Abstract
This paper investigates model congruence (= asymptotic unidentifiability) in phylogenetics for continuous-time Markov chains (CTMCs) that include models for DNA, protein, discrete trait evolution, and state-dependent diversification. Without exception, all CTMCs have infinite classes of congruent models. Congruent models vary in the number of parameters from one to infinity and may have drastically different evolutionary dynamics, and standard model selection criteria are not applicable to them. We classify the structure of a congruence class and show how the “best” model can be selected based on mathematical and biological reasoning. Thus, congruent models in CTMCs do not suffer from the model selection problem previously identified for the time-dependent diversification process. Moreover, we demonstrate that congruence may serve to explain some evolutionary phenomena, specifically linking macro-and microevolution. We also discuss other types of congruence that may occur in phylogenetics and ways to handle them.
Competing Interest Statement
The authors have declared no competing interest.
