Dear Pim,

These are two completely different techniques: 1) PCA is a parametric (indirect) ordination technique and 2) PERMANOVA is a non-parametric multivariate statistical test. You could use both to get an answer to your question.

1) Ordination is used to reveal hidden patterns in your data. So it can be used to reveal differences in species composition and show the differences on a graph. But here I recommend not to use PCA, because it assumes linear relationships between species and the underlying ecological gradients (and this is often not the case). You should better use NMDS (non-metric multidimensional scaling). It is a non-parametric ordination technique based on a dissimilarity matrix. For species abundance data, bray-curtis dissimilarity is recommended. You can use the metaMDS function from the vegan package (https://www.rdocumentation.org/packages/vegan/versions/2.4-2/topics/metaMDS)

2) PERMANOVA is more or less the multivariate counterpart of ANOVA. It is used to test the differences between groups, not in 1 variable as in ANOVA, but in multiple variables (in your case the species). You have several techniques: PERMANOVA, MRPP, ANOSIM, Mantel test, Procruste analysis. You can check earlier questions on this topic: https://www.researchgate.net/post/What_is_the_best_method_to_analyze_change_in_species_composition_over_three_years_in_different_sites

You don't need to normalise data for a PERMANOVA, but you could also estimate bootstrap confidence intervals for biodiversity indices or examine dissimilarity in species composition of each sampling (such as Bray Curtis Mantel). Use PCA as well, but for preliminary exploratory data analysis

Regarding the comparison of Difference in species composition, if you can perform the PERMANOVA, but I do not think it would be the most advisable analysis if you want to know if there is similarity in the composition of species between plant layers. It would use UNIFACTORIAL or BIFACTORIAL PERMANOVA to compare the abundance between the same layer in different places or seasons of the year. To establish the differences in species composition between the different layers, a cluster study of similarity or dissimilarity would be made using Bray-Curis or Morisita quantitative and binary Jaccard data. Then I would make an analysis of ANOSIM (PERMANOVA) to compare if the groups formed in the cluster are statistically different, you could continue with MDS and finish with a SIMPER analysis to know which species were the ones that most influenced the dissimilarity of the groups.

In relation to your question Difference in diversity for Shannon-Wiener index you can perform an analysis Diversity permutation test or Diversity t test.

References

Brower, J.E., Zar, J.H., von Ende, C.N. 1998. Field and Laboratory Methods for General Ecology.

McGraw-Hill, Boston.

Hutcheson, K. 1970. A test for comparing diversities based on the Shannon formula. Journal of

Theoretical Biology 29:151-154.

Magurran, A. 1988. Ecological Diversity and Its Measurement. Princeton University Press.

Poole, R.W. 1974. An introduction to quantitative ecology. McGraw-Hill, New York.

The PCA is used more to perform multiple correlations or to group a set of variables.

Principal components analysis (PCA) finds hypothetical variables (components) accounting for as much as possible of the variance in your multivariate data (Davis 1986, Harper 1999). These new variables are linear combinations of the original variables. PCA may be used for reduction of the data set to only two variables (the two first components), for plotting purposes. One might also hypothesize that the most important components are correlated with other underlying variables. For morphometric data, this might be size, while for ecological data it might be a physical gradient (e.g. temperature or depth). Bruton & Owen (1988) describe a typical morphometric application of PCA.

I attached the manual of Past 3.18 so you can analyze the different tests that best suit your research.

Dear Pim,

These are two completely different techniques: 1) PCA is a parametric (indirect) ordination technique and 2) PERMANOVA is a non-parametric multivariate statistical test. You could use both to get an answer to your question.

1) Ordination is used to reveal hidden patterns in your data. So it can be used to reveal differences in species composition and show the differences on a graph. But here I recommend not to use PCA, because it assumes linear relationships between species and the underlying ecological gradients (and this is often not the case). You should better use NMDS (non-metric multidimensional scaling). It is a non-parametric ordination technique based on a dissimilarity matrix. For species abundance data, bray-curtis dissimilarity is recommended. You can use the metaMDS function from the vegan package (https://www.rdocumentation.org/packages/vegan/versions/2.4-2/topics/metaMDS)

2) PERMANOVA is more or less the multivariate counterpart of ANOVA. It is used to test the differences between groups, not in 1 variable as in ANOVA, but in multiple variables (in your case the species). You have several techniques: PERMANOVA, MRPP, ANOSIM, Mantel test, Procruste analysis. You can check earlier questions on this topic: https://www.researchgate.net/post/What_is_the_best_method_to_analyze_change_in_species_composition_over_three_years_in_different_sites