Evaluating dispersion strategies in growth models subject to geometric catastrophes

TL;DR

This paper investigates how different dispersion strategies after geometric catastrophes affect population survival in stochastic growth models, revealing that the effectiveness depends on the number of new positions and other parameters.

Contribution

It introduces a comparative analysis of dispersion schemes in growth models under catastrophes, highlighting conditions where dispersion improves survival chances.

Findings

When d=2, dispersion does not improve survival.

For d=3, the benefit of dispersion depends on growth rate and survival probability.

Dispersion can be advantageous or not, based on specific parameters.

Abstract

We consider stochastic growth models to represent population dynamics subject to geometric catastrophes. We analyze different dispersion schemes after catastrophes, to study how these schemes impact the population viability and comparing them with the scheme where there is no dispersion. In the schemes with dispersion, we consider that each colony, after the catastrophe event, has $d$ new positions to place its survivors. We find out that when $d = 2$ no type of dispersion considered improves the chance of survival, at best it matches the scheme where there is no dispersion. When $d = 3$, based on the survival probability, we conclude that dispersion may be an advantage or not, depending on its type, the rate of colony growth and the probability that an individual will survive when exposed to a catastrophe.