Accurate cell type classification is critical for downstream analysis in single-cell RNA sequencing (scRNA-seq). Most existing methods rely on a single type of feature representation-such as statistical, information theory, matrix factorization, or deep learning-based features. However, each captures different aspects of the data, and no single feature type can fully represent the complex differences between cell types. Moreover, naïvely concatenating multiple features may introduce redundancy or noise, reducing model performance. To address these challenges, we propose scMFF, which is a multiple feature fusion framework that integrates four features and explores six fusion strategies in combination with various classifiers for single-cell type classification. Comprehensive evaluations on 42 disease-related datasets and an external COVID-19 dataset demonstrate that scMFF outperforms single-feature approaches in terms of performance and stability, providing a reliable and effective solution for scRNA-seq data analysis.

MOTIVATION: The collection of temporal or perturbed data is often a prerequisite for reconstructing dynamic networks in most cases. However, these types of data are seldom available for genomic studies in medicine, thus significantly limiting the use of dynamic networks to characterize the biological principles underlying human health and diseases. RESULTS: We proposed a statistical framework to recover disease risk-associated pseudo-dynamic networks (DRDNet) from steady-state data. We incorporated a varying coefficient model with multiple ordinary differential equations to learn a series of networks. We analyzed the publicly available Genotype-Tissue Expression data to construct networks associated with hypertension risk, and biological findings showed that key genes constituting these networks had pivotal and biologically relevant roles associated with the vascular system. We also provided the selection consistency of the proposed learning procedure and evaluated its utility through extensive simulations. AVAILABILITY AND IMPLEMENTATION: DRDNet is implemented in the R language, and the source codes are available at https://github.com/chencxxy28/DRDnet/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

SUMMARY: Genome-wide association studies (GWAS), particularly designed with thousands and thousands of single-nucleotide polymorphisms (SNPs) (big p) genotyped on tens of thousands of subjects (small n), are encountered by a major challenge of p ≪ n. Although the integration of longitudinal information can significantly enhance a GWAS's power to comprehend the genetic architecture of complex traits and diseases, an additional challenge is generated by an autocorrelative process. We have developed several statistical models for addressing these two challenges by implementing dimension reduction methods and longitudinal data analysis. To make these models computationally accessible to applied geneticists, we wrote an R package of computer software, HiGwas, designed to analyze longitudinal GWAS datasets. Functions in the package encompass single SNP analyses, significance-level adjustment, preconditioning and model selection for a high-dimensional set of SNPs. HiGwas provides the estimates of genetic parameters and the confidence intervals of these estimates. We demonstrate the features of HiGwas through real data analysis and vignette document in the package. AVAILABILITY AND IMPLEMENTATION: https://github.com/wzhy2000/higwas. CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Large scale genome-wide association studies (GWAS) have resulted in the identification of a wide range of genetic variants related to a host of complex traits and disorders. Despite their success, the individual single-nucleotide polymorphism (SNP) analysis approach adopted in most current GWAS can be limited in that it is usually biologically simple to elucidate a comprehensive genetic architecture of phenotypes and statistically underpowered due to heavy multiple-testing correction burden. On the other hand, multiple-SNP analyses (e.g. gene-based or region-based SNP-set analysis) are usually more powerful to examine the joint effects of a set of SNPs on the phenotype of interest. However, current multiple-SNP approaches can only draw an overall conclusion at the SNP-set level and does not directly inform which SNPs in the SNP-set are driving the overall genotype-phenotype association. RESULTS: In this article, we propose a new permutation-assisted tuning procedure in lasso (plasso) to identify phenotype-associated SNPs in a joint multiple-SNP regression model in GWAS. The tuning parameter of lasso determines the amount of shrinkage and is essential to the performance of variable selection. In the proposed plasso procedure, we first generate permutations as pseudo-SNPs that are not associated with the phenotype. Then, the lasso tuning parameter is delicately chosen to separate true signal SNPs and non-informative pseudo-SNPs. We illustrate plasso using simulations to demonstrate its superior performance over existing methods, and application of plasso to a real GWAS dataset gains new additional insights into the genetic control of complex traits. AVAILABILITY AND IMPLEMENTATION: R codes to implement the proposed methodology is available at https://github.com/xyz5074/plasso. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Detecting how genes regulate biological shape has become a multidisciplinary research interest because of its wide application in many disciplines. Despite its fundamental importance, the challenges of accurately extracting information from an image, statistically modeling the high-dimensional shape and meticulously locating shape quantitative trait loci (QTL) affect the progress of this research. In this article, we propose a novel integrated framework that incorporates shape analysis, statistical curve modeling and genetic mapping to detect significant QTLs regulating variation of biological shape traits. After quantifying morphological shape via a radius centroid contour approach, each shape, as a phenotype, was characterized as a high-dimensional curve, varying as angle θ runs clockwise with the first point starting from angle zero. We then modeled the dynamic trajectories of three mean curves and variation patterns as functions of θ. Our framework led to the detection of a few significant QTLs regulating the variation of leaf shape collected from a natural population of poplar, Populus szechuanica var tibetica. This population, distributed at altitudes 2000-4500 m above sea level, is an evolutionarily important plant species. This is the first work in the quantitative genetic shape mapping area that emphasizes a sense of 'function' instead of decomposing the shape into a few discrete principal components, as the majority of shape studies do.

How trees allocate photosynthetic products to primary height growth and secondary radial growth reflects their capacity to best use environmental resources. Despite substantial efforts to explore tree height-diameter relationship empirically and through theoretical modeling, our understanding of the biological mechanisms that govern this phenomenon is still limited. By thinking of stem woody biomass production as an ecological system of apical and lateral growth components, we implement game theory to model and discern how these two components cooperate symbiotically with each other or compete for resources to determine the size of a tree stem. This resulting allometry game theory is further embedded within a genetic mapping and association paradigm, allowing the genetic loci mediating the carbon allocation of stemwood growth to be characterized and mapped throughout the genome. Allometry game theory was validated by analyzing a mapping data of stem height and diameter growth over perennial seasons in a poplar tree. Several key quantitative trait loci were found to interpret the process and pattern of stemwood growth through regulating the ecological interactions of stem apical and lateral growth. The application of allometry game theory enables the prediction of the situations in which the cooperation, competition or altruism is an optimal decision of a tree to fully use the environmental resources it owns.

Heterochrony is known as a developmental change in the timing or rate of ontogenetic events across phylogenetic lineages. It is a key concept synthesizing development into ecology and evolution to explore the mechanisms of how developmental processes impact on phenotypic novelties. A number of molecular experiments using contrasting organisms in developmental timing have identified specific genes involved in heterochronic variation. Beyond these classic approaches that can only identify single genes or pathways, quantitative models derived from current next-generation sequencing data serve as a more powerful tool to precisely capture heterochronic variation and systematically map a complete set of genes that contribute to heterochronic processes. In this opinion note, we discuss a computational framework of genetic mapping that can characterize heterochronic quantitative trait loci that determine the pattern and process of development. We propose a unifying model that charts the genetic architecture of heterochrony that perceives and responds to environmental perturbations and evolves over geologic time. The new model may potentially enhance our understanding of the adaptive value of heterochrony and its evolutionary origins, providing a useful context for designing new organisms that can best use future resources.

Heterophylly, i.e. morphological changes in leaves along the axis of an individual plant, is regarded as a strategy used by plants to cope with environmental change. However, little is known of the extent to which heterophylly is controlled by genes and how each underlying gene exerts its effect on heterophyllous variation. We described a geometric morphometric model that can quantify heterophylly in plants and further constructed an R-based computing platform by integrating this model into a genetic mapping and association setting. The platform, named HpQTL, allows specific quantitative trait loci mediating heterophyllous variation to be mapped throughout the genome. The statistical properties of HpQTL were examined and validated via computer simulation. Its biological relevance was demonstrated by results from a real data analysis of heterophylly in a wood plant, mei (Prunus mume). HpQTL provides a powerful tool to analyze heterophylly and its underlying genetic architecture in a quantitative manner. It also contributes a new approach for genome-wide association studies aimed to dissect the programmed regulation of plant development and evolution.

The mixed linear model has been widely used in genome-wide association studies (GWAS), but its application to multi-locus GWAS analysis has not been explored and assessed. Here, we implemented a fast multi-locus random-SNP-effect EMMA (FASTmrEMMA) model for GWAS. The model is built on random single nucleotide polymorphism (SNP) effects and a new algorithm. This algorithm whitens the covariance matrix of the polygenic matrix K and environmental noise, and specifies the number of nonzero eigenvalues as one. The model first chooses all putative quantitative trait nucleotides (QTNs) with ≤ 0.005 P-values and then includes them in a multi-locus model for true QTN detection. Owing to the multi-locus feature, the Bonferroni correction is replaced by a less stringent selection criterion. Results from analyses of both simulated and real data showed that FASTmrEMMA is more powerful in QTN detection and model fit, has less bias in QTN effect estimation and requires a less running time than existing single- and multi-locus methods, such as empirical Bayes, settlement of mixed linear model under progressively exclusive relationship (SUPER), efficient mixed model association (EMMA), compressed MLM (CMLM) and enriched CMLM (ECMLM). FASTmrEMMA provides an alternative for multi-locus GWAS.

Knowledge about how changes in gene expression are encoded by expression quantitative trait loci (eQTLs) is a key to construct the genotype-phenotype map for complex traits or diseases. Traditional eQTL mapping is to associate one transcript with a single marker at a time, thereby limiting our inference about a complete picture of the genetic architecture of gene expression. Here, we implemented an ultrahigh-dimensional variable selection model to build a computing platform that can systematically scan main effects and interaction effects among all possible loci and identify a set of significant eQTLs modulating differentiation and function of gene expression. This platform, named iFORM/eQTL, was assembled by forward-selection-based procedures to tackle complex covariance structures of gene-gene interactions. iFORM/eQTL can particularly discern the role of cis-QTLs, trans-QTLs and their epistatic interactions in gene expression. Results from the reanalysis of a published genetic and genomic data set through iFORM/eQTL gain new discoveries on the genetic origin of gene expression differentiation in Caenorhabditis elegans, which could not be detected by a traditional one-locus/one-transcript analysis approach.

Evo-devo is a theory proposed to study how phenotypes evolve by comparing the developmental processes of different organisms or the same organism experiencing changing environments. It has been recognized that nonallelic interactions at different genes or quantitative trait loci, known as epistasis, may play a pivotal role in the evolution of development, but it has proven difficult to quantify and elucidate this role into a coherent picture. We implement a high-dimensional genome-wide association study model into the evo-devo paradigm and pack it into the R-based Evo-Devo-EpiR, aimed at facilitating the genome-wide landscaping of epistasis for the diversification of phenotypic development. By analyzing a high-throughput assay of DNA markers and their pairs simultaneously, Evo-Devo-EpiR is equipped with a capacity to systematically characterize various epistatic interactions that impact on the pattern and timing of development and its evolution. Enabling a global search for all possible genetic interactions for developmental processes throughout the whole genome, Evo-Devo-EpiR provides a computational tool to illustrate a precise genotype-phenotype map at interface between epistasis, development and evolution.

Linkage analysis has played an important role in understanding genome structure and evolution. However, two-point linkage analysis widely used for genetic map construction can rarely chart a detailed picture of genome organization because it fails to identify the dependence of crossovers distributed along the length of a chromosome, a phenomenon known as crossover interference. Multi-point analysis, proven to be more advantageous in gene ordering and genetic distance estimation for dominant markers than two-point analysis, is equipped with a capacity to discern and quantify crossover interference. Here, we review a statistical model for four-point analysis, which, beyond three-point analysis, can characterize crossover interference that takes place not only between two adjacent chromosomal intervals, but also over multiple successive intervals. This procedure provides an analytical tool to elucidate the detailed landscape of crossover interference over the genome and further infer the evolution of genome structure and organization.

Briefings in Bioinformatics (2016) doi: 10.1093/bib/bbw145 In the article above, the following errors have been addressed: • In Table 1, the SHS formula was incorrectly given as SHS=URdiag(ξ1+δ,⋯,ξn+δ)URT⁠. This has been corrected to SHS=URdiag(λ1+δ,⋯,λn−q+δ)URT⁠. • The running title has been changed from ‘Methodological implementation of mixed linear model’ to ‘Methodological implementation of mixed linear models’. • Reference 22 has been corrected to indicate a page range of ‘525–6’ from ‘525’.

Whole-organism metabolic rate co-varies allometrically with body mass, and is also affected by temperature through different biochemical mechanisms. Here we implement a computational platform to map specific quantitative trait loci (QTLs) that govern the dependence of metabolic rate on size and temperature. The model was formulated within settings of genetic mapping or genome-wide association studies through a mapping population genotyped by a set of molecular markers throughout the genome and phenotyped for metabolic parameters over a range of temperature. The model, estimated by a maximum-likelihood approach, allows a genome-wide search for the underlying metabolic QTLs and the estimation of genotype-specific parameters that specify the metabolism of an organism. Our model provides a tool to detect pleiotropy and epistasis that cause the size- and temperature-dependent change of metabolic rate.

Allopolyploids are a group of polyploids with more than two sets of chromosomes derived from different species. Previous linkage analysis of allopolyploids is based on the assumption that different chromosomes pair randomly during meiosis. A more sophisticated model to relax this assumption has been developed for allotetraploids by incorporating the preferential pairing behavior of homologous over homoeologous chromosomes. Here, we show that the basic principle of this model can be extended to perform linkage analysis of higher-ploidy allohexaploids, where multiple preferential pairing factors are used to characterize chromosomal-pairing meiotic features between different constituent species. We implemented the extended model into an R package, called AlloMap6, allowing the recombination fractions and preferential pairing factors to be estimated simultaneously. Allomap6 has two major functionalities, computer simulation and real-data analysis. By analyzing a real data from a full-sib family of allohexaploid persimmon, we tested and validated the usefulness and utility of this package. AlloMap6 lays a foundation for allohexaploid genetic mapping and provides a new horizon to explore the chromosomal kinship of allohexaploids.

Whole-genome search of genes is an essential approach to dissecting complex traits, but a marginal one-single-nucleotide polymorphism (SNP)/one-phenotype regression analysis widely used in current genome-wide association studies fails to estimate the net and cumulative effects of SNPs and reveal the developmental pattern of interplay between genes and traits. Here we describe a computational framework, which we refer to as two-side high-dimensional genome-wide association studies (2HiGWAS), to associate an ultrahigh dimension of SNPs with a high dimension of developmental trajectories measured across time and space. The model is implemented with a dual dimension-reduction procedure for both predictors and responses to select a sparse but full set of significant loci from an extremely large pool of SNPs and estimate their net time-varying effects on trait development. The model can not only help geneticists to precisely identify an entire set of genes underlying complex traits but also allow them to elucidate a global picture of how genes control developmental and dynamic processes of trait formation. We investigated the statistical properties of the model via extensive simulation studies. With the increasing availability of GWAS in various organisms, 2HiGWAS will have important implications for genetic studies of developmental compelx traits.

With the increasing recognition of its role in trait and disease development, it is crucial to account for genetic imprinting to illustrate the genetic architecture of complex traits. Genetic mapping can be innovated to test and estimate effects of genetic imprinting in a segregating population derived from experimental crosses. Here, we describe and assess a design for imprinting detection in natural plant populations. This design is to sample maternal plants at random from a natural population and collect open-pollinated (OP) seeds randomly from each maternal plant and germinate them into seedlings. A two-stage hierarchical platform is constructed to jointly analyze maternal and OP progeny markers. Through tracing the segregation and transmission of alleles from the parental to progeny generation, this platform allows parent-of-origin-dependent gene expression to be discerned, providing an avenue to estimate the effect of imprinting genes on a quantitative trait. The design is derived to estimate imprinting effects expressed at the haplotype level. Its usefulness and utilization were validated through computer simulation. This OP-based design provides a tool to detect the genomic distribution and pattern of imprinting genes as an important component of heritable variation that is neglected in traditional genetic studies of complex traits.

As a group of important plant species in agriculture and biology, polyploids have been increasingly studied in terms of their genome structure and organization. There are two types of polyploids, allopolyploids and autopolyploids, each resulting from a different genetic origin, which undergo meiotic divisions of a distinct complexity. A set of statistical models has been developed for linkage analysis, respectively for each type, by taking into account their unique meiotic behavior, i.e. preferential pairing for allopolyploids and double reduction for autopolyploids. We synthesized these models and modified them to accommodate the linkage analysis of less informative dominant markers. By reanalysing a published data set of varying ploidy in Arabidopsis, we corrected the estimates of the meiotic recombination frequency aimed to study the significance of polyploidization.

Unlike annuals, all perennial plants undergo seasonal transitions during ontogeny. As an adaptive response to seasonal changes in climate, the seasonal pattern of growth is likely to be under genetic control, although its underlying genetic basis remains unknown. Here, we develop a computational model that can map specific quantitative trait loci (QTLs) responsible for seasonal transitions of growth in perennials. The model is founded on functional mapping, a statistical framework to map developmental dynamics, which is reformed to integrate a seasonally adjusted growth function. The new model is equipped with a capacity to characterize the genetic effects of QTLs on seasonal alternation at different ages and then to better elucidate the genetic architecture of development. The model is implemented with a series of testing procedures, including (i) how a QTL controls an overall ontogenetic growth curve, (ii) how the QTL determines seasonal trajectories of growth within years and (iii) how it determines the dynamic nature of age-specific season response. The model was validated through computer simulation. The extension of season adjustment to other types of biological curves is statistically straightforward, facilitating a wider variety of genetic studies into ontogenetic growth and development in perennial plants.

Dynamic changes of gene expression reflect an intrinsic mechanism of how an organism responds to developmental and environmental signals. With the increasing availability of expression data across a time-space scale by RNA-seq, the classification of genes as per their biological function using RNA-seq data has become one of the most significant challenges in contemporary biology. Here we develop a clustering mixture model to discover distinct groups of genes expressed during a period of organ development. By integrating the density function of multivariate Poisson distribution, the model accommodates the discrete property of read counts characteristic of RNA-seq data. The temporal dependence of gene expression is modeled by the first-order autoregressive process. The model is implemented with the Expectation-Maximization algorithm and model selection to determine the optimal number of gene clusters and obtain the estimates of Poisson parameters that describe the pattern of time-dependent expression of genes from each cluster. The model has been demonstrated by analyzing a real data from an experiment aimed to link the pattern of gene expression to catkin development in white poplar. The usefulness of the model has been validated through computer simulation. The model provides a valuable tool for clustering RNA-seq data, facilitating our global view of expression dynamics and understanding of gene regulation mechanisms.

As an important mechanism for adaptation to heterogeneous environment, plastic responses of correlated traits to environmental alteration may also be genetically correlated, but less is known about the underlying genetic basis. We describe a statistical model for mapping specific quantitative trait loci (QTLs) that control the interrelationship of phenotypic plasticity between different traits. The model is constructed by a bivariate mixture setting, implemented with the EM algorithm to estimate the genetic effects of QTLs on correlative plastic response. We provide a series of procedure that test (1) how a QTL controls the phenotypic plasticity of a single trait; and (2) how the QTL determines the correlation of environment-induced changes of different traits. The model is readily extended to test how epistatic interactions among QTLs play a part in the correlations of different plastic traits. The model was validated through computer simulation and used to analyse multi-environment data of genetic mapping in winter wheat, showing its utilization in practice.

As the model species for woody plants, the poplar has excellent experimental properties. The studies of functional genes make up the foundation of improving genetic traits and cultivating elite lines at the molecular level. Although studies of functional genes have been carried out for many years, plenty of experimental data are still scattered across documents and are not unified by a comprehensive statistical analysis, Consequentially, the disjoint in information severely hinders systematic utilization of the accumulated data. This problem can be solved through the use of bioinformatic methodology and technology to gather and organize data to construct this Poplar Functional Gene Database (PFGD). By complining information from an array of studies, this study collected 207 poplar functional genes. 164 of the collected genes, selected for their detailed annotations, were input into Populus Database (http://ccb.bjfu.edu.cn/app/pfgd/). Many important stress genes were located in the database. As an example, we investigate the target genes function of Populus euphratica in response to salt stress. Two small cDNA libraries from P. euphratica plantlets treated with or without salt (300 mM NaCl, 3 days) in the root. Using high-throughput sequencing to identify miRNAs, we found 179 conserved miRNAs and 62 novel miRNAs which have differential expression. After the detailed analysis of these miRNAs, 1254 target genes from conserved miRNAs and 479 target genes from novel miRNAs were predicted, and functional information was annotated using the Gene Ontology databases. These information provides a primary visual field for understanding the gene regulatory network in response to salt stress in Populus.

The recent availability of high-throughput genetic and genomic data allows the genetic architecture of complex traits to be systematically mapped. The application of these genetic results to design and breed new crop types can be made possible through systems mapping. Systems mapping is a computational model that dissects a complex phenotype into its underlying components, coordinates different components in terms of biological laws through mathematical equations and maps specific genes that mediate each component and its connection with other components. Here, we present a new direction of systems mapping by integrating this tool with carbon economy. With an optimal spatial distribution of carbon fluxes between sources and sinks, plants tend to maximize whole-plant growth and competitive ability under limited availability of resources. We argue that such an economical strategy for plant growth and development, once integrated with systems mapping, will not only provide mechanistic insights into plant biology, but also help to spark a renaissance of interest in ideotype breeding in crops and trees.

Knowledge about biological shape has important implications in biology and biomedicine, but the underlying genetic mechanisms for shape variation have not been well studied. Statistical models play a pivotal role in mapping specific quantitative trait loci (QTLs) that contribute to biological shape and its developmental trajectories. We describe and assess a statistical framework for shape gene identification that incorporates shape and image analysis into a mixture-model framework for QTL mapping. Statistical parameters that define genotype-specific differences in biological shape are estimated by implementing statistical and computational algorithms. A state-of-the-art procedure is described to examine the control patterns of specific QTLs on the origin, properties and functions of biological shape. The statistical framework described will help to address many integrative biological and genetic questions and challenges in shape variation faced by the life sciences community.

Despite a tremendous effort to map quantitative trait loci (QTLs) responsible for agriculturally and biologically important traits in plants, our understanding of how a QTL governs the developmental process of plant seeds remains elusive. In this article, we address this issue by describing a model for functional mapping of seed development through the incorporation of the relationship between vegetative and reproductive growth. The time difference of reproductive from vegetative growth is described by Reeve and Huxley’s allometric equation. Thus, the implementation of this equation into the framework of functional mapping allows dynamic QTLs for seed development to be identified more precisely. By estimating and testing mathematical parameters that define Reeve and Huxley’s allometric equations of seed growth, the dynamic pattern of the genetic effects of the QTLs identified can be analyzed. We used the model to analyze a soybean data, leading to the detection of QTLs that control the growth of seed dry weight. Three dynamic QTLs, located in two different linkage groups, were detected to affect growth curves of seed dry weight. The QTLs detected may be used to improve seed yield with marker-assisted selection by altering the pattern of seed development in a hope to achieve a maximum size of seeds at a harvest time.

Over the past few decades, genome-wide association studies analyzed by efficient statistical procedures have successfully identified single-nucleotide polymorphisms (SNPs) that are associated with complex traits or human diseases. However, due to the overwhelming number of SNPs, most approaches have focused on additive genetic model without genome-wide SNP-SNP interactions. In this study, we propose an efficient statistical procedure in a genetic model-free framework for detecting SNPs exhibiting main genetic effects as well as epistatic interactions. Specifically, the association between phenotype and genotype is characterized by an unknown function to be estimated using nonparametric techniques, and a two-stage non-parametric independence screening procedure is proposed to sequentially identify potentially important main genetic effects and interactions. Finally, the subset of genetic predictors implied by two-stage non-parametric independence screening is analyzed by penalized regressions such as LASSO, and a final model is identified. In this framework, specific genetic model is not assumed and interactions are not only among marginally important SNPs. Therefore, SNPs that are involved in genetic regulatory networks but missed by previous studies are expected to be recognized. In simulation studies, we show that the procedure is computationally efficient and has an outstanding finite sample performance in selecting potential SNPs as well as SNP-SNP interactions. A real data analysis further indicates the importance of epistatic interactions in explaining body mass index.

Genetic imprinting, or called the parent-of-origin effect, has been recognized to play an important role in the formation and pathogenesis of human diseases. Although the epigenetic mechanisms that establish genetic imprinting have been a focus of many genetic studies, our knowledge about the number of imprinting genes and their chromosomal locations and interactions with other genes is still scarce, limiting precise inference of the genetic architecture of complex diseases. In this article, we present a statistical model for testing and estimating the effects of genetic imprinting on complex diseases using a commonly used case-control design with family structure. For each subject sampled from a case and control population, we not only genotype its own single nucleotide polymorphisms (SNPs) but also collect its parents' genotypes. By tracing the transmission pattern of SNP alleles from parental to offspring generation, the model allows the characterization of genetic imprinting effects based on Pearson tests of a 2 × 2 contingency table. The model is expanded to test the interactions between imprinting effects and additive, dominant and epistatic effects in a complex web of genetic interactions. Statistical properties of the model are investigated, and its practical usefulness is validated by a real data analysis. The model will provide a useful tool for genome-wide association studies aimed to elucidate the picture of genetic control over complex human diseases.

Epigenetic modifications may play an important role in the formation and progression of complex diseases through the regulation of gene expression. The systematic identification of epigenetic variants that contribute to human diseases can be made possible using genome-wide association studies (GWAS), although epigenetic effects are currently not included in commonly used case-control designs for GWAS. Here, we show that epigenetic modifications can be integrated into a case-control setting by dissolving the overall genetic effect into its different components, additive, dominant and epigenetic. We describe a general procedure for testing and estimating the significance of each component based on a conventional chi-squared test approach. Simulation studies were performed to investigate the power and false-positive rate of this procedure, providing recommendations for its practical use. The integration of epigenetic variants into GWAS can potentially improve our understanding of how genetic, environmental and stochastic factors interact with epialleles to construct the genetic architecture of complex diseases.

Traditional approaches for genetic mapping are to simply associate the genotypes of a quantitative trait locus (QTL) with the phenotypic variation of a complex trait. A more mechanistic strategy has emerged to dissect the trait phenotype into its structural components and map specific QTLs that control the mechanistic and structural formation of a complex trait. We describe and assess such a strategy, called structural mapping, by integrating the internal structural basis of trait formation into a QTL mapping framework. Electrical impedance spectroscopy (EIS) has been instrumental for describing the structural components of a phenotypic trait and their interactions. By building robust mathematical models on circuit EIS data and embedding these models within a mixture model-based likelihood for QTL mapping, structural mapping implements the EM algorithm to obtain maximum likelihood estimates of QTL genotype-specific EIS parameters. The uniqueness of structural mapping is to make it possible to test a number of hypotheses about the pattern of the genetic control of structural components. We validated structural mapping by analyzing an EIS data collected for QTL mapping of frost hardiness in a controlled cross of jujube trees. The statistical properties of parameter estimates were examined by simulation studies. Structural mapping can be a powerful alternative for genetic mapping of complex traits by taking account into the biological and physical mechanisms underlying their formation.

With the availability of gene expression data by RNA-seq, powerful statistical approaches for grouping similar gene expression profiles across different environments have become increasingly important. We describe and assess a computational model for clustering genes into distinct groups based on the pattern of gene expression in response to changing environment. The model capitalizes on the Poisson distribution to capture the count property of RNA-seq data. A two-stage hierarchical expectation–maximization (EM) algorithm is implemented to estimate an optimal number of groups and mean expression amounts of each group across two environments. A procedure is formulated to test whether and how a given group shows a plastic response to environmental changes. The impact of gene–environment interactions on the phenotypic plasticity of the organism can also be visualized and characterized. The model was used to analyse an RNA-seq dataset measured from two cell lines of breast cancer that respond differently to an anti-cancer drug, from which genes associated with the resistance and sensitivity of the cell lines are identified. We performed simulation studies to validate the statistical behaviour of the model. The model provides a useful tool for clustering gene expression data by RNA-seq, facilitating our understanding of gene functions and networks.

The formation of phenotypic traits, such as biomass production, tumor volume and viral abundance, undergoes a complex process in which interactions between genes and developmental stimuli take place at each level of biological organization from cells to organisms. Traditional studies emphasize the impact of genes by directly linking DNA-based markers with static phenotypic values. Functional mapping, derived to detect genes that control developmental processes using growth equations, has proven powerful for addressing questions about the roles of genes in development. By treating phenotypic formation as a cohesive system using differential equations, a different approach-systems mapping-dissects the system into interconnected elements and then map genes that determine a web of interactions among these elements, facilitating our understanding of the genetic machineries for phenotypic development. Here, we argue that genetic mapping can play a more important role in studying the genotype-phenotype relationship by filling the gaps in the biochemical and regulatory process from DNA to end-point phenotype. We describe a new framework, named network mapping, to study the genetic architecture of complex traits by integrating the regulatory networks that cause a high-order phenotype. Network mapping makes use of a system of differential equations to quantify the rule by which transcriptional, proteomic and metabolomic components interact with each other to organize into a functional whole. The synthesis of functional mapping, systems mapping and network mapping provides a novel avenue to decipher a comprehensive picture of the genetic landscape of complex phenotypes that underlie economically and biomedically important traits.

As a group of economically important species, linkage mapping of polysomic autotetraploids, including potato, sugarcane and rose, is difficult to conduct due to their unique meiotic property of double reduction that allows sister chromatids to enter into the same gamete. We describe and assess a statistical model for mapping quantitative trait loci (QTLs) in polysomic autotetraploids. The model incorporates double reduction, built in the mixture model-based framework and implemented with the expectation-maximization algorithm. It allows the simultaneous estimation of QTL positions, QTL effects and the degree of double reduction as well as the assessment of the estimation precision of these parameters. We performed computer simulation to examine the statistical properties of the method and validate its use through analyzing real data in tetraploid switchgrass.

The capacity of apomixis to generate maternal clones through seed reproduction has made it a useful characteristic for the fixation of heterosis in plant breeding. It has been observed that apomixis displays pronounced intra- and interspecific diversification, but the genetic mechanisms underlying this diversification remains elusive, obstructing the exploitation of this phenomenon in practical breeding programs. By capitalizing on molecular information in mapping populations, we describe and assess a statistical design that deploys linkage analysis to estimate and test the pattern and extent of apomictic differences at various levels from genotypes to species. The design is based on two reciprocal crosses between two individuals each chosen from a hermaphrodite or monoecious species. A multinomial distribution likelihood is constructed by combining marker information from two crosses. The EM algorithm is implemented to estimate the rate of apomixis and test its difference between two plant populations or species as the parents. The design is validated by computer simulation. A real data analysis of two reciprocal crosses between hickory (Carya cathayensis) and pecan (C. illinoensis) demonstrates the utilization and usefulness of the design in practice. The design provides a tool to address fundamental and applied questions related to the evolution and breeding of apomixis.

Because of its widespread occurrence and role in shaping evolutionary processes in the biological kingdom, especially in plants, polyploidy has been increasingly studied from cytological to molecular levels. By inferring gene order, gene distances and gene homology, linkage mapping with molecular markers has proven powerful for investigating genome structure and organization. Here we review and assess a general statistical model for three-point linkage analysis in autotetraploids by integrating double reduction, a phenomenon that commonly occurs in autopolyploids whose chromosomes are derived from a single ancestral species. This model does not require any assumption on the distribution of the occurrence of double reduction and can handle the complexity of multilocus linkage in terms of crossover interference. Implemented with the expectation-maximization (EM) algorithms, the model can estimate and test the recombination fractions between less informative dominant markers, thus facilitating its practical implications for any autopolyploids in most of which inexpensive dominant markers are still used for their genetic and evolutionary studies. The model was applied to reanalyze a published data in tetraploid switchgrass, validating its practical usefulness and utilization.

Genetic interactions or epistasis have been thought to play a pivotal role in shaping the formation, development and evolution of life. Previous work focused on lower-order interactions between a pair of genes, but it is obviously inadequate to explain a complex network of genetic interactions and pathways. We review and assess a statistical model for characterizing high-order epistasis among more than two genes or quantitative trait loci (QTLs) that control a complex trait. The model includes a series of start-of-the-art standard procedures for estimating and testing the nature and magnitude of QTL interactions. Results from simulation studies and real data analysis warrant the statistical properties of the model and its usefulness in practice. High-order epistatic mapping will provide a routine procedure for charting a detailed picture of the genetic regulation mechanisms underlying the phenotypic variation of complex traits.

Despite its central role in the adaptation and microevolution of traits, the genetic architecture of phenotypic plasticity, i.e. multiple phenotypes produced by a single genotype in changing environments, remains elusive. We know little about the genes that underlie the plastic response of traits to the environment, their number, chromosomal locations and genetic interactions as well as environment impact on their effects. Here we review key statistical approaches for analyzing the genetic variation of phenotypic plasticity due to genotype-environment interactions and describe the implementation of a dynamic model to map specific quantitative trait loci (QTLs) that affect the gradient expression of a quantitative trait across a range of environments. This dynamic model is distinct by incorporating mathematical aspects of phenotypic plasticity into a QTL mapping framework, thereby better unraveling the quantitative attribute of trait response to the environment. By testing the curve parameters that specify environment-dependent trajectories of the trait, the model allows a series of fundamental hypotheses to be tested in a quantitative way about the interplay between gene action/interaction and environmental sensitivity. The model can also make the dynamic prediction of genetic control over phenotypic plasticity within the context of changing environments. We demonstrate the usefulness of the model by reanalyzing a QTL data set for rice, gleaning new insights into the genetic basis for phenotypic plasticity in plant height growth.

An allotetraploid has four paired sets of chromosomes derived from different diploid species, whose meiotic behavior is qualitatively different from the underlying diploids. According to a traditional view, meiotic pairing occurs only between homologous chromosomes, but new evidence indicates that homoeologous chromosomes may also pair to a lesser extent compared with homolog pairing. Here, we describe and assess a unifying analytical framework that incorporates differential chromosomal pairing into a multilocus linkage model. The preferential pairing factor is used to quantify the probability difference of pairing occurring between homologous chromosomes and homoeologous chromosomes. The unifying framework allows simultaneous estimation of the linkage, genetic interference and preferential pairing factor using commonly existing multiplex markers. We compared the unifying approach and traditional approaches assuming random chromosomal pairing by analyzing marker data collected in a full-sib family of tetraploid switchgrass, a bioenergy species whose diploid origins are undefined, but with subgenomes that are genetically well differentiated. The unifying framework provides a better tool for estimating the meiotic linkage and constructing a genetic map for allotetraploids.

Despite our expanding knowledge about the biochemistry of gene regulation involved in host-pathogen interactions, a quantitative understanding of this process at a transcriptional level is still limited. We devise and assess a computational framework that can address this question. This framework is founded on a mixture model-based likelihood, equipped with functionality to cluster genes per dynamic and functional changes of gene expression within an interconnected system composed of the host and pathogen. If genes from the host and pathogen are clustered in the same group due to a similar pattern of dynamic profiles, they are likely to be reciprocally co-evolving. If genes from the two organisms are clustered in different groups, this means that they experience strong host-pathogen interactions. The framework can test the rates of change for individual gene clusters during pathogenic infection and quantify their impacts on host-pathogen interactions. The framework was validated by a pathological study of poplar leaves infected by fungal Marssonina brunnea in which co-evolving and interactive genes that determine poplar-fungus interactions are identified. The new framework should find its wide application to studying host-pathogen interactions for any other interconnected systems.

Genetic imprinting, by which the expression of a gene depends on the parental origin of its alleles, may be subjected to reprogramming through each generation. Currently, such reprogramming is limited to qualitative description only, lacking more precise quantitative estimation for its extent, pattern and mechanism. Here, we present a computational framework for analyzing the magnitude of genetic imprinting and its transgenerational inheritance mode. This quantitative model is based on the breeding scheme of reciprocal backcrosses between reciprocal F(1) hybrids and original inbred parents, in which the transmission of genetic imprinting across generations can be tracked. We define a series of quantitative genetic parameters that describe the extent and transmission mode of genetic imprinting and further estimate and test these parameters within a genetic mapping framework using a new powerful computational algorithm. The model and algorithm described will enable geneticists to identify and map imprinted quantitative trait loci and dictate a comprehensive atlas of developmental and epigenetic mechanisms related to genetic imprinting. We illustrate the new discovery of the role of genetic imprinting in regulating hyperoxic acute lung injury survival time using a mouse reciprocal backcross design.

Organisms usually cope with change in the environment by altering the dynamic trajectory of gene expression to adjust the complement of active proteins. The identification of particular sets of genes whose expression is adaptive in response to environmental changes helps to understand the mechanistic base of gene-environment interactions essential for organismic development. We describe a computational framework for clustering the dynamics of gene expression in distinct environments through Gaussian mixture fitting to the expression data measured at a set of discrete time points. We outline a number of quantitative testable hypotheses about the patterns of dynamic gene expression in changing environments and gene-environment interactions causing developmental differentiation. The future directions of gene clustering in terms of incorporations of the latest biological discoveries and statistical innovations are discussed. We provide a set of computational tools that are applicable to modeling and analysis of dynamic gene expression data measured in multiple environments.

All organisms face the problem of how to perform a sequence of developmental changes and transitions during ontogeny. We revise functional mapping, a statistical model originally derived to map genes that determine developmental dynamics, to take into account the entire process of ontogenetic growth from embryo to adult and from the vegetative to reproductive phase. The revised model provides a framework that reconciles the genetic architecture of development at different stages and elucidates a comprehensive picture of the genetic control mechanisms of growth that change gradually from a simple to a more complex level. We use an annual flowering plant, as an example, to demonstrate our model by which to map genes and their interactions involved in embryo and postembryonic growth. The model provides a useful tool to study the genetic control of ontogenetic growth in flowering plants and any other organisms through proper modifications based on their biological characteristics.

BACKGROUND: Despite our increasing recognition of the mechanisms that specify and propagate epigenetic states of gene expression, the pattern of how epigenetic modifications contribute to the overall genetic variation of a phenotypic trait remains largely elusive. RESULTS: We construct a quantitative model to explore the effect of epigenetic modifications that occur at specific rates on the genome. This model, derived from, but beyond, the traditional quantitative genetic theory that is founded on Mendel's laws, allows questions concerning the prevalence and importance of epigenetic variation to be incorporated and addressed. CONCLUSIONS: It provides a new avenue for bringing chromatin inheritance into the realm of complex traits, facilitating our understanding of the means by which phenotypic variation is generated.

MOTIVATION: Despite their success in identifying genes that affect complex disease or traits, current genome-wide association studies (GWASs) based on a single SNP analysis are too simple to elucidate a comprehensive picture of the genetic architecture of phenotypes. A simultaneous analysis of a large number of SNPs, although statistically challenging, especially with a small number of samples, is crucial for genetic modeling. METHOD: We propose a two-stage procedure for multi-SNP modeling and analysis in GWASs, by first producing a 'preconditioned' response variable using a supervised principle component analysis and then formulating Bayesian lasso to select a subset of significant SNPs. The Bayesian lasso is implemented with a hierarchical model, in which scale mixtures of normal are used as prior distributions for the genetic effects and exponential priors are considered for their variances, and then solved by using the Markov chain Monte Carlo (MCMC) algorithm. Our approach obviates the choice of the lasso parameter by imposing a diffuse hyperprior on it and estimating it along with other parameters and is particularly powerful for selecting the most relevant SNPs for GWASs, where the number of predictors exceeds the number of observations. RESULTS: The new approach was examined through a simulation study. By using the approach to analyze a real dataset from the Framingham Heart Study, we detected several significant genes that are associated with body mass index (BMI). Our findings support the previous results about BMI-related SNPs and, meanwhile, gain new insights into the genetic control of this trait. AVAILABILITY: The computer code for the approach developed is available at Penn State Center for Statistical Genetics web site, http://statgen.psu.edu.

MOTIVATION: Functional mapping that embeds the developmental mechanisms of complex traits shows great power to study the dynamic pattern of genetic effects triggered by individual quantitative trait loci (QTLs). A full-sib family, produced by crossing two heterozygous parents, is characteristic of uncertainties about cross-type at a locus and linkage phase between different loci. Integrating functional mapping into a full-sib family requires a model selection procedure capable of addressing these uncertainties. 3FunMap, written in VC++ 6.0, provides a flexible and extensible platform to perform full-sib functional mapping of dynamic traits. Functions in the package encompass linkage phase determination, marker map construction and the pattern identification of QTL segregation, dynamic tests of QTL effects, permutation tests and numerical simulation. We demonstrate the features of 3FunMap through real data analysis and computer simulation. AVAILABILITY: http://statgen.psu.edu/software.

MOTIVATION: Genetic interactions or epistasis may play an important role in the genetic etiology of drug response. With the availability of large-scale, high-density single nucleotide polymorphism markers, a great challenge is how to associate haplotype structures and complex drug response through its underlying pharmacodynamic mechanisms. RESULTS: We have derived a general statistical model for detecting an interactive network of DNA sequence variants that encode pharmacodynamic processes based on the haplotype map constructed by single nucleotide polymorphisms. The model was validated by a pharmacogenetic study for two predominant beta-adrenergic receptor (betaAR) subtypes expressed in the heart, beta1AR and beta2AR. Haplotypes from these two receptors trigger significant interaction effects on the response of heart rate to different dose levels of dobutamine. This model will have implications for pharmacogenetic and pharmacogenomic research and drug discovery. AVAILABILITY: A computer program written in Matlab can be downloaded from the webpage of statistical genetics group at the University of Florida. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: The characterization of the relationship between a longitudinal response process and a time-to-event has been a pressing challenge in biostatistical research. This has emerged as an important issue in genetic studies when one attempts to detect the common genes or quantitative trait loci (QTL) that govern both a longitudinal trajectory and developmental event. RESULTS: We present a joint statistical model for functional mapping of dynamic traits in which the event times and longitudinal traits are taken to depend on a common set of genetic mechanisms. By fitting the Legendre polynomial of orthogonal properties for the time-dependent mean vector, our model does not rely on any curve, which is different from earlier parametric models of functional mapping. This newly developed nonparametric model is demonstrated and validated by an example for a forest tree in which stemwood growth and the time to first flower are jointly modelled. CONCLUSION: Our model allows for the detection of specific QTL that govern both longitudinal traits and developmental processes through either pleiotropic effects or close linkage, or both. This model will have great implications for integrating longitudinal and event data to gain better insights into comprehensive biology and biomedicine.

MOTIVATION: The proper development of any organ or tissue requires the coordinated expression of its underlying genes that can be located on different genomes present in an organism. For instance, each step in the development of seed for a higher plant is the consequence of gene interactions from the maternal, embryo and endosperm genomes. RESULTS: We present a multivariate statistical model for mapping quantitative trait loci (QTL) by incorporating two important aspects of seed development in plants-QTL interactions derived from different genomes, the maternal, embryo and endosperm, and genetic correlations among phenotypic traits expressed in different genome-specific tissues. This model, which has a high dimensionality, is constructed within the maximum-likelihood context based on a finite mixture model. The implementation of the expectation-maximization algorithm allows for the efficient estimation of QTL positions, their action and interaction effects and pleiotropic effects. The application of this high-dimensional model to a real rice dataset has validated its usefulness. CONCLUSIONS: Our model was derived for self-pollinated plants, but it can be extended to cross-pollinated plants and to animals. With the burgeoning of genetic and genomic data, this high-dimensional model will have many implications for agricultural and evolutionary genetic research. AVAILABILITY: A package of software will be provided from the corresponding author upon request.

SUMMARY: Understanding the genetic control of growth is fundamental to agricultural, evolutionary and biomedical genetic research. In this article, we present a statistical model for mapping quantitative trait loci (QTL) that are responsible for genetic differences in growth trajectories during ontogenetic development. This model is derived within the maximum likelihood context, implemented with the expectation-maximization algorithm. We incorporate mathematical aspects of growth processes to model the mean vector and structured antedependence models to approximate time-dependent covariance matrices for longitudinal traits. Our model has been employed to map QTL that affect body mass growth trajectories in both male and female mice of an F2 population derived from the Large and Small mouse strains. The results from this model are compared with those from the autoregressive-based functional mapping approach. Based on results from computer simulation studies, we suggest that these two models are alternative to one another and should be used simultaneously for the same dataset.

SUMMARY: FunMap is a Web-based user interface designed to map quantitative trait loci (QTL) affecting function-valued traits or infinite-dimensional traits in well-structured pedigrees or natural populations. User input includes three files: longitudinal trait data, marker genotypes and/or a linkage map. This software allows for a systematic genome-wide scan and significance test of QTL throughout the map. The dynamic change of QTL effects during the time course of growth is automatically drawn, from which specific biological hypotheses regarding the genetic control mechanisms of growth and development can be tested. AVAILABILITY: http://web.biostat.ufl.edu/~cma/genetics/software.html