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Feasibility in MacArthur’s consumer-resource model

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Abstract

Finding the conditions that ensure the survival of species has occupied ecologists for decades. Theoretically, for mechanistic models such as MacArthur’s consumer-resource model, most of the efforts have concentrated on proving the stability of an equilibrium assuming that it is feasible, but overlooking the conditions that ensure its feasibility. Here, we address this gap by finding the range of conditions that lead to a feasible equilibrium of MacArthur’s consumer-resource model, where species competition is mediated by their consumption of similar resources, and study how changes in the system’s structural and parametric properties affect those ranges for communities of any size. We characterize the relationship between the loss of feasibility and the increase in complexity (measured by the system’s richness and connectance) by a power law that can be extended to random competition matrices. Focusing on the pool of consumers, we find that while the feasibility of the entire system decreases with the size of the pool, the expected fraction of feasible consumers increases—safety in consumer numbers. Focusing on the pool of resources, we find that if resources grow linearly, the larger the pool of resources, the lower the feasibility of the system and the expected fraction of feasible consumers—danger in resource numbers. However, if resources grow logistically, this pattern is reversed with a sublinear increase in feasibility, as it has been previously reported in experimental work. This work provides testable predictions for consumer-resource systems and is a gateway to exploring feasibility in other mechanistic models.

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Data availability

Empirical data were not used for this research.

Code availability

The code for this work is provided and will remain available via the following link: https://github.com/andrea-aparicio/FeasibilityCRM.

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Funding

Y.Y.L. acknowledges the funding support from National Institutes of Health (R01AI141529, R01HD093761, RF1AG067744, UH3OD023268, U19AI095219, and U01HL089856). A.A. acknowledges the support from National Institutes of Health (T32HL742742).

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Authors and Affiliations

  1. Channing Division of Network Medicine, Department of Medicine, Brigham and Women’s Hospital and Harvard Medical School, Boston, MA, 02115, USA

    Andrea Aparicio, Tong Wang & Yang-Yu Liu

  2. Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Serguei Saavedra

  3. Center for Artificial Intelligence and Modeling, The Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Champaign, IL, 61801, USA

    Yang-Yu Liu

Authors
  1. Andrea Aparicio
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  2. Tong Wang
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  3. Serguei Saavedra
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  4. Yang-Yu Liu
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Contributions

A.A. and Y.Y.L. conceived and designed the project; A.A. did the simulations; all authors analyzed and interpreted the data; A.A. wrote the manuscript with the help of T.W.; all authors revised the manuscript.

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Correspondence to Yang-Yu Liu.

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Aparicio, A., Wang, T., Saavedra, S. et al. Feasibility in MacArthur’s consumer-resource model. Theor Ecol 16, 225–238 (2023). https://doi.org/10.1007/s12080-023-00566-0

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