Replicates in Canonical Correspondence Analysis or PERMANOVA My problem is the statistical analysis of community data with gradients of environmental data.
I have a table of species occurrences (from metabarcoding) per sample site and measurements of environmental parameters (like pH, nutrient concentration, ...). We did all our samples in technical triplicates. That is, we took each sample three times and ran it trough our complete lab process.
Now these replicates are obviously not statistically independent from each other so I have to take that into account when doing statistical test on the data.
I want to test if the environmental data we measured explain the variance of the metabarcoding data. For this I have so far considered Canonical Correspondence Analysis and PERMANOVA. If I understand what I read correctly, in a linear model I would have to include a "random effect" of the replicate (right?). As far as I can see I can not include such an effect in the before mentioned tests.
I found in a FAQ of the vegan package the statement that this is not possible (at least in vegan) and as a work around they suggest to use partial CCA or include a "strata argument" in the PERMANOVA. I think this is not possible to use in my case, because this would imply that the effect of the replicate number is consistent over the sample sites.
The only other idea I have dome up with so fat is to average over the replicates, but I would rather find a different solution.
Any ideas or pointers would be greatly appreciated.
I cross posted this on Biostars where I got the suggestion to ask here.
 A: First I I'd like to understand your question better. When you say replicates you say that you sample the same site three times for detecting species presence via metabarcoding, right? Do you happen to have the same amount of replicates for your environmental variables? If so, it's simple you can use a two-table ordination technique (also called constrained or canonical ordination), like CCA or RDA. The choice will depend on how effectively you sampled the length of the environmental gradients you're working on. For a start I'd choose RDA and then test the significance of the first canonical axis. The "strata argument" you mentioned can also be applied in this case. It works by constraining the randomizations to determine significance to each strata (in your case the three replicates for each site), it's the same with a repeated measures design. But this would only work with you also had repeated measures for the environmental variables. If you have only data for species presence, then we'd need another solution. 
Take a look at the Chapter 5 of the Borcard's book Numerical ecology with R, it explains all that I spoke about. There's also the R scripts you might find usefull.
I cannot see how you'd use a PERMANOVA in this case, since you have two tables, not just one.
