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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.


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q-bio.PE, q-bio.PE, q-bio.GN, q-bio.QM