This function calculates the weighted l1 distance index Dl1(T) for a given rooted binary tree T. Dl1(T) is defined as
Dl1(T)= ∑ z*|f_n(z)-p_n(z)| over all possible sizes 2<=z<=n
in which n denotes the
number of leaves of T, f_n(z) denotes the frequency of pending subtrees
of size z in T and p_n(z) is the expected number of
pending subtrees of size z under the Yule model, i.e. p_n(z)=1/(n-1)
if z=n and otherwise n/(n-1)*2/(z*(z+1)).
For n=1 the function returns Dl1(T)=0.
A rooted binary tree in phylo format.
weighL1distI returns the weighted l1 distance index of the given tree.
M. G. Blum and O. François. On statistical tests of phylogenetic tree imbalance: The Sackin and other indices revisited. Mathematical Biosciences, 195(2):141-153, 2005. doi: 10.1016/j.mbs.2005.03.003.
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