A stochastic model for phylogenetic trees

TL;DR

This paper introduces a stochastic birth-death model for phylogenetic trees, capturing different evolutionary dynamics such as influenza and HIV, based on the birth rate relative to death rate.

Contribution

It presents a simple probabilistic model that explains diverse phylogenetic tree structures through birth-death processes with fitness-based selection.

Findings

Subcritical birth rate yields influenza-like trees with few types and long-lasting dominant types.

Supercritical birth rate produces HIV-like trees with many types and short-lived variants.

Model aligns well with observed phylogenetic patterns of influenza and HIV.

Abstract

We propose the following simple stochastic model for phylogenetic trees. New types are born and die according to a birth and death chain. At each birth we associate a fitness to the new type sampled from a fixed distribution. At each death the type with the smallest fitness is killed. We show that if the birth (i.e. mutation) rate is subcritical we get a phylogenetic tree consistent with an influenza tree (few types at any given time and one dominating type lasting a long time). When the birth rate is supercritical we get a phylogenetic tree consistent with an HIV tree (many types at any given time, none lasting very long).