## 5 Results and Discussion
### Confidence Regions and Cluster Probabilities
This can be done only via the estimation of Monte-Carlo pairwise cluster probabilities, especially the probabilities of the most frequent clusters/patterns. The importance of the estimation of Monte-Carlo cluster probabilities is shown in both Figures 7 and 8 as well as in the relevant spreadsheets in Supplement-S2-Tables and Dendrograms. In Figure 7, we observe that the most likely dendrogram of the dataset EG1 consists of the clusters (00110, 11000, and 00111), that is, the pairwise clusters 3-4 and 1-2 and the cluster 3-4-5 with probabilities of 0.35, 0.78, and 0.575, respectively, whereas similar is the case for the most likely dendrogram of the Sim-100 dataset. However, if we look at the probabilities of the most frequent clusters, we note that the 4-5 cluster (00011) has a significant probability equal to 0.6 for the dataset EG1 and 0.59 for Sim-100. Therefore, the MDS plots of EG1 and Sim-100 are very likely to be related to the clusters (11000, 00011, 00111), which are associated with the dendrogram obtained from the EG1 original dataset. In Figure 8, at the MDS plot of WH1, we can easily distinguish at least three clusters: They are formed by the samples 1-2 (P-Mokapu, P-Easter I), 3-11-12 (P-Moriori, P-Maori S, P-Maori N), and 4-5-6-7-8 (WP-Japan N, WP-Japan S, WP-Hainan, WP-Atayal, WP-Phillipi) with probabilities of 0.76, 0.62, and 0.90, respectively. The samples WP-Guam and WP-Ainu seem to stand alone as outliers, but if we examine the cluster probabilities, these two samples can be clustered with the cluster (4-5-6-7-8). In this case, we have the formation of two clusters with probabilities of 0.66, corresponding to the classification of the samples as \"Pacific\" (P) and \"West Pacific\" (WP) [15]. Note that all the above clusters are depicted in the most likely dendrogram. In this dendrogram, as well as in the table of the most frequent cluster, we observe that there are many other clusters, but with probabilities less than 0.4. Therefore, it is not safe to draw conclusions about these clusters. Figure 8 also shows the MDS plot of the dataset NO1. We observe that in this case, the uncertainty is so high that no safe conclusions can be drawn about clusters. Note that the high uncertainty is due to the nature of the dataset and not to the distance measure or the MDS technique used (see spreadsheet NO1 in Supplement-S2-Tables and Dendrograms). The best we can extract are two broad clusters, one with African and the other with Eurasian groups, with probabilities of only 0.16 and 0.18, respectively. Clusters with greater probability do exist, but they usually depend upon the distance measure used, except for the cluster between Af-S and Af-W, which has an average probability of about 0.31. An interesting observation derived from Figure 8 and the relevant spreadsheets _Detail-sOnFigure 8_ and _NO1_ in Supplement-S2-Tables and Dendrograms is the very low probability of the most likely dendrogram associated with a great number of dendrograms obtained from the MDS ellipses. This shows that the specific dendrograms, that is, dendrograms with a very low probability, have almost no value. Instead, the useful element of these dendrograms is the probabilities of the clusters that compose them. All these probabilities are presented by the _MAPSov()_ function in the \"Most frequent cluster probabilities from the ellipses of MDS\" table. Note that the _MAPSov()_ function also presents (a) the probability of the basic dendrogram and the probabilities of the most likely dendrograms together with the probabilities of their clusters, and (b) the most frequent MC cluster probabilities estimated when HCA is applied to the original dataset (see spreadsheet NO1 in Supplement-S2-Tables and Dendrograms). Therefore, we can easily compare the information about the clusters obtained from the direct application of HCA to a dataset to that obtained from the application of the MDS technique.