Report on Phylomania

摘要

Phylogenetics is concerned with the problem of reconstructing the evolutionary history of extant organisms from present-day molecular data such as DNA. Currently, there is much interest in further development of the mathematics that underlies computational phylogenetic methods. Hidden from view, in software packages used by biologists, are algorithms performing statistical inference using Markov models on binary trees. The mathematics involved represents a wonderful confluence of stochastic methods and probability theory (Markov chain models), discrete mathematics (combinatorics of tree space), statistical inference (maximum likelihood and Bayesian methods) and, more recently, methods taken from algebraic geometry and the representation theory of finite and infinite (Lie) groups. The latter methods fall under the heading of the emerging field of 'algebraic statistics'. There are many important theoretical problems that arise, such as statistical identifiability of models, consistency and convergence of methods. These problems can only be solved using a multi-disciplinary approach. Phylomania sought to bring together leading bio-mathematicians in this area, with the aim of attacking some of the more pressing problems.