Reconciled trees and incongruent gene and species trees

c 0000 American Mathematical Society 1052-1798/00 $1.00 + $.25 per page . We present a method for visualising and quantifying the relationship between a pair of gene and species trees that constructs a third tree termed the reconciled tree. Given a gene tree and a species tree the reconciled tree represents the history of the gene tree embedded within the species tree. The reconciled tree is constructed from one or more subtrees of the species tree, and contains the gene tree as a subtree. The relationship between the gene and species tree can be expressed in terms of the number of gene duplications and gene losses required to construct the reconciled tree. This number can be used as an optimality criterion for selecting the species tree that best accounts for the observed gene tree.