  The Sackin and Colless indices are two widely-used metrics for measuring the
balance of trees and for testing evolutionary models in phylogenetics. This
short paper contributes two results about the Sackin and Colless indices of
trees. One result is the asymptotic analysis of the expected Sackin and Colless
indices of a tree shape (which are full binary rooted unlabelled trees) under
the uniform model where tree shapes are sampled with equal probability. Another
is a short elementary proof of the closed formula for the expected Sackin index
of phylogenetic trees (which are full binary rooted trees with leaves being
labelled with taxa) under the uniform model.
