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

TL;DR

This paper analyzes the accuracy of maximum parsimony in reconstructing ancestral states in phylogenetic trees, providing new theoretical results for 2-state and multi-state characters under a symmetric model.

Contribution

It introduces new identities and inequalities for ancestral state prediction accuracy using a coupling argument and a simplified coin toss model.

Findings

New theoretical bounds for 2-state characters

Results extend to r-state characters with r>2

Coupling argument simplifies analysis of reconstruction accuracy

Abstract

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 ($r>2$). 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.