Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-25T04:53:27.882Z Has data issue: false hasContentIssue false
  • English
  • Français

Expected size distributions in models of group dynamics

Part of: Markov processes Applications

Published online by Cambridge University Press:  14 July 2016

Byron J. T. Morgan
Byron J. T. Morgan*
Affiliation:
University of Kent
*
∗ Postal address: Institute of Mathematics and Statistics, The University of Kent, Cornwallis Building, Canterbury, Kent CT2 7NF, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers several models for biological processes in which animate individuals live and die as members of groups which can split to form smaller groups. Resulting distributions of individuals over groups are compared and contrasted. In particular, two qualitatively different types of distributions are identified. It is clear that distinguishing between models giving rise to the same distribution types is difficult. Implications for more complex models are discussed and avenues for further research are outlined.

Keywords

BIRTH-DEATH PROCESSANIMATE INDIVIDUALSPOPULATION PROCESSGROUPING OF INDIVIDUALSBRANCHING PROCESSCELL-SIZE DEPENDENCE

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J85: Applications of branching processes 62P10: Applications to biology and medical sciences 92D25: Population dynamics (general) 92D50: Animal behavior
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 1 , March 1993 , pp. 1 - 16
Copyright
Copyright © Applied Probability Trust 1993 

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, M. and Stegun, I. A. (1964) Handbook of Mathematical Functions. Dover, New York.Google Scholar
Bromwich, T. (1955) An Introduction to the Theory of Infinite Series. 2nd edn. Macmillan, London.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
Gibbs, K. G. (1980) Mathematical Models for Population Growth with Special Reference to the African Mountain Gorilla. Unpublished M.Sc. dissertation, University of Kent, Canterbury, UK.Google Scholar
Grimmett, G. R. (1980) A linear cell-size dependent branching process. Stoch. Proc. Appl. 10, 105–113.Google Scholar
Harcourt, A. H., Stewart, K. J. and Fossey, D. (1976) Male emigration and female transfer in wild mountain gorilla. Nature 263, 226–227.CrossRefGoogle Scholar
Morgan, B. J. T. (1974) On the distribution of inanimate marks over a linear birth-and-death process. J. Appl. Prob. 11, 423–436.Google Scholar
Morgan, B. J. T. (1976) Stochastic models of grouping changes. Adv. Appl. Prob. 8, 30–57.Google Scholar
Morgan, B. J. T. (1977) Models for the behaviour of animate individuals living in groups. Unpublished manuscipt.Google Scholar
Morgan, B. J. T. (1979) Four approaches to solving the linear birth-and-death (and similar). Int. J. Math. Educ. Sci. Technol. 10, 51–64.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
Morris, E. O. (1958) Yeast growth. The Chemistry and Biology of Yeasts, ed. Cook, A. H., Chapter VI. Academic Press, London.Google Scholar
Whittle, P. (1965a) Statistical processes of aggregation and polymerisation. Proc. Camb. Phil. Soc. 61, 475–495.Google Scholar
Whittle, P. (1965b) The equilibrium statistics of a clustering process in the uncondensed phase. Proc. R. Soc. A 285, 501–519.Google Scholar