  Ancestral mixture model, proposed by Chen and Lindsay (2006), is an important
model to build a hierarchical tree from high dimensional binary sequences.
Mixture trees created from ancestral mixture models involve in the inferred
evolutionary relationships among various biological species. Moreover, it
contains the information of time when the species mutates. Tree comparison
metric, an essential issue in bioinformatics, is to measure the similarity
between trees. However, to our knowledge, the approach to the comparison
between two mixture trees is still under development. In this paper, we propose
a new metric, named mixture distance metric, to measure the similarity of two
mixture trees. It uniquely considers the factor of evolutionary times between
trees. In addition, we also further develop two algorithms to compute the
mixture distance between two mixture trees. One requires O(n^2) and the other
requires O(nh) computation time with O(n) preprocessing time, where n denotes
the number of leaves in the two mixture trees, and h denotes the minimum height
of these two trees.
