Parity Splits by Triple Point Distances in *X*-Trees

Jörgen Backelin^{1} and Svante Linusson^{2}

joeb@math.su.se

linusson@math.kth.se

Annals of Combinatorics 10 (1) p.1-18 March, 2006

Abstract:

At the conference Andreas Dress defined parity split maps by triple point distance
and asked for a characterisation of such maps coming from binary phylogenetic X-trees. This
article gives an answer to that question. The characterisation for *X*-trees can be easily described
as follows: If all restrictions of a split map to sets of five or fewer elements is a parity split map
for an X-tree, then so is the entire map.
To ensure that the parity split map comes from an X-tree which is binary and phylogenetic,
we add two more technical conditions also based on studying at most five points at a time.

References:

1. S. Böcker and A. Dress, Recovering symbolically dated, rooted trees from symbolic ultrametrics, Adv. Math. 138 (1998) 105--125.

2. A. Dress and M. Steel, Mapping edge sets to splits in trees: the path index and parsimony, preprint, 2005.

3. A. Dress, Talk at the PCA04 conference in Uppsala, Sweden, July 5--9, 2004.

4. C. Semple and M. Steel, Phylogenetics, Oxford University Press, 2003.

5. T. Strachan and A.P. Read, Human molecule genetics, 2nd Ed., BIOS Scientific Publishers Ltd., 1999.