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Ergodicity of age structure in populations with Markovian vital rates, III: Finite-state moments and growth rate; an illustration

Published online by Cambridge University Press:  01 July 2016

Joel E. Cohen
Joel E. Cohen*
Affiliation:
The Rockefeller University, New York
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Abstract

Leslie (1945) models the evolution in discrete time of a closed, single-sex population with discrete age groups by multiplying a vector describing the age structure by a matrix containing the birth and death rates. We suppose that successive matrices are chosen according to a Markov chain from a finite set of matrices. We find exactly the long-run rate of growth and expected age structure. We give two approximations to the variance in age structure and total population size. A numerical example illustrates the ergodic features of the model using Monte Carlo simulation, finds the invariant distribution of age structure from a linear integral equation, and calculates the moments derived here.

Keywords

ERGODIC SETSLESLIE MATRICESNON-NEGATIVE MATRICESPOPULATION DYNAMICSPRODUCTS OF RANDOM MATRICESSTOCHASTIC POPULATION MODELS
Type
Research Article
Information
Advances in Applied Probability , Volume 9 , Issue 3 , September 1977 , pp. 462 - 475
Copyright
Copyright © Applied Probability Trust 1977 

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References

Cohen, J. E. (1976) Ergodicity of age structure in populations with Markovian vital rates, I: Countable states. J. Amer. Statist. Assoc. 71, 335–339.Google Scholar
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* Typographical errors on p. 22 of this paper should be corrected. In Theorem 3(iv), the region of integration should be Z, not C. In Theorem 3(v), II.3 and 4, x should be x' and y should be y'.Google Scholar