When can we reconstruct the ancestral state? A unified theory

TL;DR

This paper develops a unified theoretical framework for understanding when ancestral state reconstruction is reliably possible across different evolutionary models, linking discrete and continuous trait analyses.

Contribution

It establishes necessary and sufficient conditions for consistent ancestral state reconstruction across multiple models, unifying previous disparate results.

Findings

Conditions are equivalent for nested trees with bounded heights across models.

Counter-example shows equivalence breaks down with unbounded tree heights.

Provides a comprehensive theoretical foundation for ancestral state reconstruction.

Abstract

Ancestral state reconstruction is one of the most important tasks in evolutionary biology. Conditions under which we can reliably reconstruct the ancestral state have been studied for both discrete and continuous traits. However, the connection between these results is unclear, and it seems that each model needs different conditions. In this work, we provide a unifying theory on the consistency of ancestral state reconstruction for various types of trait evolution models. Notably, we show that for a sequence of nested trees with bounded heights, the necessary and sufficient conditions for the existence of a consistent ancestral state reconstruction method under discrete models, the Brownian motion model, and the threshold model are equivalent. When tree heights are unbounded, we provide a simple counter-example to show that this equivalence is no longer valid.