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

We study the number N k of (spaced) word matches between pairs of evolutionarily related DNA sequences depending on the word length or pattern weight k , respectively. We show that, under the Jukes-Cantor model, the number of substitutions per site that occurred since two sequences evolved from their last common ancestor, can be esti-mated from the slope of a certain function of N k . Based on these considerations, we implemented a software program for alignment-free sequence comparison called Slope-SpaM . Test runs on simulated sequence data show that Slope-SpaM can estimate phylogenetic dis-tances with high accuracy for up to around 0.5 substitutions per po-sitions. The statistical stability of our results is improved if spaced words are used instead of contiguous k -mers. Unlike previous methods that are based on the number of (spaced) word matches, our approach can deal with sequences that share only local homologies.