Multi-SpaM: A Maximum-Likelihood Approach to Phylogeny Reconstruction Using Multiple Spaced-Word Matches and Quartet Trees

Abstract

Motivation: Word-based or 'alignment-free' methods for phylogeny reconstruction are much faster than traditional approaches, but they are generally less accurate. Most of these methods calculate pairwise distances for a set of input sequences, for example from word frequencies, from so-called spaced-word matches or from the average length of common substrings. Results: In this paper, we propose the first word-based approach to tree reconstruction that is based on multiple sequence comparison and Maximum Likelihood. Our algorithm first samples small, gap-free alignments involving four taxa each. For each of these alignments, it 1 arXiv:1803.09222v2 [q-bio.PE] 28 Apr 2018 then calculates a quartet tree and, finally, the program Quartet Max-Cut is used to infer a super tree topology for the full set of input taxa from the calculated quartet trees. Experimental results show that trees calculated with our approach are of high quality. Availability: The source code of the program is available at https://github.com/tdencker/multi-SpaM

Benchmarking of alignment-free sequence comparison methods

“…The best-performing tools for the plant data set are co-phylog [21], mash [9] and Multi-SpaM [23], all of which almost perfectly recovered the reference tree topology of the plant species (with an nRF = 0.09 for all three programs). In each of the trees produced by these programs, there was exactly one species placed at an incorrect position compared to its position in the reference tree, namely, in the speciation order in the Brassicaceae family for co-phylog (Additional file 2: Figure S4), mash (Additional file 2: Figure S5) and for Multi-SpaM, the last of which placed Carica papaya outside the Brassicales order (Additional file 2: Figure S6).…”

“…The sequences of 25 whole mitochondrial genomes of fish species from the suborder Labroidei and the species tree were taken from Fischer et al [48]. The set of 29 E. coli genome sequences was originally compiled by Yin and Jin [21] and has been used in the past by other groups to evaluate AF programs [22,23,68]. Finally, the set of 14 plant genomes is from Hatje et al [69].…”

“…Two sketches are compared to provide an estimate of the Jaccard index (i.e., the fraction of shared hashes) and the Mash distance, which estimates the rate of sequence mutation under an evolutionary model. [23], similarly to FSWM, starts with a binary pattern P of length l representing "match positions" and "don't care positions". It then searches for four-way Spaced-word Matches (SpaMs) w.r.t.…”

“…A wide array of AF approaches to sequence comparison have been developed. These approaches include methods based on word or k-mer counts [12][13][14][15][16], the length of common substrings [17][18][19][20], micro-alignments [21][22][23][24][25], sequence representations based on chaos theory [26,27], moments of the positions of the nucleotides [28], Fourier transformations [29], information theory [30] and iterated-function systems [30,31]. Currently, the most widely used AF approaches are based on k-mer counts [32].…”

The number of spaced-word matches between twoDNAsequences as a function of the underlying pattern weight

“…Most of these approaches calculate heuristic measures of sequence (dis-)similarity that are difficult to interpret. At the same time, alignment-free methods have been proposed that can accurately estimate phylogenetic distances between sequences based on stochastic models of DNA or protein evolution, using the length of common substrings [22,35] or so-called micro alignments [54,21,30,29,12].…”