Beta diversity measures

The following beta diversity measures are available:

where $ n$ is the number of OTUs and $ x_i^A$ and $ x_i^B$ are the abundances of OTU $ i$ in samples $ A$ and $ B$, respectively.

The following distances are also available:

where $ n$ is the number of branches in the phylogenetic tree, $ b_i$ is the length of branch $ i$; $ p_i^A$ and $ p_i^B$ are the proportion of taxa descending from branch $ i$ for samples $ A$ and $ B$, respectively; and the indicator functions $ I(p_i^A>0)$ and $ I(p_i^B>0)$ assume the value of $ 1$ if any taxa descending from branch $ i$ is present in samples $ A$ and $ B$, 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 $ d^{(0.5)}$ offers a robust tradeoff [Chen et al., 2012].