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Méndez V, Assaf M, Horsthemke W, et al. Stochastic foundations in nonlinear density-regulation growth. Phys Rev E. 2017;96(2):022147doi: 10.1103/PhysRevE.96.022147.
Méndez, V., Assaf, M., Horsthemke, W., & Campos, D. (2017). Stochastic foundations in nonlinear density-regulation growth. Physical review. E, 96(2), 022147. https://doi.org/10.1103/PhysRevE.96.022147
Méndez, Vicenç, et al. "Stochastic foundations in nonlinear density-regulation growth." Physical review. E vol. 96,2 (2017): 022147. doi: https://doi.org/10.1103/PhysRevE.96.022147
Méndez V, Assaf M, Horsthemke W, Campos D. Stochastic foundations in nonlinear density-regulation growth. Phys Rev E. 2017 Aug;96(2):022147. doi: 10.1103/PhysRevE.96.022147. Epub 2017 Aug 24. PMID: 28950645.
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Phys Rev E. 2017 Aug;96(2):022147. doi: 10.1103/PhysRevE.96.022147. Epub 2017 Aug 24.

Stochastic foundations in nonlinear density-regulation growth.

Physical review. E

Vicenç Méndez, Michael Assaf, Werner Horsthemke, Daniel Campos

Affiliations

  1. Grup de Física Estadística, Departament de Física, Facultat de Ciències, Edifici Cc, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain.
  2. Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
  3. Department of Chemistry, Southern Methodist University, Dallas, Texas 75275-0314, USA.

PMID: 28950645 DOI: 10.1103/PhysRevE.96.022147

Abstract

In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We also study the effect of internal fluctuations on the long-time dynamics for the different models that have been widely used in the literature, such as the theta-logistic and Savageau models. In particular, we determine the conditions for population extinction and calculate the mean time to extinction. If the population does not become extinct, we obtain analytical expressions for the population abundance distribution. Our theoretical results are based on WKB theory and the probability generating function formalism and are verified by numerical simulations.

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