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Predator-prey models with component Allee effect for predator reproduction.

Alan J Terry1

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Summary

This study extends Allee effect definitions to predator-prey models, revealing predator extinction risks with small populations. It also explores coexistence dynamics and implications for pest control strategies.

Keywords:
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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • The Allee effect describes reduced per capita growth rates at low population densities.
  • Extending Allee effect definitions from single-species to predator-prey models presents challenges.
  • Understanding these dynamics is crucial for ecological management and conservation.

Purpose of the Study:

  • To extend the definitions of component and demographic Allee effects to predator-prey models.
  • To analyze four distinct predator-prey models incorporating a component Allee effect on predator reproduction.
  • To investigate the conditions for predator extinction, coexistence, and population cycles.

Main Methods:

  • Numerical simulations were used to analyze predator-prey models.
  • Analytical methods were employed to examine model stability and equilibrium points.
  • The study explored model behavior under fixed and variable prey population assumptions.

Main Results:

  • Predator extinction is a stable fixed point, occurring with small initial predator or prey populations.
  • Coexistence fixed points and stable limit cycles were identified through simulations.
  • Analytical conditions for coexistence trapping regions were derived for three models.

Conclusions:

  • Customary Allee effect definitions require careful extension for predator-prey systems.
  • Small initial populations can lead to predator extinction, impacting ecological balance.
  • Findings have implications for biological pest control and understanding population resurgences.