Dynamical Ising model of spatially coupled ecological oscillators

Area of Science:

• Ecology
• Statistical Physics
• Complex Systems

Background:

• Long-range synchrony often emerges from short-range interactions in biological and physical systems.
• Many biological systems exhibiting synchrony belong to the Ising universality class, allowing simple models to replicate static spatial properties.
• While static properties are understood, the dynamics of these systems are often of greater interest.

Purpose of the Study:

• To investigate if a dynamical Ising model can accurately represent universal and non-universal features of ecological systems.
• To use noisy coupled metapopulation models with two-cycle dynamics as a case study for dynamical modeling.
• To assess the correspondence between ecological dynamics and a modified Ising model that incorporates memory.

Main Methods:

• Developed an Ising model with memory to account for the tendency of local dynamics to maintain their oscillation phase.
• Fitted the two parameters of the Ising model with memory to simulated ecological dynamics.
• Assessed model correspondence by comparing critical boundary locations, local phase change probabilities, and predictive capabilities.

Main Results:

• The Ising model with memory demonstrated a reasonable ability to represent key properties of ecological metapopulations.
• The model successfully captured aspects of synchrony, dynamics, and phase changes.
• The critical boundary between synchronous and asynchronous dynamics was well-represented.

Conclusions:

• The Ising model with memory provides a valuable tool for understanding the dynamics of complex biological systems, particularly ecological ones.
• The correspondence suggests that the Ising universality class can be extended to model dynamic ecological processes.
• This research opens avenues for using simplified models to gain deeper insights into biological synchrony and spatial patterns.