Constructing Semi-Directed Level-1 Phylogenetic Networks from Quarnets

Abstract: We introduce two algorithms for reconstructing semi-directed level-1 phylogenetic networks from their complete set of 4-leaf subnetworks, known as quarnets. The first algorithm, the sequential method, begins with a single quarnet and adds on one leaf at a time until all leaves have been placed. The second algorithm, the cherry-blob method, functions similarly to cherry-picking algorithms for phylogenetic trees by identifying exterior network structures from the quarnets.