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Expected size distributions in models of group dynamics

Part of: Applications Markov processes

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.
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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 

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