Asymptotic properties of infinite Leslie matrices

The stable population theory is classically applicable to populations in which there is a maximum age after which individuals die. Demetrius [1972. On an infinite population matrix. Math. Biosci. 13, 133–137] extended this theory to infinite Leslie matrices, in which the longevity of individuals is...

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Veröffentlicht in:	Journal of theoretical biology 2009-01, Vol.256 (2), p.157-163
Hauptverfasser:	Gosselin, Frédéric, Lebreton, Jean-Dominique
Format:	Artikel
Sprache:	eng
Schlagworte:	Age Distribution Demography Dynamical Systems Environmental Sciences Humanities and Social Sciences Humans Infinite matrix Leslie matrix Longevity Mathematics Models, Biological Population Growth Reproduction Senescence Stable population theory Survival Rate Usher matrix
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Beschreibung
Zusammenfassung:	The stable population theory is classically applicable to populations in which there is a maximum age after which individuals die. Demetrius [1972. On an infinite population matrix. Math. Biosci. 13, 133–137] extended this theory to infinite Leslie matrices, in which the longevity of individuals is potentially infinite. However, Demetrius had to assume that the survival probability per time step tends to 0 with age. We generalise here the conditions of application of the stable population theory to infinite Leslie matrix models and apply these results to two examples, including or not senescence.
ISSN:	0022-5193 1095-8541
DOI:	10.1016/j.jtbi.2008.09.018