Quantifying the accuracy of ancestral state prediction in a phylogenetic tree under maximum parsimony

In phylogenetic studies, biologists often wish to estimate the ancestral discrete character state at an interior vertex v of an evolutionary tree T from the states that are observed at the leaves of the tree. A simple and fast estimation method-maximum parsimony-takes the ancestral state at v to be any state that minimises the number of state changes in T required to explain its evolution on T. In this paper, we investigate the reconstruction accuracy of this estimation method further, under a simple symmetric model of state change, and obtain a number of new results, both for 2-state characters, and r-state characters ([Formula: see text]). Our results rely on establishing new identities and inequalities, based on a coupling argument that involves a simpler 'coin toss' approach to ancestral state reconstruction.