Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T05:19:16.474Z Has data issue: false hasContentIssue false
  • English
  • Français

The expected population size in a cell-size-dependent branching process

Published online by Cambridge University Press:  14 July 2016

Aidan Sudbury
Aidan Sudbury*
Affiliation:
Monash University
*
∗Postal address: Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia.
Get access Rights & Permissions [Opens in a new window]

Abstract

In cell-size-dependent growth the probabilistic rate of division of a cell into daughter-cells and the rate of increase of its size depend on its size. In this paper the expected number of cells in the population at time t is calculated for a variety of models, and it is shown that population growths slower and faster than exponential are both possible. When the cell sizes are bounded conditions are given for exponential growth.

Keywords

CELL-SIZE-DEPENDENTBRANCHING PROCESSBIRTH-AND-DEATH PROCESSINTEGRAL OPERATORS
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 65 - 75
Copyright
Copyright © Applied Probability Trust 

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

Abramowitz, A. and Stegun, I. A. (1964) Handbook of Mathematical Functions. Dover, New York.Google Scholar
Bell, G. I. and Anderson, E. C. (1967) Cell growth and division I. Biophys. J. 7, 329–351.CrossRefGoogle ScholarPubMed
Clifford, P. and Sudbury, A. (1972) The linear cell-size-dependent branching process. J. Appl. Prob. 9, 687–696.Google Scholar
Gani, J. and Saunders, I. W. (1976) On the parity of individuals in a branching process. J. Appl. Prob. 13, 219–230.Google Scholar
Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.Google Scholar
Morgan, B. J. T. and Leventhal, B. (1977) A model for blue-green algae and gorillas. J. Appl. Prob. 14, 675–688.Google Scholar
Schumitzky, A. and Wenska, T. (1975) An operator residue theorem with applications to branching processes and renewal type integral equations. SIAM J. Math. Anal. 6, 229–235.CrossRefGoogle Scholar