Statistical Shape Analysis - Sebastian Kurtek
Shape refers to the external appearance of an object as produced by its outline. Statistical analysis of shapes has played an important role in various biological applications including disease diagnosis based on brain morphometry, bioinformatics (structural analysis of proteins) or the study of leaf shapes. During this project the students will develop tools for generating comparisons between shapes, computing statistical summaries of shapes such as the mean and covariance, defining probability distributions on shape classes, and studying clustering and classification of shapes. These tools will then be applied to different types of biological data.
It will be useful if students have a background in statistics and experience with computing (preferably MATLAB). Exposure to directional statistics would be helpful, but not required. Motivated students without this type of experience can learn everything that is required during the program.
Statistical Phylogenetics - Laura Kubatko
Phylogenetic trees are graphs that display ancestry-descent relationships among a set of present-day species. A fundamental goal in evolutionary biology is the inference of a phylogenetic tree given some data, often in the form of DNA sequences, for the species of interest. In this project, students will study the main ideas involved in the estimation of phylogenetic trees from DNA sequence data. They will then apply this knowledge to a real-world DNA sequence data set, with the goal of estimating a phylogenetic tree as well as quantifying the error in the estimate. The estimated phylogeny will then be used to examine questions of interest concerning the organisms under study. Examples of such questions are the directionality of trait evolution, the phylogeographic movement of ancestral populations, the compatibility of molecular and morphological data, or whether speciation has occurred via hybridization.