## Beta diversity measures

The following beta diversity measures are available:

• Bray-Curtis:
• Jaccard:
• Euclidean:
where is the number of OTUs and and are the abundances of OTU in samples and , respectively.

The following distances are also available:

• Unweighted UniFrac:
• Weighted UniFrac:
• Weighted UniFrac not normalized:
• D_0 UniFrac: The generalized UniFrac distance
• D_0.5 UniFrac: The generalized UniFrac distance
where is the number of branches in the phylogenetic tree, is the length of branch ; and are the proportion of taxa descending from branch for samples and , respectively; and the indicator functions and assume the value of if any taxa descending from branch is present in samples and , respectively, or 0 otherwise.

The unweighted UniFrac distance gives comparatively more importance to rare lineages, while the weighted UniFrac distance gives more important to abundant lineages. The generalized UniFrac distance offers a robust tradeoff [Chen et al., 2012].