This article proposes a stochastic growth model that starts as a Yule process and is subsequently joined with a Prendiville process when the population attains certain prescribed critical size. In other words, the model assumes exponential growth in an early stage and logistic growth later on to reflect growth retardation caused by overcrowding. In the case that the population starts with a single unit, closed form expressions are given for the distribution of the population size and for the mean and variance functions of the process. Numerical solutions are briefly discussed for the process that starts with more than one unit.
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