Phylogenetic Closure Operations and Homoplasy-Free Evolution

Phylogenetic closure operations on partial splits and quartet trees turn out to be both mathematically interesting and computationally useful. Although these operations were defined two decades ago, until recently little had been established concerning their properties. Here we present some further new results and links between these closure operations, and show how they can be applied in phylogeny reconstruction and enumeration. Using the operations we study how effectively one may be able to reconstruct phylogenies from evolved multi-state characters that take values in a large state space (such as may arise with certain genomic data).