Skip to main content
Log in

On the dynamics of vegetation: Markov chains as models of succession

  • Published:
Vegetatio Aims and scope Submit manuscript

Summary

An important problem in the study of successional change is the question whether succession is Markovian, or, in other words, whether a knowledge of past vegetation is necessary in order to predict the future vegetation of a site. One approach to this problem would be to perform perturbation studies on actual vegetation.

Since experimental perturbations of most vegetation types are extremely time consuming, however, a test for the importance of historical effects which can be performed on observational data would be preferable. Such a test can be found in the theory of Markov processes. the statistical tests for testing the Markovity assumption and some additional applications of the theory to vegetation dynamics are discussed. Appropriate data, however, are hard to find and the data set used here can only illustrate some other applications of the Markov chain model. One salient conclusion is that, the classical conception to the contrary, ecological succession appears to be highly indeterminate. This clearly calls for a stochastic rather than a deterministic description.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anderson, T.W. & L.A. Goodman. 1957. Statistical inference about Markov Chains. Ann. Math. Statist. 28: 89–110.

    Article  Google Scholar 

  • Billingsley, P. 1961. Statistical methods in Markov chains. Ann. Math. Statist. 32: 12–40.

    Article  Google Scholar 

  • Dacey, M.F. & W.C. Krumbein. 1970. Markovian models in stratigraphic analysis. J. Int. Ass. Math. Geol. 2: 175–191

    Article  Google Scholar 

  • Davis, J.C. 1973. Statistics and data analysis in geology. Wiley, New York, 550 pp.

    Google Scholar 

  • Drury, W.H. & I.C.T. Nisbet. 1973. Succession. J. Arnold Arb. 54: 331–368.

    Google Scholar 

  • Feller, W. 1968. An Introduction to Probability Theory and its Applications. Vol. I. 3rd ed. Wiley, New York, 509 pp.

    Google Scholar 

  • Ferschl, F. 1970. Markovketten. Nr 35 in: Lecture Notes in Operations Research and Mathematical Systems. Springer, Berlin, 168 pp.

    Book  Google Scholar 

  • Harbaugh, J.W. & G. Bonham-Carter. 1970. Computer simulation in geology. Wiley-Interscience, New York, 575 pp.

    Google Scholar 

  • Horn, H.S. 1974. The ecology of secondary succession. Ann. Rev. Ecol. Syst. 4: 25–37.

    Article  Google Scholar 

  • Horn, H.S. 1976. Markovian properties of forest succession. In: J.M. Diamond & M.L. Cody (eds.). Ecology of Communities, p. 187–204. Harvard University Press, Cambridge, Mass.

    Google Scholar 

  • Hulst, R.van. 1978. The dynamics of vegetation: Patterns of environmental and vegetational change. Vegetatio 38: 65–75.

    Article  Google Scholar 

  • Hulst, R.van 1979. The dynamics of vegetation: Succession in, model communities. Vegetatio 39/2: 85–96.

    Article  Google Scholar 

  • Karlin, S. 1966. A first course in stochastic processes. Academic Press, New York, 502 pp.

    Google Scholar 

  • Kemeny, J.G. & J.L. Snell. 1962. Mathematical models in the social sciences. Ginn, Boston, 145 pp.

    Google Scholar 

  • Kemeny, J.G., J.L. Snell & A.W. Knapp. 1960. Denumerable Markov chains. Van Nostrand, Princeton, 439 pp.

    Google Scholar 

  • Krumbein, W.C. & M.F. Dacey. 1969. Markov chains and embedded chains in geology. J. Int. Ass. Math. Geol. 1: 79–96.

    Article  Google Scholar 

  • Lewontin, R.C. 1974. The genetic basis of evolutionary change. Columbia University Press, New York and London, 346 pp.

    Google Scholar 

  • MacArthur, R.H. 1958. A note on stationary age distributions in single-species populations and stationary species populations in a community. Ecology 39: 146–147.

    Article  Google Scholar 

  • MacArthur, R.H. 1961. Community. In: P. Gray (ed.). The Encyclopedia of the Biological Sciences, p. 207–209. Reinhold, New York.

    Google Scholar 

  • Parzen, E. 1965. Stochastic processes. Holden-Day, San Francisco, 324 pp.

    Google Scholar 

  • Pielou, E.C. 1969. Introduction to mathematical ecology. Wiley, New York, 286 pp.

    Google Scholar 

  • Romanovsky, V.I. 1970. Discrete Markov chains. (Translated from Russian by E. Seneta.) Wolters-Noordhoff, Groningen, The Netherlands. 408 pp.

    Google Scholar 

  • Walker, D. 1970. Direction and rate in some British postglacial hydroseres In: D. Walker & R. West (eds.): The Vegetational History of the British Isles, p. 117–139. Cambridge University Press, Cambridge.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The author gratefully acknowledges the critical support he received from Professor László Orlóci. This paper forms part of a wider research program supported by NRC grant to Professor Orlóci.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Van Hulst, R. On the dynamics of vegetation: Markov chains as models of succession. Vegetatio 40, 3–14 (1979). https://doi.org/10.1007/BF00052009

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00052009

Keywords

Navigation