Confirmation about PERMANOVA and Variance partitioning (permutest)
Permutational Multivariate Analysis of Variance (PERMANOVA) assumes no distribution which means it is a non-parameteric statistical test. According to the assumption of PERMANOVA test, each group must have same dispersion in the data. Before performing any statistical test, we must check the underlying assumptions. Variance partitioning (permutest) is a confirmatory test to check the assumption (similar dispersion). You can use permutest.betadisper for permutest. After that you can perform PERMANOVA test using adonis().
Interpretation of PERMANOVA test –

If p value is small (&lt;0.05 ) we reject the null hypothesis (No difference between the groups) otherwise we accept the null hypothesis (Significant difference between the groups).

Coefficient of determination, R-squared value indicates the variation in the distances being explained by groups under the study. Higher value indicates a better fit.


You can further look into the confidence interval for each group.
Hope this confirms the answer to your question.