Description Usage Arguments Value Author(s) References Examples
This function calculates the Colijn-Plazzotta rank CP(T) for a
given rooted tree T.
For a binary tree T, the Colijn-Plazzotta rank CP(T) is
recursively defined as CP(T)=1 if T consists of only
one leaf and otherwise
CP(T)=1/2*CP(T1)(CP(T1)-1)+CP(T2)+1
with CP(T1)>=CP(T2) being the ranks of the two pending
subtrees rooted at the children of the root of T. This rank
of T corresponds to its position in the
lexicographically sorted list of (i,j): (1),(1,1),(2,1),(2,2),(3,1),...
The Colijn-Plazzotta rank of binary trees has been shown to be an imbalance index.
For an arbitrary tree T whose maximal number of children of any vertex is l,
the Colijn-Plazzotta rank CP(T) is recursively defined as CP(T)=0
if T is the empty tree (with no vertices), CP(T)=1 if T consists
of only one leaf and otherwise CP(T)=ā_{i=1,...,l} binom{CP(T_i)+i-1,i}
(with CP(T_1)<=...<=CP(T_l)). If there are only k<l pending subtrees
rooted at the children of the root of T, then T_1,...,T_{l-k} are empty trees,
i.e. CP(T_1)=...=CP(T_{l-k})=0, and CP(T_{l-k+1}),...,CP(T_l) are the
increasingly ordered CP-ranks of the k pending subtrees rooted at the
children of the root of T. Note that if k=l there are no empty trees.
For n=1 the function returns CP(T)=1 and a warning.
Note that problems can sometimes arise even for trees with small leaf numbers due
to the limited range of computable values (ranks can reach INF quickly).
1 | colPlaLab(tree, method)
|
tree |
A rooted tree in phylo format. |
method |
The method must be one of: "binary" or "arbitrary". Note that (only) in the arbitrary case vertices of out-degree 1 are allowed. |
colPlaLab
returns the Colijn-Plazotta rank of the given tree
according to the chosen method.
Sophie Kersting, Luise Kuehn
C. Colijn and G. Plazzotta. A Metric on Phylogenetic Tree Shapes. Systematic Biology, doi: 10.1093/sysbio/syx046.
N. A. Rosenberg. On the Colijn-Plazzotta numbering scheme for unlabeled binary rooted trees. Discrete Applied Mathematics, 2021. doi: 10.1016/j.dam.2020.11.021.
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