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

Abstract

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 D₂^S and D₂^*. For D₂^S, 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 D₂^S 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.