A statistical framework for genome-wide scanning and testing of imprinted quantitative trait loci

Non-equivalent expression of alleles at a locus results in genomic imprinting. In this article, a statistical framework for genome-wide scanning and testing of imprinted quantitative trait loci (iQTL) underlying complex traits is developed based on experimental crosses of inbred line species in backcross populations. The joint likelihood function is composed of four component likelihood functions with each of them derived from one of four backcross families. The proposed approach models genomic imprinting effect as a probability measure with which one can test the degree of imprinting. Simulation results show that the model is robust for identifying iQTL with various degree of imprinting ranging from no imprinting, partial imprinting to complete imprinting. Under various simulation scenarios, the proposed model shows consistent parameter estimation with reasonable precision and high power in testing iQTL. When a QTL shows Mendelian effect, the proposed model also outperforms traditional Mendelian model. Extension to incorporate maternal effect is also given. The developed model, built within the maximum likelihood framework and implemented with the EM algorithm, provides a quantitative framework for testing and estimating iQTL involved in the genetic control of complex traits.     

Zero-inflated generalized Poisson regression mixture model for mapping quantitative trait loci underlying count trait with many zeros

Phenotypes measured in counts are commonly observed in nature. Statistical methods for mapping quantitative trait loci (QTL) underlying count traits are documented in the literature. The majority of them assume that the count phenotype follows a Poisson distribution with appropriate techniques being applied to handle data dispersion. When a count trait has a genetic basis, “naturally occurring” zero status also reflects the underlying gene effects. Simply ignoring or miss-handling the zero data may lead to wrong QTL inference. In this article, we propose an interval mapping approach for mapping QTL underlying count phenotypes containing many zeros. The effects of QTLs on the zero-inflated count trait are modelled through the zero-inflated generalized Poisson regression mixture model, which can handle the zero inflation and Poisson dispersion in the same distribution. We implement the approach using the EM algorithm with the Newton-Raphson algorithm embedded in the M-step, and provide a genome-wide scan for testing and estimating the QTL effects. The performance of the proposed method is evaluated through extensive simulation studies. Extensions to composite and multiple interval mapping are discussed. The utility of the developed approach is illustrated through a mouse F₂ intercross data set. Significant QTLs are detected to control mouse cholesterol gallstone formation.     

Functional mapping of quantitative trait loci underlying growth trajectories using a transform-both-sides logistic model

The incorporation of developmental control mechanisms of growth has proven to be a powerful tool in mapping quantitative trait loci (QTL) underlying growth trajectories. A theoretical framework for implementing a QTL mapping strategy with growth laws has been established. This framework can be generalized to an arbitrary number of time points, where growth is measured, and becomes computationally more tractable, when the assumption of variance stationarity is made. In practice, however, this assumption is likely to be violated for age-specific growth traits due to a scale effect. In this article, we present a new statistical model for mapping growth QTL, which also addresses the problem of variance stationarity, by using a transform-both-sides (TBS) model advocated by Carroll and Ruppert (1984, Journal of the American Statistical Association 79, 321-328). The TBS-based model for mapping growth QTL cannot only maintain the original biological properties of a growth model, but also can increase the accuracy and precision of parameter estimation and the power to detect a QTL responsible for growth differentiation. Using the TBS-based model, we successfully map a QTL governing growth trajectories to a linkage group in an example of forest trees. The statistical and biological properties of the estimates of this growth QTL position and effect are investigated using Monte Carlo simulation studies. The implications of our model for understanding the genetic architecture of growth are discussed.     

Quantifying genomic imprinting in the presence of linkage

Genomic imprinting decreases the power of classical linkage analysis, in which paternal and maternal transmissions of marker alleles are equally weighted. Several methods have been proposed for taking genomic imprinting into account in the model-free linkage analysis of binary traits. However, none of these methods are suitable for the formal identification and quantification of genomic imprinting in the presence of linkage. In addition, the available methods are designed for use with pure sib-pairs, requiring artificial decomposition in cases of larger sibships, leading to a loss of power. We propose here the maximum likelihood binomial method adaptive for imprinting (MLB-I), which is a unified analytic framework giving rise to specific tests in sibships of any size for (i) linkage adaptive to imprinting, (ii) genomic imprinting in the presence of linkage, and (iii) partial versus complete genomic imprinting. In addition, we propose an original measure for quantifying genomic imprinting. We have derived and validated the distribution of the three tests under their respective null hypotheses for various genetic models, and have assessed the power of these tests in simulations. This method can readily be applied to genome-wide scanning, as illustrated here for leprosy sibships. Our approach provides a novel tool for dissecting genomic imprinting in model-free linkage analysis, and will be of considerable value for identifying and evaluating the contribution of imprinted genes to complex diseases.     

Mapping of a new quantitative trait locus for resistance to malaria in mice by a comparative mapping approach with human Chromosome 5q31-q33

A number of linkage studies in human populations have identified a locus (pfbi) on Chromosome 5q31-q33 controlling Plasmodiun falciparum blood infection levels. This region contains numerous candidate genes encoding immunological molecules such as cytokines, growth factors and growth-factor receptors. We have used an F₁₁ advance intercross line (AIL) population of mice infected with Plasmodium chabaudi to identify additional mouse quantitative trait loci (QTL) for control of parasitaemia on Chrs 11 and 18, which carry regions homologous to human Chr 5q31-q33. Herein, we report a novel QTL for parasitaemia control (char8) on the mouse Chr 11, linked to marker D11Mit242, and involved in the clearance stages of the parasites from the bloodstream. Strikingly, several Th2 cytokines that are located within char8 have been identified to play a predominant role in the late stages of the infection.     

A dynamic model for functional mapping of biological rhythms

Functional mapping is a statistical method for mapping quantitative trait loci (QTLs) that regulate the dynamic pattern of a biological trait. This method integrates mathematical aspects of biological complexity into a mixture model for genetic mapping and tests the genetic effects of QTLs by comparing genotype-specific curve parameters. As a way of quantitatively specifying the dynamic behaviour of a system, differential equations have proved to be powerful for modelling and unravelling the biochemical, molecular, and cellular mechanisms of a biological process, such as biological rhythms. The equipment of functional mapping with biologically meaningful differential equations provides new insights into the genetic control of any dynamic processes. We formulate a new functional mapping framework for a dynamic biological rhythm by incorporating a group of ordinary differential equations (ODE). The Runge–Kutta fourth-order algorithm was implemented to estimate the parameters that define the system of ODE. The new model will find its implications for understanding the interplay between gene interactions and developmental pathways in complex biological rhythms.     

A general model for detecting genetic determinants underlying longitudinal traits with unequally spaced measurements and nonstationary covariance structure

A mixture model for determining quantitative trait loci (QTL) affecting growth trajectories has been proposed in the literature. In this article, we extend this model to a more general situation in which longitudinal traits for each subject are measured at unequally spaced time intervals, different subjects have different measurement patterns, and the residual correlation within subjects is nonstationary. We derive an EM-simplex hybrid algorithm to estimate the allele frequencies, Hardy-Weinberg disequilibrium, and linkage disequilibrium between QTL in the original population and parameters contained in the growth equation and in the covariance structure. A worked example of head circumference growth in 145 children is used to validate our extended model. A simulation study is performed to examine the statistical properties of the parameter estimation obtained from this example. Finally, we discuss the implications and extensions of our model for detecting QTL that affect growth trajectories.     

Constructing a new integrated genetic linkage map and mapping quantitative trait loci for vegetative mycelium growth rate in Lentinula edodes

The most saturated linkage map for Lentinula edodes to date was constructed based on a monokaryotic population of 146 single spore isolates (SSIs) using sequence-related amplified polymorphism (SRAP), target region amplification polymorphism (TRAP), insertion–deletion (InDel) markers, and the mating-type loci. Five hundred and twenty-four markers were located on 13 linkage groups (LGs). The map spanned a total length of 1006.1 cM, with an average marker spacing of 2.0 cM. Quantitative trait loci (QTLs) mapping was utilized to uncover the loci regulating and controlling the vegetative mycelium growth rate on various synthetic media, and complex medium for commercial cultivation of L. edodes. Two and 13 putative QTLs, identified respectively in the monokaryotic population and two testcross dikaryotic populations, were mapped on seven different LGs. Several vegetative mycelium growth rate-related QTLs uncovered here were clustered on LG4 (Qmgr1, Qdgr1, Qdgr2 and Qdgr9) and LG6 (Qdgr3, Qdgr4 and Qdgr5), implying the presence of main genomic areas responsible for growth rate regulation and control. The QTL hotspot region on LG4 was found to be in close proximity to the region containing the mating-type A (MAT-A) locus. Moreover, Qdgr2 on LG4 was detected on different media, contributing 8.07 %–23.71 % of the phenotypic variation. The present study provides essential information for QTL mapping and marker-assisted selection (MAS) in L. edodes.     

A genetic model and molecular markers for wild oat (Avena fatua L.) seed dormancy

Seed dormancy allows weed seeds to persist in agricultural soils. Wild oat (Avena fatua L.) is a major weed of cereal grains and expresses a range of seed dormancy phenotypes. Genetic analysis of wild oat dormancy has been complicated by the difficulty of phenotypic classification in segregating populations. Therefore, little is known about the nature of the genes that regulate dormancy in wild oat. The objectives of our studies were to develop methods to classify the germination responses of segregating wild oat populations and to find molecular markers linked to quantitative trait loci (QTL) that regulate seed dormancy in wild oat. RAPD markers OPX-06 and OPT-04 explained 12.6% and 6.8% respectively, of the F₂ phenotypic variance. OPF-17 was not significant in a simple regression model, but it was linked in repulsion to OPT-04. A three-locus model of seed dormancy in wild oat is presented based on the 41-day germination profiles of F₁, F₂, F₃, BC₁P₁F₁, BC₁P₁F₂, and BC₁P₂F₁ generations, and the 113 day germination profile of 126 F₇ recombinant inbred lines. Loci G ₁ and G ₂ promote early germination, and the D locus promotes late germination. If at least one copy of the dominant G ₁ or G ₂ alleles are present regardless of the genotype at D locus, then the individual will be nondormant. If the genotype is g ₁ g ₁ g ₂ g ₂ D_, then the phenotype will be dormant. Received: 1 December 1998 / Accepted: 1 February 1999     

Genotype-by-environment interaction in genetic mapping of multiple quantitative trait loci

The interval mapping method is widely used for the genetic mapping of quantitative trait loci (QTLs), though true resolution of quantitative variation into QTLs is hampered with this method. Separation of QTLs is troublesome, because single-QTL is models are fitted. Further, genotype-by-environment interaction, which is of great importance in many quantitative traits, can only be approached by separately analyzing the data collected in multiple environments. Here, we demonstrate for the first time a novel analytic approach (MQM mapping) that accommodates both the mapping of multiple QTLs and genotype-by-environment interaction. MQM mapping is compared to interval mapping in the mapping of QTLs for flowering time in Arabidopsis thaliana under various photoperiod and vernalization conditions.     

Modelling the genetic architecture of flowering time control in barley through nested association mapping

Background

Barley, globally the fourth most important cereal, provides food and beverages for humans and feed for animal husbandry. Maximizing grain yield under varying climate conditions largely depends on the optimal timing of flowering. Therefore, regulation of flowering time is of extraordinary importance to meet future food and feed demands. We developed the first barley nested association mapping (NAM) population, HEB-25, by crossing 25 wild barleys with one elite barley cultivar, and used it to dissect the genetic architecture of flowering time.

Results

Upon cultivation of 1,420 lines in multi-field trials and applying a genome-wide association study, eight major quantitative trait loci (QTL) were identified as main determinants to control flowering time in barley. These QTL accounted for 64% of the cross-validated proportion of explained genotypic variance (p_G). The strongest single QTL effect corresponded to the known photoperiod response gene Ppd-H1. After sequencing the causative part of Ppd-H1, we differentiated twelve haplotypes in HEB-25, whereof the strongest exotic haplotype accelerated flowering time by 11 days compared to the elite barley haplotype. Applying a whole genome prediction model including main effects and epistatic interactions allowed predicting flowering time with an unmatched accuracy of 77% of cross-validated p_G.

Conclusions

The elaborated causal models represent a fundamental step to explain flowering time in barley. In addition, our study confirms that the exotic biodiversity present in HEB-25 is a valuable toolbox to dissect the genetic architecture of important agronomic traits and to replenish the elite barley breeding pool with favorable, trait-improving exotic alleles.

     

A disequilibrium model for detecting genetic mutations for cancer

It has been recognized that genetic mutations in specific nucleotides may give rise to cancer via the alteration of signaling pathways. Thus, the detection of those cancer-causing mutations has received considerable interest in cancer genetic research. Here, we propose a statistical model for characterizing genes that lead to cancer through point mutations using genome-wide single nucleotide polymorphism (SNP) data. The basic idea of the model is that mutated genes may be in high association with their nearby SNPs because of evolutionary forces. By genotyping SNPs in both normal and cancer cells, we formulate a polynomial likelihood to estimate the population genetic parameters related to cancer, such as allele frequencies of cancer-causing alleles, mutation rates of alleles derived from maternal or paternal parents, and zygotic linkage disequilibria between different loci after the mutation occurs. We implement the EM algorithm to estimate some of these parameters because of the missing information in the likelihood construction. The model allows the elegant tests of the significant associations between mutated cancer genes and genome-wide SNPs, thus providing a way for predicting the occurrence and formation of cancer with genetic information. The model, validated through computer simulation, may help cancer geneticists design efficient experiments and formulate hypotheses for cancer gene identification.     

Bias Reduction and a Solution for Separation of Logistic Regression with Missing Covariates

Summary Logistic regression is an important statistical procedure used in many disciplines. The standard software packages for data analysis are generally equipped with this procedure where the maximum likelihood estimates of the regression coefficients are obtained iteratively. It is well known that the estimates from the analyses of small‐ or medium‐sized samples are biased. Also, in finding such estimates, often a separation is encountered in which the likelihood converges but at least one of the parameter estimates diverges to infinity. Standard approaches of finding such estimates do not take care of these problems. Moreover, the missingness in the covariates adds an extra layer of complexity to the whole process. In this article, we address these three practical issues—bias, separation, and missing covariates by means of simple adjustments. We have applied the proposed technique using real and simulated data. The proposed method always finds a solution and the estimates are less biased. A SAS macro that implements the proposed method can be obtained from the authors.     

A quantitative genetic model for analyzing species differences in outcrossing species

A genetic model based on a two-level intra- and interspecific mating design is proposed to estimate the genetic architecture of species differences and heterosis for outcrossing species. The underlying genetic analyses make use of classical quantitative genetic theories and recent results from molecular genetic studies. Gene effects across different quantitative trait loci (QTL) can be approximated by a geometric series. Under natural selection, gene effects are often associated with allele frequencies in a particular way, which can be approximated by the gamma distribution. By incorporating these approximations into family structural analyses in the mating design, we are able to estimate a number of genetic parameters that contribute to quantitative genetic variation based on a nonlinear optimization approach. These parameters include the number of QTL, their gene effects, and their allele frequencies in the parental populations. We perform simulation studies and illustrate an example to demonstrate the statistical property and procedure of the method.     

两个位点主基因控制的质量—数量性状的遗传分析

应用极大似然法和EM算法提出了关于两个位点主基因控制的质量．数量性状的遗传分析方法,参照质量性状两位点互作在F_2代的分离比率建立了7种遗传假设及其似然比测验的程序,讨论了应用这一方法时应注意的几个问题．