  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.
