On the Inference of Large Phylogenies with Long Branches: How Long Is Too Long?

Elchanan Mossel, Sébastien Roch, Allan Sly
2010 Bulletin of Mathematical Biology  
The accurate reconstruction of phylogenies from short molecular sequences is an important problem in computational biology. Recent work has highlighted deep connections between sequence-length requirements for high-probability phylogeny reconstruction and the related problem of the estimation of ancestral sequences. In Daskalakis et al. (in Probab. Theory Relat. Fields 2010), building on the work of Mossel (Trans. Am. Math. Soc. 356(6):2379-2404, 2004), a tight sequencelength requirement was
more » ... ained for the simple CFN model of substitution, that is, the case of a two-state symmetric rate matrix Q. In particular the required sequence length for high-probability reconstruction was shown to undergo a sharp transition (from O(log n) to poly(n), where n is the number of leaves) at the "critical" branch length g ML (Q) (if it exists) of the ancestral reconstruction problem defined roughly as follows: below g ML (Q) the sequence at the root can be accurately estimated from sequences at the leaves on deep trees, whereas above g ML (Q) information decays exponentially quickly down the tree. Here, we consider a more general evolutionary model, the GTR model, where the q × q rate matrix Q is reversible with q ≥ 2. For this model, recent results of Roch E.
doi:10.1007/s11538-010-9584-6 pmid:20931293 fatcat:bfjxipzjnvhsxkr5zna2jvnjea