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A Unified Approach to Evolution Models With Allee Effects
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ABSTRACT
Allee effects reduce per capita growth at low densities and can arise from mechanisms such as mate limitation, predator saturation, cooperation, inbreeding, just to name a few. Yet in many eco‐evolutionary models, they are imposed phenomenologically, obscuring how mechanisms and functional form shape persistence and extinction. We develop a unified framework for discrete‐time eco‐evolutionary dynamics with multiplicative Allee effects by embedding a broad class of continuously differentiable Allee‐inducing functions into Beverton–Holt and Ricker models coupled to trait evolution. Classifying Allee functions as increasing, decreasing, or unimodal, we derive general conditions for the existence and stability of extinction, axial, and interior equilibria. We show that evolutionary feedback can generate not only classical weak and strong Allee effects, but also generalized multi‐threshold regimes with more than two interior equilibria. Our results demonstrate that evolutionary dynamics may either amplify or mitigate extinction risk depending on parameters and mechanisms, yielding new insights into persistence thresholds and evolutionary tipping points, with implications for conservation, invasion, and biological control.
Title: A Unified Approach to Evolution Models With Allee Effects
Description:
ABSTRACT
Allee effects reduce per capita growth at low densities and can arise from mechanisms such as mate limitation, predator saturation, cooperation, inbreeding, just to name a few.
Yet in many eco‐evolutionary models, they are imposed phenomenologically, obscuring how mechanisms and functional form shape persistence and extinction.
We develop a unified framework for discrete‐time eco‐evolutionary dynamics with multiplicative Allee effects by embedding a broad class of continuously differentiable Allee‐inducing functions into Beverton–Holt and Ricker models coupled to trait evolution.
Classifying Allee functions as increasing, decreasing, or unimodal, we derive general conditions for the existence and stability of extinction, axial, and interior equilibria.
We show that evolutionary feedback can generate not only classical weak and strong Allee effects, but also generalized multi‐threshold regimes with more than two interior equilibria.
Our results demonstrate that evolutionary dynamics may either amplify or mitigate extinction risk depending on parameters and mechanisms, yielding new insights into persistence thresholds and evolutionary tipping points, with implications for conservation, invasion, and biological control.
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A study of the strong Allee effect with fuzzy parameters for its application in economics
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