NDLI: Restricted Trees: Simplifying Networks with Bottlenecks

Content Provider	Springer Nature Link
Author	Willson, Stephen J.
Copyright Year	2011
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.
Starting Page	2322
Ending Page	2338
Page Count	17
File Format	PDF
ISSN	00928240
Journal	Bulletin of Mathematical Biology
Volume Number	73
Issue Number	10
e-ISSN	15229602
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-02-26
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Digraph Network Tree Connected Hybrid Phylogeny Homomorphism Restricted Phylogenetic network Mathematical and Computational Biology Cell Biology Life Sciences
Content Type	Text
Resource Type	Article
Subject	Neuroscience Biochemistry, Genetics and Molecular Biology Mathematics Pharmacology Immunology Computational Theory and Mathematics Environmental Science Agricultural and Biological Sciences

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