Applications of Perron-Frobenius Theory to Population Dynamics

Details Applications of Perron-Frobenius Theory to Population Dynamics Applications of Perron-Frobenius Theory to Population Dynamics

2001-09-02

arxiv.org/abs/math/0109008v1

Mathematics

Rings and Algebras

Also math demography

Scientific paper

By the use of Perron-Frobenius theory, simple proofs are given of the Fundamental Theorem of Demography and of a theorem of Cushing and Yicang on the net reproductive rate occurring in matrix models of population dynamics. The latter result is further refined with some additional nonnegative matrix theory. When the fertility matrix is scaled by the net reproductive rate, the growth rate of the model is 1. More generally, we show how to achieve a given growth rate for the model by scaling the fertility matrix. Demographic interpretations of the results are given.

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