Phylogeny,
Real Trees, Metric Geometry, and Dirichlet Forms
Modern phylogenetics seeks to
reconstruct evolutionary family trees of contemporary species
using data such as DNA sequences. Important in this enterprise
are various random mechanisms for wandering around "tree
space" by a sequence of simple rearrangements, and this motivates
questions about how such mechanisms behave on large trees. As
the number of leaves goes to infinity, one is led to consider
stochastic processes that move around continuously in a space
of tree-like metric spaces. The study of these limiting dynamics
uses ideas from metric geometry such as the Gromov-Hausdorff distance
and analytic tools such as Dirichlet forms. Also, it is intimately
connected with Aldous's continuum random tree, a canonical model
for the limit of many natural families of large random trees.
