Mathematical and Computational Evolutionary Genomics Lecture Series: Eric Tannier

Macromolecules (DNA, RNA, proteins) are long sequences over small alphabets which contain informations about the functionning of the carrier organisms as well as traces of their descent, the history of individuals, populations, species, up to the deep history of life.

As every lineage records its own events, the comparison of molecules with dedicated algorithms allows to decipher the information stored in these chemical strings. This series of four lectures is devoted to some of the mathematics and algorithms designed for analyzing molecular data and their evolution.

In particular I will present some solutions to genomes rearrangement problems. Thought historically rearrangements were the first mutations discovered, they are poorly exploited in evolutionary biology compared to sequence substitutions because of the combinatorial complexity of the objects commonly used to model them. Solutions will consist in modeling random walks in large discrete spaces, and determining shortest paths or likely paths between a start and an end point of the walk.

Then I will talk about models for phylogeny, and in particular how they cope with gene transfers, that is, the exchange of genetic material between different species. Models of gene evolution with transfers can help dating in the deep past of the living world, in the absence of fossil reconrd.