Abstract
A phylogenetic network is a graphtheoretical tool that is used by biologists to represent the evolutionary history of a collection of species. One potential way of constructing such networks is via a distancebased approach, where one is asked to find a phylogenetic network that in some way represents a given distance matrix, which gives information on the evolutionary distances between presentday taxa. Here, we consider the following question. For which k are unrooted levelk networks uniquely determined by their distance matrices? We consider this question for shortest distances as well as for the case that the multisets of all distances is given. We prove that level1 networks and level2 networks are reconstructible from their shortest distances and multisets of distances, respectively. Furthermore we show that, in general, networks of level higher than 1 are not reconstructible from shortest distances and that networks of level higher than 2 are not reconstructible from their multisets of distances.
Original language  English 

Article number  102075 
Journal  Advances in Applied Mathematics 
Volume  120 
Early online date  3 Jul 2020 
DOIs  
Publication status  Published  Sep 2020 
Profiles

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