A polynomial time algorithm for calculating the probability of a ranked gene tree given a species tree

TL;DR

This paper presents a polynomial time algorithm for computing the probability of a ranked gene tree given a species tree, focusing on cases with polynomially many internal vertex orderings.

Contribution

It introduces a polynomial time algorithm for calculating gene tree probabilities with ranked topologies, addressing cases with polynomially many internal vertex orderings.

Findings

Polynomial time algorithm for ranked gene tree probability

Efficient computation when internal vertex orderings are polynomial

Complexity remains unknown for exponential orderings

Abstract

In this paper, we provide a polynomial time algorithm to calculate the probability of a {\it ranked} gene tree topology for a given species tree, where a ranked tree topology is a tree topology with the internal vertices being ordered. The probability of a gene tree topology can thus be calculated in polynomial time if the number of orderings of the internal vertices is a polynomial number. However, the complexity of calculating the probability of a gene tree topology with an exponential number of rankings for a given species tree remains unknown.