On Certain Functions Useful in Population Evolution Studies

Spinrad, B.I. (1979). On Certain Functions Useful in Population Evolution Studies. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-79-010

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The problem of the size of a cell population, descendant from a single cell or a small group of cells, each of which is subject to the alternative fates of death or division into two new cells, is a prototype problem for a number of different types of population models. I first came across it while studying models for the penetration of mutations into a population, for example. At that time, about 20 years ago I could not find an exact solution in the literature available to me, although asymptotic properties were well known.

I recently reviewed the problem, primarily as a mathematical recreation. In so doing, I blundered into the solution. I do not know whether it has been published, either before 1958 or by 1978. This memorandum may be useful to researchers dealing with the problem or with its analysis. I write it partly for its potential value as a collection, in one place, of properties of the solutions of the stated problem. However, I must also admit that, to a certain extent, it is written to illustrate that scientific research is much more often dominated by heuristics and serendipity than by pure logical inference.

Item Type: Monograph (IIASA Working Paper)
Research Programs: Energy Program (ENP)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 01:46
Last Modified: 27 Aug 2021 17:09
URI: https://pure.iiasa.ac.at/1173

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