# Density-dependent feedback in age-structured populations

## TL;DR

This paper provides a rigorous mathematical analysis of how population density and age structure influence population stability and extinction, highlighting the role of the newborn function and the Allee effect.

## Contribution

It introduces a new stability criterion based solely on the newborn function and establishes a threshold population size for extinction in age-structured models.

## Key findings

- Global stability depends only on the newborn function.
- Existence of a population threshold leading to extinction.
- Analysis of positive and negative density effects in age-structured populations.

## Abstract

The population size has far-reaching effects on the fitness of the population, that, in its turn influences the population extinction or persistence. Understanding the density- and age-dependent factors will facilitate more accurate predictions about the population dynamics and its asymptotic behaviour. In this paper, we develop a rigourous mathematical analysis to study positive and negative effects of increased population density in the classical nonlinear age-structured population model introduced by Gurtin \& MacCamy in the late 1970s. One of our main results expresses the global stability of the system in terms of the newborn function only. We also derive the existence of a threshold population size implying the population extinction, which is well-known in population dynamics as an Allee effect.