PCA with clustering according to facial pattern
I am comparing animal species based on their facial color pattern in Rstudio. The relatively new used packages resulted in a lot of principal components (1 for each sample). Only the first 2 (possibly 3) PCs are of importance in determining if species are statistically different, opposed to visually on a PCA.

                  PC1    PC2    PC3

Sample 1 : group 1 … … …
Sample 2 : group 1 … … …
Sample 3 : group 2 … … …
Sample 4 : group 2 … … …
Sample 5 : group 3 … … …
Sample 6 : group 3 … … …
…..

A univariate Mann-Whitney U test was chosen as a result of the amount of assumption violations. Altough this was succesful, I want to try a multivariate Mann-Whitney U test, where multiple pairwise comparisons are made (7 species over +- 540 samples, unequally divided) with eventual measures to further strengthen interpretation. My current thought process was to include Melanobis distance as a measure for multivariat effect size (group sample size and spread) and a power estimate. I only found the package “MultNonParam” which specifies this in their description: “Methods include adjustments for multiple comparisons, implementation of multivariate Mann-Whitney-Wilcoxon testing”. I do not see an appropriat function for it and certainly not one for calculating power which would be done with advanced simulations, bootstrapping as I understand it.

Additionally, I am not sure if I am asking to much from my dataset due to the distributions of the groups and sample size being different.