BackgroundVarious approaches to alignment-free sequence comparison are based on the length of exact or inexact word matches between pairs of input sequences. Haubold et al. (J Comput Biol 16:1487–1500, 2009) showed how the average number of substitutions per position between two DNA sequences can be estimated based on the average length of exact common substrings.ResultsIn this paper, we study the length distribution of k-mismatch common substrings between two sequences. We show that the number of substitutions per position can be accurately estimated from the position of a local maximum in the length distribution of their k-mismatch common substrings.

Word-based or 'alignment-free' sequence comparison has become an active area of research in bioinformatics. While previous wordfrequency approaches calculated rough measures of sequence similarity or dissimilarity, some new alignment-free methods are able to accurately estimate phylogenetic distances between genomic sequences. One of these approaches is Filtered Spaced Word Matches. Herein, we extend this approach to estimate evolutionary distances between complete or incomplete proteomes; our implementation of this approach is called Prot-SpaM. We compare the performance of Prot-SpaM to other alignment-free methods on simulated sequences and on various groups of eukaryotic and prokaryotic taxa. Prot-SpaM can be used to calculate high-quality phylogenetic trees from whole-proteome sequences in a matter of seconds or minutes and often outperforms other alignmentfree approaches. The source code of our software is available through Github:https://github.com/jschellh/ProtSpaM