  A central task in the study of molecular sequence data from present-day
species is the reconstruction of the ancestral relationships. The most
established approach to tree reconstruction is the maximum likelihood (ML)
method. In this method, evolution is described in terms of a discrete-state
continuous-time Markov process on a phylogenetic tree. The substitution rate
matrix, that determines the Markov process, can be estimated using the
expectation maximization (EM) algorithm. Unfortunately, an exhaustive search
for the ML phylogenetic tree is computationally prohibitive for large data
sets. In such situations, the neighbor-joining (NJ) method is frequently used
because of its computational speed. The NJ method reconstructs trees by
clustering neighboring sequences recursively, based on pairwise comparisons
between the sequences. The NJ method can be generalized such that
reconstruction is based on comparisons of subtrees rather than pairwise
distances. In this paper, we present an algorithm for simultaneous substitution
rate estimation and phylogenetic tree reconstruction. The algorithm iterates
between the EM algorithm for estimating substitution rates and the generalized
NJ method for tree reconstruction. Preliminary results of the approach are
encouraging.
