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Molecular phylogenetic techniques do not generally account for such commonevolutionary events as site insertions and deletions (known as indels). Insteadtree building algorithms and ancestral state inference procedures typicallyrely on substitution-only models of sequence evolution. In practice thesemethods are extended beyond this simplified setting with the use of heuristicsthat produce global alignments of the input sequences--an important problemwhich has no rigorous model-based solution. In this paper we consider a newversion of the multiple sequence alignment in the context of stochastic indelmodels. More precisely, we introduce the following {\em trace reconstructionproblem on a tree} (TRPT): a binary sequence is broadcast through a treechannel where we allow substitutions, deletions, and insertions; we seek toreconstruct the original sequence from the sequences received at the leaves ofthe tree. We give a recursive procedure for this problem with strongreconstruction guarantees at low mutation rates, providing also an alignment ofthe sequences at the leaves of the tree. The TRPT problem without indels hasbeen studied in previous work (Mossel 2004, Daskalakis et al. 2006) as abootstrapping step towards obtaining optimal phylogenetic reconstructionmethods. The present work sets up a framework for extending these works toevolutionary models with indels.

Global Alignment of Molecular Sequences via Ancestral State Reconstruction