Functional Mapping: Towards High-Dimensional Biology
Functional Mapping: Simplicity from Complexity
Functional Mapping: Biomedical Implications
Polyploid Mapping
Joint Interval and Linkage Disequilibrium Mapping
Sequencing Complex Traits with HapMap
Mapping Seed Development
Statistical Algorithms
Functional Mapping: Towards High-Dimensional Biology
Many complex traits inherently undergo remarked developmental changes during ontogeny. Traditional mapping approaches that analyze phenotypic data measured at a single point are too simple to take into account such a high-dimensional biological issue. We have developed a general framework, called functional mapping, in which the foundation is established for mapping quantitative trait loci (QTL) that underlie variation in a complex trait of dynamic feature. Functional mapping provides a useful quantitative and testable framework for assessing the interplay between gene action, development, sex, genetic background and environment.
Functional Mapping: Simplicity from Complexity
Functional mapping incorporates fundamental principles behind biological processes or networks that are bridged with mathematical functions into a QTL mapping framework. Thus, instead of estimating the genetic effects, variances and covariances among all points within a particular biological network, functional mapping estimates mathematical parameters that determine shape and function of this network. This statistical treatment largely simplifies the complexity of a developmental process. We have implemented a number of parametric (such as autoregressive, transform-both-side and structured antedependence models) and nonparametric approaches to model the structure of variance-covariance matrix among different but related points.
Functional Mapping: Biomedical Implications
Although functional mapping was originally proposed for growth analysis, it has been extended to attack many different biomedical problems. Several successful examples include genetic mapping of drug response, HIV dynamics, tumor growth, circadian rhythms and gene expression dynamics. We anticipate that the integration between functional mapping and biomedical processes will open a novel avenue for functional studies for complex diseases and drug response in the post-genomic era.
Polyploid Mapping
Polyploids are extremely important in agriculture and have been thought to play a central role in evolution and speciation of higher plants. The genetic mapping of polyploids is one of the most difficult tasks in statistical genetic research. Some uniqueness of polyploids, such as preferential chromosomal pairing and double reduction, makes their genetic analyses qualitatively different from those of diploids. Unlike the traditional classification (allo- and autopolyploids), we used Peloaquin's (1961) idea to sort polyploids into bivalent and multivalent polyploids based on the pairing patterns of homologous chromosomes during meiosis. We have constructed a host of statistical models for linkage analysis, map construction and QTL mapping separately for bivalent and multivalent polyploids.
Joint Interval and Linkage Disequilibrium Mapping
The non-random association between different genes, termed linkage disequilibrium (LD), provides a powerful tool for high-resolution mapping of QTL underlying complex traits. This LD-based mapping approach can be made more efficient when it is coupled with interval mapping characterizing the genetic distance between markers and QTL. We provide a closed-form solution for joint estimation of quantitative genetic parameters describing QTL effects, QTL position, residual variances, and population genetic parameters describing allele frequencies and QTL-marker LD.
Sequencing Complex Traits with HapMap
Determining the patterns of DNA sequence variation in the human genome is a useful first step towards identifying the genetic basis of a common disease. A haplotype map, or HapMap, aimed at describing these variation patterns across the entire genome has been recently developed by the International HapMap Consortium. We have derived a novel statistical model for directly characterizing specific sequence variants that are responsible for disease risk based on the haplotype structure provided by HapMap.
Mapping Seed Development
Coordinated expression of maternal, embryo and endosperm tissues is required for proper seed development. The coordination among these three issues is controlled by the interactions between multiple genes derived from the maternal, embryo and endosperm genomes. We have developed a series of statistical models for estimating epistatic effects among QTL derived from the maternal, embryo and endosperm genomes. Our models have power to map imprinted loci that trigger parent-of-origin specific control over gene expression during seed development. Collaborated with Dr. Brian Larkins at the University of Arizona and Dr. Chunhai Shi and Dr. Jun Zhu at Zhejiang University, we have successfully identified interacting QTL from the maternal, embryo and endosperm genomes that regulate endosperm-specific traits in maize and rice. By integrating QTL mapping within the context of seed development, we are among the first to provide insightful ideas for the understanding of the genetic architecture of seed quality traits.
Statistical Algorithms
We derive a closed-form of the EM algorithm for estimating linkage analysis between any kind of marker systems, fully vs. partially informative, or codominant vs. dominant. This more efficient EM algorithm has been extended for linkage disequilibrium mapping and joint interval and linkage disequilibrium mapping.