Growth and Extinction in Randomly Varying Environments: Modelling and Optimization Using Stochastic Differential Equations

Abstract

This paper presents a brief overview of a range of applications of stochastic differential equations (SDE) in describing the growth of wildlife populations living in randomly varying environments and the associated risks of extinction, including profit optimization issues in the particular case of fish or other populations subjected to harvesting. The same basic ideas apply also to the growth of individual animals and how to optimize the profit of the farmers that raise such animals.