Stochastic models for horizontal gene transfer: Taking a random walk through tree space

Horizontal gene transfer (HGT) plays a critical role in evolution across all domains of life with important biological and medical implications. I propose a simple class of stochastic models to examine HGT using multiple orthologous gene alignments. The models function in a hierarchical phylogenetic framework. The top level of the hierarchy is based on a random walk process in tree space that allows for the development of a joint probabilistic distribution over multiple gene trees and an unknown, but estimable species tree. I consider two general forms of random walks. The first form is derived from the subtree prune and regraft (SPR) operator that mirrors the observed effects that HGT has on inferred trees. The second form is based on walks over complete graphs and offers numerically tractable solutions for an increasing number of taxa. The bottom level of the hierarchy utilizes standard phylogenetic models to reconstruct gene trees given multiple gene alignments conditional on the random walk process. I develop a well-mixing Markov chain Monte Carlo algorithm to fit the models in a Bayesian framework. I demonstrate the flexibility of these stochastic models to test competing ideas about HGT by examining the complexity hypothesis. Using 144 orthologous gene alignments from six prokaryotes previously collected and analyzed, Bayesian model selection finds support for (1) the SPR model over the alternative form, (2) the 16S rRNA reconstruction as the most likely species tree, and (3) increased HGT of operational genes compared to informational genes.