Statistical considerations underpinning an alignment-free sequence comparison method

The D2 statistic is defined as the number of word matches of prespecified length k, with up to t mismatches, shared between two given sequences. This statistic finds its application in alignment-free comparisons of biological sequences. It has two main advantages over alignment-based methods for nucleotide and amino-acid sequence comparisons, such as BLAST (basic local alignment search tool). These are (i) D2 does not assume that homologous segments are contiguous, and (ii) the algorithm is computationally extremely fast, the runtime being proportional to the size of the sequences in the case of exact matches. This review article summarises results to date on determining the distributional properties of the D2 statistic for a range of biologically relevant parameters, describes existing applications of the method, and outlines future research directions.