test for significant differences in communtiy composition between habitats? required PERMANOVA sample size?

Question

I sampled spiders in 5 different forest-stands. I originally had a sample size of 32 per forest-type, but as I had to pool the data I now just have 8 samples per forest type.

I did an ordination with spider-data in order to evalutate differences in the community structure (Index: Morisita-Horn). The colours reprensent the forest types, the triangle and circles the region. The ellipses show the standard deviation.

I want to find a way to see if the differences between the forest types and also between the regions are statistically significant. For that I wanted to use a Permanova (adonis2 from the vegan package).

I first checked if the dispersion varies significantly between the stands:

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

Analysis of Variance Table

Response: Distances
          Df  Sum Sq  Mean Sq F value Pr(>F)
Groups     4 0.06117 0.015292  1.0219 0.4096
Residuals 35 0.52376 0.014965 

which it does not. Same goes for 'region'.

I then proceeded by running the adonis2 function:

perma_stands_results <- adonis2(horn_dist~stand, data=matrix_env_plot, permutations=999)

> print(perma_stands_results)
Permutation test for adonis under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 999

adonis2(formula = horn_dist ~ stand, data = matrix_env_plot, permutations = 999)
         Df SumOfSqs      R2      F Pr(>F)  
stand     4   1.8350 0.17689 1.8804  0.027 *
Residual 35   8.5387 0.82311                
Total    39  10.3736 1.00000                
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> 

according to which there are indeed signficant differences in the community structure between the forest types. I extracted distance matrixes for every pair and applied adonis2 again.

D_DB_test <- adonis2(D_DB_dist ~ stand, data=D_DB)

I also correct the p-values for multiple testing

> p.adjust(pairwise.p, method="BH")
      D_DB        D_B       D_FB        D_F       B_DB       B_FB        B_F       F_DB       F_FB 
0.05666667 0.03000000 0.05666667 0.72000000 0.72000000 0.95400000 0.08600000 0.06250000 0.10166667 
     DB_FB 
0.86222222

my questions are:

1. Is perfoming an anova the right way of analysing the global differences regarding differences in the dispersion? or do I first have to check if the assumptions that anova makes are violated (variance of homogenity...)
2. Is running an Peranova for every pair of forest types a valid way of doing pairwise comparisons?
3. Is it in any way problematic, that I only have 8 samples per group?
4. Anova and the adonis function tell me that there are differnces in the community composition, but can I also draw a conclusion about the strength of the differences?

Thanks a lot, as you can see I am not an statistic expert, and really appreciate every explanation!

Answer 1

If I understood correctly, you have a nested (or hierarchical) design, with forest type nested within region. If you want to test for a difference in composition dissimilarity you need to account for that. In PERMANOVA, for example, you would need to constrain the permutations to within region only. It doesn't make sense doing this two-step procedure you did nor doing PERMANOVA for each pair of forest types. If the factor forest type were significant, after accounting for region, you can them condoct post-hoc tests. $R^2$ and F would provide you with the strength of the influence of forest type on and how much it explained of community dissimilarity.