Optimal Sequence Length Requirements for Phylogenetic Tree Reconstruction with Indels
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We consider the phylogenetic tree reconstruction problem with insertions and deletions (indels). Phylogenetic algorithms proceed under a model where sequences evolve down the model tree, and given sequences at the leaves, the problem is to reconstruct the model tree with high probability. Traditionally, sequences mutate by substitution-only processes, although some recent work considers evolutionary processes with insertions and deletions. In this paper, we improve on previous work by giving a reconstruction algorithm that simultaneously has O(poly n) sequence length and tolerates constant indel probabilities on each edge. Our recursively-reconstructed distance-based technique provably outputs the model tree when the model tree has O(poly n) diameter and discretized branch lengths, allowing for the probability of insertion and deletion to be non-uniform and asymmetric on each edge. Our polylogarithmic sequence length bounds improve significantly over previous polynomial sequence length bounds and match sequence length bounds in the substitution-only models of phylogenetic evolution, thereby challenging the idea that many global misalignments caused by insertions and deletions when p_indel is large are a fundamental obstruction to reconstruction with short sequences.
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