On the challenge of reconstructing level1 phylogenetic networks from triplets and clusters
Abstract
Phylogenetic networks have gained prominence over the years due to their ability to represent complex nontreelike evolutionary events such as recombination or hybridization. Popular combinatorial objects used to construct them are triplet systems and cluster systems, the motivation being that any network $N$ induces a triplet system $\mathcal R(N)$ and a softwired cluster system $\mathcal S(N)$. Since in realworld studies it cannot be guaranteed that all triplets/softwired clusters induced by a network are available it is of particular interest to understand whether subsets of $\mathcal R(N)$ or $\mathcal S(N)$ allow one to uniquely reconstruct the underlying network $N$. Here we show that even within the highly restricted yet biologically interesting space of level1 phylogenetic networks it is not always possible to uniquely reconstruct a level1 network $N$ even when all triplets in $\mathcal R(N)$ or all clusters in $\mathcal S(N)$ are available. On the positive side, we introduce a reasonably large subclass of level1 networks the members of which are uniquely determined by their induced triplet/softwired cluster systems. Along the way, we also establish various enumerative results, both positive and negative, including results which show that certain special subclasses of level1 networks $N$ can be uniquely reconstructed from proper subsets of $\mathcal R(N)$ and $\mathcal S(N)$. We anticipate these results to be of use in the design of, for example, algorithms for phylogenetic network inference.
 Publication:

arXiv eprints
 Pub Date:
 November 2015
 arXiv:
 arXiv:1511.08056
 Bibcode:
 2015arXiv151108056G
 Keywords:

 Mathematics  Combinatorics