Growth Models Under Uniform Catastrophes

TL;DR

This paper analyzes stochastic population growth models with colonies facing uniform catastrophes, deriving explicit survival probabilities and comparing effects of different catastrophe types on population persistence.

Contribution

It provides explicit formulas for survival chances and extinction times under uniform catastrophes, and compares these with binomial and geometric models.

Findings

Explicit survival probability formulas derived

Uniform catastrophes impact persistence differently than binomial or geometric

Comparison quantifies effects of catastrophe types on population viability

Abstract

We consider stochastic growth models for populations organized in colonies and subject to uniform catastrophes. To assess population viability, we analyze scenarios in which individuals adopt dispersion strategies after catastrophic events. For these models, we derive explicit expressions for the survival probability and the mean time to extinction, both with and without spatial constraints. In addition, we complement this analysis by comparing uniform catastrophes with binomial and geometric catastrophes in models with dispersion and no spatial restrictions. Here, the terms uniform, binomial and geometric refer to the probability distributions governing the number of individuals that survive immediately after a catastrophe. This comparison allows us to quantify the impact of different types of catastrophic events on population persistence.