Raising Leslie matrices to powers: a method and applications to demography
Article
Revised:
- 71 Downloads
- 1 Citations
Abstract
An illustrative method, labelled Strip and Mask, to raise a Leslie matrix to powers is introduced. Starting from a recent article in this journal, the Strip and Mask method is utilized to determine the primitivity pattern of a Leslie matrix, and to discuss some properties of the corresponding population model.
Key words
Matrix powers Leslie matrix Index of primitivity Convergence Stable age distributionPreview
Unable to display preview. Download preview PDF.
References
- Goodman, L. A.: On the reconciliation of mathematical theories of population growth. J. Roy. Stat. Soc. A 130, 541–554 (1967)Google Scholar
- Lefkovich, L. P.: Some comments on the invariants of population growth. In: Statistical ecology, Vol. 2 (Patil, G. P., Pielou, E. C., Waters, W. E., eds.), pp. 337–360. Pennsylvania State University Press, Philadelphia, 1971Google Scholar
- Leslie, P. H.: On the use of matrices in certain population mathematics. Biometrika 33, 183–212 (1945)Google Scholar
- Leslie, P. H.: Some further notes on the use of matrices in population mathematics. Biometrika 35, 213–245 (1948).Google Scholar
- Pollard, J. H.: Mathematical models for the growth of human populations. New York: Cambridge Univ. Press 1973Google Scholar
- Sykes, Z. M.: On discrete stable population theory. Biometrics 25, 285–293 (1969).Google Scholar
- Tuljapurkar, S. D.: Primitivity and convergence to stability. J. Math. Biol. 13, 241–246 (1981)Google Scholar
- Usher, M. B.: Development in the Leslie matrix model. In: Mathematical models in ecology (J. N. R. Jeffers, ed.), ph. 29–60. Oxford-London-Edinburgh-Melbourne: Blackwell 1972Google Scholar
- Williamson, M. H.: Some extensions of the use of matrices in population theory. Bull. Math. Biophysics 21, 13–17 (1959)Google Scholar
Copyright information
© Springer-Verlag 1983