A Framework for Representing Reticulate Evolution

Abstract

Acyclic directed graphs (ADGs) are increasingly being viewed as more appropriate for representing certain evolutionary relationships, particularly in biology, than rooted trees. In this paper, we develop a framework for the analysis of these graphs which we call hybrid phylogenies. We are particularly interested in the problem whereby one is given a set of phylogenetic trees and wishes to determine a hybrid phylogeny that 'embeds' each of these trees and which requires the smallest number of hybridisation events. We show that this quantity can be greatly reduced if additional species are involved, and investigate other combinatorial aspects of this and related questions.

Trinets encode tree-child and level-2 phylogenetic networks

“…In Section 5, we then use alternative techniques to prove that tree-child networks are also encoded by their trinets (Theorem 4). Note that this class of networks includes the class of regular networks [1]. Thus it is interesting to note that a regular network is encoded by the set of trees 1 that it contains [28], but that this is not the case for tree-child networks (e.g.…”

Reconstruction of certain phylogenetic networks from the genomes at their leaves

“…Basic models of recombination were suggested by Hein (1990Hein ( , 1993. General frameworks are discussed in Bandelt and Dress (1992), Baroni et al (2004), Moret et al (2004), and Nakhleh et al (2005).…”

“…Another is a kind of time consistency at hybridization events, roughly that the parents of a hybrid be possibly contemporaneous (''temporal representation'' for , ''coexistence in time'' for Moret et al, 2004). Another is a condition called ''regularity'' in Baroni et al (2004) in which, among other properties, no two vertices have the same set of leaves as descendents.…”

Bounding the Number of Hybridisation Events for a Consistent Evolutionary History

“…[4,6,11,16]). In this setting, we expect that the following concept introduced in [2] will prove useful (see also [7,9,11,16,17] where related concepts are presented).…”