Alignment-Free Sequence Comparison (II): Theoretical Power of Comparison Statistics

Abstract

Rapid methods for alignment-free sequence comparison make large-scale comparisons between sequences increasingly feasible. Here we study the power of the statistic D 2 , which counts the number of matching k-tuples between two sequences, as well as D 2 * , which uses centralized counts, and D 2 S , which is a self-standardized version, both from a theoretical viewpoint and numerically, providing an easy to use program. The power is assessed under two alternative hidden Markov models; the first one assumes that the two sequences share a common motif, whereas the second model is a pattern transfer model; the null model is that the two sequences are composed of independent and identically distributed letters and they are independent. Under the first alternative model, the means of the tuple counts in the individual sequences change, whereas under the second alternative model, the marginal means are the same as under the null model. Using the limit distributions of the count statistics under the null and the alternative models, we find that generally, asymptotically D 2 S has the largest power, followed by D 2 * , whereas the power of D 2 can even be zero in some cases. In contrast, even for sequences of length 140,000 bp, in simulations D 2 * generally has the largest power. Under the first alternative model of a shared motif, the power of D 2 * approaches 100% when sufficiently many motifs are shared, and we recommend the use of D 2 * for such practical applications. Under the second alternative model of pattern transfer, the power for all three count statistics does not increase with sequence length when the sequence is sufficiently long, and hence none of the three statistics under consideration can be recommended in such a situation. We illustrate the approach on 323 transcription factor binding motifs with length at most 10 from JASPAR CORE (October 12, 2009 version)

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.…”

Scalable alignment-free approaches in microbial phylogenomics

“…Certain other AF methods may fit uncomfortably into these classes, or lie outside them altogether 30 . In the present context, the motivating concept is the same: substrings (perhaps defined by k-mers) that meet certain criteria, and are shared by a set of sequences, can be considered as capturing part of the homology signal and are thus potentially informative on phylogeny.…”

“…For instance, regions of ribosomal RNA (16S or 23S for bacteria, 18S or 28S for eukaryotes) are more highly conserved compared to genes coding for metabolic functions 30,31 . For a given protein however the evolutionary rate can be modelled as constant across evolutionary time and among the different lineages.…”

“…MSA is also complicated by local structure variation (such as genetic recombination, duplication, gene gain and loss) yielding ambiguously aligned regions, or not aligned at all ( Figure 3). Simplified workflow of phylogenomic approaches 64 . A simplified workflow of (A) the classical and (B) an alternative phylogenetic approaches, given a set of homologous sequences and reference phylogeny shown on top.…”