Estimating evolutionary distances between genomic sequences from spaced-word matches

Abstract

Alignment-free methods are increasingly used to calculate evolutionary distances between DNA and protein sequences as a basis of phylogeny reconstruction. Most of these methods, however, use heuristic distance functions that are not based on any explicit model of molecular evolution. Herein, we propose a simple estimator dN of the evolutionary distance between two DNA sequences that is calculated from the number N of (spaced) word matches between them. We show that this distance function is more accurate than other distance measures that are used by alignment-free methods. In addition, we calculate the variance of the normalized number N of (spaced) word matches. We show that the variance of N is smaller for spaced words than for contiguous words, and that the variance is further reduced if our spaced-words approach is used with multiple patterns of ‘match positions’ and ‘don’t care positions’. Our software is available online and as downloadable source code at: http://spaced.gobics.de/.

Fast and accurate phylogeny reconstruction using filtered spaced-word matches

“…To describe our algorithm, we are using the terminology from our previous papers (Leimeister and Morgenstern, 2014; Morgenstern et al , 2015). For an alphabet Σ, a sequence S of length L and $0<i\le L,\hspace{0.17em}S[i]$ denotes the i th symbol of S .…”

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

“…Spacedword matches or spaced seeds have been introduced in database searching as an alternative to exact k-mer matches [8,34,31]. The main advantage of spaced words compared to contiguous k-mers is the fact that results based on spaced words are statistically more stable than results based on k-mers [24,13,10,9,36,38]. Quite obviously, approximations (4) and (5) remain valid if we define X k to be the number of spaced-word matches for a given pattern P of weight k, and we can generalize the definition of F (k) accordingly: if we consider a maximum pattern weight K and a given set of patterns {P k , 1 ≤ k ≤ K} where k is the weight of pattern P k , then we can define N k as the empirical number of spaced-word matches with respect to pattern P k between two observed DNA sequences.…”

“…Skmer [47] is a further improvement of this approach. In a previous paper, we proposed another way to infer evolutionary distances between DNA sequences based on the number of word matches between them, and we generalized this to so-called spaced-word matches [36]. Here, a spaced-word match is a pair of words from two sequences that are identical at certain positions, specified by a pre-defined binary pattern of match and don't-care positions.…”

“…The distance function proposed in [36] is now used by default in the program Spaced [27]. Theoretically, this distance measure is based on a simple model of molecular evolution without insertions or deletions.…”

“…In [36], we used this equation to estimate the match probability p for two observed sequences using a moment-based approach, by replacing the expected number E(X k ) by the empirical number N k of word matches or spaced-word matches, respectively. Although in equation (1), an indel-free model is assumed, we could show in our previous paper, that this approach gives still reasonable estimates of p for sequences with insertions and deletions, as long as the sequences are globally related, i.e.…”