Alignment-Free Sequence Comparison (I): Statistics and Power

Abstract

Large-scale comparison of the similarities between two biological sequences is a major issue in computational biology; a fast method, the D2 statistic, relies on the comparison of the k-tuple content for both sequences. Although it has been known for some years that the D2 statistic is not suitable for this task, as it tends to be dominated by single-sequence noise, to date no suitable adjustments have been proposed. In this article, we suggest two new variants of the D2 word count statistic, which we call D2S and D2∗. For D2S, which is a self-standardized statistic, we show that the statistic is asymptotically normally distributed, when sequence lengths tend to infinity, and not dominated by the noise in the individual sequences. The second statistic, D2∗, outperforms D2S in terms of power for detecting the relatedness between the two sequences in our examples; but although it is straightforward to simulate from the asymptotic distribution of D2∗, we cannot provide a closed form for power calculations.

G-MAPSEQ – a new method for mapping reads to a reference genome

“…Such techniques were proposed as a fast alternative to much more time-consuming alignment methods, but at the expense of accuracy. Some detailed reviews of k-mer algorithms for sequence comparison (as well as others approaches based on information theory) were presented by Vinga et al [17], Reinert et al [16] and Wan et al [18]. The main idea of using k-mers in sequences comparison usually boils down to two stages.…”

A Simple Shortcut to Unsupervised Alignment-Free Phylogenetic Genome Groupings, Even From Unassembled Sequencing Reads

“…To this end, theoretical aspects of k-mer statistics for biological sequence comparison have been studied in detail before. [7][8][9][10] Previous work has shown a similar approach of studying optimal length of peptides shared among close homologues for ultra-fast protein searches. 11 As also shown previously, simple oligonucleotide or peptide overlap measures between two genomes can be indicative of their phylogenetic distance.…”

Weighted k-word matches: a sequence comparison tool for proteins

“…In all calculations, q ab was taken from the background probabilities of the blosum62 matrix at the reblosum web page [7]. Although other generalisations of the D 2 statistic exist, such as D * 2 and D S 2 proposed by Reinert et al [8], as far as we are aware, D …”