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

  • Aidan Sudbury (a1)

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.

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Postal address: Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia.

References

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Abramowitz, A. and Stegun, I. A. (1964) Handbook of Mathematical Functions. Dover, New York.
Bell, G. I. and Anderson, E. C. (1967) Cell growth and division I. Biophys. J. 7, 329351.
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Gani, J. and Saunders, I. W. (1976) On the parity of individuals in a branching process. J. Appl. Prob. 13, 219230.
Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.
Morgan, B. J. T. and Leventhal, B. (1977) A model for blue-green algae and gorillas. J. Appl. Prob. 14, 675688.
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, 229235.

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

  • Aidan Sudbury (a1)

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