I am working with a data set containing species level relative cover estimates in a number of replicates over time that are under ambient conditions or that have received chronic N addition (treatment vs control). I am trying to determine how the community (or communities depending on how you view the landscape) is changing over time with N addition. I think that a shift in community space is a much different response than a dispersion of the replicates (i.e. change in beta diversity) so I want to determine both if the community is shifting and whether it is dispersing. When I use a PERMANOVA (Anderson, 2006) to look for a shift in community space between the two treatments, I get a significant P value (at alpha = 0.05), but when I run a PERMDISP to look for a change in dispersion I also get a significant P value. Now, one of the assumptions of PERMANOVA is equal variance between groups because PERMANOVA will pick up differences in the mean as well as differences in variance (this is shown through PERMDISP). So my question is: when both PERMANOVA and PERMDISP are significant, yet it is difficult to discern which is happening from an NMDS plot, how do you determine whether the community change is a shift of all replicates in multivariate space, a change in heterogeneity of localized communities, or both? I have done a bit of digging on this topic without much success so any feedback would be much appreciated!
Thanks
The sensitivity of MANOVA based on permutation testing to unequal variance in groups will depend on (1) the dissimilarity function that is used for the computation of the sum of squares (less problematic with Euclidean distances) and (2) whether the experimental design is balanced or unbalanced regarding the number of replicates per treatments (there is no hope with unbalanced designs). Thus, if you use Euclidean distances and your design is balanced, it is likely that both differences in group means and dispersions are real. You can find more details in
Pillar, V.D. 2013. How accurate and powerful are randomization tests in multivariate analysis of variance? Community Ecology 14: 153-163 (http://dx.doi.org/10.1556/ComEc.14.2013.2.5)
You should see this article by Anderson and Walsh:
Marti J. Anderson and Daniel C. I. Walsh 2013. PERMANOVA, ANOSIM, and the Mantel test in the face of heterogeneous dispersions: What null hypothesis are you testing? Ecological Monographs 83:557–574
I would recomend a paper by Anderson and a simple and explanatory post about Permanova. http://www.ncbi.nlm.nih.gov/pubmed/21070562. http://thebiobucket.blogspot.de/2011/04/assumptions-for-permanova-with-adonis.html#more. Greets.
You may try to perform variance partitioning following multivariate analysis (e.g.RDA) for which you could assess both the specific effect of space (e.g. PCNM) and dispersion. You could distinguish their specific influence on the community as well as the proportion of variance that can be explained by both of these parameters. A paper that perform a analysis similar to the one you could perform is :
Sweetman, J., K. Rühland, et al. (2010). Environmental and spatial factors influencing the distribution of cladocerans in lakes across the central Canadian Arctic treeline region. Journal of Limnology 69: 76-87.
Good luck!
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