Empirical parameterisation and dynamical analysis of the allometric Rosenzweig-MacArthur equations

Area of Science:

• Ecology
• Theoretical Ecology
• Mathematical Biology

Background:

• Allometric scaling is crucial for understanding ecological patterns across different organism sizes.
• Population dynamics models often require simplification for broad applicability.
• The Rosenzweig-MacArthur model is a foundational predator-prey model.

Purpose of the Study:

• To develop a size-scaled Rosenzweig-MacArthur model that eliminates prey-mass dependency.
• To analytically study the contribution of scaling parameters to species coexistence.
• To reconcile theoretical predictions with empirical observations in metabolic theory.

Main Methods:

• Parameterization of the size-scaled Rosenzweig-MacArthur differential equations.
• Definition of the functional response term based on empirical data.
• Analysis of dynamical properties including equilibria, population cycling, and predator-prey abundance relationships.

Main Results:

• The model accurately represents predator-prey dynamics across 15 orders of magnitude of mass.
• Dynamical properties such as equilibrium distributions and population cycling scale consistently with empirical data.
• The parameterization successfully incorporates scaling parameters' effects on coexistence.

Conclusions:

• The developed allometric model provides a parsimonious yet accurate representation of population dynamics.
• This minimal model advances the analytic study of ecological systems by integrating scaling effects.
• The findings support the utility of allometric approaches in ecology for understanding system-level effects.