title: 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 well-defined procedures that yield a tree given a network N. A useful tool toward this end is a connected surjective digraph (CSD) map φ: N → 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 u ∉ W from which there is an arc into W, thus yielding a bottleneck in N. A CSD map φ: N → 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 well-defined 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.
authors.affiliation: Department of Mathematics, Iowa State University, Ames, IA 50011, USA. swillson@iastate.edu
authors.forename: Stephen J
authors.initials: SJ
authors.lastname: Willson
mesh_terms: D000465:Algorithms; D005075:Biological Evolution; D055641:Mathematical Concepts; D008957:Models, Genetic; D010802:Phylogeny