Critical habitat size of organisms diffusing with stochastic resetting

Area of Science:

• Ecology
• Population Dynamics
• Mathematical Biology

Background:

• Population persistence relies on critical patch size, the minimum habitat area for survival.
• Traditional models often assume simple diffusive movement, neglecting complex behaviors.
• Understanding how additional movement patterns affect habitat needs is crucial for ecological insights.

Purpose of the Study:

• To investigate the impact of stochastic resetting on critical patch size.
• To model behaviors like homing, refuge-seeking, or resource-seeking using stochastic resetting.
• To analytically derive population growth and critical patch size under these conditions.

Main Methods:

• Analytical derivation of population growth and critical patch size.
• Agent-based simulations to validate theoretical results.
• Analysis of how reset rate, position, and environmental hostility influence outcomes.

Main Results:

• Stochastic resetting significantly affects critical patch size.
• The impact of resetting on critical patch size can be either an increase or a decrease.
• Outcomes depend on specific parameters: reset rate, reset position, and environmental hostility.

Conclusions:

• Intermittent relocation, modeled by stochastic resetting, shapes ecological thresholds.
• Findings offer insights for ecological modeling and conservation planning in fragmented landscapes.
• This research highlights the importance of incorporating complex movement behaviors into ecological studies.