2022/04/28 by Hellmuth, Marc, Schaller, David, Stadler, Peter F. · 1 citation
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Mathematics #Molecular Networks (q-bio.MN) #Populations and Evolution (q-bio.PE)
paper · doi:10.48550/arxiv.2204.13466
Rooted acyclic graphs appear naturally when the phylogenetic relationship of a set X of taxa involves not only speciations but also recombination, horizontal transfer, or hybridization, that cannot be captured by trees. A variety of classes of such networks have been discussed in the literature, including phylogenetic, level-1, tree-child, tree-based, galled tree, regular, or normal networks as models of different types of evolutionary processes. Clusters arise in models of phylogeny as the sets \mathttC(v) of descendant taxa of a vertex v. The clustering system \mathscrCN comprising the clusters of a network N conveys key information on N itself. In the special case of rooted phylogenetic trees, T is uniquely determined by its clustering system \mathscrCT. Although this is no longer true for networks in general, it is of interest to relate properties of N and \mathscrCN. Here, we systematically investigate the relationships of several well-studied classes of networks and their clustering systems. The main results are correspondences of classes of networks and clustering system of the following form: If N is a network of type \mathbbX, then CN satisfies \mathbbY, and conversely if \mathscrC is a clustering system satisfying \mathbbY then there is network N of type \mathbbX such that \mathscrC⊆\mathscrCN.This, in turn, allows us to investigate the mutual dependencies between the distinct types of networks in much detail.