| In this dissertation, I adopt a hierarchical modeling framework under a Bayesian paradigm to appropriately model complex evolutionary phenomenon. I provide a solution to the problem of how to appropriately model evolutionary histories under the influence of recombination, reassortment, horizontal gene transfer and other such non-vertical process. Before moving to the exact problem itself, I review molecular phylogenetic research under a Bayesian framework.;After this review, I focus on viral applications under the influence of recombination. In these applications, specific regions of the molecular sequence alignment will support differing topologies due to the effect of recombination. To alleviate this, I introduce the random tips model. The random tips model works by utilizing an evolutionary history with an unknown number of taxa; because of this, the model removes the independence assumption plaguing previous methods. Furthermore the random tips model can easily handle multiple recombinant sequences.;Next, I extend the random tips model using ancestral recombination graphs (ARGs). ARGs fully specify an evolutionary history by jointly modeling both vertical and non-vertically transfered data. Building from this, I introduce a Bayesian model for multilocus data under the influence of vertical and non-vertical evolution. I also extend this model to allow for rate variation.;Moving away from multilocus datasets and non-vertical evolution, I turn my attention to the inference of variable population dynamics. In particular, I demonstrate how the Bayesian paradigm allows for joint inference of population dynamics and the evolutionary history. Moreover, I outline a method to compare the population dynamics across multiple populations. |
