A few logs suffice to build (almost) all trees (l): part I
Random Structures & Algorithms
A Short Proof that Phylogenetic Tree Reconstruction by Maximum Likelihood Is Hard
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Approximate Maximum Parsimony and Ancestral Maximum Likelihood
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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Ancestral maximum likelihood (AML) is a method that simultaneously reconstructs a phylogenetic tree and ancestral sequences from extant data (sequences at the leaves). The tree and ancestral sequences maximize the probability of observing the given data under a Markov model of sequence evolution, in which branch lengths are also optimized but constrained to take the same value on any edge across all sequence sites. AML differs from the more usual form of maximum likelihood (ML) in phylogenetics because ML averages over all possible ancestral sequences. ML has long been know to be statistically consistent - that is, it converges on the correct tree with probability approaching 1 as the sequence length grows. However, the statistical consistency of AML has not been formally determined, despite informal remarks in a literature that dates back 20 years. In this short note we prove a general result that implies that AML is statistically inconsistent. In particular we show that AML can 'shrink' short edges in a tree, resulting in a tree that has no internal resolution as the sequence length grows. Our results apply to any number of taxa.