Collective Evolution Under Catastrophes.

We introduce the following discrete time model. Each site of N 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. [ABSTRACT FROM AUTHOR]