A discrete mathematical method for the analysis of spatial pattern

Abstract

A discrete mathematical method, based on the Jakó Iterative Canonical Forms (ICF) of Boolean functions is proposed for the analysis of species combinations and the detection of characteristic areas in plant communities. Information on species combinations (or florulas) appearing in a sample is expressed in compact form to reveal fundamental properties of community pattern. The new method provides a complementary tool for the florula diversity approach: whereas florula diversity is indicative of the frequency distribution of species combinations regardless their interrelationships, the new procedure detects complexity in the abstract structure of species combinations. Graph-theoretical representations of the ICF promote understanding the new method and visualizing its results. A cellular automata model and field data provide illustrative examples.

Abbreviations

CA:

Cellular Automata

CDNF:

Canonical Disjunctive Normal Form

FD:

Florula Diversity

ICF:

Iterative Canonical Form

NSC:

Number of species combinations

References

  1. Bartha, S. 1992. Preliminary scaling for multi-species coalitions in primary succession. Abstracta Botanica 16:31–41.

    Google Scholar 

  2. Bartha, S., T. Czárán and J. Podani. 1998. Exploring plant community dynamics in abstract coenostate spaces. Abstracta Botanica 22:49–66.

    Google Scholar 

  3. Bartha, S., T. Rédei, Gy. Szollát, J. Bódis and L. Mucina. 1998. Compositional diversity and fine-scale spatial patterns of dolomite grasslands on contrasting slopes. In: Csontos, P. (ed.), Sziklagyepek szünbotanikai kutatása. Zólyomi Bálint professzor emlékének. Scientia Kiadó, Budapest. pp. 159–182.

    Google Scholar 

  4. Collins, S.L. 1992. Fire frequency and community heterogeneity in tallgrass prairie vegetation. Ecology 73: 2001–2006.

    Article  Google Scholar 

  5. Dale, M.R.T. 1977. Graph theoretical analysis of the phytosociological structure of plant communities: the theoretical basis. Vegetatio 34: 137–154.

    Article  Google Scholar 

  6. Erschbamer, B., G. Grabherr and H. Reisigl. 1983. Spatial pattern in dry grassland communities of the Central Alps and its ecophysiological significance. Plant Ecology 54: 143–151.

    Article  Google Scholar 

  7. Frolov, A. and É. Jakó. 1991. Algorithms for recognition of partially ordered objects and their application. Scripta Technica 29: 109–118.

    Google Scholar 

  8. Greig-Smith, P. 1983. Quantitative Plant Ecology. 2nd ed. Blackwell, Oxford.

    Google Scholar 

  9. Herben, T., F. Krahulec, V. Hadincová and S. Pecháčková. 1997. Is a grassland community composed of coexisting species with low and high spatial mobility? Folia Geobot. Phytotax. 29:459–468.

    Article  Google Scholar 

  10. Jakó, É. 1983. Iterative Canonical Decomposition of Boolean Functions and its Application to Logical Design.. PhD Thesis, Technical University, Moscow.

    Google Scholar 

  11. Jakó, É. (manuscript). Recognition and classification of discrete objects by Iterative Canonical Forms (ICF) of Boolean functions. Journal of Mathematical Chemistry.

  12. Jakó É. and P. Ittzés. 1998. A discrete mathematical approach to the analysis of spatial pattern. Abstracta Botanica 22:121–142.

    Google Scholar 

  13. Juhász-Nagy, P. 1976. Spatial dependence of plant populations. I. Equivalence analysis (an outline for a new model). Acta Bot. Hung. 22: 61–78.

    Google Scholar 

  14. Juhász-Nagy, P. and J. Podani. 1983. Information theory methods for the study of spatial processes and succession. Vegetatio 51:129–140.

    Article  Google Scholar 

  15. Klimeš, L. 1999. Small-scale plant mobility in a species-rich grassland. Journal of Vegetation Science 10: 209–218.

    Article  Google Scholar 

  16. Kun, A., P. Ittzés and D. Krasser. 2000. Coenological gradients in the Hungarian rocky vegetation I. Landscape-level studies. V. Magyar Ökológus Kongresszus elõadásainak és posztereinek kivonatai. Debrecen, 2000. p. 93.

  17. McIntosh, R. 1973. Matrix and plexus techniques. In: R. H. Whittaker (ed.), Ordination and Classification of Plant Communities. Junk, The Hague. pp. 157–191.

    Chapter  Google Scholar 

  18. Mucina, L. and S. Bartha. 1999. Variance in species richness and guild proportionality in two contrasting dry grassland communities. Biologia (Bratislava) 54: 67–75.

    Google Scholar 

  19. Pärtel, M. and M. Zobel. 1995. Small-scale dynamics and species richness in successional alvar plant communities. Ecography 18: 83–90.

    Article  Google Scholar 

  20. Podani, J. 1984. Analysis of mapped and simulated vegetation patterns by means of computerized sampling techniques. Acta Bot. Hung. 30: 403–425.

    Google Scholar 

  21. Podani, J. 1994. Multivariate analysis in ecology and systematics. SPB Publishing, The Hague, The Netherlands.

    Google Scholar 

  22. Podani, J., T. Czárán and S. Bartha. 1993. Pattern, area and diversity: the importance of spatial scale in species assemblages. Abstracta Botanica 17:37–52.

    Google Scholar 

  23. Szõcs, Z. 1977. New computer-oriented methods for the study of natural and simulated vegetation structure. In: L. Orlóci, C. R. Rao and W. M. Stiteler (eds.), Multivariate Methods in Ecological Work. International Co-operative Publishing House, Burtonsville, MD, USA. pp. 301–308

    Google Scholar 

  24. van der Maarel, E. 1996. Pattern and process in the plant community: fifty years after A.S. Watt. Journal of Vegetation Science 7: 19–28.

    Article  Google Scholar 

  25. Wikberg, S. and B.M. Svensson. 2003. Ramet demography in a ring-forming clonal sedge. Journal of Ecology 91: 847–854.

    Article  Google Scholar 

  26. Wimberly, M.C. and T.A. Spies. 2001. Influences of environment and disturbance on forest patterns in coastal Oregon watersheds. Ecology 82: 1443–1459.

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to J. Podani.

Rights and permissions

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Cite this article

Ittzés, P., Jakó, É., Kun, Á. et al. A discrete mathematical method for the analysis of spatial pattern. COMMUNITY ECOLOGY 6, 177–190 (2005). https://doi.org/10.1556/ComEc.6.2005.2.6

Download citation

Keywords

  • Boolean functions
  • Cellular automata
  • Graphs
  • Species pattern
  • Vegetation