[R-sig-eco] adonis or other multi-variate approaches to examine community change over time given main effect of treatment

[Chris Holmes]

Hello All,
I have a large data set where I am interested in answering the question 
of whether initial conditions (i.e. our initial treatments) influenced 
the community composition over time. We have 10 replicates for each 
treatment and species abundances for 15+ species. My question is, I have 
seen approaches to use adonis and capscale to analyze the question of do 
sites change over time (omitting the treatment factor, as I have in my 
design). A summary of those codes can be found in this paper:
http://www.esajournals.org/doi/full/10.1890/10-2138.1

However, my question is, is what I seek to do able to be properly done 
using adonis and/or capscale? In short, I am interested in the 
interactive treatment x time interaction.

For example, Consider a case in which I expect to see no effect of time 
or treatment:
#DATA
speciesmatrix <- matrix(rnorm(3 * 6 * 20, 50, 10), nrow = 3 * 6, ncol = 20,
          dimnames = list(1:18, paste("Sp", 1:20, sep = "")))
#TIME AND TREATMENT VECTORS
time <- as.ordered(rep(1:3, 6))
site <- gl(6, 3)
treatment <- gl(3,6)
#ADONIS
adonis(speciesmatrix~treatment*time,permutations=1000, method="bray")

Call:
adonis(formula = speciesmatrix ~ treatment * time, permutations = 1000, 
method = "bray")

Contrast this when I add an effect of treatment by adding 100 to each 
treatment 3:
#Add 100 to each species in treatment 3
speciesmatrix[treatment==3,] <-  speciesmatrix[treatment==3,] + 100

#Adonis
adonis(speciesmatrix~treatment*time,permutations=1000, method="bray")

After this, I see an effect of treatment. Great!
Now let's add 50 to each species in time 2, and 75 to each species at 
time 3 (still having the effect of treatment by 100 being added to 
treatment 3 in the previous analysis) to see if this will produce a 
treatment x time effect
speciesmatrix[time==2,] <- speciesmatrix[time==2,] + 50
speciesmatrix[time==3,] <- speciesmatrix[time==3,] + 75

adonis(speciesmatrix~treatment*time,permutations=1000, method="bray")
According to this, I see the effect that I expected. However, my 
question is, is this the proper way to analyze this data? I have seen 
others treat each site as a strata, but when I incorporate those into my 
models the results I expect to see given my toy data fall apart. For 
example, I wouldn't see an effect of treatment after adding 100 to 
treatment 3.

Any help would be very much appreciated because I have been struggling 
with this problem for a long time!

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