Nonidentifiability of state-dependent diversification models (SSEs) is ubiquitous but not problematic for phylogenetics

Λ recent study (Louca and Pennell, 2020) spotlighted the issue of model congruence, or asymptotic unidentifiability, in timedependent birth-death models used for reconstructing species diversification histories on phylogenetic trees. The phenomenon of model congruence implies that any given timetree can be equally likely explained by various diversification scenarios. The present work investigates this issue in state-dependent speciation and extinction (SSE) models, which are widely employed to study trait-dependent diversification. We demonstrate that model unidentifiability is universal for SSEs, with every SSE belonging to an infinite class of congruent models. Importantly, we find that any trait-independent model is congruent with a trait-dependent model that possesses the same or fewer parameters, raising significant concerns for model selection and hypothesis testing. To address this challenge, we propose an analytical solution and discuss its implication for comparative phylogenetics and model development. Our results indicate that while SSE congruence is critical to avoiding unidentifiability in diversification studies, no fundamental change to phylogenetic methodologies is needed. Instead, congruence opens up new opportunities for modeling trait-dependent diversification. ### Competing Interest Statement The authors have declared no competing interest.