Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-17T14:17:43.315Z Has data issue: false hasContentIssue false
  • English
  • Français

Spatial patterns arising from plant dispersal as modelled by a correlated random walk

Published online by Cambridge University Press:  14 July 2016

R. D. Routledge
R. D. Routledge*
Affiliation:
Simon Fraser University
*
∗Postal address: Department of Mathematics and Statistics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6.
Get access Rights & Permissions [Opens in a new window]

Abstract

A correlated random walk in the plane is studied for which the direction of a step depends on the direction of the previous step. Both step direction and step length are continuous random variables. Such a random walk has been used to model the vegetative dispersal of certain plant populations. The analysis provides general conclusions about dependencies on parameters, an efficient scheme for generating numerical results, and testable predictions for plant populations.

Keywords

RHIZOME ARCHITECTUREFUNCTIONAL DIFFERENTIAL EQUATIONSPOLYMER CHAINSELEOCHARIS PALUSTRIS
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 1 , March 1990 , pp. 1 - 13
Copyright
Copyright © Applied Probability Trust 1990 

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

Barlow, R. E. and Proschan, F. (1965) Mathematical Theory of Reliability. Wiley, New York.Google Scholar
Bell, A.D. and Tomlinson, P. B. (1980) Adaptive architecture in rhizomatous plants. Bot. J. Linnean Soc. 80, 125–160.CrossRefGoogle Scholar
Breiman, L. (1968) Probability. Addison-Wesley, Reading, Massachusetts.Google Scholar
Churchill, R. V., Brown, J. W. and Verhey, R. F. (1974) Complex Variables and Applications, 3rd edn. McGraw-Hill, New York.Google Scholar
Cook, R. E. (1983) Clonal plant populations. Amer. Scientist 71, 244–253.Google Scholar
Cowie, J. M. G. (1967) Polymers: Chemistry and Physics of Modern Materials. International Textbook, Aylesbury.Google Scholar
Cox, D. R. (1967) Renewal Theory. Science Paperback edition, Science Paperbacks.Google Scholar
Daletski, Y. L. and Krein, M. G. (1974) Stability of Solutions of Differential Equations in Banach Space (Smith, S., translator), American Mathematical Society, Providence, Rhode Island.Google Scholar
Daniels, H. E. (1952) The statistical theory of stiff chains. Proc. Roy. Soc. Edin. A 43, 290–311.Google Scholar
Iossif, G. (1986) Return probabilities for correlated random walks. J. Appl. Prob. 23, 201–207.Google Scholar
Kac, M. (1959) Probability and Related Topics in Physical Sciences. Interscience, New York.Google Scholar
Kingman, J. F. C. (1982) The thrown string (with discussion). J. R. Statist. Soc. B 44, 109–138.Google Scholar
Lukacs, E. (1970) Characteristic Functions, 2nd edn. Griffin, London.Google Scholar
Routledge, R. D. (1987) Rhizome architecture for dispersal in Eleocharis palustris. Can. J. Bot. 65, 1218–1223.Google Scholar
Walters, S. M. (1950) On the vegetative morphology of Eleocharis R. Br. New Phytol. 49, 1–7.Google Scholar
Weinberger, H. F. (1965) A First Course in Partial Differential Equations. Blaisdell, New York.Google Scholar