Fast Phylogenetic Tree Reconstruction Using Locality-Sensitive Hashing

Abstract

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.

LSHPlace: Fast phylogenetic placement using locality-sensitive hashing

“…9 For binary characters, r 2 converges to 1 2 ; similar constants can be computed for other mutation models, alphabets, and baseline letter frequencies.…”

“…These include TreePhyler 12 and CARMA. 13 While much progress has been made in fast phylogeny reconstruction in recent years, 9,14,15 reconstructing the full tree remains much slower than other classification methods.…”

“…For a more detailed discussion of the theoretical issues in this method, the reader is referred to our previous paper on phylogeny reconstruction. 9 …”

“…These dependencies could be ameliorated by using some of the techniques discussed in our previous paper. 9 We leave that as future work.…”

Learning partial correlation graphs and graphical models by covariance queries

“…Hwang et al (2018) give an extensive discussion of computational challenges of massive amounts of gene expression data and note that issues of computational complexity made researchers rely on pairwise notions of dependence; see, for example, Chan et al (2016); Zhang et al (2011). Scalable algorithms are also of interest in phylogenetics, where the problem is to reconstruct the evolutionary relationships between tens to hundreds of thousands of DNA sequences (Price et al (2010); Brown & Truszkowski (2012). Another example leading to large networks is building human brain functional connectivity networks using functional MRI data.…”