Hi, everyone,
I have a general question about dissimilarity within-between groups, to which I could not find a conclusive answer so far.
Broadly speaking, I have 5 samples per lake per time point (3 time points per year, 2 years, 2 different species) and I’m interested to see if the community composition of my samples within the same lake is more or less similar than the composition between lakes.
So, first of all, I transformed my data using the “clr” option from the microbiome package in R (centered log-ratio) and after that I’ve done an adonis test (with strata=lake) considering the output of the dissimilarity test using euclidean distance (vegan package). Ok. See below just as an example:
a <- adonis(dt.Rt_2nd ~ altitude_sc + lakearea_sc, data = meta_Rt2nd, permutations=9999, method="euclidean",strata=lake)
Blocks: strata
Permutation: free
Number of permutations: 9999
Terms added sequentially (first to last)
Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
altitude_sc 1 13229 13228.6 3.0853 0.06690 1
lakearea_sc 1 13000 13000.0 3.0320 0.06575 1
Residuals 40 171504 4287.6 0.86735
Total 42 197733 1.00000
(unfortunately, nothing significant) 
However, it only shows me if the factors have an influence or not (p-value) on the community composition and how much it explains (R2). So, here is my first question: can I use the f-value of an adonis test to say something about the ratio of between group- and within-group variation? If so, how can I interpret this value to be able to say if my community within the same lake is more or less similar then the communities of other lakes?
Following the same idea, anosim is also used to compare dissimilarity within and between groups (https://sites.google.com/site/mb3gustame/hypothesis-tests/anosim), however when I do the test, I only get one R-value, which doesn’t tell much about the community composition within- and between lakes.
anosim(dt.Rt_2nd, meta_Rt2nd$altitude_sc + meta_Rt2nd$lakearea_sc, permutations = 9999, distance = "euclidean", strata = lake)
ANOSIM statistic R: 0.7453
Significance: 1
Blocks: strata
Permutation: free
Number of permutations: 9999
So, is it really useful for checking within-between community variation? Or sticking with adonis is still more reliable even though it doesn’t give a clear statement about this?
Last, but not least (sorry, I know it is already too long!), there is the Kendall’s W test (Kendall coefficient of concordance), also used to compare within and between groups variation. So, if I only had samples and OTUs as data, it would look similar to this:
sample1 sample2 sample3
OTU1 abundance ... ...
OTU2 abundance ... ...
OTU3 abundance ... ...
...
However, I have samples nested in lakes, so I don’t know how to include this information on the table, since the test doesn’t give the strata option or anything similar to this. And it would also be a huge table, with more than 20.000 rows to include a column manually and give numbers for the different lakes. So, here is my third question: would Kendall’s W be also a possible option to evaluate the within-between group variation or it doesn’t apply for microbiome data?
Thanks a lot for the feedback and sorry for creating such a long question