Phylogenetic automata, pruning, and multiple alignment

We present an extension of Felsenstein's algorithm to indel models defined on entire sequences, without the need to condition on one multiple alignment. The algorithm makes use of a generalization from probabilistic substitution matrices to weighted finite-state transducers. Our approach may equivalently be viewed as a probabilistic formulation of progressive multiple sequence alignment, using partial-order graphs to represent ensemble profiles of ancestral sequences. We present a hierarchical stochastic approximation technique which makes this algorithm tractable for alignment analyses of reasonable size.