Abstract
Data on the presence of a number of vegetation ‘states’ (defined in terms of species dominance in areas of 10×10 cm) and transition probabilities were derived from permanent quadrats in a number of recently burned heath stands. Data were taken from a species-rich community, a species-poor type and a high-level Calluna-Eriophorum bog. Simple Markovian models were constructed using these data, and the model predictions were compared with known or expected trends. Models for species-rich heath yielded poor simulations of expected trends since matrices derived from data for the first years after fire did not contain sufficient information on transitions to states important later in the developmental sequence. Model results for the simpler species-poor and bog communities were more satisfactory and simulated expected trends. In these types all species recovered quickly after fire and less rearrangement of species abundances took place. Maximum likelihood statistics carried out on the transition matrices produced inconclusive results for the species-rich and species-poor types, but indicated that the data from the Calluna-Eriophorum bog approximated a first-order time-homogeneous Markov chain. It was concluded that Markov models lack predictive ability except in relatively simple systems, but that they may be useful in illustrating variations in short-term community dynamics.
Similar content being viewed by others
References
Acevedo, L. M. F., 1981. On Horn's Markovian model of forest dynamics with particular reference to tropical forests. Theor. Pop. Biol. 19: 230–250.
Anderson, T. W. & Goodman, L. A., 1957. Statistical inference about Markov chains. Ann. Math. Statist. 28: 89–109.
Austin, M. P. & Belbin, L., 1981. An analysis of succession along an environmental gradient using data from a lawn. Vegetatio 46: 19–30.
Bellefleur, P., 1981. Markov models of forest-type secondary succession in British Columbia. Can. J. For. Res. 11: 18–29.
Binkley, C. S., 1980. Is succession in hardwood forest a stationary Markov process? Forest Sci. 26: 566–570.
Collins, L., 1975. An introduction to Markov chain analysis. Concepts and techniques in modern Geography, 1. University of East Anglia, Norwich. 36 pp.
Debussche, M., Godron, M., Lepart, J. & Romane, F., 1977. An account of the use of a transition matrix. Agro-Ecosystems 3: 81–92.
Enright, N. & Ogden, J., 1979. Applications of transition matrix models in forest dynamics: Araucaria in Papua New Guinea and Nothofagus in New Zealand. Aust. J. Ecol. 3: 3–23.
Gibson, C. W. D., Guilford, T. C., Hambler, C. & Sterling, P. H., 1983. Transition matrix models and succession after release from grazing on Aldabra atoll. Vegetatio 52: 151–159.
Gimingham, C. H., 1972. Ecology of Heathlands. Chapman & Hall, London. 266 pp.
Gimingham, C. H., Hobbs, R. J. & Mallik, A. U., 1981. Community dynamics in relation to management of heathland vegetation in Scotland. Vegetatio 46: 149–155.
Godron, M. & Lepart, J., 1973. Sur la représentation de la dynamique de la végétation au moyen des matrices de succession. In: R., Tüxen (ed.), Sukzessionsforschung, Ber. Symp. Int. Ver. Vegetationskunde, Rinteln, 1973, pp. 269–287. Cramer, Vaduz.
Grant, S. A., Hunter, R. F. & Cross, C., 1963. The effects of muirburning on Molinea-dominant communities. J. Brit. Grassland Soc. 18: 249–257.
Henderson, W. & Wilkins, C. W., 1975. The interaction of bushfires and vegetation. Search 6: 130–133.
Hill, M. O., 1982. Review of: van der Maarel, E. (ed.) (1980) Succession. Symposium on Advances in Vegetation Sciences, Nijmegen, The Netherlands, May 1979. Advances in Vegetation Science 3. J. Ecol. 70: 703.
Hobbs, R. J., 1981. Post-fire succession in heathland communities. Unpubl. Ph.D. Thesis, University of Aberdeen, Scotland. 371 pp.
Hobbs, R. J. & Gimingham, C. H., 1984. Studies on fire in Scottish heathland communities II. Post-fire vegetation development. J. Ecol. 72 (in press).
Hobbs, R. J. & Legg, C. J., 1983. Markov models and initial floristic composition in heathland vegetation dynamics. Vegetatio 56: 31–43.
Horn, H. S., 1975. Markovian properties of forest succession. In: M. L., Cody & J. M., Diamond (eds.), Ecology and Evolution of Communities, pp. 196–211. Belknap, Harvard Univ. Press, Cambridge, Massachusetts.
Hulst, R.van, 1979. On the dynamics of vegetation: Markov chains as models of succession. Vegetatio 40: 3–14.
Hulst, R.van, 1980. Vegetation dynamics or ecosystem dynamics. Dynamic sufficiency in succession theory. Vegetatio 43: 147–151.
Jeffers, J. N. R., 1978. An Introduction to Systems Analysis: with Ecological Applications. Arnold, London. 198 pp.
Kullback, S., Kupperman, M. & Ku, H. H., 1962. Tests for contingency tables and Markov chains. Technometrics 4: 572–608.
Legg, C. J., 1978. Succession and homeostasis in heathland vegetation. Unpubl. Ph.D. Thesis, Univ. of Aberdeen, Scotland. 219 pp.
Legg, C. J., 1980. A Markovian approach to the study of heath vegetation dynamics. Bull. Ecol. 11: 393–404.
Miles, J., Welch, D. & Chapman, S. B., 1978. Vegetation and management in the uplands. In: O. W. Heal (ed.). Upland Land Use in England and Wales, pp. 77–95. Countryside Commission Publ. CCP111, Leeds.
Noble, I. R. & Slatyer, R. O., 1981. Concepts and models of succession in vascular plant communities subject to recurrent fire. In: A. M., Gill, R. O., Groves & I. R., Noble (eds.). Fire and the Australian Biota, pp. 319–335. Australian Academy of Science, Canberra.
Rawes, M. & Hobbs, R., 1979. Management of semi-natural blanket bog in the northern Pennines. J. Ecol. 67: 789–807.
Smith, A. J. E., 1978. The Moss Flora of Britain and Ireland. Cambridge University Press, London. 706 pp.
Tutin, T. G., Heywood, V. H., Burges, N. A., Valentine, D. H., Walters, S. M. & Webb, D. A., 1964–80. Flora Europaea Vols. I-V. Cambridge University Press, London.
Usher, M. B., 1979. Markovian approaches to ecological succession. J. Anim. Ecol. 48: 413–426.
Usher, M. B., 1981. Modelling ecological succession, with particular reference to Markovian models. Vegetatio 46: 11–18.
Waggoner, P. E. & Stephens, G. R., 1970. Transition probabilities for a forest. Nature (London) 225: 1160–1161.
Watt, A. S., 1947. Pattern and process in the plant community. J. Ecol. 35: 1–22.
Author information
Authors and Affiliations
Additional information
Nomenclature follows Tutin et al. (1964–80) for vascular plants and Smith (1978) for mosses.
I am grateful to Prof. C. H. Gimingham for help and advice during this study, which was carried out during tenure of a Natural Environment Research Council studentship. Thanks are also due to Dr M. B. Usher and an anonymous referee for their comments on the draft.
Rights and permissions
About this article
Cite this article
Hobbs, R.J. Markov models in the study of post-fire succession in heathland communities. Vegetatio 56, 17–30 (1984). https://doi.org/10.1007/BF00036133
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00036133