Alpha diversity measures

The available diversity measures are:

where $ n$ is the number of features; $ D$ is the number of distinct features observed in the sample; $ f_1$ is the number of features for which only one read has been found in the sample; $ f_2$ is the number of features for which two reads have been found in the sample; and $ p_i$ is the fraction of reads that belong to feature $ i$.

Note that Chao-based methods deal with singletons and doubletons, i.e., rows with exactly one or two reads (counts) associated. These measures are thus not available for whole metagenome taxonomic profiles that are characterized by coverage estimate.

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$ is the proportion of taxa descending from branch $ i$; and the indicator function $ I(p_i>0)$ and $ I(p_i^B>0)$ assumes the value of $ 1$ if any taxa descending from branch $ i$ is present in the sample or 0 otherwise.