An equation describing the dynamics of single species populations is derived. The model allows for variations in the physiological characteristics of animals of different ages and sizes. An analytical solution which holds under certain specific conditions is found. It is shown that Von Foerster's equation, the logistic equation and other prior models are special cases of the new model.

A partial differential equation which describes the dynamics of a single species population for animals reproducing by fission is set forth. The equation is then applied to Dugesia tigrina. Whenever possible, experimental results are used to determine pertinent parameters. Tests are performed to determine those parameters upon which the model has a critical dependence. The model gives results which are qualitatively in agreement with empirical populations.

Partial differential equations which describe the dynamics of single species populations are applied to Daphnia pulex. Whenever possible, experimental results are used to determine pertinent parameters. Tests are performed to find parameters upon which the model has a critical dependence. The model gives results which are qualitatively in agreement with empirical populations.