On the mapping between evolutionary scenarios and governing rules in state-dependent speciation-extinction models.

Biologists often wish to explain why one trait is more common than its alternatives among species in a clade: is it due to asymmetries in diversification or character evolution processes? State-dependent speciation-extinction (SSE) models provide a flexible framework for jointly modeling such processes. Here, we derive mathematical results that define functional relationships ("rulesets") among rate parameters, establish a mapping between rulesets and evolutionary scenarios, and characterize how these scenarios give rise to different long-term tip state distributions. In particular, we show that multiple evolutionary scenarios can produce identical stationary distributions of tip state frequencies. Performing inference on simulated data from extant-only trees, we find that not all scenarios are equally favored for explaining datasets constructed solely from extant species. This bias could arise from the interplay between mixing rates, elapsed time, and the conditioning inherent in tree likelihoods. As a proof of concept, we apply our framework to the binary SSE (BiSSE) model across multiple Squamate clades and conduct a literature survey of previous BiSSE analyses on Angiosperm phylogeny. We show that, to some extent, the preference for certain scenarios observed in simulations is also reflected in analyses of empirical trees. This study provides a theoretical ground to directly link data-generating process and observed tip state frequencies under an SSE framework.