Impact of environmental colored noise in single-species population dynamics

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.

10 pages, 3 figures

References in corpus (7)

• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Demographic noise can reverse the direction of deterministic selection
• Extinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach
• Fixation in finite populations evolving in fluctuating environments
• Species coexistence in a neutral dynamics with environmental noise
• Stochasticity enhances the gaining of bet-hedging strategies in contact-process-like dynamics
• Stability of two-species communities: drift, environmental stochasticity, storage effect and selection

Cited by in corpus (4)

• Stochastic spatial models in ecology: a statistical physics approach
• A comprehensive phase diagram for logistic populations in fluctuating environment
• Mitigation of rare events in multistable systems driven by correlated noise
• Fluctuating Environments Favor Extreme Reproductive Delays and Penalize Intermediate Ones