Collective behavior under catastrophes
Probability
2022-11-03 v1
Abstract
We introduce the following discrete time model. Each natural number represents an ecological niche and is assigned a fitness in . All the sites are updated simultaneously at every discrete time. At any given time the environment may be normal with probability or a catastrophe may occur with probability . 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.
Cite
@article{arxiv.2211.00751,
title = {Collective behavior under catastrophes},
author = {Rinaldo B. Schinazi},
journal= {arXiv preprint arXiv:2211.00751},
year = {2022}
}