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Mechanistic derivation and qualitative analysis of a predator-prey population model with strong Allee effect in the predator

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Title: Mechanistic derivation and qualitative analysis of a predator-prey population model with strong Allee effect in the predator
Author(s): Karjalainen, Miko
Contributor: University of Helsinki, Faculty of Science
Degree program: Master 's Programme in Mathematics and Statistics
Specialisation: Mathematics and applied mathematics
Language: English
Acceptance year: 2023
Abstract:
Predator-prey models are mathematical models widely used in ecology to study the dynamics of predator and prey populations, to better understand the stability of such ecosystems and to elucidate the role of various ecological factors in these dynamics. An ecologically important phenomenon studied with these models is the so-called Allee effect, which refers to populations where individuals have reduced fitness at low population densities. If an Allee effect results in a critical population threshold below which a population cannot sustain itself it is called a strong Allee effect. Although predator-prey models with strong Allee effects have received a lot of research attention, most of the prior studies have focused on cases where the phenomenon directly impacts the prey population rather than the predator. In this thesis, the focus is placed on a particular predator-prey model where a strong Allee effect occurs in the predator population. The studied population-level dynamics are derived from a set of individual-level behaviours so that the model parameters retain their interpretation at the level of individuals. The aim of this thesis is to investigate how the specific individual-level processes affect the population dynamics and how the population-level predictions compare to other models found in the literature. Although the basic structure of the model precedes this paper, until now there has not been a comprehensive analysis of the population dynamics. In this analysis, both the mathematical and biological well-posedness of the model system are established, the feasibility and local stability of coexistence equilibria are examined and the bifurcation structure of the model is explored with the help of numerical simulations. Based on these results, the coexistence of both species is possible either in a stable equilibrium or in a stable limit cycle. Nevertheless, it is observed that the presence of the Allee effect has an overall destabilizing effect on the dynamics, often entailing catastrophic consequences for the predator population. These findings are largely in line with previous studies of predator-prey models with a strong Allee effect in the predator.
Keyword(s): Predator-prey model Population model Allee effect Linear stability analysis Local stability analysis Bifurcation analysis Mechanistic derivation


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