The longest branches in a non-Markovian phylogenetic tree

TL;DR

This paper investigates the asymptotic lengths of the longest branches in a non-Markovian Bellman-Harris branching process, analyzing both living and deceased lineages at a given time.

Contribution

It provides new asymptotic results for the longest branches in non-Markovian branching processes, extending understanding beyond Markovian models.

Findings

Asymptotic behavior characterized for pendant branches

Asymptotic behavior characterized for interior branches

Results applicable to non-Markovian branching processes

Abstract

Consider a Bellman--Harris-type branching process, in which individuals evolve independently of one another, giving birth after a random time $T$ to a random number $L$ of children. In this article, we study the asymptotic behaviour of the length of the longest branches of this branching process at time $t$, both pendant branches (corresponding to individuals still alive at time $t$) and interior branches (corresponding to individuals dead before time $t$).