Leibovich2022 - multispecies eco-competition describes by Master equation

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We are using a minimal model of interacting multispecies ecological communities that incorporates competition, immigration, and demographic noise. Importantly, the dynamics of the system are described by a birth-death process with interactions, whereby the abundance (the number of individuals) of any species is discrete, where the number of individuals from a given species increases or decreases by one following given birth or death rates (respectively). We find rich behavior with many unexpected regimes. We apply the insights and implications of our model to the range of behaviors observed experimentally in different ecosystems—from bacteria to the immune system. This repository stores the code used to study the population dynamics described in the PNAS publication: Phenomenology and Dynamics of Competitive Ecosystems Beyond the Niche-Neutral Regimes by Nava Leibovich, Jeremy Rothschild, Sidhartha Goyal and Anton Zilman. See more at (https://github.com/jbRothschild/project-abundance/tree/PNAS)
Python (3.6)
Related Publication
  • Phenomenology and dynamics of competitive ecosystems beyond the niche-neutral regimes.
  • Leibovich N, Rothschild J, Goyal S, Zilman A
  • Proceedings of the National Academy of Sciences of the United States of America , 10/ 2022 , Volume 119 , Issue 43 , pages: e2204394119 , PubMed ID: 36251996
  • Department of Physics, University of Toronto, Toronto, ON M5S 1A7, Canada.
  • Structure, composition, and stability of ecological populations are shaped by the inter- and intraspecies interactions within their communities. It remains to be fully understood how the interplay of these interactions with other factors, such as immigration, controls the structure, the diversity, and the long-term stability of ecological systems in the presence of noise and fluctuations. We address this problem using a minimal model of interacting multispecies ecological communities that incorporates competition, immigration, and demographic noise. We find that a complete phase diagram exhibits rich behavior with multiple regimes that go beyond the classical "niche" and "neutral" regimes, extending and modifying the "rare biosphere" or "niche-like" dichotomy. In particular, we observe regimes that cannot be characterized as either niche or neutral where a multimodal species abundance distribution is observed. We characterize the transitions between the different regimes and show how these arise from the underlying kinetics of the species turnover, extinction, and invasion. Our model serves as a minimal null model of noisy competitive ecological systems, against which more complex models that include factors such as mutations and environmental noise can be compared.
Submitter of the first revision: Nava leibovich
Submitter of this revision: Nava leibovich
Modellers: Nava leibovich

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Model files

gillespie.py run the Gillespie algorithm 13.10 KB Preview | Download

Additional files

gillespie_models.py Gillespie model function 29.50 KB Preview | Download
settings.py setting of model 2.83 KB Preview | Download
theory_equations.py theory equation functions 70.64 KB Preview | Download

  • Model originally submitted by : Nava leibovich
  • Submitted: Dec 8, 2022 3:36:52 PM
  • Last Modified: Dec 8, 2022 3:36:52 PM
  • Version: 1 public model Download this version
    • Submitted on: Dec 8, 2022 3:36:52 PM
    • Submitted by: Nava leibovich
    • With comment: Import of Leibovich2022 - multispecies eco-competition describes by Master equation