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.

Controlling the Mean Time to Extinction in Populations of Bacteria

“…At the same time, these systems are exposed to changing environments, including periodic changes, such as seasonal variations and daily changes in sunlight and darkness, and random changes, such as outbreaks of diseases, catastrophes, and climate variations. In the last decade, much activity has been invested in studying the interplay of demographic and external fluctuations and their impacts on the temporary or final fate of the respective systems [1][2][3][4][5][6][7][8][9]. Population dynamics under environmental conditions, which are frequently or even continually switching between favorable and adverse conditions, were previously studied in [1,2] in a population of two strains, one growing slightly faster than the other, particularly their fixation (one strain takes over the population) properties.…”

“…In a similar system with two strains and a randomly switching carrying capacity, the correlations between the population size and its composition were determined, particularly for conditions under which a public good produced by one of the strains is beneficial [3]. The authors of [6] focused on the establishment probability of a population and the mean time for establishment in a time-varying environment. Finally, the impact of demographic and environmental fluctuations on the mean time to extinction (MTE) was studied in a stochastic branching-annihilation process in a time-modulated environment in [7], in populations consisting of two phenotypes of bacteria in [8], and more recently, for two species interacting via competition in [9].…”

Extrinsic noise effects on ribosomal traffic during the translation process

“…Specifically, like any cellular process, the three stages of translation are stochastic in nature and in the context of the translation process account for IN. However, the rates of the three stages can themselves be stochastically fluctuating, which has its basis in EN [36,38,46]. In fact, despite a lot of interest and activity in theoretical and computational studies on this aspect of the central dogma, the role of EN on mRNA translation has been barely studied.…”

Extrinsic noise acts to lower protein production at higher translation initiation rates

“…Specifically, like any cellular process, the three stages of translation are stochastic in nature and in the context of the translation process account for intrinsic noise. However, the rates of the three stages can themselves be stochastically fluctuating, which has its basis in extrinsic noise (EN) [36,38,41].…”