Phylogenies, the evolutionary histories of groups of organisms, play a major role in representing the interrelationships among biological entities. Although many biological processes can be effectively modeled and summarized as a binary tree, others cannot: recombination, hybrid speciation, and horizontal gene transfer result in networks of relationships rather than trees of relationships.
Maximum parsimony (MP) is one of the most popular methods used for phylogenetic tree reconstruction. Roughly, this method is based on the assumption that "evolution is parsimonious", that is, the best evolutionary trees are the ones that minimize the number of changes along the edges of the tree.
In previous works, we formulated a maximum parsimony (MP) criterion for reconstructing and evaluating phylogenetic networks, and demonstrated its quality on biological as well as synthetic datasets. In this work, we show further theoretical insights and results regarding various aspects of the MP criterion of phylogenetic networks.