FRACTION OF TREES WITH GIVEN ROOT TRAITS - THE LIMIT OF LARGE TREES

An evolutionary tree is considered as a rooted binary tree, with leaves representing taxa assigned particular traits. Interior nodes of the tree are assigned traits in a parsimonious fashion, including the concept of an ambiguous state. The ambiguous state arises if two offspring nodes have different definite traits, and may be resolved by joining with other definite traits. For a single characteristic with two possible trait values, the fraction of trees that root in a particular trait is known for small values of n, the total number of taxa under consideration. This paper presents formulae for the fraction of trees with a given root trait asymptotically as n → ∞, for a specified fractionation of traits at the leaves, or terminal taxa. For example, if the terminal taxa are evenly split between the two traits, then the fraction of trees that parsimoniously root with definitively one of those traits is, in the limit of large trees, exactly 1/3. © 1990 Academic Press Limited.