Permanova for microbiome analysis with repeated measures

Dear all,

I have the following experimental design: 9 mice (mouseID) were assigned to
three different treatments (3 mice per treatment level) and we estimated
the composition of microbial species in the gut at 5 time points (same time
points for each mouse). I would like to know if the community differs
between the 3 treatment levels and I am not really interested in the
treatment*time interaction, but I would like to take into account that the
samples are not independent.

I was thinking of using adonis from the R vegan package to test for this,
but I have doubts as to what is the best way of setting the model?

I have looked through the answers on the list (particularly the replies
form Stephen Brewer) and have seen a  the model formulated as:

*adonis(matrix~treatment + mouseID,data=data,strata=mouseID)*

But it is unclear to me why the "random" variable needs to be included in
the fixed effects and why should we not simply use:

*adonis(matrix~treatment,data=data,strata=mouseID)*


Any thoughts on this would be of great help,


Ramiro