title: Closure operations in phylogenetics.
abstract: Closure operations are a useful device in both the theory and practice of tree reconstruction in biology and other areas of classification. These operations take a collection of trees (rooted or unrooted) that classify overlapping sets of objects at their leaves, and infer further tree-like relationships. In this paper we investigate closure operations on phylogenetic trees; both rooted and unrooted; as well as on X-splits, and in a general abstract setting. We derive a number of new results, particularly concerning the completeness (and incompleteness) and complexity of various types of closure rules.
authors.affiliation: Allan Wilson Centre for Molecular Ecology and Evolution, Biomathematics Research Centre, University of Canterbury, Christchurch, New Zealand. stefan@picb.ac.cn
authors.forename: Stefan
authors.initials: S
authors.lastname: Grünewald
authors.forename: Mike
authors.initials: M
authors.lastname: Steel
authors.forename: M Shel
authors.initials: MS
authors.lastname: Swenson
mesh_terms: D005075:Biological Evolution; D008433:Mathematics; D008957:Models, Genetic; D010802:Phylogeny