Allee Effects Plus Noise Induce Population Dynamics Resembling Binary Markov Highs and Lows

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Allee effects describe how reduced per capita growth rates at low population densities can hinder population recovery.
• Environmental and demographic noise are crucial factors influencing population dynamics, often leading to unpredictable fluctuations.

Purpose of the Study:

• To introduce a novel, flexible deterministic model for attenuated Allee effects.
• To investigate the impact of incorporating environmental and demographic noise into this model.
• To analyze the resulting stochastic population dynamics and their characteristics.

Main Methods:

• Development of a new deterministic model for attenuated Allee effects, bridging logistic and standard Allee models.
• Incorporation of environmental and demographic noise into the model.
• Solution of the resulting Kolmogorov forward equation to analyze population state distributions.
• Simulation of sample paths to observe population dynamics over time.

Main Results:

• The model demonstrates a dichotomous distribution of residence times, with populations frequently occupying high (near saturation) and low states.
• Attenuated Allee effects and noise together drive alternating, sustained periods of low and high population levels.
• Transition times between population states are approximately exponentially distributed, suggesting an approximately Markovian process.

Conclusions:

• The combination of attenuated Allee effects and noise generates complex population dynamics characterized by alternating low and high density phases.
• The developed model provides a flexible framework for studying these phenomena.
• The findings highlight the importance of considering both density-dependent effects and stochasticity in population ecology.