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Allee effects introduced by density dependent phenology.

Timothy J Pervenecki1, Sharon Bewick2, Garrett Otto3

  • 1Department of Mathematics and Computer Science, University of Wisconsin-Superior, Superior, WI 54880, United States of America.

Mathematical Biosciences
|May 26, 2024
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Summary
This summary is machine-generated.

This study introduces a hybrid population model where density influences species timing, revealing strong Allee effects and overcompensation. Population dynamics are complex, ranging from stable states to chaos, driven by emergence timing distributions.

Keywords:
Allee effectPhenologyovercompensation

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Area of Science:

  • Population Ecology
  • Mathematical Biology
  • Ecological Dynamics

Background:

  • Phenology, the timing of biological events, significantly impacts population dynamics.
  • Density-dependent processes are crucial for understanding population regulation and stability.
  • Allee effects, where population growth rate decreases at low densities, can lead to extinction risk.

Purpose of the Study:

  • To investigate a hybrid population model incorporating density-dependent phenology for stage transitions.
  • To analyze the emergence of Allee effects and overcompensation within this model.
  • To explore the influence of density-dependent emergence timing distributions on population dynamics.

Main Methods:

  • Development of a hybrid population model for an annual species.
  • Mathematical modeling of density-dependent phenology governing stage transitions.
  • Numerical simulations using a density-dependent gamma distribution for emergence timing.

Main Results:

  • The model successfully demonstrates a strong Allee effect and overcompensation.
  • Density-dependent emergence timing distributions were found to be critical drivers of population dynamics.
  • Simulations revealed a wide spectrum of dynamic behaviors, including stable equilibria, limit cycles, and chaotic dynamics.

Conclusions:

  • Hybrid models with density-dependent phenology offer a robust framework for understanding complex population dynamics.
  • The timing of population emergence significantly shapes ecological outcomes, including stability and the presence of Allee effects.
  • This research highlights the potential for rich and unpredictable population dynamics arising from simple density-dependent mechanisms.