Online Trick

library(vegan)

# two similar populations:
dat1a<-matrix(sample(c(0,1,1,1),200,replace=T),10,20)
dat1b<-matrix(sample(c(0,1,1,1),200,replace=T),10,20)

# generating a third sample from the same population, but with reduced
# number of species occurrences. this set will have higher
# beta-diversity (or "multivariate spread"):
dat2<-matrix(sample(c(0,0,0,1),200,replace=T),10,20)
 


# distance matrices:
fac<-gl(2,10)
dist11<-vegdist(rbind(dat1a,dat1b))
dist12<-vegdist(rbind(dat1a,dat2)): 

# when computing sets with same beta-dispersion we get a
# correct adonis result with no sign. group differences
# in species composition:
anova(betadisper(dist11,fac))
adonis(rbind(dat1a,dat1b)~fac)

# when using sets with different beta-diversity you may
# get false significant adonis results - the location/composition
# is actually the same (!) this result is due to different
# multivariate spread in dat1 and dat2:
anova(betadisper(dist12,fac))
adonis(rbind(dat1a,dat2)~fac)

# see ordination diagram where location (centroids) between dat1 and dat2
# is not shifted more than for dat1a dat1b, still you yield a (false)
# sign. adonis result
# plot:

windows(10,5)

opar<-par()
par(mfrow=c(1,2))
plot(meta11<-metaMDS(dist11,zerodist=ignore),type="n",
main="same beta-disp\nsame location")
points(meta11,select=which(fac==1),col="red")
points(meta11,select=which(fac==2),col="blue")
ordispider(meta11,group=fac)

plot(meta12<-metaMDS(dist12,zerodist=ignore),type="n",
main="diff beta-disp\nsame location")
points(meta12,select=which(fac==1),col="red")
points(meta12,select=which(fac==2),col="blue")
ordispider(meta12,group=fac)

par(opar)