Many-body perturbation theory and fluctuation relations for interacting population dynamics

Area of Science:

• Ecology
• Mathematical Biology
• Statistical Physics

Background:

• Population dynamics models explain organism adaptation to environments.
• Existing models often lack organism interactions, crucial for collective phenomena.
• Recent work showed fluctuation relations for organism fitness in general settings.

Purpose of the Study:

• To propose and analyze interacting models for population dynamics.
• To incorporate inter-organism interactions into ecological modeling.
• To derive a variational principle and fluctuation relations for interacting populations.

Main Methods:

• Development of novel interacting population dynamics models.
• Application of perturbative theory to analyze these models.
• Derivation of a variational principle and fluctuation relations.

Main Results:

• Successfully formulated interacting models for population dynamics.
• Established a perturbative theory for these interacting systems.
• Derived key variational principles and fluctuation relations.

Conclusions:

• Interacting models provide a more comprehensive framework for population dynamics.
• The derived fluctuation relations offer new insights into ecological systems.
• This work bridges concepts from statistical physics and population ecology.