Hi all,
As we know, PCoA is one type of eigenanalysis. Each PCo is associated with an eigenvalue. The sum of the eigenvalues will equal the sum of the variance of all variables in the data set. The relative eigenvalues thus tell how much variation that a PCo is able to ‘explain’.Axes are ranked by their eigenvalues. Thus, the first axis has the highest eigenvalue and thus explains the most variance, the second axis has the second highest eigenvalue, etc.
However, I recently found that Eigenvalues that generated by Qiime2, R package "ape" and PRIMERe software are different.
For consistency, I used the same dataset (braycurtis):

R: import relative abundance table, and generate braycurtis dissimilarity indices using vegdist() in vegan package and acquire eigenvalues/relative eigenvalues using pcoa() function from age package

Qiime 2: obtained braycurtis distance matrix and then convert it to qzv and view it from qiime 2 view

PRIMER: import braycurtis distance matrix, then PCoA it
My questions:
 Could anyone help explain what eigenvalues does qiime2 use? Eigenvalues or Relative eigenvalues or Relative eigenvalues after Lingoes or Cailliez correction?
 Could anyone let me know which result I should trust? Qiime2 or ape or PRIMERe considering the results are not inconsistent.
 From the options I found in pcoA() function in ape package, there are many values I can extract from the result list: Eigenvalues, Relative eigenvalues, Corrected eigenvalues (Lingoes correction) and Relative eigenvalues after Lingoes or Cailliez correction. If ape package is right one to choose, which value "PCo1 (? %)" should be used in the figure? My understanding is relative eigenvalues, but I am not sure whether Relative eigenvalues after Lingoes or Cailliez correction is more accurate to explain the variance of microbiome.
Attached are three different outcomes:
 Eigenvalues/Relative eigenvalues from ape package
 Axis 1: ~50% / Axis 2: ~ 13%
 "Eigenvalues" from Qiime 2 (not sure it is Eigenvalues or Relative Eigenvalues)
 Axis 1: ~16% / Axis 2: ~ 12.25%
 "Eigenvalues" from PRIMER (not sure it is Eigenvalues or Relative Eigenvalues)
 Axis 1: ~18.3% / Axis 2: ~ 14%
Last but not the least, thank you in advance for helping me solve my questions
Best Regard,
Godric