Towards a Practical O(n logn) Phylogeny Algorithm

2012

Biocomputing 2013

Self Cite

We consider the problem of phylogenetic placement, in which large numbers of sequences (often nextgeneration sequencing reads) are placed onto an existing phylogenetic tree. We adapt our recent work on phylogenetic tree inference, which uses ancestral sequence reconstruction and locality-sensitive hashing, to this domain. With these ideas, new sequences can be placed onto trees with high fidelity in strikingly fast runtimes. Our results are two orders of magnitude faster than existing programs for this domain, and show a modest accuracy tradeoff. Our results offer the possibility of analyzing many more reads in a next-generation sequencing project than is currently possible.

Section: Related Workmentioning

confidence: 99%

LSHPlace: Fast phylogenetic placement using locality-sensitive hashing

2012

Biocomputing 2013

Self Cite

“…FastTree [20] reconstructs phylogenies without computing the full distance matrix, which results in O(n 1.5 log n) runtime. Our own recent algorithm, QTree [1,2], runs in O(n log n) time, using an incremental approach to building trees. No theoretical guarantees exist for the quality of solutions obtained from these fast algorithms, however, under realistic assumptions about the evolutionary model, for short sequences.…”

Section: Practical Algorithmsmentioning

confidence: 99%

“…As biologists start to need trees for hundreds of thousands of taxa [10], even traditionally faster distance methods, such as neighbour joining, become unacceptably slow. Researchers have developed sub-quadratic time heuristics [20,1], but they lack theoretical performance guarantees, so it is unclear whether their use is universally appropriate.…”

Section: Introductionmentioning

confidence: 99%

Fast Phylogenetic Tree Reconstruction Using Locality-Sensitive Hashing

Lecture Notes in Computer Science

2012

Self Cite

We present the first sub-quadratic time algorithm that with high probability correctly reconstructs phylogenetic trees for short sequences generated by a Markov model of evolution. Due to rapid expansion in sequence databases, such very fast algorithms are becoming necessary. Other fast heuristics have been developed for building trees from very large alignments [20,1], but they lack theoretical performance guarantees. Our new algorithm runs in O(n 1+γ(g) log 2 n) time, where γ is an increasing function of an upper bound on the branch lengths in the phylogeny, the upper bound g must be below 1 2 − 1 8 ≈ 0.15, and γ(g) < 1 for all g. For phylogenies with very short branches, the running time of our algorithm is close to linear. For example, if all branch lengths correspond to a mutation probability of less than 0.02, the running time of our algorithm is roughly O(n 1.2 log 2 n). Via a prototype and a sequence of large-scale experiments, we show that many large phylogenies can be reconstructed fast, without compromising reconstruction accuracy.

“…When combined with local search, our algorithm can produce trees on the full taxa set whose accuracy is almost identical to that of FastTree, while being substantially faster. This paper is an expanded version of our earlier conference publication [4]. …”

Section: Introductionmentioning

confidence: 99%

Towards a practical O(n logn) phylogeny algorithm

Hao

2012

Algorithms Mol Biol

Self Cite

Recently, we have identified a randomized quartet phylogeny algorithm that has O(nlogn) runtime with high probability, which is asymptotically optimal. Our algorithm has high probability of returning the correct phylogeny when quartet errors are independent and occur with known probability, and when the algorithm uses a guide tree on O(loglogn) taxa that is correct with high probability. In practice, none of these assumptions is correct: quartet errors are positively correlated and occur with unknown probability, and the guide tree is often error prone. Here, we bring our work out of the purely theoretical setting. We present a variety of extensions which, while only slowing the algorithm down by a constant factor, make its performance nearly comparable to that of Neighbour Joining , which requires Θ(n3) runtime in existing implementations. Our results suggest a new direction for quartet-based phylogenetic reconstruction that may yield striking speed improvements at minimal accuracy cost. An early prototype implementation of our software is available at http://www.cs.uwaterloo.ca/jmtruszk/qtree.tar.gz.