Phylogenetic closure operations, and homoplasy-free evolution


             Tobias Dezulian and Mike Steel


                          Abstract 

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 decade 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). 

Keywords: Phylogenetic tree, quartet tree, closure operations, random cluster model.