Mathematics

Ms. Sangeeta Bhatia
Western Sydney University

Phylogenetics is the study of evolutionary relationships among the different life forms .The arrangement of genes along chromosomes is (very) roughly analogous to that of beads on a necklace. Variations in the arrangements of genes constitute an important clue about the evolutionary relationships and have been used to inform phylogenetic studies since the 1930s.  It is no surprise therefore that in designing algorithms for comparison of genome arrangements,  permutations have constituted the construct of choice for representing genomes. Our work attempts to exploit the the rich theory of permutation groups to study the problems related to comparison of genomic arrangements. In this talk, I will describe two important models that we have developed.
Our first model is an algebraic translation of a universal genome rearrangement operator called double cut and join (DCJ).  In the second part, I’ll discuss a model that makes use of the well developed theory of rewriting systems to design a flexible framework for determining weighted rearrangement distances. The proposed framework can be adapted to a number of different rearrangement models and presents an important contribution to the study of weighted distances in genome rearrangement literature. Our work is the first to utilise the theory of rewriting systems to a problem in phylogenetics thereby linking these two separate fields.