Adonis output with or without strata

Hi Jakob,

Thank you for your time and useful answers. I had tried to include Island as a fixed factor earlier and had a significant result for both factors. I got confused on how to interpret this output.

I was interested in the difference between Healthy and Diseased but Island had an effect too so I thought: should I test the interaction factor then? Also, what does it tell me about which of Island or Disease has the most influence etc. this sort of questions. Since we are here and if you have time, maybe we could go through it.

I ran this model:

adonis <- adonis(dist ~ Island + Dis, data = meta)

and obtained this output:

                Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)

Island      1    0.9302 0.93024  2.6688 0.18269  0.001 ***

Dis           1    0.6759 0.67592  1.9392 0.13275  0.002 **

Residuals  10    3.4856 0.34856         0.68456

Total      12    5.0918                 1.00000

Q1: Does the model test the effect of Island within the Healthy group and the Diseased group separately or does it test an Island effect on the whole data set?

Q2: If I visualize my data using an NMDS, there is a clear separation of the Healthy and Diseased groups (see pdf enclosed) meaning that healthy samples are ?closer? to each other than diseased samples from the same island? but now the adonis seems to say that Island has a strong effect too. How do I distinguish between the two factors, how do I know which factor has the ?strongest effect? on the microbiomes?

Cheers,

Ga?lle

________________________________
De : Jakob Russel <russel2620 at gmail.com>
Envoy? : vendredi 10 avril 2020 10:04
? : Ga?lle Quere <gaellequere at hotmail.com>
Objet : Re: Adonis output with or without strata

Dear Ga?lle,

I have just received your email through r-sig-ecology, so it seems to have passed through.

Q1:
Yes, your model tests whether the microbiomes of Healthy and Diseased algae are different, regardless of island. (Under the assumption that the Bray-Curtis dissimilarity captures this difference in microbiome composition)

Q2:
If you are not interested in the islands, I would say your model is correct. You could try to include islands as a fixed effect to see the effect size, but if you have a balanced experimental design it will not affect the Dis factor. If your design is unbalanced the order matters and you should add the island as the first fixed effect adonis <- adonis(dist ~ Island + Dis, data = meta).

Regards,
Jakob

Den fre. 10. apr. 2020 kl. 11.28 skrev <gaellequere at hotmail.com<mailto:gaellequere at hotmail.com>>:
Dear Jakob,

Sorry for sending a private email. I tried to reply directly on the forum but it keeps getting rejected and I don't understand why.

Here was my answer:

Dear Jakob,

Thank you for your prompt reply. May I take the opportunity to ask two related additional questions?

As mentioned in my first post, my research question is to compare microbiomes depending on health status of the host algae (Healthy vs Diseased). Healthy and diseased samples were collected in different islands.

So far, this is the model I have been using to answer my research question:
Variable: Bray-Curtis dissimilarity matrix (dist)
Fixed factor: Disease (Dis)
Random factor: Island

adonis<- adonis(dist ~ Dis, strata = Island, data = meta)

Q1: If I understood correctly, this model compares Healthy and Diseased samples within each island, is that correct? The p-value being significant, does it mean that Healthy and Diseased samples are different within each island or can I make a general statement like: overall Healthy and Diseased microbiomes are different regardless of the island. In other words, microbiomes associated with diseased samples share significant similarities among island and are distinct from healthy samples?

Q2: Is my model correct or should I consider Island as a fixed factor and consider potential interactions as well in order to test the effect of both Island and Dis on the microbiomes?

Thanks once more,
Ga?lle

<quote author='Jakob Russel'>
Dear Ga?lle,

The p-values in PERMANOVA are generated by permutations. These permutations
are by default free, but they can be constrained by the strata factor.
The strata argument only affects the permutations, and hence will only
affect the p-value.
The Sum of Squares (and R2) are only based on the fixed effects.

Regards,
Jakob

Den fre. 10. apr. 2020 kl. 09.42 skrev Ga?lle Quere <GaelleQUERE at hotmail.com<mailto:GaelleQUERE at hotmail.com>