Tukukkk

I am testing differences in community composition between fished and no-take areas, and while the nmds seems to indicate the two levels overlap considerably, ANOSIM and ADONIS suggest there are significant differences. Have I done something wrong or is there a reason for this significant difference that I can't see?

species



env=species[,1]

species=species[,-1]

species = species[,colSums(species) > 2]



nmds=metaMDS(species, distance="bray", k=3, type="n", trymax=100)

nmds

env$Protection=as.factor(env$Protection)

pointvec <- c(21, 21)

bgvec <- c("black","white")

with(env, levels(Protection))

plot(nmds,type="n",xaxt='n',xlab="",cex.lab=1.5,cex.axis=1.4,xlim=c(-1.5,1.5),ylim=c(-1.2,1))

axis(side=1)

with(env, points(nmds,pch=pointvec[Protection],cex=1,bg = bgvec[Protection],type="p" ,display="sites"))

ordiellipse(nmds, groups=env$Protection, kind = "se", conf = 0.95)

legend("topleft", "A", bty="n",cex=1.5,inset=-0.02,adj=1) 

legend("bottomright", "Stress = 0.182", bty="n",cex=1.5) 

with(env,legend("topright", legend =  levels(Protection),inset=-0.007,cex=1.5,bty="n",pt.bg =    bgvec,pch=pointvec))

spe.dist <- vegdist(species,method='bray')

spe.ano <- anosim(spe.dist, env$Protection)

summary(spe.ano)



#Call:

#anosim(x = spe.dist, grouping = env$Protection) 

#Dissimilarity: bray 



#ANOSIM statistic R: 0.04693 

      #Significance: 0.029 



#Permutation: free

#Number of permutations: 999



#Upper quantiles of permutations (null model):

   #90%    95%  97.5%    99% 

#0.0290 0.0398 0.0487 0.0593 



#Dissimilarity ranks between and within classes:

       # 0%     25%     50%     75% 100%    N

#Between  1 655.625 1193.50 1771.25 2317 1184

#fished   3 750.500 1360.00 1896.50 2317  666

 #no-take  2 358.125  837.25 1525.00 2285  496

And then the permanova gives a similar result

adonis(species~env$Protection,method='bray')



#Call:

#adonis(formula = species ~ env$Protection, method = "bray") 

#Permutation: free

#Number of permutations: 999

#Terms added sequentially (first to last)



              # Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)   

#env$Protection  1    0.9517 0.95174  2.8946 0.04141  0.002 **

#Residuals      67   22.0296 0.32880         0.95859          

#Total          68   22.9813                 1.00000          

 #---

#Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Firstly, the NMDS graphics and your tests are inconsistent: tests are for the location of class centroids, but the graph shows the spread of observations. ordiellipse(..., kind = "se", conf = 0.95) would be more consistent with the tests. Secondly, the tests (in particular, adonis -- I would not use anosim) are based on the full n-dimensional space interpreted as Euclidean, whereas NMDS is a two-dimensional mapping of a non-Euclidean dissimilarity (although the NMDS plot itself is Euclidean). It may be that your groups differ in third dimension that you have not estimated.