On the inference of large phylogenies with long branches: How long is too long?

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.'09], building on the work of [Mossel'04], a tight sequence-length requirement was obtained for the CFN model. In particular the required sequence length for high-probability reconstruction was shown to undergo a sharp transition (from $O(\log n)$ to $\hbox{poly}(n)$, where $n$ is the number of leaves) at the "critical" branch length \critmlq (if it exists) of the ancestral reconstruction problem. Here we consider the GTR model. For this model, recent results of [Roch'09] show that the tree can be accurately reconstructed with sequences of length $O(\log(n))$ when the branch lengths are below \critksq, known as the Kesten-Stigum (KS) bound. Although for the CFN model \critmlq = \critksq, it is known that for the more general GTR models one has \critmlq \geq \critksq with a strict inequality in many cases. Here, we show that this phenomenon also holds for phylogenetic reconstruction by exhibiting a family of symmetric models $Q$ and a phylogenetic reconstruction algorithm which recovers the tree from $O(\log n)$-length sequences for some branch lengths in the range (\critksq,\critmlq). Second we prove that phylogenetic reconstruction under GTR models requires a polynomial sequence-length for branch lengths above \critmlq

Reconstructing (super)trees from data sets with missing distances: Not all is lost

The wealth of phylogenetic information accumulated over many decades of biological research, coupled with recent technological advances in molecular sequence generation, present significant opportunities for researchers to investigate relationships across and within the kingdoms of life. However, to make best use of this data wealth, several problems must first be overcome. One key problem is finding effective strategies to deal with missing data. Here, we introduce Lasso, a novel heuristic approach for reconstructing rooted phylogenetic trees from distance matrices with missing values, for datasets where a molecular clock may be assumed. Contrary to other phylogenetic methods on partial datasets, Lasso possesses desirable properties such as its reconstructed trees being both unique and edge-weighted. These properties are achieved by Lasso restricting its leaf set to a large subset of all possible taxa, which in many practical situations is the entire taxa set. Furthermore, the Lasso approach is distance-based, rendering it very fast to run and suitable for datasets of all sizes, including large datasets such as those generated by modern Next Generation Sequencing technologies. To better understand the performance of Lasso, we assessed it by means of artificial and real biological datasets, showing its effectiveness in the presence of missing data. Furthermore, by formulating the supermatrix problem as a particular case of the missing data problem, we assessed Lasso's ability to reconstruct supertrees. We demonstrate that, although not specifically designed for such a purpose, Lasso performs better than or comparably with five leading supertree algorithms on a challenging biological data set. Finally, we make freely available a software implementation of Lasso so that researchers may, for the first time, perform both rooted tree and supertree reconstruction with branch lengths on their own partial datasets