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2 results

  • Stepping stone models for population growth

  • E. Renshaw
  • Journal:
    Journal of Applied Probability / Volume 11 / Issue 1 / March 1974
    Published online by Cambridge University Press:
    14 July 2016, pp. 16-31
    Print publication:
    March 1974

  • A population is composed of an infinite number of colonies situated at the integer points of a single co-ordinate axis. Each colony develops according to a simple birth and death process and migration is allowed between nearest neighbours. An approximate solution is obtained for the probability structure of the population size, and exact results are derived for the process when immigration is introduced into a single colony from outside the system.

  • Interconnected population processes

  • E. Renshaw
  • Journal:
    Journal of Applied Probability / Volume 10 / Issue 1 / March 1973
    Published online by Cambridge University Press:
    14 July 2016, pp. 1-14
    Print publication:
    March 1973

  • This paper investigates the effect of migration between two colonies each of which undergoes a simple birth and death process. Expressions are obtained for the first two moments and approximate solutions are developed for the probability generating function of the colony sizes.