Branching random walks with ageing

TL;DR

This paper investigates how ageing impacts the dynamics of branching random walks, analyzing how changes in parameters and reproduction rates influence the process's long-term behavior.

Contribution

It introduces a model incorporating ageing into branching processes and explores its effects on population evolution and extinction probabilities.

Findings

Ageing significantly alters the process's growth and extinction dynamics.

Modified parameters can either mitigate or exacerbate the effects of ageing.

The study provides insights into real-world populations with declining reproductive capacity.

Abstract

Branching processes are models used to describe populations that reproduce and die over time. In the classical setting, an individual's reproductive capacity remains constant throughout its lifetime. However, in real-world situations, reproductive capacity typically undergoes ageing - that is, after reaching a peak, it decreases over time. In this work, we study the influence of ageing on the behaviour of the process and how modifying its parameters, along with reproduction rates, affects the destiny of the process.