Large deviations of a random walk model with emerging territories

Area of Science:

• Complex systems
• Theoretical ecology
• Statistical physics

Background:

• Understanding spatial dynamics and resource competition is crucial in ecology.
• Agent-based models (ABMs) offer a powerful framework for simulating complex biological interactions.
• Territory formation and evasion are fundamental behaviors influencing species distribution and survival.

Purpose of the Study:

• To investigate the distribution of territory sizes in a one-dimensional agent-based model.
• To explore the occurrence and characteristics of atypically small and large territories.
• To identify potential large deviation principles governing these territory size distributions.

Main Methods:

• Development and simulation of a one-dimensional agent-based model for territory marking and evasion.
• Application of sophisticated sampling techniques to analyze territory size distributions.
• Statistical analysis of the rate function for the right tail of the distribution.

Main Results:

• Hints supporting the validity of a large deviation principle for territory sizes were observed.
• The shape of the rate function for the extreme right tail of the distribution was characterized.
• Insights into the structural properties of atypical territory realizations were gained.

Conclusions:

• The study suggests that territory size distributions may follow a large deviation principle.
• Atypical territory sizes, though rare, exhibit specific structural characteristics.
• Further research can refine the understanding of these principles in ecological contexts.