about betadisper() interpretation

[Gian77]

Hello,

I I am using the function betadisper() after adonis() to test for homogeneity of variances. I have used it a lot in the years but I never get to look at the boxplots output with the necessary attention.

So this is my code.

permdisp <- betadisper(vegdist(otu, method="bray"), metadata$Origin)
par(mfrow=c(1,2))
plot(permdisp, main="PCoA")
boxplot(permdisp, main="Distance to centroids")

In the ordination plot looks like the Root samples should have smaller distances to centroids respect to the Soil samples. However, this is not what we see int he boxplot. is it because the PCoA is in 2D but in reality there are many axes, so the distances to the centroids might be bigger than what seen in PC1 & PC2.

So I tried to plot the distance manually and I got this

boxplot(permdisp$distances, permdisp$group)

SAM110 SAM111 SAM37 SAM112 SAM113 SAM114 SAM115 SAM116 SAM117 SAM118 SAM119 SAM120 Root Root Root Soil Soil Soil Soil Root Root Root Root Soil Levels: Root Soil

Levels 1 and 2 correspond exactly to Root and Soil. This plot makes more sense to me in relation to the PCoA graph.
So, I am wondering if:

• does the default function boxplot() on the betadisper object (as showed above) calculates distance distribution across all axis?
• does the boxplot() plotted manually actually show the distances seen in the 2D PCoA?
• Does then anova [anova(permdisp, permutations = 9999)] used tests for differences across group centroids using all PCoA axis or just the first 2?

Thanks you very much,

Gian

[jarioksa]

Your Box plot is wrongly constructed (or at least, it is unlikely to show what you want it to show). With this command

boxplot(permdisp$distances, permdisp$group)

the plot will show two variables: the ungrouped distances (left) and the group values of 1 and 2 (right). If you want to show the distances by groups, you should use

boxplot(permdisp$distances ~ permdisp$group)

This latter version is constructed by vegan:::boxplot.betadisper.

The PCoA plot shows only two first axes, but all calculations are based on all axes (or actually, in the original full space). So the boxplot is not based on only two axes, but on all. The distances returned by betadisper are also calculated in the full space over all dimensions, and vegan:::anova.betadisper uses those distances in its analysis.

[Gian77]

Hello @jarioksa,

thanks so much for your answer. it makes a lot of sense, and I could not find it in the betadisper help.

I think it is just kind of weird, for example in my case, that the PCoA shows a pattern of dispersion (based on 2 axis, 2D) that is opposite to what the all PCoA axes (original full space) is showing.

Thanks,

G.