Stephen J. Willson. Restricted trees: simplifying networks with bottlenecks. In BMB, Vol. 73(10):23222338, 2011. Keywords: from network, phylogenetic network. Note: http://arxiv.org/abs/1005.4956.
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"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 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 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. © 2011 The Author(s)."
