Mathematical Approaches to Evolutionary Trees and Networks (17w5104)

The Banff International Research Station will host the "Mathematical Approaches to Evolutionary Trees and Networks" workshop from February 12th to February 17th, 2017.

New technologies for sequencing DNA mean that we can probe evolution in more detail than ever before. By sequencing hundreds, thousands or even tens of thousands of individual viruses or bacteria, we can learn how these pathogens evade immune systems, gain resistance to vaccines and drugs, and more fundamentally, how they evolve. This understanding is gained with the help of evolutionary trees, like the ``tree of life''. These trees describe the ancestry of a group of organisms back through time. This can provide information about how an infection spreads, where drug resistance comes from, and can even help us to predict which strains of a virus we should be worried about next.

However, accomplishing these goals requires new ways to understand evolutionary trees, and to take into account that evolution does not always happen in a tree-like way: even simple organisms like bacteria can have more than one “parent''. In this workshop we will focus on three key areas where these questions are driving new mathematics, which in turn have immediate applications. The first is in building better ways to understand what evolutionary trees should look like under different models of what is driving diversity. For example, if an infection is spreading mostly from a few ``super-spreaders'', does the tree look different than when an infection is spreading more evenly? The second is in coping with the vast sizes and complex shapes of the space of possible evolutionary trees for a dataset. There are far more possible trees than there are atoms in the universe, even when only 100 viral sequences are in a dataset! Finally, better ways to summarize the shape and structure of evolutionary trees are needed. These questions link biology with several distinct areas of modern mathematics including modelling, probability, geometry and combinatorics.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).