Which Phylogenetic Networks are Merely Trees with Additional Arcs?
Bottom Line: Here, we establish a precise and easily tested criterion (based on "2-SAT") that efficiently determines whether or not any given network can be realized in this way.Moreover, the proof provides a polynomial-time algorithm for finding one or more trees (when they exist) on which the network can be based.A number of interesting consequences are presented as corollaries; these lead to some further relevant questions and observations, which we outline in the conclusion.
Affiliation: Centre for Research in Mathematics, School of Computing, Engineering and Mathematics, University of Western Sydney, Australia;Show MeSH
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Mentions: It might seem plausible that the antichain-to-leaf property is also a sufficient condition for a network to be tree-based. Alas, this is not the case, and Fig. 3 shows a particular case where the antichain-to-leaf property holds, yet the network is not tree-based.Figure 3.
Affiliation: Centre for Research in Mathematics, School of Computing, Engineering and Mathematics, University of Western Sydney, Australia;