English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

To a given gene tree topology $G$ and species tree topology $S$ with leaveslabeled bijectively from a fixed set $X$, one can associate a set of ancestralconfigurations, each of which encodes a set of gene lineages that can be foundat a given node of the species tree. We introduce a lattice structure onancestral configurations, studying the directed graphs that provide graphicalrepresentations of lattices of ancestral configurations. For a matching genetree topology and species tree topology $G=S$, we present a method for definingthe digraph of ancestral configurations from the tree topology by usingiterated cartesian products of graphs. We show that a specific set of paths onthe digraph of ancestral configurations is in bijection with the set of labeledhistories -- a well-known phylogenetic object that enumerates possible temporalorderings of the coalescences of a tree. For each of a series of tree families,we obtain closed-form expressions for the number of labeled histories by usingthis bijection to count paths on associated digraphs. Finally, we prove thatour lattice construction extends to nonmatching tree pairs, and we use it tocharacterize pairs $(G,S)$ having the maximal number of ancestralconfigurations for a fixed $G$. We discuss how the construction provides newmethods for performing enumerations of combinatorial aspects of gene andspecies trees.

A lattice structure for ancestral configurations arising from the relationship between gene trees and species trees