Hostname: page-component-cb9f654ff-mwwwr Total loading time: 0 Render date: 2025-08-30T22:59:16.655Z Has data issue: false hasContentIssue false
  • English
  • Français

A model for blue-green algae and gorillas

Published online by Cambridge University Press:  14 July 2016

Byron J. T. Morgan  and
B. Leventhal
Byron J. T. Morgan
Affiliation:
University of Kent, Canterbury
B. Leventhal*
Affiliation:
Audits of Great Britain Ltd.
*
*Postal address: Audit House, Field End Road, Eastcote, Ruislip, Middlesex HA4 9LT.
Get access Rights & Permissions [Opens in a new window]

Abstract

The linear birth-and-death process is elaborated to allow the elements of the process to live as members of linear clusters which have the possibility of breaking up. For the supercritical case, expressions, based on an approximation, are derived for the mean numbers of clusters of the various sizes as time → ∞. These expressions compare very well with exact solutions obtained by the method of Runge-Kutta. Exact solutions for the mean values for all time are given for when the death rate is zero.

Keywords

ALGAEAPPROXIMATIONBIRTH-AND-DEATH PROCESSGORILLASLINEAR CLUSTERSRUNGE-KUTTA

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 4 , December 1977 , pp. 675 - 688
Copyright
Copyright © Applied Probability Trust 1977 

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.)

Article purchase

Temporarily unavailable

References

Fossey, D. (1971) More days with African mountain gorillas. National Geographic 140, 574–585.Google Scholar
Fossey, D. (1972) Vocalizations of the Mountain Gorilla (Gorilla gorilla beringei). Anim. Behav. 20, 36–53.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
Groom, A. F. G. (1973) Squeezing out the mountain gorilla. Oryx 12, 207–215.Google Scholar
Harcourt, A. H. and Groom, A. F. G. (1972) Gorilla Census. Oryx 11, 355–363.Google 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. and Hinde, J. P. (1976) On an approximation made when analysing stochastic processes. J. Appl. Prob. 13, 672–683.Google Scholar
Ralston, A. (1965) A First Course in Numerical Analysis. McGraw-Hill, New York.Google Scholar
Saunders, I. W. (1976) A convergence theorem for parities in a birth-and-death process. J. Appl. Prob. 13, 231–238.Google Scholar
Wilcox, M. (1970) One dimensional pattern found in blue-green algae. Nature (London) 228, 686–687.Google Scholar
Wilcox, M., Mitchison, G. J. and Smith, R. J. (1975) Spatial control of differentiation in the blue-green alga Anabaena. Microbiology 29, 453–463.Google Scholar