Date of Award:

12-2025

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Mathematics and Statistics

Committee Chair(s)

Luis Gordillo

Committee

Luis Gordillo

Committee

Brynja Kohler

Committee

Erin Beckman

Abstract

The Allee effect is an ecological phenomenon characterized by a per capita growth rate that increases as the population size increases in the context of low population density. The Allee effect can lead to rapid extinction events. Consequently, ecologists can attempt to control the strength of the Allee effect to help increase the population (in the case of endangered species) or decrease the population (in the case of parasites or pests).

This research aimed to study not the strength of the Allee effect, but the intensity of the Allee effect, or how rapidly cooperation between individuals causes the per capita growth rate to increase as the population size increases. We used a logistic-derived Allee effect equation to discover how the intensity of the Allee effect, along with internal stochastic noise, affected the dynamics of a population.

We found that when the intensity of the Allee effect is small, the parameters of the deterministic model may not accurately represent a population. Consequently, in the case of an endangered population, a stochastic model may lead to an extinction event at small parameter values, even when this is not predicted by the deterministic model. We also concluded that the time spent in the bottleneck region when there is stochasticity does not follow the inverse square-root scaling law, as in the deterministic case, for cases of low intensity of the Allee effect. This, in practice, indicates that the population will go to extinction faster in the stochastic setting than in the deterministic setting.

Our results highlight the importance of measuring the intensity of the Allee effect in a particular population, especially in conjunction with internal stochastic noise, which is how most populations behave. Ecologists who are trying to control a population need to know not only the strength of the Allee effect in a population, but also its intensity, so that the population can be controlled to a desired outcome.

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Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

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