Ancestral reconstruction, lateral gene transfer, and the joys of leaping between trees

In part 1, I will present some recent results with Olivier Gascuel on how accurately we can expect to predict ancestral states at the interior nodes of a phylogenetic tree from discrete character data at the extant leaves.

In part 2, I will describe a second project on species tree reconstruction when genes have evolved under a simple model of random lateral gene transfer (LGT). The aim is to answer questions such as: 'could we reconstruct a species tree on (say) 200 species from a large number of gene trees, if each gene has been laterally transferred into other lineages, on average, ten times?' and 'can LGT lead to inconsistent tree estimation?' Our analysis involves a curious connection to random walks on cyclic graphs.