Relational Data in Phylogenetics

In the course of investigation evolutionary relationships found in the genomes a set of species, several binary relations appear. For example “best matches” refer pairs of genes x and y so that y is one of the closest relatives of x in the species that harbors y. Orthology designates pairs of genes whose last common ancestor is a speciation event. Horizontal gene transfer is related to the lower diverence time relation, satisfied by a pair of genes that is younger than the divergence of the species in which they reside. I will sketch the connections between the relations and the the information that they convey about the gene trees, the phylogeny of the underlying species, and the reconciliation of gene and species trees.