# 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:

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

where,

$p_i^n$ = proportion of sequences from community i descendant from branch n.

$p_j^n$ = proportion of sequences from community j descendant from branch n.

$\underset{c}{max}(p_c^n)$ = maximum proportion of sequences from any community c descendant from branch n.

$\underset{c}{min}(p_c^n)$ = minimum proportion of sequences from any community c descendant from branch n.

$W_n$ = weight or length of branch n.

$N$ = number of branches in the tree spanned by 'all' communities.

### Points-of-interest

• $D_{WCL}$ 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)