PAGE 5 OF 9 Nucleic Acids Research, 2008, Vol. 36, No. 5 e33 Figure 2. The accuracy of all ﬁve metrics on dataset 2 with the NJ method. Figure 3. The accuracies of the ﬁve metrics on dataset 3 with the NJ method. model trees to simulate dataset 2. Figure 2 shows the accuracies of all ﬁve distance estimators with the NJ method on dataset 2. Although the advantage of the k-tuple distance matrix is not as obvious as in dataset 1, we can see that k-tuple distance accuracy is above the other distance matrices most of the time. In fact, the k-tuple distance has the best performance for 127 of the 210 trees. Another very important advantage that is not very clearly shown in the ﬁgure is the stability of the k-tuple distance. It has a leading average accuracy of 0.51568 with the lowest standard deviation of 0.09604. Jukes–Cantor ranked second in terms of average accuracy (=0.43574) but has the highest standard deviation (=0.20702) among the ﬁve estimators. Kimura and F84 scored almost the same with an average accuracy of 0.42759 and 0.42550, respectively, and a standard devia- tion of 0.01831 and 0.18175, respectively. Tamura–Nei has the lowest average accuracy (0.35853) with a standard deviation of 0.19900. It is clear that, in additional to its high accuracy, the k-tuple distance also produced a much smaller standard deviation, which is an equally important factor in judging the performance of a metric. BioNJ trees gave a slightly better accuracy for all ﬁve estimators but the diﬀerence was very subtle (Table 2). Figure 3 shows the performance comparison of ﬁve estimators on dataset 3 generated by random trees with sequence lengths from 500 to 1500 bp. It is interesting to note that as the number of taxa increases in the trees (the trees are arranged along the x-axis according to the ascending order of the number of taxa that trees contain), the accuracy of F84, Kimura and Juke–Cantor signiﬁ- cantly dropped. Tamura–Nei and k-tuple distance main- tained their accuracy regardless of the change of the number of taxa. As shown in Figure 3, after the 100th tree sample, which contained 150 taxa, F84, Jukes–Cantor and Kimura basically had the same performance as random clustering. The k-tuple distance achieved the highest average accuracy of 0.30889 with a standard deviation of 0.04278. Tamura–Nei had the second highest average Figure 4. The accuracies of the ﬁve metrics on dataset 4 with the NJ method. accuracy of 0.16092 with a standard deviation of 0.03402. Kimura and F84 matrices performed similarly, with an average accuracy of 0.04410 and 0.04484, respectively, and a standard deviation of 0.08308 and 0.08374, respectively. Jukes–Cantor matrix ranked last with the lowest average accuracy of 0.03222 and a standard deviation of 0.07173. Figure 4 shows the comparison of accuracies of the metrics with the NJ method for dataset 4. Compared to results from other datasets, the accuracy diﬀerence decreased considerably, with the highest average accuracy of 0.64871 for Jukes–Cantor and the lowest 0.50200 for the F84 matrix. Tamura–Nei, k-tuple distance and Kimura ranked second, third and fourth with an average accuracy of 0.58316, 0.52836 and 0.50406, respectively. Despite the loss of advantage in accuracy, the k-tuple distance still maintained its leading position in terms of performance stability with the lowest standard deviation