I am planning on using perMANOVA to test for differences in biodiversity (macroinvertebrate taxa) in Great Salt Lake wetland ponds between years and between ponds. I am still uncertain as to whether these can be considered independent replications because species composition during the last sample period is dependent on what was there previously and species composition in nearby ponds are dependent on species composition in ponds near them. Would this be considered a violation of the assumption of independence of replicates in perMANOVA?
Typically, I'd say this violates the independence assumption and reduces your degrees of freedom. However, I'm not familiar with this methodology per say but ANOVA in general. I did find this directly from PERMANOVA user manual:
"Recall that for traditional one-way ANOVA, the assumptions
are that the errors are independent, that they are
normally distributed with a mean of
zero and a common variance, and that the
treatment effects are additive. In the
case of a one-way analysis, th
e PERMANOVA test using permutations assumes only that
the observation units are
exchangeable under a true null hypothesis
. There are no explicit assumptions regarding the distributions of the
original variables; they are certainly not assumed to be normally distributed. However, implicit in the notion of
exchangeability is the notion of independence, for if observa
tions are correlated with one another (e.g., temporally or
spatially), then randomly shuffling them will destroy this kind
of inherent structure, if it is there. Thus, in general, we
would assume that the
observation units
are independent of one another. In contrast, we do not at all expect the
individual variables which have been measured on the same observation units (in the multivariate case) to be
independent of one another, and this is not assumed. "
I have no experience with perMANOVA, but you should take into acount the compositional character of your data. Quite probably, these methods are not subcompositionally coherent, you might even get contradictory results if you consider a smaller or larger number of species. I would recommend to work on coordinates (ilr-transformation) (see Chapters 2 and 3 of the book "Compositional Data Analysis" published by Wiley and edited by myself and A. Buccianti). As mentioned by John Aitchison, classical methods are not suitable for compositional data.
PERMANOVA was new to me, thanks for introducing. But after going through the manual http://www.stat.auckland.ac.nz/~mja/prog/PERMANOVA_UserNotes.pdf (probably you know), I found the answer to your question as 'No'. Please read the 'Assumptions' section in page 9 carefully, PERMANOVA explicitly assumes that spatial or temporal dependence exists in the variables. What you need to control in 'adonis' by restricting permutations (as Eduard suggested) is built in PERMANOVA. If you want to be more sure, input time and space as covariables (time points, coordinates etc.) where you expect the covariance to occur. Take care of the design variables (factors and levels) to make sure that dissimilarities are computed as the way you wanted. I would rather go for 'adonis' function of 'vegan' package to obtain more freedom, but PERMANOVA would certainly serve your purpose I believe.
I'd also say, you cannot do this. hovewer, looking for covariates - time, place etc. - you should tell us, how mwny replications you have.
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