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Updated: Oct 15, 2025

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
Published on: July 30, 2019
Path-integral solution of MacArthur's resource-competition model for large ecosystems with random species-resources
A R Batista-Tomás1, Andrea De Martino2, Roberto Mulet1
1Group of Complex Systems and Statistical Physics, Department of Applied Physics, Physics Faculty, University of Havana, La Habana 10400, Cuba.
Abstract:
We solve MacArthur's resource-competition model with random species-resource couplings in the "thermodynamic" limit of infinitely many species and resources using dynamical path integrals à la De Domincis. We analyze how the steady state picture changes upon modifying several parameters, including the degree of heterogeneity of metabolic strategies (encoding the preferences of species) and of maximal resource levels (carrying capacities), and discuss its stability. Ultimately, the scenario obtained by other approaches is recovered by analyzing an effective one-species-one-resource ecosystem that is fully equivalent to the original multi-species one. The technique used here can be applied for the analysis of other model ecosystems related to the version of MacArthur's model considered here.
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