Population switching under a time-varying environment

Abstract

We examine the switching dynamics of a stochastic population subjected to a deterministically time-varying environment. Our approach is demonstrated in the realm of ecology on a problem of population establishment. Here, by assuming a constant immigration pressure along with a strong Allee effect, at the deterministic level one obtains a critical population size beyond which the system experiences establishment. Notably the latter has been shown to be strongly influenced by the interplay between demographic and environmental noise. We consider two prototypical examples for environmental variations: a temporary environmental change, and a periodically-varying environment. By employing a semi-classical approximation we compute, within exponential accuracy, the change in the establishment probability and mean establishment time of the population, due to the environmental variability. Our analytical results are verified by using a modified Gillespie algorithm which accounts for explicitly time-dependent reaction rates. Finally, our theoretical approach can also be useful in studying switching dynamics in gene regulatory networks under extrinsic variations.

9 pages, 8 figures

References in corpus (8)

• Analytical distributions for stochastic gene expression
• Extinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach
• Exponential sensitivity of noise-driven switching in genetic networks
• Demographic stochasticity and extinction in populations with Allee effect
• Persistence of instanton connections in chemical reactions with time dependent rates
• Population Extinction under Bursty Reproduction in a Time Modulated Environment
• Time Distribution for Persistent Viral Infection
• Reducing the extinction risk of stochastic populations via non-demographic noise

Cited by in corpus (4)

• First detection of threshold crossing events under intermittent sensing
• Extremal statistics for first-passage trajectories of drifted Brownian motion under stochastic resetting
• Epidemic extinction in a simplicial susceptible-infected-susceptible model
• Reconstructing an epigenetic landscape using a genetic `pulling' approach