  The Minimal Ancestral Deviation (MAD) method is a recently introduced
procedure for estimating the root of a phylogenetic tree, based only on the
shape and branch lengths of the tree. The method is loosely derived from the
midpoint rooting method, but, unlike its predecessor, makes use of all pairs of
OTUs when positioning the root. In this note we establish properties of this
method and then describe a fast and memory efficient algorithm. As a proof of
principle, we use our algorithm to determine the MAD roots for simulated
phylogenies with up to 100,000 OTUs. The calculations take a few minutes on a
standard laptop.
