Abstract
Abstract There are two main streams in the mathematical study of populations. The theory of branching processes, in its general formulations, describes the development in time of populations where each member has a random life length and at its death begets a random number of new individuals, or, in physical cases, splits into a random number of new particles. The basic assumptions of the so called stable population theory, on the other side, are often more implicit. But in all formulations of it an important feature is that individuals may give birth not only when they die. Whereas the theory of branching processes is rigorous but with a more limited scope of application (elementary particles, cells, bacteria), stable population theory is a vague but exciting blend of mathematics and intuitive reasoning. Whereas branching processes are stochastic, stable population theory is pseudo-deterministic; only conclusions concerning expectations are arrived at but intuitive probabilistic arguments are often relied upon.
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