A study of some diffusion models of population growth.

The stochastic differential equations of many diffusion processes which arise in studies of population growth in random environments can be transformed, if the Stratonovich stochastic calculus is employed, to the equation of the Wiener process. If the transformation function has certain properties then the transition probability density function and quantities relating to the time to first attain a given population size can be obtained from the known results for the Wiener process. Some other random growth processes can be derived from the Omstein-Uhlenbeck process. These transformation methods are applied to the random processes of Malthusian growth, Pearl-Verhulst logistic growth and a recent model of density independent growth due to Levins.