  We have developed an alignment-free method that calculates phylogenetic
distances using a maximum likelihood approach for a model of sequence change on
patterns that are discovered in unaligned sequences. To evaluate the
phylogenetic accuracy of our method, and to conduct a comprehensive comparison
of existing alignment-free methods (freely available as Python package decaf+py
at http://www.bioinformatics.org.au), we have created a dataset of reference
trees covering a wide range of phylogenetic distances. Amino acid sequences
were evolved along the trees and input to the tested methods; from their
calculated distances we infered trees whose topologies we compared to the
reference trees.
  We find our pattern-based method statistically superior to all other tested
alignment-free methods on this dataset. We also demonstrate the general
advantage of alignment-free methods over an approach based on automated
alignments when sequences violate the assumption of collinearity. Similarly, we
compare methods on empirical data from an existing alignment benchmark set that
we used to derive reference distances and trees. Our pattern-based approach
yields distances that show a linear relationship to reference distances over a
substantially longer range than other alignment-free methods. The pattern-based
approach outperforms alignment-free methods and its phylogenetic accuracy is
statistically indistinguishable from alignment-based distances.
