Analytical approaches to genomic evolution.

We model the non-local mechanisms of genomic evolution and propose methods for studying the evolutionary divergence of species based on these models. Mechanisms include the movement of segments of genomes within a single chromosome (transpositions), the reciprocal translocation of segments between two chromosomes, and the inversion of segments. Each of these is studied in the context of a different type of genomic data. We introduce the theory of phylogenetic invariants for evolutionary inference based on very long macromolecular sequences.