  The Multiple Sequence Alignment (MSA) is a computational abstraction that
represents a partial summary either of indel history, or of structural
similarity. Taking the former view (indel history), it is possible to use
formal automata theory to generalize the phylogenetic likelihood framework for
finite substitution models (Dayhoff's probability matrices and Felsenstein's
pruning algorithm) to arbitrary-length sequences. In this paper, we report
results of a simulation-based benchmark of several methods for reconstruction
of indel history. The methods tested include a relatively new algorithm for
statistical marginalization of MSAs that sums over a stochastically-sampled
ensemble of the most probable evolutionary histories. For mammalian
evolutionary parameters on several different trees, the single most likely
history sampled by our algorithm appears less biased than histories
reconstructed by other MSA methods. The algorithm can also be used for
alignment-free inference, where the MSA is explicitly summed out of the
analysis. As an illustration of our method, we discuss reconstruction of the
evolutionary histories of human protein-coding genes.
