Immortal Branching Processes

TL;DR

This paper introduces an immortal variant of the critical branching process, where certain particles or stem cells cannot die, leading to new dynamical behaviors and potential long-term survival.

Contribution

It proposes and analyzes a novel immortal critical branching process, extending classical models by incorporating immortality mechanisms.

Findings

New dynamical behaviors identified in immortal branching processes

Conditions under which populations avoid extinction due to immortality

Theoretical framework for analyzing immortal stem cell lineages

Abstract

We introduce and study the dynamics of an \emph{immortal} critical branching process. In the classic, critical branching process, particles give birth to a single offspring or die at the same rates. Even though the average population is constant in time, the ultimate fate of the population is extinction. We augment this branching process with immortality by positing that either: (a) a single particle cannot die, or (b) there exists an immortal stem cell that gives birth to ordinary cells that can subsequently undergo critical branching. We discuss the new dynamical aspects of this immortal branching process.