The distributions under two species-tree models of the number of root ancestral configurations for matching gene trees and species trees

TL;DR

This paper investigates the distribution of the number of root ancestral configurations in matching gene and species trees under two models, aiding in understanding the computational complexity of gene tree probability calculations.

Contribution

It introduces a study of the distribution of root ancestral configurations under two species-tree models for matching gene and species trees, highlighting their role in computational complexity.

Findings

Distribution patterns vary under different models

Enumeration of configurations helps assess computational complexity

Results inform gene tree probability calculations

Abstract

For a pair consisting of a gene tree and a species tree, the ancestral configurations at an internal node of the species tree are the distinct sets of gene lineages that can be present at that node. Ancestral configurations appear in computations of gene tree probabilities under evolutionary models conditional on fixed species trees, and the enumeration of root ancestral configurations -- ancestral configurations at the root of the species tree -- assists in describing the complexity of these computations. In the case that the gene tree matches the species tree in topology, we study the distribution of the number of root ancestral configurations of a random labeled tree topology under each of two models.