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1 results

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

  • Joel E. Cohen
  • Journal:
    Advances in Applied Probability / Volume 9 / Issue 3 / September 1977
    Published online by Cambridge University Press:
    01 July 2016, pp. 462-475
    Print publication:
    September 1977

  • 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.