Guifang Fu

A dynamic model for genome-wide association studies

Although genome-wide association studies (GWAS) are widely used to identify the genetic and environmental etiology of a trait, several key issues related to their statistical power and biological relevance have remained unexplored. Here, we describe a novel statistical approach, called functional GWAS or fGWAS, to analyze the genetic control of traits by integrating biological principles of trait formation into the GWAS framework through mathematical and statistical bridges. fGWAS can address many fundamental questions, such as the patterns of genetic control over development, the duration of genetic effects, as well as what causes developmental trajectories to change or stop changing. In statistics, fGWAS displays increased power for gene detection by capitalizing on cumulative phenotypic variation in a longitudinal trait over time and increased robustness for manipulating sparse longitudinal data.

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.

Genome-Wide Association Studies for Bivariate Sparse Longitudinal Data

Objective: Longitudinal measurements with bivariate response have been analyzed by several authors using two separate models for each response. However, for most of the biological or medical experiments, the two responses are highly correlated and hence a separate model for each response might not be a desirable way to analyze such data. A single model considering a bivariate response provides a more powerful inference as the correlation between the responses is modeled appropriately. In this article, we propose a dynamic statistical model to detect the genes controlling human blood pressure (systolic and diastolic). Methods: By modeling the mean function with orthogonal Legendre polynomials and the covariance matrix with a stationary parametric structure, we incorporate the statistical ideas in functional genome-wide association studies to detect SNPs which have significant control on human blood pressure. The traditional false discovery rate is used for multiple comparisons. Results: We analyze the data from the Framingham Heart Study to detect such SNPs by appropriately considering gender-gene interaction. We detect 8 SNPs for males and 7 for females which are most significant in controlling blood pressure. The genotype-specific mean curves and additive and dominant effects over time are shown for each significant SNP for both genders. Simulation studies are performed to examine the statistical properties of our model. The current model will be extremely useful in detecting genes controlling different traits and diseases for humans or non-human subjects.

EM Algorithm for Mapping Quantitative Trait Loci in Multivalent Tetraploids

Multivalent tetraploids that include many plant species, such as potato, sugarcane, and rose, are of paramount importance to agricultural production and biological research. Quantitative trait locus (QTL) mapping in multivalent tetraploids is challenged by their unique cytogenetic properties, such as double reduction. We develop a statistical method for mapping multivalent tetraploid QTLs by considering these cytogenetic properties. This method is built in the mixture model-based framework and implemented with the EM algorithm. The method allows the simultaneous estimation of QTL positions, QTL effects, the chromosomal pairing factor, and the degree of double reduction as well as the assessment of the estimation precision of these parameters. We used simulated data to examine the statistical properties of the method and validate its utilization. The new method and its software will provide a useful tool for QTL mapping in multivalent tetraploids that undergo double reduction.

A statistical model for mapping morphological shape

BackgroundLiving things come in all shapes and sizes, from bacteria, plants, and animals to humans. Knowledge about the genetic mechanisms for biological shape has far-reaching implications for a range spectrum of scientific disciplines including anthropology, agriculture, developmental biology, evolution and biomedicine.ResultsWe derived a statistical model for mapping specific genes or quantitative trait loci (QTLs) that control morphological shape. The model was formulated within the mixture framework, in which different types of shape are thought to result from genotypic discrepancies at a QTL. The EM algorithm was implemented to estimate QTL genotype-specific shapes based on a shape correspondence analysis. Computer simulation was used to investigate the statistical property of the model.ConclusionBy identifying specific QTLs for morphological shape, the model developed will help to ask, disseminate and address many major integrative biological and genetic questions and challenges in the genetic control of biological shape and function.

Statistical Models for Genetic Mapping in Polyploids: Challenges and Opportunities

Statistical methods for genetic mapping have well been developed for diploid species but are lagging in the more complex polyploids. The genetic mapping of polyploids, where genome number is higher than two, is complicated by uncertainty about the genotype-phenotype correspondence, inconsistent meiotic mechanisms, heterozygous genome structures, and increased allelic (action) and nonallelic (interaction) combinations. According to their meiotic configurations, polyploids can be classified as bivalent polyploids, in which only two chromosomes pair during meiosis at a time, and multivalent polyploids, where multiple chromosomes pair simultaneously. For some polyploids, these two types of pairing occur at the same time, leading to a mixed category. This chapter reviews several challenges due to the complexities of linkage analysis in polyploids and describes statistical models and algorithms that have been developed for linkage mapping based on their distinct meiotic characteristics. We discuss several issues that should be addressed to better understand the genome structure and organization of polyploids and the genetic architecture of complex traits for this unique group of plants.

A Graphical Weighted Power Improving Multiplicity Correction Approach for SNP Selections

Controlling for the multiplicity effect is an essential part of determining statistical significance in large-scale single-locus association genome scans on Single Nucleotide Polymorphisms (SNPs). Bonferroni adjustment is a commonly used approach due to its simplicity, but is conservative and has low power for large-scale tests. The permutation test, which is a powerful and popular tool, is computationally expensive and may mislead in the presence of family structure. We propose a computationally efficient and powerful multiple testing correction approach for Linkage Disequilibrium (LD) based Quantitative Trait Loci (QTL) mapping on the basis of graphical weighted-Bonferroni methods. The proposed multiplicity adjustment method synthesizes weighted Bonferroni-based closed testing procedures into a powerful and versatile graphical approach. By tailoring different priorities for the two hypothesis tests involved in LD based QTL mapping, we are able to increase power and maintain computational efficiency and conceptual simplicity. The proposed approach enables strong control of the familywise error rate (FWER). The performance of the proposed approach as compared to the standard Bonferroni correction is illustrated by simulation and real data. We observe a consistent and moderate increase in power under all simulated circumstances, among different sample sizes, heritabilities, and number of SNPs. We also applied the proposed method to a real outbred mouse HDL cholesterol QTL mapping project where we detected the significant QTLs that were highlighted in the literature, while still ensuring strong control of the FWER.

Systems mapping: how to map genes for biomass allocation toward an ideotype

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.

Holm multiple correction for large-scale gene-shape association mapping

BackgroundLinkage Disequilibrium (LD) is a powerful approach for the identification and characterization of morphological shape, which usually involves multiple genetic markers. However, multiple testing corrections substantially reduce the power of the associated tests. In addition, the principle component analysis (PCA), used to quantify the shape variations into several principal phenotypes, further increases the number of tests. As a result, a powerful multiple testing correction for simultaneous large-scale gene-shape association tests is an essential part of determining statistical significance. Bonferroni adjustments and permutation tests are the most popular approaches to correcting for multiple tests within LD based Quantitative Trait Loci (QTL) models. However, permutations are extremely computationally expensive and may mislead in the presence of family structure. The Bonferroni correction, though simple and fast, is conservative and has low power for large-scale testing.ResultsWe propose a new multiple testing approach, constructed by combining an Intersection Union Test (IUT) with the Holm correction, which strongly controls the family-wise error rate (FWER) without any additional assumptions on the joint distribution of the test statistics or dependence structure of the markers. The power improvement for the Holm correction, as compared to the standard Bonferroni correction, is examined through a simulation study. A consistent and moderate increase in power is found under the majority of simulated circumstances, including various sample sizes, Heritabilities, and numbers of markers. The power gains are further demonstrated on real leaf shape data from a natural population of poplar, Populus szechuanica var tietica, where more significant QTL associated with morphological shape are detected than under the previously applied Bonferroni adjustment.ConclusionThe Holm correction is a valid and powerful method for assessing gene-shape association involving multiple markers, which not only controls the FWER in the strong sense but also improves statistical power.

Quantitative gene–gene and gene–environment mapping for leaf shape variation using tree-based models

Leaf shape traits have long been a focus of many disciplines, but the complex genetic and environmental interactive mechanisms regulating leaf shape variation have not yet been investigated in detail. The question of the respective roles of genes and environment and how they interact to modulate leaf shape is a thorny evolutionary problem, and sophisticated methodology is needed to address it. In this study, we investigated a framework-level approach that inputs shape image photographs and genetic and environmental data, and then outputs the relative importance ranks of all variables after integrating shape feature extraction, dimension reduction, and tree-based statistical models. The power of the proposed framework was confirmed by simulation and a Populus szechuanica var. tibetica data set. This new methodology resulted in the detection of novel shape characteristics, and also confirmed some previous findings. The quantitative modeling of a combination of polygenetic, plastic, epistatic, and gene-environment interactive effects, as investigated in this study, will improve the discernment of quantitative leaf shape characteristics, and the methods are ready to be applied to other leaf morphology data sets. Unlike the majority of approaches in the quantitative leaf shape literature, this framework-level approach is data-driven, without assuming any pre-known shape attributes, landmarks, or model structures.