Topology and inference for Yule trees with multiple states.

Area of Science:

• Evolutionary biology
• Theoretical biology
• Mathematical modeling

Background:

• Trait dependence is crucial in species evolution.
• Existing models often lack multi-state capabilities.
• Understanding evolutionary processes requires robust modeling frameworks.

Purpose of the Study:

• Introduce novel random tree models for multi-state trait evolution.
• Generalize existing Markov propagation and Yule processes.
• Enable inference of model parameters from empirical data.

Main Methods:

• Developed a discrete-time model (multiple state ERM tree).
• Developed a continuous-time model (multiple state Yule tree).
• Analyzed state-dependent topological properties and derived asymptotic results.

Main Results:

• The models generalize existing random tree mechanisms (ERM, Yule).
• State-dependent topological properties were analyzed.
• Asymptotic results facilitate parameter inference from leaf and near-leaf state data.

Conclusions:

• The introduced models offer a flexible framework for studying trait dependence in evolution.
• The models allow for inferring evolutionary parameters from observed trait distributions.
• These advancements contribute to a deeper understanding of evolutionary processes through mathematical modeling.