I am currently trying to figure out the differences between Adonis {vegan} and Analysis of Molecular Variances AMOVA {e.g. Ade4}. I know that Adonis tests if the position of the centroids (belonging to groups or species) are different and that this is an approximation of compositional (beta diversity) similarity of the sample (groups/species) to the other samples (group/species). AMOVA on the other hand, is just an non-parametric version of ANOVA, usually applied in population genetics but can be extended to 'ecology' in general since it works on any distance metric. It tests the hypothesis that genetic (or whatever distance) diversity within populations (or groups/species) is not significantly different from that which would result from pooling the two populations (Excoffier et al., 1992; Anderson, 2001; Martin, 2002). Both methods calculate P-values using permutations. 

So my question is; if I would use the same distance metric with the same factor-levels, would Adonis and AMOVA produce the same or at least (extremely) similar results?

I am also wondering the difference between Betadisper {vegan} and HOMOVA (Homogeneity of Molecular Variance). The only difference here is that Betadisper seems to be based on Levene's test for homogeneity of variances while HOMOVA implements Barlett's test.

Any thoughts or comments on this would be highly appreciated, thanks! 


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