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

Given a gene tree topology and a species tree topology, a coalescent historyrepresents a possible mapping of the list of gene tree coalescences toassociated branches of a species tree on which those coalescences take place.Enumerative properties of coalescent histories have been of interest in theanalysis of relationships between gene trees and species trees. The simplestenumerative result identifies a bijection between coalescent histories for amatching caterpillar gene tree and species tree with monotonic paths that donot cross the diagonal of a square lattice, establishing that the associatednumber of coalescent histories for $n$-taxon matching caterpillar trees ($n\geqslant 2$) is the Catalan number $C_{n-1} = \frac{1}{n} {2n-2 \choose n-1}$.Here, we show that a similar bijection applies for \emph{non-matching}caterpillars, connecting coalescent histories for a non-matching caterpillargene tree and species tree to a class of \emph{roadblocked} monotonic paths.The result provides a simplified algorithm for enumerating coalescent historiesin the non-matching caterpillar case. It enables a rapid proof of a knownresult that given a caterpillar species tree, no non-matching caterpillar genetree has a number of coalescent histories exceeding that of the matching genetree. Additional results on coalescent histories can be obtained by a bijectionbetween permissible roadblocked monotonic paths and Dyck paths. We study thenumber of coalescent histories for non-matching caterpillar gene trees thatdiffer from the species tree by nearest-neighbor-interchange andsubtree-prune-and-regraft moves, characterizing the non-matching caterpillarwith the largest number of coalescent histories. We discuss the implications ofthe results for the study of the combinatorics of gene trees and species trees.

Roadblocked monotonic paths and the enumeration of coalescent histories for non-matching caterpillar gene trees and species trees