Overlaid species forests

Abstract

Introgression is an evolutionary process in which genes or other types of genetic material are introduced into a genome. It is an important evolutionary process that can, for example, play a fundamental role in speciation. Recently the concept of an overlaid species forest (OSF) was introduced as a discrete way to model introgression. Basically, an OSF consists of a gene history in the form of a phylogenetic tree, a collection of lineage trees or forest for some species of interest, and a map that overlays the gene tree onto the forest. In this paper we shall study mathematical properties of OSFs and their relationship with other structures in phylogenetics, such as lateral gene transfer models, subtree prune and regraft operations, and phylogenetic networks. In particular, we show that a certain algorithm called OSF-Builder for constructing an OSF is guaranteed to produce a special type of OSF with a minimum number of introgressions, as well as providing some characterizations for networks that can arise from OSFs. We also give bounds on how much an OSF can change when the underlying gene tree or forest is perturbed. We expect that these results will be useful in developing new algorithms for deriving introgression histories, a rapidly growing area of interest in phylogenomics.