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Overview
While alpha diversity examines differences within treatment groups, beta diversity measures the similarity (or dissimilarity) between samples.
Each variable is plotted on Principal coordinates analysis (PCoA) plots, to examine the variance between samples based on a dissimilarity matrix. A detailed explanation of PCoA and other ordination methods can be seen here: http://albertsenlab.org/ampvis2-ordination/
Sample distance has been measured using 3 distance-based ordination methods (plotted on 2 separate PCoA plots per variable). These methods are:
Bray–Curtis dissimilarity measures the fraction of overabundant counts.
Sorenson, T. (1948) “A method of establishing groups of equal amplitude in plant sociology based on similarity of species content.” Kongelige Danske Videnskabernes Selskab 5.1-34: 4-7.
Cao index is a minimally biased index for high beta diversity and variable sampling intensity. Chao index tries to take into account the number of unseen species pairs.
Cao, Y., Bark, A. W., & Williams, W. P. (1997). Analysing benthic macroinvertebrate community changes along a pollution gradient: a framework for the development of biotic indices. Water Research, 31(4), 884-892.
Jaccard similarity index measures the fraction of unique features, regardless of abundance..
Jaccard, P. (1908). “Nouvellesrecherches sur la distribution florale.” Bull. Soc. V and. Sci. Nat., (44):223-270.
Significance tests
For each beta diversity method, both overall significance and pairwise significance were calculated using a Permutational Multivariate Analysis of Variance (PERMANOVA), a non-parametric multivariate statistical test. This was done in R using the adonis function from the vegan: Community Ecology Package. A sample-sample distance matrix was first generated from relative (normalised) abundance tables (except for Cao index, which used absolute abundances) using the vegdist function with each of the three distance-based ordination methods (Bray-Curtis, Cao and Jaccard). On this distance matrix PERMANOVA R and p values were calculated using adonis. The R-squared value represents the percentage of variance explained by the examined groups. E.g. if R = 0.23 then 23% of the total diversity is explained by groupwise differences. PERMANOVA is based on groupwise differences, thus cannot be applied to continuous data.