Restricted trees: simplifying networks with bottlenecks
Abstract
Suppose N is a phylogenetic network indicating a complicated relationship among individuals and taxa. Often of interest is a much simpler network, for example, a species tree T, that summarizes the most fundamental relationships. The meaning of a species tree is made more complicated by the recent discovery of the importance of hybridizations and lateral gene transfers. Hence it is desirable to describe uniform welldefined procedures that yield a tree given a network N. A useful tool toward this end is a connected surjective digraph (CSD) map f from N to N' where N' is generally a much simpler network than N. A set W of vertices in N is "restricted" if there is at most one vertex from which there is an arc into W, thus yielding a bottleneck in N. A CSD map f from N to N' is "restricted" if the inverse image of each vertex in N' is restricted in N. This paper describes a uniform procedure that, given a network N, yields a welldefined tree called the "restricted tree" of N. There is a restricted CSD map from N to the restricted tree. Many relationships in the tree can be proved to appear also in N.
 Publication:

arXiv eprints
 Pub Date:
 May 2010
 arXiv:
 arXiv:1005.4956
 Bibcode:
 2010arXiv1005.4956W
 Keywords:

 Quantitative Biology  Populations and Evolution;
 Mathematics  Combinatorics;
 92D15 (Primary);
 05C20 (Secondary);
 05C05
 EPrint:
 17 pages, 2 figures