adonis2 model structure: Handling block design

[sharminakteranu]

Hi all,
I’m analysing microbial community data from a factorial experiment with a randomised block design. Treatments were assigned within spatial blocks (Block is a random factor), and samples were destructively collected across multiple time points. Each plot (Plot_ID) was sampled independently at each time, so there are no true repeated measures.
Each Plot_ID × Time combination includes multiple technical replicates (e.g., three samples per plot). These were not averaged but kept as separate entries in the dataset.

I’m using the adonis2 function with a Bray-Curtis distance matrix. I’ve seen the following model used:

adonis2(dist ~ Treatment * Time, data = meta, strata = meta$Block)

My questions are:

1. Is it scientifically valid to use strata = Block without including Block in the formula, given that Block is a random factor?
2. Would including + Block in the formula be statistically inappropriate in this context?
3. Should technical replicates per Plot_ID be accounted for via strata = Plot_ID instead?
4. If both Block and Plot_ID are relevant, how should permutation structure be handled in adonis2 (e.g., nested strata or alternative approach)?

[gavinsimpson]

You won't be able to use strata for this as you have variation at two levels:

1. the spatial Block level, and
2. the Plot_ID level,

and strata cannot handle that.

Is it scientifically valid to use strata = Block without including Block in the formula, given that Block is a random factor?

Usually you want to exclude differences between blocks from the variation that can be attributed to your other covariates of interest (here Treatment and Time), and hence it should in general be in the formula, or better, use dbRDA() and put Block inside Condition() in the formula.

Would including + Block in the formula be statistically inappropriate in this context?

Yes you can just add + Block, but I don't think that can certainly remove the block effect first; it would just model the conditional mean of each block given the other terms in the model, which is not necessarily the same as partialling out (Condition()-ing on) Block.

Should technical replicates per Plot_ID be accounted for via strata = Plot_ID instead?

Yes they should be accounted for, no, you can't do this optimally via strata.

If both Block and Plot_ID are relevant, how should permutation structure be handled in adonis2 (e.g., nested strata or alternative approach)?

I would use dbRDA(); it is doing the same thing as adoins2() but allows Condition() in the formula. You should use the permutations argument, and set up the permutation design using how() from the permute package (which vegan depends on and loads when you load vegan). See the vignette for permute for more details and there are several examples in the Discussions section here that are similar to yours. If you have trouble figuring this out mention that here and I can provide more detail when I am back at the keyboard tomorrow/later.

[sharminakteranu]

Thanks, @gavinsimpson, for your detailed explanation. I've read through the vignette and tried exploring. If I switch from using adonis2() to dbrda() as you suggested, would the following nested permutation setup correctly reflect my design?

Nested permutation control for Plot_ID within Block

ctrl_nested <- how(nperm = 999,
blocks = meta$Block,
plots = Plots(strata = meta$Plot_ID, type = "none"),
within = Within(type = "free")) # destructive sampling

Distance-based RDA with Block partialled out

mod_nested <- dbrda(dist_mat ~ Treatment * Time + Condition(Block), data = meta)

Marginal tests with nested permutation structure

anova(mod_nested, permutations = ctrl_nested, by = "margin")

1. Does this approach, with Plot_ID nested within Block and samples permuted freely within each Plot_ID, represent the correct and most appropriate fit for my design?

2. Is Within(type = "free") the right choice for destructive sampling, with series only relevant if the temporal order must be preserved?

[SalmaSarker]

Hi @gavinsimpson, I have a similar question and would greatly appreciate your insights. I look forward to your response.