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Ziebur's matrix equation for population growth

Published online by Cambridge University Press:  17 February 2009

A. Brown
A. Brown
Affiliation:
Department of Theoretical Physics, Research School of Physical Sciences, Australian National University, G.P.O. Box 4, Canberra, A.C.T. 2601
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Abstract

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The paper examines a matrix equation given by Ziebur [6] for the growth of a population in which the birth-rate and death-rate are age-dependent. For convenience the population was sub-divided into four age groups, with the same birth-rate and death-rate for individuals in a particular group, and the matrix equation relates the numbers in each sub-division in consecutive years. This avoids delay terms and makes it easier to modify the growth equation but it is shown that the form suggested by Ziebur for the transition matrix leads to some difficulties.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 2 , October 1986 , pp. 220 - 228
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Lefkovitch, L.P., “The study of population growht in organisms grouped by stages” Biometrics 21 (1965), 1–18.CrossRefGoogle Scholar
[2]Leslie, P.H., “On the use of matrices in certain population mathematics” Biometrika 33 (1945), 183–212.CrossRefGoogle ScholarPubMed
[3]Leslie, P.H., “Some further notes on the use of matrices in population mathematics” Biometrika 35 (1948), 213–245.CrossRefGoogle Scholar
[4]Pielou, E.C., An introduction to mathematical ecology (Wiley, New York, 1969), 33–42.Google Scholar
[5]Peilou, M.H., The analysis of biological populations (Arnold, London, 1972), 21–26.Google Scholar
[6]Ziebur, A.D., “Age-dependent models of population growth” Theoret. Population Biol. 26 (1984), 315–319.CrossRefGoogle ScholarPubMed