# Extinction and the Allee Effect in an Age-structured Ricker Population Model with Inter-stage Interaction

## TL;DR

This paper analyzes how age-structured populations with stage interactions and Allee effects evolve over time, revealing conditions for extinction and surprising survival scenarios without interior fixed points.

## Contribution

It introduces a model incorporating inter-stage interactions in an age-structured Ricker population and explores their impact on extinction thresholds and equilibrium shifts.

## Key findings

- Inter-stage interactions can enable survival without interior fixed points.
- Extinction and Allee thresholds are unaffected by shifts in interior equilibria.
- Conditions for convergence to extinction are characterized under time-dependent vital rates.

## Abstract

We study the evolution in discrete time of certain age-structured populations, such as adults and juveniles, with a Ricker fitness function. We determine conditions for the convergence of orbits to the origin (extinction) in the presence of the Allee effect and time-dependent vital rates. We show that when stages interact, they may survive in the absence of interior fixed points, a surprising situation that is impossible without inter-stage interactions. We also examine the shift in the interior Allee equilibrium caused by the occurrence of interactions between stages and find that the extinction or Allee threshold does not extend to the new boundaries set by the shift in equilibrium, i.e. no interior equilibria are on the extinction threshold.