skbio.diversity.alpha.faith_pd(counts, otu_ids, tree, validate=True)[source]

Compute Faith’s phylogenetic diversity metric (PD)

State: Experimental as of 0.4.1.

  • counts (1-D array_like, int) – Vectors of counts/abundances of OTUs for one sample.

  • otu_ids (list, np.array) – Vector of OTU ids corresponding to tip names in tree. Must be the same length as counts.

  • tree (skbio.TreeNode) – Tree relating the OTUs in otu_ids. The set of tip names in the tree can be a superset of otu_ids, but not a subset.

  • validate (bool, optional) – If False, validation of the input won’t be performed. This step can be slow, so if validation is run elsewhere it can be disabled here. However, invalid input data can lead to invalid results or error messages that are hard to interpret, so this step should not be bypassed if you’re not certain that your input data are valid. See skbio.diversity for the description of what validation entails so you can determine if you can safely disable validation.


The phylogenetic diversity (PD) of the samples.

Return type



ValueError, MissingNodeError, DuplicateNodeError – If validation fails. Exact error will depend on what was invalid.


Faith’s phylogenetic diversity, often referred to as PD, was originally described in 1.

If computing Faith’s PD for multiple samples, using skbio.diversity.alpha_diversity will be much faster than calling this function individually on each sample.

This implementation differs from that in PyCogent (and therefore QIIME versions less than 2.0.0) by imposing a few additional restrictions on the inputs. First, the input tree must be rooted. In PyCogent, if an unrooted tree was provided that had a single trifurcating node (a newick convention for unrooted trees) that node was considered the root of the tree. Next, all OTU IDs must be tips in the tree. PyCogent would silently ignore OTU IDs that were not present the tree. To reproduce Faith PD results from PyCogent with scikit-bio, ensure that your PyCogent Faith PD calculations are performed on a rooted tree and that all OTU IDs are present in the tree.

This implementation of Faith’s PD is based on the array-based implementation of UniFrac described in 2.



Faith, D. P. Conservation evaluation and phylogenetic diversity. Biol. Conserv. (1992).


Hamady M, Lozupone C, Knight R. Fast UniFrac: facilitating high- throughput phylogenetic analyses of microbial communities including analysis of pyrosequencing and PhyloChip data. ISME J. 4(1):17-27 (2010).


Assume we have the following abundance data for a sample u, represented as a counts vector. These counts represent the number of times specific Operational Taxonomic Units, or OTUs, were observed in the sample.

>>> u_counts = [1, 0, 0, 4, 1, 2, 3, 0]

Because Faith PD is a phylogenetic diversity metric, we need to know which OTU each count corresponds to, which we’ll provide as otu_ids.

>>> otu_ids = ['OTU1', 'OTU2', 'OTU3', 'OTU4', 'OTU5', 'OTU6', 'OTU7',
...            'OTU8']

We also need a phylogenetic tree that relates the OTUs to one another.

>>> from io import StringIO
>>> from skbio import TreeNode
>>> tree =
...                      '(((((OTU1:0.5,OTU2:0.5):0.5,OTU3:1.0):1.0):0.0,'
...                      '(OTU4:0.75,(OTU5:0.5,((OTU6:0.33,OTU7:0.62):0.5'
...                      ',OTU8:0.5):0.5):0.5):1.25):0.0)root;'))

We can then compute the Faith PD of the sample.

>>> from skbio.diversity.alpha import faith_pd
>>> pd = faith_pd(u_counts, otu_ids, tree)
>>> print(round(pd, 2))