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

Jody C McKerral1, Maria Kleshnina2, Vladimir Ejov1

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This study presents an allometric population dynamics model that accurately describes predator-prey interactions across vast size ranges. The model simplifies complex ecological dynamics, offering insights into species coexistence and population cycles.

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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.