Relating coupled map lattices to integro-difference equations: dispersal-driven instabilities in coupled map lattices

Area of Science:

• Ecological dynamics
• Mathematical modeling
• Population interactions

Background:

• Growing interest in ecological communities regarding populations coupled solely by dispersal.
• Existing models lack sufficient theoretical validation for dispersal-coupled population dynamics.
• Need for theoretical frameworks to understand discrete-time population dynamics influenced by dispersal.

Purpose of the Study:

• To present a theoretical framework for understanding ecological interactions in populations coupled by dispersal.
• To extend discrete-time population models using coupled map lattices (CMLs).
• To derive conditions for dispersal-driven instabilities in these models.

Main Methods:

• Development of a general form for coupled map lattices (CMLs).
• Linking CMLs to integro-difference equations using a redistribution kernel.
• Derivation of general conditions for dispersal-driven instabilities.
• Application of the theory to discrete-time predator-prey and host-pathogen models.

Main Results:

• Established a theoretical basis for analyzing dispersal-coupled populations with discrete time dynamics.
• Identified general conditions under which dispersal can drive population instabilities.
• Demonstrated the applicability of the developed theory to ecological models.

Conclusions:

• The presented theory provides a robust framework for analyzing spatial population dynamics driven by dispersal.
• The findings are applicable to various ecological scenarios, including predator-prey and host-pathogen systems.
• This work bridges the gap between modeling and theory in the study of dispersal-coupled populations.