Finding analytical approximations for discrete, stochastic, individual-based models of ecology

Area of Science:

• Ecological modeling
• Theoretical ecology
• Mathematical biology

Background:

• Spatially explicit individual-based models (IBMs) are crucial for understanding population dynamics.
• Approximating complex IBMs with simpler 'top-down' models remains a significant challenge in ecology.
• Understanding the relationship between individual-level interactions and emergent population-level dynamics is key.

Purpose of the Study:

• To develop and validate new analytical approximations for spatially explicit individual-based models with contest competition.
• To investigate how individual-based interactions and dispersal influence large-scale population dynamics and stability.
• To bridge the gap between 'bottom-up' individual-based approaches and 'top-down' macroscopic models.

Main Methods:

• Simulations of spatially explicit individual-based models with contest competition.
• Characterization of population oscillations using spatial correlation analysis.
• Development of two novel approximation methods: one based on local interactions and another for long-range interactions.
• Calculation of extinction probabilities and analysis of model convergence.

Main Results:

• The individual-based model exhibits large-scale discrete population oscillations.
• Dispersal was found to stabilize population dynamics.
• The developed approximations successfully capture demographic stochasticity and emergent dynamics.
• Convergence was demonstrated between local and global approximations under specific conditions.

Conclusions:

• New analytical approximations provide a deeper understanding of complex spatial population dynamics.
• Dispersal plays a critical role in stabilizing ecological systems modeled by individual-based approaches.
• The study offers a framework for linking individual behavior to population-level phenomena in spatially extended systems.