## 5 Results and Discussion
### Effect of Adding a Constant  
To examine the effect of adding a fixed value to the input distances, we have proceeded to the following qualitative and quantitative tests: The qualitative tests involved the visual inspection of plots of 95% confidence ellipses created with and without a fixed value added to the initial distances, like the plots in Figure 5. In the quantitative tests, we examined (a) the percent difference between the stability measures estimated with and without adding a constant and (b) the effect of the added constant on the cluster probabilities obtained from 95% confidence ellipses. Indicative quantitative tests are shown in Tables 1-3 and Figure 6.  
Figure 4: **(left)**. Dependence of the stability measure \(STma\) upon \(n\) calculated using the MAPSov method, the MD1 distance measure, and the mMDS and nMDS techniques. Points indicate values averaged over 5 datasets per \(n\) value. Bars show \(\pm\) one standard deviation. Curves have been calculated from \(STma\) = 34.926 \(n^{-1.425}\) (mMDS) and \(STma\) = 8.7242 \(n^{-0.967}\) (nMDS) (**right**). Dependence of the probability of the most likely dendrograms upon \(n\) when they are created from data from confidence ellipses of the mMDS and nMDS techniques using MD1 simulated distances and the MAPSov method. Points indicate values averaged over 5 datasets per \(n\) value. Bars show \(\pm\) one standard deviation. Curves have been calculated from \(Pr=0.114\ln(n)+0.0133\) (mMDS) and \(Pr=0.1154\ln(n)-0.0124\) (nMDS). \begin{table}
\begin{tabular}{l l l l l l l l l l l} \hline  & & & **EG1** & **EG1** & **EG1** & **EG2** & **EG2** & **EG2** & **WH1** & **WH1** & **WH1** \\ \hline \hline
**MDS** & **Stability** & **MD1-m** & **MD1-av** & **cMD1** & **MD1-m** & **MD1-av** & **cMD1** & **MD1-m** & **MD1-av** & **cMD1** \\ \hline mMDS & STvr & 0.65 & 7.41 & 0.05 & 0.2 & 5.85 & 0.46 & 2.07 & 5.82 & 1.12 \\ mMDS & STov & 2.17 & 6.42 & 1.34 & 5.25 & 9.25 & 5.31 & 0.28 & 1.06 & 0.08 \\ mMDS & STma & 28.6 & 61.5 & 21.3 & 0.67 & 5.08 & 3.34 & 12.8 & 35.6 & 14.7 \\ nMDS & STvr & 0.52 & 4.67 & 0.14 & 0.02 & 1.04 & 0.09 & 0.01 & 0.05 & 0.01 \\ nMDS & STov & 1.02 & 3.80 & 0.88 & 2.46 & 6.96 & 2.03 & 0.02 & 0.01 & 0 \\ nMDS & STma & 8.53 & 23.9 & 4.84 & 0.18 & 8.02 & 0.07 & 0.34 & 1.00 & 0.28 \\ PCoA & STvr & 0.05 & 2.85 & 0.16 & 0.47 & 0.54 & 0.39 & 0.06 & 0.37 & 0.03 \\ PCoA & STov & 0.70 & 1.74 & 0.36 & 2.22 & 6.28 & 1.86 & 0.24 & 0.62 & 0.2 \\ PCoA & STma & 5.18 & 18.85 & 2.11 & 0.75 & 10.62 & 0.55 & 4.68 & 10.92 & 5.42 \\ \hline \hline
**MDS** & **Stability** & **ED-m** & **ED-av** & **cED** & **ED-m** & **ED-av** & **cED** & **ED-m** & **ED-av** & **cED** \\ \hline mMDS & STvr & 0.19 & 5.13 & 0.08 & 0.32 & 7.03 & 0.22 & 0.41 & 4.21 & 0.19 \\ mMDS & STov & 1.97 & 6.78 & 1.27 & 7.28 & 13.53 & 6.05 & 0.2 & 0.57 & 0.22 \\ mMDS & STma & 33.8 & 102.4 & 23.0 & 4.28 & 6.78 & 7.33 & 9.7 & 43.9 & 7.98 \\ nMDS & STvr & 0.22 & 3.3 & 0.02 & 0.61 & 0.31 & 0.11 & 0.02 & 0.05 & 0.04 \\ nMDS & STov & 1.3 & 4.11 & 0.99 & 4.38 & 13.5 & 2.61 & 0.04 & 0.16 & 0.03 \\ nMDS & STma & 10.14 & 39.5 & 5.32 & 0.45 & 6.21 & 1.89 & 0.94 & 3.74 & 2.08 \\ PCoA & STvr & 0.19 & 1.95 & 0.1 & 0.83 & 1.05 & 0.2 & 0.07 & 0.08 & 0.1 \\ PCoA & STov & 0.98 & 2.85 & 0.5 & 4.1 & 10.77 & 2.47 & 0.07 & 0.26 & 0.12 \\ PCoA & STma & 6.03 & 31.36 & 2.59 & 0.3 & 8.35 & 2.58 & 3.91 & 17.1 & 3.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Percent difference between the stability measures estimated with and without an added constant in the distance measures of the datasets EG1, EG2, and WH1. Figure 5: 95% confidence ellipses obtained from the WH1 dataset when using the distance measure MD1 and the mMDS and nMDS techniques. The added constant to the distance values is equal to 0 (**left**) and the average MD1 values (**right**). Populations: (1) P-Mokapu, (2) P-Easter I, (3) P-Moriori, (4) WP-Japan N, (5) WP-Japan S, (6) WP-Hainan, (7) WP-Atayal, (8) WP-Phillipi, (9) WP-Guam, (10) WP-Ainu, (11) P-Maori S, and (12) P-Maori N.