Population dynamics in an intermittent refuge

TL;DR

This paper investigates how intermittent refuges affect the long-term survival of populations in heterogeneous environments, providing analytical expressions for minimal refuge size needed for persistence under different temporal regimes.

Contribution

It introduces a model incorporating spatial heterogeneity and temporal refuge variability, deriving conditions for population survival in different time scale limits.

Findings

Derived minimal refuge size for population survival.

Analyzed slow and fast refuge fluctuation regimes.

Provided analytical and numerical insights into population persistence.

Abstract

Population dynamics is constrained by the environment, which needs to obey certain conditions to support population growth. We consider a standard model for the evolution of a single species population density, that includes reproduction, competition for resources and spatial spreading, while subject to an external harmful effect. The habitat is spatially heterogeneous, there existing a refuge where the population can be protected. Temporal variability is introduced by the intermittent character of the refuge. This scenario can apply to a wide range of situations, from a lab setting where bacteria can be protected by a blinking mask from ultraviolet radiation, to large scale ecosystems, like a marine reserve where there can be seasonal fishing prohibitions. Using analytical and numerical tools, we investigate the asymptotic behavior of the total population as a function of the size and characteristic time scales of the refuge. We obtain expressions for the minimal size required for population survival, in the slow and fast time scale limits.