## 6 Conclusions  
The present paper first reviewed four stability methods for MDS plots, that is, methods proposed to evaluate the stability of MDS solutions, in order to choose the most appropriate one for producing reliable MDS confidence ellipses. It was found that the most effective of the methods studied is the MAPsov method, which involves the generation of simulated distances based on the original multivariate dataset and then the creation of MDS maps that are scaled, reflected, rotated, translated, and finally superimposed to construct confidence ellipses.  
The MDS techniques used in the MAPsov method were the metric (mMDS) and nonmetric (nMDS) MDS based on the SMACOF algorithm, the metric MDS based on Principal Coordinates Analysis (PCoA), and an approach adopted in the present study based on the maximum correlation between initial and MDS distances (corMDS). The MAPsov method was used to assess the uncertainty in the MDS plots of squared Euclidean and Mahalanobis distances with and without correction for small sample sizes, as well as the corresponding distances for binary data. Since the correction for small sample sizes can lead to negative distance values, making it impossible to apply the MDS technique, the addition of a fixed value to the distances was thoroughly investigated. It was found that this addition is almost insignificant for the nonmetric nMDS technique, is rather small for the PCoA, and may become significant when using the metric mMDS. By construction, the corMDS is not affected by adding a fixed value to the input distances.  
The application of the MAPsov method showed that the confidence ellipses in MDS plots of (bio)distances provide a good visualization of the (bio)distance map of the populations under study because they take into account the effect of the uncertainty in the computed distances on the distribution of the populations in the MDS map. This visualization is much better than that obtained from the single points of the MDS plots. However, to quantify the uncertainty and its effect on the determination of clusters of samples, we must apply the approach proposed in this paper. That is, we should apply hierarchical cluster analysis to the data of the 95% confidence ellipses and estimate all possible cluster probabilities related to these ellipses. This procedure can also be used to estimate the most probable dendrograms, their cluster probabilities, and the probability of their appearance.  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/a16120535/s1](https://www.mdpi.com/article/10.3390/a16120535/s1)]([https://www.mdpi.com/article/10.3390/a16120535/s1](https://www.mdpi.com/article/10.3390/a16120535/s1)), Supplement S1: Instructions and Code; Supplement S2: Tables and Dendrograms.  
Conceptualization, P.N. and E.N.; methodology, P.N. and E.N.; software, P.N.; validation, E.N.; formal analysis, E.N.; investigation, P.N.; writing--original draft preparation, P.N.; writing--review and editing, E.N.; project administration, P.N.; funding acquisition, E.N. All authors have read and agreed to the published version of the manuscript.  
This paper was written in the context of the MetaMobility project. The project is implemented under the program of social cohesion \"THALIA 2021-2027\", co-funded by the European Union, through the Research and Innovation Foundation [EXCELLENCE/0421/0376].  
Data Availability Statement: All raw data have been extracted from online repositories, as indicated in the text.