Overlaid species forests

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