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On a population model with density dependence and Allee effect.

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This study explores a discrete population model combining Beverton-Holt and Ricker maps, revealing complex dynamics and the Allee effect. The research demonstrates a transition from extinction to complex behaviors, with high complexity leading to near-certain extinction.

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Area of Science:

  • Population Dynamics
  • Mathematical Ecology
  • Discrete Dynamical Systems

Background:

  • Ecological models often simplify population dynamics.
  • Understanding transitions between simple and complex dynamics is crucial.
  • The Allee effect significantly impacts population viability.

Purpose of the Study:

  • To investigate the dynamics of a discrete population model.
  • To analyze the interplay between pre-adult (Beverton-Holt) and adult (Ricker) stages.
  • To explore the influence of the Allee effect on population persistence and extinction.

Main Methods:

  • Development of a discrete dynamical model combining Beverton-Holt and Ricker maps.
  • Analysis of the model's phase space and bifurcation behavior.
  • Investigation of conditions leading to simple (extinction) and complex population dynamics.

Main Results:

  • The combined model exhibits the Allee effect.
  • The model demonstrates a transition from deterministic extinction to complex dynamics.
  • High levels of dynamical complexity are associated with almost sure extinction.

Conclusions:

  • Discrete models integrating different life stages can yield rich population dynamics.
  • The Allee effect plays a critical role in population persistence under complex dynamics.
  • Understanding these dynamics is key for predicting population fate, especially under environmental pressures.