Bounded environmental stochasticity generates secondary Allee thresholds

Area of Science:

• Ecology
• Population Dynamics
• Mathematical Biology

Background:

• The Allee effect describes a critical population density below which extinction is probable.
• Classical models often assume normal environmental variation, predicting inevitable extinction.
• Realistic environmental fluctuations are bounded and not always normally distributed.

Purpose of the Study:

• To analyze population dynamics under Allee effects with bounded environmental fluctuations.
• To investigate the impact of realistic environmental variation on population persistence.
• To develop more accurate models for conservation and management.

Main Methods:

• Utilized piecewise deterministic Markov models (PDMPs).
• Incorporated finite-state Markov chains for environmental dynamics.
• Analyzed population persistence through threshold densities and stochastic bistability.

Main Results:

• Identified two threshold densities: one for deterministic extinction, one for deterministic persistence.
• Demonstrated stochastic bistability at intermediate densities, with probabilities of extinction or persistence.
• Found persistence impossible when carrying capacity in one environment falls below the Allee threshold in another.

Conclusions:

• Bounded environmental fluctuations significantly alter population persistence predictions compared to classical models.
• Realistic environmental modeling is crucial for accurate conservation and management strategies.
• Non-monotonic effects of environment on growth rates can lead to persistence challenges.