Three mathematical issues in reconstructing ancestral genome

Abstract

With the advances in comparative genomics methods in the past decade, bioinformatics has become a feasible approach to reconstructing ancestral genomes. It reconstructs an ancestral genome by aligning extant genomes and inferring different types of evolutionary events in the evolutionary history, among which two important events are substitution event and duplication event. In this thesis, we study three mathematical issues arising from this approach: (1) seed optimization for homology search and sequence alignment; (2) calculating and asymptotically analyzing the reconstruction accuracy of the Fitch method for reconstructing the ancestral states; (3) counting tandem duplication trees and inferring the relationship between rooted and unrooted duplication trees.