An algorithm for reconstructing level-2 phylogenetic networks from trinets

Evolutionary histories for species that cross with one another or exchange genetic material can be represented by leaf-labelled, directed graphs called phylogenetic networks . A major challenge in the burgeoning area of is to develop algorithms building such amalgamating small into a single large network. The level network measure its deviation from being tree; higher network, less treelike it becomes. Various have been developed level-1 networks. However, may not able capture complexity some data sets. In this paper, we present polynomial-time algorithm constructing rooted binary level-2 collection 3-leaf trinets Moreover, prove will correctly reconstruct if given all as input. runs time O ( t ⋅ n + 4 ) number input and leaves. We also show there fundamental obstruction level-3 trinets, so new approaches need level-networks. • First trinets. Algorithm polynomial any set guaranteed construct correct are Example showing encoded