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Impact of environmental colored noise in single-species population dynamics

Tommaso Spanio, Jorge Hidalgo, and Miguel A. Muñoz
Phys. Rev. E 96, 042301 – Published 2 October 2017

Abstract

Variability on external conditions has important consequences for the dynamics and the organization of biological systems. In many cases, the characteristic timescale of environmental changes as well as their correlations play a fundamental role in the way living systems adapt and respond to it. A proper mathematical approach to understand population dynamics, thus, requires approaches more refined than, e.g., simple white-noise approximations. To shed further light onto this problem, in this paper we propose a unifying framework based on different analytical and numerical tools available to deal with “colored” environmental noise. In particular, we employ a “unified colored noise approximation” to map the original problem into an effective one with white noise, and then we apply a standard path integral approach to gain analytical understanding. For the sake of specificity, we present our approach using as a guideline a variation of the contact process—which can also be seen as a birth-death process of the Malthus-Verhulst class—where the propagation or birth rate varies stochastically in time. Our approach allows us to tackle in a systematic manner some of the relevant questions concerning population dynamics under environmental variability, such as determining the stationary population density, establishing the conditions under which a population may become extinct, and estimating extinction times. We focus on the emerging phase diagram and its possible phase transitions, underlying how these are affected by the presence of environmental noise time-correlations.

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  • Received 12 July 2017

DOI:https://doi.org/10.1103/PhysRevE.96.042301

©2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsPhysics of Living SystemsInterdisciplinary Physics

Authors & Affiliations

Tommaso Spanio1,2, Jorge Hidalgo2,*, and Miguel A. Muñoz1

  • 1Instituto Carlos I de Física Teórica y Computacional and Departamento Electromagnetismo y Física de la Materia, Universidad de Granada, 18071 Granada, Spain
  • 2Dipartimento di Fisica “G. Galilei” and CNISM, INFN, Università di Padova, Via Marzolo 8, 35131 Padova, Italy

  • *hidalgo@pd.infn.it

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Issue

Vol. 96, Iss. 4 — October 2017

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