  Mutation rate variation across loci is well known to cause difficulties,
notably identifiability issues, in the reconstruction of evolutionary trees
from molecular sequences. Here we introduce a new approach for estimating
general rates-across-sites models. Our results imply, in particular, that large
phylogenies are typically identifiable under rate variation. We also derive
sequence-length requirements for high-probability reconstruction.
  Our main contribution is a novel algorithm that clusters sites according to
their mutation rate. Following this site clustering step, standard
reconstruction techniques can be used to recover the phylogeny. Our results
rely on a basic insight: that, for large trees, certain site statistics
experience concentration-of-measure phenomena.
