# An algebraic metric for phylogenetic trees

## (By R. Alberich, G. Cardona, F. Rosselló, G. Valiente)

### Supplementary Material

- Phylogenetic trees with up to 7 taxa:
The
*i*-th line in the file corresponding to *n*
holds a Newick string identifying the *i*-th (starting with *i=0*) tree with *n* taxa.

- Distances between all pairs of trees up to 6 taxa:
Each line is of the form "
*i j dRF dTR dNS*",
where *dRF, dTR, dNS* are, respectively, the
Robinson-Foulds, transposition and nodal splitted distance between the *i*-th and the *j*-th tree with *n* taxa.

- Distributions of distances between all pairs of trees up to 7 taxa:
For each of the considered
*n*, the corresponding file
contains:
- Global statistics of distances: These lines are of the form
"
*(dRF,dTR,dNS) k*", meaning that there are *k*
unordered pairs of trees whose Robinson-Foulds, transposition
and nodal splitted distances are, respectively, *dRF, dTR,
dNS*.
- Three separate statistics for each of the Robinson-Foulds, transposition
and nodal splitted distances: These lines are of the form "
*d k*", where *k* is the
number of (unordered) pairs of trees at distance *d*.

Some statistical parameters of these distributions are also available
here.

- Distributions of distances between all pairs of trees
within a random sample of trees with number of taxa from 8 to 14:
The syntax of these files is the same as above, including also the
size of the random sample of trees.

Some statistical parameters of these distributions are also available
here.

- Distributions of the transposition distances (with the usual ordering of
the leaves and the reversed one) between all pairs of trees
trees with number of taxa from 3 to 7:
Each line is of the form "
*dTR1 dTR2 k*",
meaning that there are *k* unordered pairs whose distance with
respect to the usual ordering is *dTR1* and with respect to the
reversed one is *dTR2*.
- Python package: A pre-release version of the python package used to
make these computations can be downloaded here.