Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T16:10:37.166Z Has data issue: false hasContentIssue false
  • English
  • Français

A population process with offspring distribution depending on both population size and generation

Published online by Cambridge University Press:  14 July 2016

Pedro Saavedra Santana  and
Miguel Sanchez Garcia
Pedro Saavedra Santana*
Affiliation:
Universidad de La Laguna
Miguel Sanchez Garcia*
Affiliation:
Universidad de La Laguna
*
∗ Postal address: Department of Statistics, University of La Laguna, La Laguna-Tenerife, Spain.
∗ Postal address: Department of Statistics, University of La Laguna, La Laguna-Tenerife, Spain.
Get access Rights & Permissions [Opens in a new window]

Abstract

A population process {Zn} is defined, with offspring distribution depending on both population size and generation number. As is well known, in models where the offspring distribution depends only on the size, under most conditions extinction surely results. The model we now introduce would mean that if history has an influence on evolution of the population, it is possible to obtain models for which a probability as high as desired exists that the population size balances between two given values.

Keywords

DESCENDANCYPOPULATION BALANCE
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 4 , December 1989 , pp. 866 - 872
Copyright
Copyright © Applied Probability Trust 1989 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Athreya, K. B. and Ney, P. E. (1972) Branching Processes. Springer-Verlag, Berlin.Google Scholar
[2] Church, J. D. (1967) Composition limit theorems for probability generating functions. Math. Research Center Report 732.Google Scholar
[3] Feller, W. (1971) An Introduction to Probability Theory and its Applications, I. Wiley, New York.Google Scholar
[4] Jagers, P. (1975) Branching Processes with Biological Applications. Wiley, New York.Google Scholar
[5] Jagers, P. (1974) Galton-Watson processes in varying environments. J. Appl. Prob. 11, 174–178.Google Scholar
[6] Klebaner, F. C. (1984) On population size-dependent branching processes. Adv. Appl. Prob. 16, 30–55.Google Scholar
[7] Saavedra Santana, P. (1987) Cuestiones Notables sobre Procesos Discretos: Algunos Modelos de Aplicacion. Tesis Doctoral.Google Scholar