is closely related to the weighted pair-wise correlation statistic. Because these statistics are known to be liberal, we propose a permutation test to evaluate significance. We applied the Mantel statistic to the autosomal data from the genome-wide scan of the Collaborative Study on the Genetics of Alcoholism with the Affymetrix Genotype 10 K array that was provided for the Genetic Analysis Workshop 14. Four regions on chromosome 4, 8, 16, and 20 showed p-values less than 0.005 with a minimum p-value of < 0.0001 on chromosome 16 (tsc0520638 at 72.8 cM). Three of these four regions located on chromosome 4, 16, and 20 have been reported previously in the Genetic Analysis Workshop 11.     

Sibling-based tests of linkage and association for quantitative traits.

The transmission/disequilibrium test (TDT) developed by Spielman et al. can be a powerful family-based test of linkage and, in some cases, a test of association as well as linkage. It has recently been extended in several ways; these include allowance for implementation with quantitative traits, allowance for multiple alleles, and, in the case of dichotomous traits, allowance for testing in the absence of parental data. In this article, these three extensions are combined, and two procedures are developed that offer valid joint tests of linkage and (in the case of certain sibling configurations) association with quantitative traits, with use of data from siblings only, and that can accommodate biallelic or multiallelic loci. The first procedure uses a mixed-effects (i.e., random and fixed effects) analysis of variance in which sibship is the random factor, marker genotype is the fixed factor, and the continuous phenotype is the dependent variable. Covariates can easily be accommodated, and the procedure can be implemented in commonly available statistical software. The second procedure is a permutation-based procedure. Selected power studies are conducted to illustrate the relative power of each test under a variety of circumstances.     

Parallel and serial computing tools for testing single-locus and epistatic SNP effects of quantitative traits in genome-wide association studies

Background  

Genome-wide association studies (GWAS) using single nucleotide polymorphism (SNP) markers provide opportunities to detect epistatic SNPs associated with quantitative traits and to detect the exact mode of an epistasis effect. Computational difficulty is the main bottleneck for epistasis testing in large scale GWAS.     

Structural model analysis of multiple quantitative traits

We introduce a method for the analysis of multilocus, multitrait genetic data that provides an intuitive and precise characterization of genetic architecture. We show that it is possible to infer the magnitude and direction of causal relationships among multiple correlated phenotypes and illustrate the technique using body composition and bone density data from mouse intercross populations. Using these techniques we are able to distinguish genetic loci that affect adiposity from those that affect overall body size and thus reveal a shortcoming of standardized measures such as body mass index that are widely used in obesity research. The identification of causal networks sheds light on the nature of genetic heterogeneity and pleiotropy in complex genetic systems.     

A powerful and flexible multilocus association test for quantitative traits

Association mapping of complex traits typically employs tagSNP genotype data to identify a trait locus within a region of interest. However, considerable debate exists regarding the most powerful strategy for utilizing such tagSNP data for inference. A popular approach tests each tagSNP within the region individually, but such tests could lose power as a result of incomplete linkage disequilibrium between the genotyped tagSNP and the trait locus. Alternatively, one can jointly test all tagSNPs simultaneously within the region (by using genotypes or haplotypes), but such multivariate tests have large degrees of freedom that can also compromise power. Here, we consider a semiparametric model for quantitative-trait mapping that uses genetic information from multiple tagSNPs simultaneously in analysis but produces a test statistic with reduced degrees of freedom compared to existing multivariate approaches. We fit this model by using a dimension-reducing technique called least-squares kernel machines, which we show is identical to analysis using a specific linear mixed model (which we can fit by using standard software packages like SAS and R). Using simulated SNP data based on real data from the International HapMap Project, we demonstrate that our approach often has superior performance for association mapping of quantitative traits compared to the popular approach of single-tagSNP testing. Our approach is also flexible, because it allows easy modeling of covariates and, if interest exists, high-dimensional interactions among tagSNPs and environmental predictors.     

A unified Haseman-Elston method for testing linkage with quantitative traits

The Haseman and Elston (H-E) method uses a simple linear regression to model the squared trait difference of sib pairs with the shared allele identical by descent (IBD) at marker locus for linkage testing. Under this setting, the squared mean-corrected trait sum is also linearly related to the IBD sharing. However, the resulting slope estimate for either model is not efficient. In this report, we propose a simple linkage test that optimally uses information from the estimates of both models. We also demonstrate that the new test is more powerful than both the traditional one and the recently revisited H-E methods.     

A general test of association for quantitative traits in nuclear families

High-resolution mapping is an important step in the identification of complex disease genes. In outbred populations, linkage disequilibrium is expected to operate over short distances and could provide a powerful fine-mapping tool. Here we build on recently developed methods for linkage-disequilibrium mapping of quantitative traits to construct a general approach that can accommodate nuclear families of any size, with or without parental information. Variance components are used to construct a test that utilizes information from all available offspring but that is not biased in the presence of linkage or familiality. A permutation test is described for situations in which maximum-likelihood estimates of the variance components are biased. Simulation studies are used to investigate power and error rates of this approach and to highlight situations in which violations of multivariate normality assumptions warrant the permutation test. The relationship between power and the level of linkage disequilibrium for this test suggests that the method is well suited to the analysis of dense maps. The relationship between power and family structure is investigated, and these results are applicable to study design in complex disease, especially for late-onset conditions for which parents are usually not available. When parental genotypes are available, power does not depend greatly on the number of offspring in each family. Power decreases when parental genotypes are not available, but the loss in power is negligible when four or more offspring per family are genotyped. Finally, it is shown that, when siblings are available, the total number of genotypes required in order to achieve comparable power is smaller if parents are not genotyped.     

famCNV: copy number variant association for quantitative traits in families

A program package to enable genome-wide association of copy number variants (CNVs) with quantitative phenotypes in families of arbitrary size and complexity. Intensity signals that act as proxies for the number of copies are modeled in a variance component framework and association with traits is assessed through formal likelihood testing. AVAILABILITY AND IMPLEMENTATION: The Java package is made available at www.imperial.ac.uk/medicine/people/m.falchi/. CONTACT: m.falchi@imperial.ac.uk.     

A genome-wide association study for quantitative traits in schizophrenia in China

Few genome-wide association studies (GWAS) of schizophrenia have included Chinese populations, and verification of positive genetic findings from other ethnic groups is rare in Chinese groups. We used fluid intelligence as the quantitative trait reflecting schizophrenia dysfunction in Chinese populations, and determined the impact of genetic variation on fluid intelligence phenotypic patterns to identify genetic influences in schizophrenia. The study sample comprised 98 patients with schizophrenia and 60 healthy controls. The general fluid intelligence of participants was assessed with Cattell's Culture-Free Intelligence Test (CCFIT). Subjects were genotyped using the Illumina HumanHap 660 beadchip. We identified the methionine sulfoxide reductase A (MSRA) gene on chromosome 8 as having an association with fluid intelligence. However, only CCFIT subtest 1 (series score) demonstrated a significant result for the interaction term using the criteria of the quantitative trait (QT) analysis of 10(-5) for at least three SNPs. There were 15 haplotype blocks of MSRA gene SNPs identified using Haploview 4.2 with solid spine D' > 0.80. The strongest QT interaction was noted in Block 3, with the most common haplotypes being AAACAGCAG and CGCAGAAGA. In conclusion, we report data from a GWAS with quantitative traits design from Chinese first-episode schizophrenia patients and matched controls. Although the gene identified requires confirmation in an independent sample, the MSRA gene located on chromosome 8 was found to be associated with the phenotype of schizophrenia.     

Multiparent intercross populations in analysis of quantitative traits

Most traits of interest to medical, agricultural and animal scientists show continuous variation and complex mode of inheritance. DNA-based markers are being deployed to analyse such complex traits, that are known as quantitative trait loci (QTL). In conventional QTL analysis, F2, backcross populations, recombinant inbred lines, backcross inbred lines and double haploids from biparental crosses are commonly used. Introgression lines and near isogenic lines are also being used for QTL analysis. However, such populations have major limitations like predominantly relying on the recombination events taking place in the F1 generation and mapping of only the allelic pairs present in the two parents. The second generation mapping resources like association mapping, nested association mapping and multiparent intercross populations potentially address the major limitations of available mapping resources. The potential of multiparent intercross populations in gene mapping has been discussed here. In such populations both linkage and association analysis can be conductted without encountering the limitations of structured populations. In such populations, larger genetic variation in the germplasm is accessed and various allelic and cytoplasmic interactions are assessed. For all practical purposes, across crop species, use of eight founders and a fixed population of 1000 individuals are most appropriate. Limitations with multiparent intercross populations are that they require longer time and more resource to be generated and they are likely to show extensive segregation for developmental traits, limiting their use in the analysis of complex traits. However, multiparent intercross population resources are likely to bring a paradigm shift towards QTL analysis in plant species.