SQUARED-CHANGE PARSIMONY RECONSTRUCTIONS OF ANCESTRAL STATES FOR CONTINUOUS-VALUED CHARACTERS ON A PHYLOGENETIC TREE

A direct algorithm is described to reconstruct on a phylogenetic tree the ancestral states of a continuous-valued character, using a parsimony criterion that minimizes the sum of squared changes along the branches. It is shown that when the squared changes are inversely weighted by the lengths of the branches, the squared-change parsimony reconstruction is that which has maximum posterior probability under a Brownian motion model of evolution. The squared-change parsimony estimates are also closely related to the contrasts in Felsenstein's test of character correlation.