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Alpha diversity measures

The available diversity measures are:

Total number: The number of features (e.g. OTUs when doing out clustering, GO terms when building functional profiles or organisms when performing taxonomic profiling) observed in the sample.
Chao 1 bias-corrected: $\textrm{Chao1-bc} = D + \frac{f_1(f_1-1)}{2(f_2+1)}$ .
Chao 1: $\textrm{Chao1} = D + \frac{f_1^2}{2 f_2}$ .
Simpson's index: $\textrm{SI} =1- \sum\limits_{i=1}^{n} p_i^2$ .
Shannon entropy: $\textrm{H} = \sum\limits_{i=1}^{n} p_i \log_2 p_i$ .

where

is the number of features;

is the number of distinct features observed in the sample;

is the number of features for which only one read has been found in the sample;

is the number of features for which two reads have been found in the sample; and

is the fraction of reads that belong to feature

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:

Phylogenetic diversity: $PD = \sum\limits_{i=1}^{n} b_i I(p_i >0)$

where

is the number of branches in the phylogenetic tree,

is the length of branch

;

is the proportion of taxa descending from branch

; and the indicator function

and

assumes the value of

if any taxa descending from branch

is present in the sample or 0 otherwise.

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Alpha diversity measures