The number of k-mer matches between two DNA sequences as a function of k and applications to estimate phylogenetic distances

Abstract

We study the number N k of length-k word matches between pairs of evolutionarily related DNA sequences, as a function of k. We show that the Jukes-Cantor distance between two genome sequences-i.e. the number of substitutions per site that occurred since they evolved from their last common ancestor-can be estimated from the slope of a function F that depends on N k and that is affine-linear within a certain range of k. Integers k min and k max can be calculated depending on the length of the input sequences, such that the slope of F in the relevant range can be estimated from the values F(k min ) and F(k max ). This approach can be generalized to so-called Spaced-word Matches (SpaM), where mismatches are allowed at positions specified by a user-defined binary pattern. Based on these theoretical results, we implemented a prototype software program for alignment-free sequence comparison called Slope-SpaM. Test runs on real and simulated sequence data show that Slope-SpaM can accurately estimate phylogenetic distances for distances up to around 0.5 substitutions per position. The statistical stability of our results is improved if spaced words are used instead of contiguous words. Unlike previous alignment-free methods that are based on the number of (spaced) word matches, Slope-SpaM produces accurate results, even if sequences share only local homologies. OPEN ACCESSCitation: Röhling S, Linne A, Schellhorn J, Hosseini M, Dencker T, Morgenstern B (2020) The number of k-mer matches between two DNA sequences as a function of k and applications to estimate phylogenetic distances. PLoS ONE 15(2): e0228070. https://doi.org/10. Data Availability Statement:The source code of our software is freely available through GitHub Traditionally, phylogenetic distances are inferred from pairwise or multiple sequence alignments. For the huge amounts of sequence data that are now available, however, sequence alignment has become too slow. Therefore, considerable efforts have been made in recent years, to develop fast alignment-free approaches that can estimate phylogenetic distances without the need to calculate full alignments of the input sequences, see [3][4][5][6][7] for recent review articles. Alignment-free approaches are not only used in phylogeny reconstruction, but are also important in metagenomics [8][9][10], to find genome rearrangements [11] and in epidemiology [12] and other medical applications, for example to identify drug-resistant bacteria [13] or to classify viruses [14,15]. In all these applications, it is crucial to rapidly estimate pairwise similarity or dissimilarity values in large sets of sequence data.Some alignment-free approaches are based on word frequencies [16,17] or on the length of common substrings [18][19][20]. Other methods use variants of the D 2 distance which is defined as the number of word matches of a pre-defined length between two sequences [15,[21][22][23]; a review focusing on these methods is given in [24]. kWIP [25] is a further development of this concept that uses information-theoretical...

An Alignment-free Method for Phylogeny Estimation using Maximum Likelihood

“…From Figure 5, it can be seen that several other popular methods have RF distances very close to K-Phylo. It should be noted that results on this dataset are surprising as methods performing well on the rest of the datasets performed poorly here and vice versa as claimed in [15]. The tree estimated by K-Phylo on this dataset and the benchmark tree are available in Figure S1 of Supplementary Data.…”

“…The limitation of this selection process is that it is solely dependent on sequence length and does not take into account resemblances between sequences. Another mechanism in [15] explains a method of finding a range of feasible values of k as a Figure 2: First, different k-mers are listed from the input sequences. Then separate binary matrices from all these k-mer counts are produced.…”

k-mer proximity index for phylogeny comparison of SARS-CoV-2 with other pathogens

“…One of the fundamental tasks of genomics is to compare these sequences for phylogenetic analysis. Several methods are available to compare genetic sequences, either through sequence alignment [1,2] or alignment-free approach [3,4,5,6,7]. Due to large size of genomic data, the sequence alignment approaches are not time and memory e cient and also have some shortcomings [8,9].…”

Read-SpaM: assembly-free and alignment-free comparison of bacterial genomes with low sequencing coverage

“…In recent years, a large number of alignment-free approaches to phylogeny reconstruction have been developed and applied, since these methods are much faster than traditional, alignment-based phylogenetic methods, see [50,39,3,25] for recent review papers. Most alignment-free approaches are based on k-mer statistics [21,44,7,48,17], but there are also approaches based on the length of common substrings [47,8,27,37,32,46], on word or spaced-word matches [38,33,35,34,1,41] or on so-called micro-alignments [49,20,29,28]. As has been mentioned by various authors, an additional advantage of many alignment-free methods is that they can be applied not only to complete genome sequences, but also to unassembled reads.…”