Abstract
In phylogenetics, distances are often used to measure the incongruence between a pair of phylogenetic trees that are reconstructed by different methods or using different regions of genome. Motivated by the maximum parsimony principle in tree inference, we recently introduced the maximum parsimony (MP) distance, which enjoys various attractive properties due to its connection with several other wellknown tree distances, such as tbr and spr. Here we show that computing the MP distance between two trees, a NPhard problem in general, is fixed parameter tractable in terms of the tbr distance between the tree pair. Our approach is based on two reduction rules – the chain reduction and the subtree reduction – that are widely used in computing tbr and spr distances. More precisely, we show that reducing chains to length 4 (but not shorter) preserves the MP distance. In addition, we describe a generalization of the subtree reduction which allows the pendant subtrees to be rooted in different places, and show that this still preserves the MP distance. On a slightly different note we also show that Monadic Second Order Logic (MSOL), posited over an auxiliary graph structure known as the display graph (obtained by merging the two trees at their leaves), can be used to obtain an alternative proof that computation of MP distance is fixed parameter tractable in terms of tbrdistance. We conclude with an extended discussion in which we focus on similarities and differences between MP distance and TBR distance and present a number of open problems. One particularly intriguing question, emerging from the MSOL formulation, is whether two trees with bounded MP distance induce display graphs of bounded treewidth.
Original language  English 

Pages (fromto)  115 
Number of pages  15 
Journal  Theoretical Computer Science 
Volume  646 
Early online date  16 Jul 2016 
DOIs  
Publication status  Published  20 Sep 2016 
Keywords
 Phylogenetics
 Parsimony
 Fixed parameter tractability
 Chain
 Incongruence
 Treewidth
Profiles

Vincent Moulton
 School of Computing Sciences  Professor in Computational Biology
 Norwich Epidemiology Centre  Member
 Computational Biology  Member
Person: Research Group Member, Academic, Teaching & Research

Taoyang Wu
 School of Computing Sciences  Lecturer in Computing Sciences
 Computational Biology  Member
Person: Research Group Member, Academic, Teaching & Research