  Cellular automata are widely used to model real-world dynamics. We show using
the Domany-Kinzel probabilistic cellular automata that alternating two
supercritical dynamics can result in subcritical dynamics in which the
population dies out. The analysis of the original and reduced models reveals
generality of this paradoxical behavior, which suggests that autonomous or
man-made periodic or random environmental changes can cause extinction in
otherwise safe population dynamics. Our model also realizes another scenario
for the Parrondo's paradox to occur, namely, spatial extensions.
