Discrete Stochastic Models

Abstract

In the deterministic and stochastic models of the previous chapters, population size was treated as a continuous variable. But animals come in discrete units. For large populations, a continuous variable may be a reasonable approximation; a model which predicts a population size of 11,924.38 is not much different from one that predicts a population of 11,924. But in small populations the difference may be important; a prediction of 5 animals is more reasonable than a prediction of 5.42. This is especially true when one considers the question of extinction, where the dynamics of small populations are of fundamental interest. A more realistic model should consider population size as a discrete variable restricted to the nonnegative integers.