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.