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Discrete and continuous methods of demography. (English) Zbl 1100.92048

Lenski, Wolfgang (ed.), Logic versus approximation. Essays dedicated to Michael M. Richter on the occasion of his 65th birthday. Berlin: Springer (ISBN 3-540-22562-5/pbk). Lecture Notes in Computer Science 3075, 43-58 (2004).
Summary: A discrete model of population growth in the spirit of Fibonacci’s rabbits, but with arbitrary fixed times for the beginning and the end of fertility and for death is investigated. Working with generating functions for linear recursions we pursue the idea to give asymptotic estimates for the number of existing individuals by means of the powers of one single main root \(z\) of the function’s denominator. The mathematical problem of mortality is easy to handle. While the outlines of such a paradigm are recognizable in the case of perpetual fertility, there remain open problems with the localization of roots on unexpected “bubbles”, if fertility gets lost at a finite time. Therefore, an alternative method of asymptotic approximation via convolution techniques is given.
A generalization of this model to realistic situations with age dependent fertility rates is straightforward. Modern computing techniques admit a convenient survey over the existing roots. In competition with continuous models of demography the results seem to clarify the global influence of the demographic data in the so called stable models of demography. This model is basic for prognostics, when – more general – dynamic changes of the demographic parameters occur.
For the entire collection see [Zbl 1052.68005].

MSC:

92D25 Population dynamics (general)
91D20 Mathematical geography and demography
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