title: Testing the variance of betadisper() output
body: <p>I have some population genomics data where I have allele frequencies of SNPs with respect to the ancestral genome for each treatment.</p>
  
  <p>I wanted to look whether beta diversity was different between treatments so used the <code>vegan</code> package and <code>betadisper()</code> on euclidean distances.</p>
  
  <p>After extracting all the information from the model and putting it into dataframes so that ggplot2 likes it I can get this plot.</p>
  
  <p><a href="https://i.stack.imgur.com/sTfvR.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/sTfvR.png" alt="enter image description here"></a></p>
  
  <p>Although to my eye this shows higher beta diversity in mixed (circle) than static (triangle) treatments, the <code>anova()</code>, <code>permutest()</code> and <code>TukeyHSD()</code> methods give results where we do not reject the null hypothesis of homogeneity of variances. In addition, the p values for most of these tests are p > 0.8.</p>
  
  <p>From what I can work out, these tests on a <code>betadisper()</code> model object look at differences in the mean distance to the centroid, which is not different across treatments.</p>
  
  <p><a href="https://i.stack.imgur.com/bSH4F.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/bSH4F.png" alt="enter image description here"></a></p>
  
  <p>However the spread of distance to centroid does seem to be different between the treatments.</p>
  
  <p>I was just wondering if I am ok doing something like a Bartlett test or levene test (in the <code>car</code> package) to look at differences in the variance of the distances from the centroid for each group as another metric of "beta diversity" (variance across groups). Or if there are methods within vegan that anyone knows to look at the variance of distance to centroid as well as the changes in the mean distance to centroid.</p>