Hello William,

Probably this article could help you. PERMANOVA, ANOSIM, and the Mantel test in the face of heterogeneous dispersions: What null hypothesis are you testing? Andersons and Walsh 2013

Hi William

The R-statistic in ANOSIM is a ratio between within-group and between-group dissimilarities. The steps in the analysis are:

1. calculate a matrix of dissimilarity scores for every pair of sites

2. convert the dissimilarities to ranks

3. calculate the R statistic as the ratio between dissimilarities between sites within a group (e.g. high grazing pressure) and the dissimilarities between sites that are in different groups. The closer this value is to 1, the more the sites within a group are similar to each other and dissimilar to sites in other groups.

4. The significance of the R-statistic is determined by permuting the membership of sites in groups.

I think you can also try Generalized Linear model after Correspondance Analysis. You can check three level of grazing pressure using AIC or AICc  in GLM. 

Hi William,

Description of the ANOSIM algorithm is given by David. Below is an extra bit on what actually the result mean.  When you print the result of ANOSIM  (I am assuming here that you used vegan) you get 1) the global R value (the test statistics for ANOSIM) followed by the p-value 2) The type of permutation done and the number of permutation 3) distribution of the test statistic (R) obtained under the null hypothesis. This can equally be shown graphically as histograms. But in vegan you get numerical summaries of R as quantiles 4) finally you get summary of the between group and within group rank dissimilarities. Here too you get the distributional summaries of A) the between group rank dissimilarities  from the minimum (0%) to the maximum (100%) B) the within group rank dissimilarity from the minimum (0%) to the maximum (100%) C) the number of observation (replicates) "N".

Hi all,

thanks a lot for your explanations, this is more clear now !!