On the number of ranked species trees producing anomalous ranked gene trees

TL;DR

This paper investigates the prevalence of anomalous ranked gene trees (ARGTs) in species trees, showing that as the number of species grows, nearly all such trees produce ARGTs, which are more probable than the species tree itself.

Contribution

It provides exact enumerations and asymptotic estimates for classes of ranked species trees, demonstrating that ARGT-producing trees dominate as species count increases.

Findings

Fraction of ARGT-producing trees approaches 1 with more species

Exact enumeration and asymptotic estimates for tree classes

Extends previous existence results to probabilistic frequency

Abstract

Analysis of probability distributions conditional on species trees has demonstrated the existence of anomalous ranked gene trees (ARGTs), ranked gene trees that are more probable than the ranked gene tree that accords with the ranked species tree. Here, to improve the characterization of ARGTs, we study enumerative and probabilistic properties of two classes of ranked labeled species trees, focusing on the presence or avoidance of certain subtree patterns associated with the production of ARGTs. We provide exact enumerations and asymptotic estimates for cardinalities of these sets of trees, showing that as the number of species increases without bound, the fraction of all ranked labeled species trees that are ARGT-producing approaches 1. This result extends beyond earlier existence results to provide a probabilistic claim about the frequency of ARGTs.