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We solve MacArthur's resource-competition model with random species-resourcecouplings in the `thermodynamic' limit of infinitely many species and resourcesusing dynamical path-integrals a la De Domincis. We analyze how the steadystate picture changes upon modifying several parameters, including the degreeof heterogeneity of metabolic strategies (encoding the preferences of species)and of maximal resource levels (carrying capacities), and discuss itsstability. Ultimately, the scenario obtained by other approaches is recoveredby analyzing an effective one-species-one-resource ecosystem that is fullyequivalent to the original multi-species one. The technique used here can beapplied for the analysis of other model ecosystems related to the version ofMacArthur's model considered here.

Path-integral solution of MacArthur's resource-competition model for large ecosystems with random species-resources couplings