Bayesian phylogenetic models for relaxed clock and trait evolution

Abstract

Bayesian Markov chain Monte Carlo (MCMC) has become a common approach for phylogenetic inference. While huge amount of data provides signi cant information of evolution, phylogenetic inference of larger data sets requires more e cient MCMC methods. In the meantime, it remains challenging to estimate phylogenetic trees relying merely on molecular data, especially when fossils and extinct species are included. To address the issues, this research aims to propose e cient algorithms for MCMC sampling and develop probabilistic models for trait evolution. A new algorithm is presented to improve the e ciency of MCMC sampling for evolutionary models that include a per-branch rate parameter in phylogenetic trees. The proposed kernel changes evolutionary rates and divergence times at the same time, under the constraint that the implied genetic distances remain constant. Results demonstrate that the algorithm is able to provide better computational e ciency measured by e ective samples per hour and overall mixing performance. An integrative model is proposed to jointly estimate phylogenetic trees using continuous traits, molecular sequences and fossils, where the evolution of continuous traits is modelled by a Brownian motion process. Methods that scale well with tree size and the number of traits are implemented to evaluate the probability density of observing trait data in an e cient fashion. The proposed model is applied to estimating a phylogeny of Carnivora, in which the paradigm of a total-evidence approach for Bayesian phylogenetic analysis is illustrated. With the motivation to analyse continuous and discrete traits in a uni ed probabilistic framework, a liability model is introduced to associate di erent types of trait observations by assuming underlying continuous random variables. Based on the liability model, evolutionary process of multiple types of traits can be estimated simultaneously, including evolutionary rates, trait correlations and ancestral states. Through a series of simulation studies, the performance and predictability of the liability model are discussed.