| Living 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 of spectrum of scientific disciplines including anthropology, agriculture, developmental biology, evolution and biomedicine. Despite the fundamental importance of morphological shape, the difficulty in quantifying the shape and modeling the ultra-high dimension of the image data make the task of genetic mapping on it increasingly difficult.;In this dissertation, we derived several statistical models for mapping specific genes or quantitative trait loci (QTLs) that govern the variation of morphological shape. We are pioneer in the functional shape genetics area and able to detect several significant genes that control the static allometry of the leaf shape traits by incorporating image analysis, statistical model and marker-based linkage disequilibrium (LD) analysis.;After quantifying the morphological shapes numerically through RCC (Radius Centroid Contour) skills, each phenotype, as a datum, is in the form of samples of functional curves or trajectories with high dimension. In the first model, we decreased the dimension by PCA and illustrated the shape variation piece by piece. In the second model, we developed a nonparametric method to model the mean curve by GEE (Generalized Estimating Equation) local polynomial kernel and model the covariance matrix by functional PCA (Principal Component Analysis. Through functional PCA, we characterized the dominant modes of variation around the overall mean trend function and avoided facing directly the extremely huge dimensional covariance matrix. The models are 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.;Through incorporating these procedures into the LD based mapping framework, our model led to the detection of several individual significant QTLs responsible for global and local shape variability, addressed many questions in the genetic control of biological shape, and simultaneously estimated QTL allele frequency and marker-QTL linkage disequilibrium. The statistical behavior of the model and its utilization were verified by both real data analysis on the leaf data from China, and computer simulated data. |
