Identifiability of a Simple Model of Lateral Gene Transfer

RESUMO

In evolutionary biology, factors like lateral gene transfer complicate the tree of life, making inference of a species tree more difficult. The phenomenon of lateral gene transfer allows genetic material to be passed between organisms as opposed to inheritance, causing the tree for a particular gene to differ from the species tree. In this work, we define a model of lateral gene transfer on site patterns. In the case where lateral gene transfer is restricted to occur only between closely related species, we show that the unrooted topology of the species tree is identifiable from SNP data on the taxa. Our proof involves showing a connection between our lateral gene transfer model and graphical models on a related tree, and uses ranks of flattenings to identify splits in the tree. We also report on results of using the singular value decomposition on flattening matrices to identify the unrooted topology in simulated data.