Operads and the Tree of Life. This week Lisa and I are visiting her 90-year-old mother in Montréal. Friday I’m giving a talk at the Université du Québec à Montréal. The main person I know there is André Joyal, an expert on category theory and algebraic topology. So, I decided to give a talk explaining how some ideas from these supposedly ‘pure’ branches of math show up in biology. My talk is called ‘Operads and the Tree of Life’. Trees In biology, trees are very important: So are trees of a more abstract sort: phylogenetic trees describe the history of evolution.
Its structure is far from fully understood. Abstracting still further, we can also think of a tree as a kind of purely mathematical structure, like this: Trees are important in combinatorics, but also in algebraic topology. With n inputs and one output as a little tree like this: We can also draw the various ways of composing these operations.
An operation with n inputs and one output is called an n-ary operation. But how do operads show up in biology? Where Why? Carl Boettiger's Open Notebook. BEACON | Center for the Study of Evolution in Action. Greg Lang's Open Notebook.