Methods for genetic linkage analysis using trisomies.

Certain genetic disorders are rare in the general population, but more common in individuals with specific trisomies. Examples of this include leukemia and duodenal atresia in trisomy 21. This paper presents a linkage analysis method for using trisomic individuals to map genes for such traits. It is based on a very general gene-specific dosage model that posits that the trait is caused by specific effects of different alleles at one or a few loci and that duplicate copies of "susceptibility" alleles inherited from the nondisjoining parent give increased likelihood of having the trait. Our mapping method is similar to identity-by-descent-based mapping methods using affected relative pairs and also to methods for mapping recessive traits using inbred individuals by looking for markers with greater than expected homozygosity by descent. In the trisomy case, one would take trisomic individuals and look for markers with greater than expected homozygosity in the chromosomes inherited from the nondisjoining parent. We present statistical methods for performing such a linkage analysis, including a test for linkage to a marker, a method for estimating the distance from the marker to the trait gene, a confidence interval for that distance, and methods for computing power and sample sizes. We also resolve some practical issues involved in implementing the methods, including how to use partially informative markers and how to test candidate genes.     

Variation in pattern and frequency of acrocentric association in normal and trisomy-21 individuals

Summary Chromosomally normal and trisomy-21 individuals were studied for the ability of their nucleolus-organising chromosomes to form satellite associations in G-banded lymphocyte metaphases. Two types of parameter, absolute association frequency and relative association frequency, were used. There was no significant difference between females and males or between Caucasoids and Mongoloids for either type of association parameter in the controls, nor was there significant correlation between age (17–40 years) and either type of parameter in the controls.The pattern of two chromosome associations is accounted for by two related models in both normal and trisomic individuals. These models imply that there is an extensive polymorphism for associating ability and that this ability may be zero in individual chromosomes. Homologous do not associate preferentially with each other. The absolute frequency of acrocentric association is lower in trisomy 21 individuals than disomic controls, but the relative involvement of chromosome 21 (after correction for the trisomic state) is higher than in the controls.     

DSLINK: a computer program for gene-centromere linkage analysis in families with a trisomic offspring.

Trisomic individuals provide information for gene-centromere mapping, since two of the four chromatids in a meiotic tetrad can be recovered. When centromeric markers are available, linkage analysis between the centromere and any marker locus can be performed in nuclear families having one or more trisomic offspring. Since conventional linkage programs consider only disomic individuals, we have written a FORTRAN computer program, DSLINK, that performs gene-centromere linkage analysis on the basis of information on trisomic and disomic offspring. This program makes it possible to study the relationship between recombination and chromosome segregation.     

Bayesian robust analysis for genetic architecture of quantitative traits

MOTIVATION: In most quantitative trait locus (QTL) mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may affect the accuracy of QTL detection and lead to detection of spurious QTLs. To improve the robustness of QTL mapping methods, we replaced the normal distribution for residuals in multiple interacting QTL models with the normal/independent distributions that are a class of symmetric and long-tailed distributions and are able to accommodate residual outliers. Subsequently, we developed a Bayesian robust analysis strategy for dissecting genetic architecture of quantitative traits and for mapping genome-wide interacting QTLs in line crosses. RESULTS: Through computer simulations, we showed that our strategy had a similar power for QTL detection compared with traditional methods assuming normal-distributed traits, but had a substantially increased power for non-normal phenotypes. When this strategy was applied to a group of traits associated with physical/chemical characteristics and quality in rice, more main and epistatic QTLs were detected than traditional Bayesian model analyses under the normal assumption.     

Model selection in binary trait locus mapping

Quantitative trait locus (QTL) mapping methodology for continuous normally distributed traits is the subject of much attention in the literature. Binary trait locus (BTL) mapping in experimental populations has received much less attention. A binary trait by definition has only two possible values, and the penetrance parameter is restricted to values between zero and one. Due to this restriction, the infinitesimal model appears to come into play even when only a few loci are involved, making selection of an appropriate genetic model in BTL mapping challenging. We present a probability model for an arbitrary number of BTL and demonstrate that, given adequate sample sizes, the power for detecting loci is high under a wide range of genetic models, including most epistatic models. A novel model selection strategy based upon the underlying genetic map is employed for choosing the genetic model. We propose selecting the "best" marker from each linkage group, regardless of significance. This reduces the model space so that an efficient search for epistatic loci can be conducted without invoking stepwise model selection. This procedure can identify unlinked epistatic BTL, demonstrated by our simulations and the reanalysis of Oncorhynchus mykiss experimental data.     

Use of randomization testing to detect multiple epistatic QTLs

Here, we describe a randomization testing strategy for mapping interacting quantitative trait loci (QTLs). In a forward selection strategy, non-interacting QTLs and simultaneously mapped interacting QTL pairs are added to a total genetic model. Simultaneous mapping of epistatic QTLs increases the power of the mapping strategy by allowing detection of interacting QTL pairs where none of the QTL can be detected by their marginal additive and dominance effects. Randomization testing is used to derive empirical significance thresholds for every model selection step in the procedure. A simulation study was used to evaluate the statistical properties of the proposed randomization tests and for which types of epistasis simultaneous mapping of epistatic QTLs adds power. Least squares regression was used for QTL parameter estimation but any other QTL mapping method can be used. A genetic algorithm was used to search for interacting QTL pairs, which makes the proposed strategy feasible for single processor computers. We believe that this method will facilitate the evaluation of the importance at epistatic interaction among QTLs controlling multifactorial traits and disorders.     

Linkage disequilibrium analysis of biallelic DNA markers, human quantitative trait loci, and threshold-defined case and control subjects

Linkage disequilibrium (LD) mapping has been applied to many simple, monogenic, overtly Mendelian human traits, with great success. However, extensions and applications of LD mapping approaches to more complex human quantitative traits have not been straightforward. In this article, we consider the analysis of biallelic DNA marker loci and human quantitative trait loci in settings that involve sampling individuals from opposite ends of the trait distribution. The purpose of this sampling strategy is to enrich samples for individuals likely to possess (and not possess) trait-influencing alleles. Simple statistical models for detecting LD between a trait-influencing allele and neighboring marker alleles are derived that make use of this sampling scheme. The power of the proposed method is investigated analytically for some hypothetical gene-effect scenarios. Our studies indicate that LD mapping of loci influencing human quantitative trait variation should be possible in certain settings. Finally, we consider possible extensions of the proposed methods, as well as areas for further consideration and improvement.     

Dimension reduction for mapping mRNA abundance as quantitative traits

The advent of sophisticated genomic techniques for gene mapping and microarray analysis has provided opportunities to map mRNA abundance to quantitative trait loci (QTL) throughout the genome. Unfortunately, simple mapping of each individual mRNA trait on the scale of a typical microarray experiment is computationally intensive, subject to high sample variance, and therefore underpowered. However, this problem can be addressed by capitalizing on correlation among the large number of mRNA traits. We present a method to reduce the dimensionality for mapping gene expression data as quantitative traits. We used a blind method, principal components, and a sighted method, hierarchical clustering seeded by disease relevant traits, to define new traits composed of a small collection of promising mRNAs. We validated the principle of our approach by mapping the expression levels of metabolism genes in a population of F(2)-ob/ob mice derived from the BTBR and C57BL/6J strains. We found that lipogenic and gluconeogenic mRNAs, which are known targets of insulin action, were closely associated with the insulin trait. Multiple interval mapping and Bayesian interval mapping of this new trait revealed significant linkages to chromosome regions that were contained in loci associated with type 2 diabetes in this same mouse sample. As a further statistical refinement, we show that principal component analysis also effectively reduced dimensions for mapping phenotypes composed of mRNA abundances.     

Increased male reproductive success in Ts65Dn “Down syndrome” mice

The Ts65Dn mouse is trisomic for orthologs of about half the genes on Hsa21. A number of phenotypes in these trisomic mice parallel those in humans with trisomy 21 (Down syndrome), including cognitive deficits due to hippocampal malfunction that are sufficiently similar to human that “therapies” developed in Ts65Dn mice are making their way to human clinical trials. However, the impact of the model is limited by availability. Ts65Dn cannot be completely inbred and males are generally considered to be sterile. Females have few, small litters and they exhibit poor care of offspring, frequently abandoning entire litters. Here we report identification and selective breeding of rare fertile males from two working colonies of Ts65Dn mice. Trisomic offspring can be propagated by natural matings or by in vitro fertilization (IVF) to produce large cohorts of closely related siblings. The use of a robust euploid strain as recipients of fertilized embryos in IVF or as the female in natural matings greatly improves husbandry. Extra zygotes cultured to the blastocyst stage were used to create trisomic and euploid embryonic stem (ES) cells from littermates. We developed parameters for cryopreserving sperm from Ts65Dn males and used it to produce trisomic offspring by IVF. Use of cryopreserved sperm provides additional flexibility in the choice of oocyte donors from different genetic backgrounds, facilitating rapid production of complex crosses. This approach greatly increases the power of this important trisomic model to interrogate modifying effects of trisomic or disomic genes that contribute to trisomic phenotypes.     

An Evaluation of High-Throughput Approaches to QTL Mapping in Saccharomyces cerevisiae

Dissecting the molecular basis of quantitative traits is a significant challenge and is essential for understanding complex diseases. Even in model organisms, precisely determining causative genes and their interactions has remained elusive, due in part to difficulty in narrowing intervals to single genes and in detecting epistasis or linked quantitative trait loci. These difficulties are exacerbated by limitations in experimental design, such as low numbers of analyzed individuals or of polymorphisms between parental genomes. We address these challenges by applying three independent high-throughput approaches for QTL mapping to map the genetic variants underlying 11 phenotypes in two genetically distant Saccharomyces cerevisiae strains, namely (1) individual analysis of >700 meiotic segregants, (2) bulk segregant analysis, and (3) reciprocal hemizygosity scanning, a new genome-wide method that we developed. We reveal differences in the performance of each approach and, by combining them, identify eight polymorphic genes that affect eight different phenotypes: colony shape, flocculation, growth on two nonfermentable carbon sources, and resistance to two drugs, salt, and high temperature. Our results demonstrate the power of individual segregant analysis to dissect QTL and address the underestimated contribution of interactions between variants. We also reveal confounding factors like mutations and aneuploidy in pooled approaches, providing valuable lessons for future designs of complex trait mapping studies.     

Bayesian quantitative trait loci mapping for multiple traits

Most quantitative trait loci (QTL) mapping experiments typically collect phenotypic data on multiple correlated complex traits. However, there is a lack of a comprehensive genomewide mapping strategy for correlated traits in the literature. We develop Bayesian multiple-QTL mapping methods for correlated continuous traits using two multivariate models: one that assumes the same genetic model for all traits, the traditional multivariate model, and the other known as the seemingly unrelated regression (SUR) model that allows different genetic models for different traits. We develop computationally efficient Markov chain Monte Carlo (MCMC) algorithms for performing joint analysis. We conduct extensive simulation studies to assess the performance of the proposed methods and to compare with the conventional single-trait model. Our methods have been implemented in the freely available package R/qtlbim (http://www.qtlbim.org), which greatly facilitates the general usage of the Bayesian methodology for unraveling the genetic architecture of complex traits.     

Multiple-Trait Genomic Selection Methods Increase Genetic Value Prediction Accuracy

Genetic correlations between quantitative traits measured in many breeding programs are pervasive. These correlations indicate that measurements of one trait carry information on other traits. Current single-trait (univariate) genomic selection does not take advantage of this information. Multivariate genomic selection on multiple traits could accomplish this but has been little explored and tested in practical breeding programs. In this study, three multivariate linear models (i.e., GBLUP, BayesA, and BayesCπ) were presented and compared to univariate models using simulated and real quantitative traits controlled by different genetic architectures. We also extended BayesA with fixed hyperparameters to a full hierarchical model that estimated hyperparameters and BayesCπ to impute missing phenotypes. We found that optimal marker-effect variance priors depended on the genetic architecture of the trait so that estimating them was beneficial. We showed that the prediction accuracy for a low-heritability trait could be significantly increased by multivariate genomic selection when a correlated high-heritability trait was available. Further, multiple-trait genomic selection had higher prediction accuracy than single-trait genomic selection when phenotypes are not available on all individuals and traits. Additional factors affecting the performance of multiple-trait genomic selection were explored.     

A mixture model approach to the mapping of QTL controlling endosperm traits with bulked samples

Endosperm traits are of triploid inheritance and have become a focus of breeding effort for their close relations with the grain quality. Current methods for mapping quantitative trait loci (QTL) underlying endosperm traits are restricted to the use of the phenotypes of single grain samples as input data set, which are often not available in practice due to the small size of the cereal seeds. This paper proposed a statistical model for one specially tailored mapping strategy, where the marker genotypes are obtained from the maternal plants in the segregation population and the phenotypic responses are replaced by the trait means of composite endosperm samples pooled from each plant. It should therefore be more practical and have wide applicability in mapping endosperm traits. The method was implemented by fitting the phenotypic means of endosperms into a Gaussian mixture model. Both the exact and approximate Expectation-Maximization algorithms were proposed to estimate the model parameters. The presence of the QTL was determined by likelihood ratio test statistics. Statistical power and other properties of the new method were investigated and compared to the current single-seed method under a variety of scenarios through simulation studies. The simulations suggest a reasonable sample size should be used to ensure reliable results. The proposed method was also applied to a simulated genome data for further evaluation. As an illustration, a real data of maize was analyzed to find the loci responsible for the popping expansion volume.     

Strategies for genetic mapping of categorical traits

The search for efficient and powerful statistical methods and optimal mapping strategies for categorical traits under various experimental designs continues to be one of the main tasks in genetic mapping studies. Methodologies for genetic mapping of categorical traits can generally be classified into two groups, linear and non-linear models. We develop a method based on a threshold model, termed mixture threshold model to handle ordinal (or binary) data from multiple families. Monte Carlo simulations are done to compare its statistical efficiencies and properties of the proposed non-linear model with a linear model for genetic mapping of categorical traits using multiple families. The mixture threshold model has notably higher statistical power than linear models. There may be an optimal sampling strategy (family size vs number of families) in which genetic mapping reaches its maximal power and minimal estimation errors. A single large-sibship family does not necessarily produce the maximal power for detection of quantitative trait loci (QTL) due to genetic sampling of QTL alleles. The QTL allelic model has a marked impact on efficiency of genetic mapping of categorical traits in terms of statistical power and QTL parameter estimation. Compared with a fixed number of QTL alleles (two or four), the model with an infinite number of QTL alleles and normally distributed allelic effects results in loss of statistical power. The results imply that inbred designs (e.g. F₂ or four-way crosses) with a few QTL alleles segregating or reducing number of QTL alleles (e.g. by selection) in outbred populations are desirable in genetic mapping of categorical traits using data from multiple families. This revised version was published online in July 2006 with corrections to the Cover Date.     

Quantitative-trait homozygosity and association mapping and empirical genomewide significance in large, complex pedigrees: fasting serum-insulin level in the Hutterites

We present methods for linkage and association mapping of quantitative traits for a founder population with a large, known genealogy. We detect linkage to quantitative-trait loci (QTLs) through a multipoint homozygosity-mapping method. We propose two association methods, one of which is single point and uses a general two-allele model and the other of which is multipoint and uses homozygosity by descent for a particular allele. In all three methods, we make extensive use of the pedigree and genotype information, while keeping the computations simple and efficient. To assess significance, we have developed a permutation-based test that takes into account the covariance structure due to relatedness of individuals and can be used to determine empirical genomewide and locus-specific P values. In the case of multivariate-normally distributed trait data, the permutation-based test is asymptotically exact. The test is broadly applicable to a variety of mapping methods that fall within the class of linear statistical models (e.g., variance-component methods), under the assumption of random ascertainment with respect to the phenotype. For obtaining genomewide P values, our proposed method is appropriate when positions of markers are independent of the observed linkage signal, under the null hypothesis. We apply our methods to a genome screen for fasting insulin level in the Hutterites. We detect significant genomewide linkage on chromosome 19 and suggestive evidence of QTLs on chromosomes 1 and 16.     

Fitness minimization and dynamic instability as a consequence of predator-prey coevolution

Summary We analyse dynamic models of the coevolution of continuous traits that determine the capture rate of a prey species by a predator. The goal of the analysis is to determine conditions when the coevolutionary dynamics will be unstable and will generate population cycles. We use a simplified model of the evolutionary dynamics of quantitative traits in which the rate of change of the mean trait value is proportional to the rate of increase of individual fitness with trait value. Traits that increase ability in the predatory interaction are assumed to have negative effects on another component of fitness. We concentrate on the role of equilibrial fitness minima in producing cycles. In this case, the mean trait of a rapidly evolving species minimizes its fitness and it is chased around this equilibrium by adaptive evolution in the other species. Such cases appear to be most likely if the capture rate of prey by predators is maximal when predator and prey phenotypes match each other. They are possible, but less likely when traits in each species determine a one-dimensional axis of ability related to the interaction. Population dynamics often increase the range of parameter values for which cycles occur, relative to purely evolutionary models, although strong prey self-regulation may stabilize an evolutionarily unstable subsystem.     

The ribosomal RNA gene cluster in aneuploid chickens: evidence for increased gene dosage and regulation of gene expression

In the chicken, the nucleolus organizer regions, or sites of the genes encoding 18S, 5.8S, and 28S ribosomal RNA (rRNA), map to one pair of microchromosomes that can be identified by silver nitrate cytochemistry. This nucleolar organizer chromosome also contains the major histocompatibility complex. Chickens aneuploid for this chromosome have been identified and reproduced for over seven generations. Crossing two trisomic parents results in the production of viable disomic, trisomic, and tetrasomic progeny, showing two, three, and four nucleoli and nucleolar organizers per cell, respectively. A molecular analysis of rRNA genes was undertaken to establish the gene copy numbers in the aneuploid genotypes, and to determine if elevated numbers of rRNA genes are stably maintained and inherited over multiple generations. Gene copy numbers were determined using hybridization analysis of erythrocyte DNA obtained from individuals comprising a family which segregated disomic, trisomic, and tetrasomic genotypes. The values obtained were 290, 420, and 570 rDNA repeats per cell for disomic, trisomic, and tetrasomic animals, respectively. These results provide molecular confirmation of the two aneuploid states and show that elevated gene copy numbers have been maintained over multiple generations. Fibroblasts derived from disomic and tetrasomic embryos were found to grow at similar rates in culture, and mature rRNA levels in chicken embryo fibroblasts from disomic, trisomic and tetrasomic embryos were also found to have similar levels of mature rRNA. Therefore, despite the increase in rDNA content, the level of rRNA is regulated to diploid amounts in aneuploid fibroblasts.     

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.     

Joint mapping of quantitative trait Loci for multiple binary characters

Joint mapping for multiple quantitative traits has shed new light on genetic mapping by pinpointing pleiotropic effects and close linkage. Joint mapping also can improve statistical power of QTL detection. However, such a joint mapping procedure has not been available for discrete traits. Most disease resistance traits are measured as one or more discrete characters. These discrete characters are often correlated. Joint mapping for multiple binary disease traits may provide an opportunity to explore pleiotropic effects and increase the statistical power of detecting disease loci. We develop a maximum-likelihood method for mapping multiple binary traits. We postulate a set of multivariate normal disease liabilities, each contributing to the phenotypic variance of one disease trait. The underlying liabilities are linked to the binary phenotypes through some underlying thresholds. The new method actually maps loci for the variation of multivariate normal liabilities. As a result, we are able to take advantage of existing methods of joint mapping for quantitative traits. We treat the multivariate liabilities as missing values so that an expectation-maximization (EM) algorithm can be applied here. We also extend the method to joint mapping for both discrete and continuous traits. Efficiency of the method is demonstrated using simulated data. We also apply the new method to a set of real data and detect several loci responsible for blast resistance in rice.