  We introduce the following discrete time model. Each natural number
represents an ecological niche and is assigned a fitness in $(0,1)$. All the
sites are updated simultaneously at every discrete time. At any given time the
environment may be normal with probability $p$ or a catastrophe may occur with
probability $1-p$. If the environment is normal the fitness of each site is
replaced by the maximum of its current fitness and a random number. If there is
a catastrophe the fitness of each site is replaced by a random number. We
compute the joint fitness distribution of any finite number of sites at any
fixed time. We also show convergence of this system to a stationary
distribution. This too is computed explicitly.
