Nested studydesign - Necessary to restrict permutations in betadisper?

Question

I have the following study design: 8 locations, 5 forest types (Plots) per location (D,DB,B,FB,F). In every plot I sampled spiders and identified them. I did an NMDS with Morisita-Horn index.

Additionally I wanted to check whether the differences in the community composition are statistically significant. For that I used adonis2 with restricted permutations because of the nested study design. With the following code I made sure that permutations are only allowed within the locations but not between.

CTRL.t <- how(within = Within(type = "free"),
              plots = Plots(type = "none"),
              blocks = matrix_plot$location,
              nperm = 999,
              observed = TRUE)

I then used adonis2

adonis2(matrix_plot[,2:49] ~ location + stand,
        data = matrix_plot,
        method="horn",
        permutations = CTRL.t)

which returned a significant p-value

> adonis2(matrix_plot[,2:49] ~ location + stand,
+         data = matrix_plot,
+         method="horn",
+         permutations = CTRL.t)
Permutation test for adonis under reduced model
Terms added sequentially (first to last)
Blocks:  matrix_plot$location 
Permutation: free
Number of permutations: 999

adonis2(formula = matrix_plot[, 2:49] ~ location + stand, data = matrix_plot, permutations = CTRL.t, method = "horn")
         Df SumOfSqs      R2      F Pr(>F)   
location  7   2.8907 0.27866 2.0473  0.009 **
stand     4   1.8350 0.17689 2.2743  0.009 **
Residual 28   5.6479 0.54445                 
Total    39  10.3736 1.00000                 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

My question is now: Do I also have to restrict the permuations when I want to use betadisper () from vegan to determine whether the effect of stand type is due to an dispersion or location effect?

So far I used betadisper like this

dispersion_stands<- betadisper(horn_dist, matrix_plot$stand, type="centroid")

and restricted the permutations with the same code as above for the permutest

permutest(dispersion_stands, permutations = CTRL.t)

Is this necessary and correct?

Answer 1

Your CTRL.t is fine; the plots = Plots(type = "none") bit is redundant as you aren't specifying any strata (plots) anyway and type = "none" is the default.

When doing betadisper(), and testing if the stands have different dispersions, I think you do need to use the same permutation design because you don't want systematic differences between locations to bleed into the test of homogeneity of variances among the levels of stand. As we don't have a way to residualise with respect to location in this analysis you'll need to stop permutation of observations between locations.

Just an FYI:

which returned a significant p-value

p values cannot be significant, they just are values. They indicate how unusual (or not) the observed test statistic (and hence and "effect") is under the null hypothesis. A p value can indicate if an effect is statistically significant.