Ergodicity of age structure in populations with Markovian vital rates, III: Finite-state moments and growth rate; an illustration
- 1 September 1977
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 9 (3) , 462-475
- https://doi.org/10.2307/1426109
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
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