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# Weighted complete tree phylogenetic beta-diversity measure

The weighted complete tree (CT) measure calculates the dissimilarity between a pair of communities by considering the proportion of sequences descendant from branches within a tree spanning *all* sequences from *all* communities. It is an weighted or quantitative measure as it explicitly considers the abundance of each sequence. This calculator can be used with the phylo.betadiversity command. The dissimilarity between communities *i* and *j* is given by:

<math>D_{WCL} = \frac{\sum_{n=0}^N |p_i^n - p_j^n|W_n}{\sum_{n=0}^N (\underset{c}{max}(p_c^n) - \underset{c}{min}(p_c^n))W_n}</math>

where,

<math>p_i^n</math> = proportion of sequences from community *i* descendant from branch *n*.

<math>p_j^n</math> = proportion of sequences from community *j* descendant from branch *n*.

<math>\underset{c}{max}(p_c^n)</math> = maximum proportion of sequences from any community *c* descendant from branch *n*.

<math>\underset{c}{min}(p_c^n)</math> = minimum proportion of sequences from any community *c* descendant from branch *n*.

<math>W_n</math> = weight or length of branch *n*.

<math>N</math> = number of branches in the tree spanned by 'all' communities.

### Mathematical properties

### Points-of-interest

- <math>D_{WCL}</math> is the phylogenetic extension of the Gower OTU-based similarity measure.

### Further information

Parks, DH and Beiko, RG. (2011). **Quantifying phylogenetic β-diversity over rooted and unrooted trees**. (in preparation)