We suggest a classificatory approach for land cover analysis that integrates fuzzy set theory with permutation techniques. It represents a non parametric alternative and/or a complement of traditional multivariate statistics when data are scarce, missing, burdened with high degree of uncertainty and originated from different sources and/or times. According to this approach, the Operational Geographic Units (OGUs) in which landscape is subdivided and sampled are classified with hierarchical clustering methods. The clusters of a classification which are significantly sharp are used to define fuzzy sets. In this way, the original data scores are transformedbydegreesofbelonging. Weintroduce the conceptsof endogenous and exogenous fuzzy sets and we suggest to apply the Mantel test between the similarity matrices of these fuzzy sets to test the predictivity of internal variables with respect to external variables. The approach is applied to OGUs corresponding to the smallest administrative units (kebeles) of the Ethiopian Rift Valley, a degrading area with high risk of further degradation. We found that: 1) there is a high correlation between geo-physical features of the landscape (geology, rainfall and elevation) and some indicators of the human pressure such as land use/cover, land management for livestock breeding and human, household and livestock densities, 2) there is a high correlation between land degradation, measured with relative loss of Normalized Difference Vegetation Index (NDVI) and the human pressure. However, the correlation is higher when the human pressure is considered in the geo-physical context of the landscape. The approach can be easily applied to produce maps useful for planning purposes thanks to geographical information system (GIS) technology that is becoming available at low cost even to small administrative units of developing countries.
Correspondence between Classifications
Correlation between Similarity Matrices
Digital Elevation Model
Normalized Difference Vegetation Index
Operational Geographic Unit
Sharpness of Exogenous classifications
Universal Soil Loss Equation
Anderson, M.J. and P. Legendre. 1999. An empirical comparison of permutation methods for tests of partial regression coefficient in a linear model. J. Stat. Comput. Simul. 62: 271–303.
Anderson, M.J. and C. ter Braak. 2003. Permutation tests for multi-factorial analysis of variance. J. Stat. Comput. Simul. 73: 85–113.
Azzali, S. and M. Menenti. 2000. Mapping vegetation-soil-climate complexes in southern Africa using temporal Fourier analysis of NOAA-AVHRR data. Int. J. Remote Sens. 21: 973–996.
Biondini, M.E., P.W. Mielke Jr. and E.F. Redente. 1991. Permutation techniques based on Euclidean analysis spaces: a new and powerful statistic method for ecological research. In: E. Feoli and L. Orlóci (eds.), Computer Assisted Vegetation Analysis. Kluwer, Boston. pp. 221–240.
Bonnet, E. and Y. Van de Peer. 2002. ZT: a software tool for simple and partial Mantel tests. J. Stat. Software 7(10): 1–12.
Box, E.O., B.N. Holben and V. Kalb. 1989. Accuracy of the AVHRR Vegetation Index as a predictor of biomass, primary productivity and net CO2 flux. Vegetatio 80: 71–89.
Burba, N., E. Feoli, M. Malaroda and V. Zuccarello. 1992. Un sistema informativo per la vegetazione. Software per l’archiviazione della vegetazione italiana e per l’elaborazione di tabelle. Manuale di utilizzo dei programmi. Quad. CETA n.12 pp. 78. Gorizia.
Burba, N., E. Feoli, M. Malaroda and V. Zuccarello. 2008. MATE-DIT: a software tool supporting the application of similarity theory in community ecology. Submitted to Community Ecol.
Carranza, L., E. Feoli and P. Ganis. 1998. Analysis of vegetation structural diversity by Burnaby’s similarity index. Plant Ecol. 138: 77–87.
Dainelli, N., M. Benvenuti and M. Sagri. 2000. Geological Map of the Ziway-Shala Lakes Basin (Ethiopia). D.B. Map, Firenze.
Davenport, M.L. and S.E. Nicholson. 1993. On the relation between rainfall and the Normalized Difference Vegetation Index for diverse vegetation types in East Africa. Int. J. Remote Sens. 14(12): 2369–2389.
De Jong, S.M. 1994. Applications of Reflective Remote Sensing for Land Degradation Studies in a Mediterranean Environment. Netherlands Geographical Studies 177, Utrecht, p. 237.
Dregne, H.E. 1983. Desertification of Arid Lands. Harwood Academic Publishers, London.
Duncan, D. 1997. Analysis and Comparison of Two AVHRR NDVI Time Series. Aerospace Engineering and Engineering Mechanics. Austin, University of Austin.
Egziabher, Tewolde, E. Feoli, M. Fernetti, G. Oriolo, Zerihun Woldu. 1998. Vegetation mapping by integration of floristic analysis, GIS and remote sensing. An example from Tigray. Plant Biosyst. 132: 39–51.
Estabrook, C.B. and G.F. Estabrook. 1989. Actus: a solution to the problem of small samples in the analyses of two-way contingency tables. Historical Meth. 82: 5–8.
Fatovich, R. 1997. The peopling of the Tigrean Plateau of ancient and medieval times (ca 4000 B. C. - A. D. 1500): Evidence and synthesis. In: K.A. Bard (ed.), The Environmental History and Human Ecology of Northern Ethiopia in Late Holocene: Preliminary Results of Multidisciplinary Project. Istituto Universitario Orientale, Napoli, pp. 82–105.
Feoli, E. and Zerihun Woldu. 2000. Fuzzy set analysis of the Ethiopian Rift Valley vegetation. Plant Ecol. 147: 219–22.
Feoli, E. and V. Zuccarello. 1986. Ordination based on classification: yet another solution? Abstr. Bot. 10: 203–219.
Feoli, E. and V. Zuccarello. 1988. Syntaxonomy, a source of useful fuzzy sets for environmental analysis? Coenoses 3: 65–70.
Feoli, E. and V. Zuccarello. 1996. Spatial pattern of ecological processes: the role of similarity in GIS applications for landscape analysis. In: M. Fisher, H. Scholten and D. Unwin (eds.), Spatial Analytical Perspectives on GIS. Taylor and Francis, London. pp. 175–185.
Feoli, E., L. Gallizia-Vuerich and Zerihun Woldu. 2002a. Processes of environmental degradation and opportunities for rehabilitation in Adwa, Northern Ethiopia. Landscape Ecol. 17: 315–325.
Feoli, E., L. Gallizia-Vuerich and Zerihun Woldu. 2002b. Evaluation of the environmental degradation innorthern Ethiopia using GIS to integrate vegetation, geomorphologic, erosion and socio-economic factors. Agriculture, Environment and Ecosystem 91: 313–325.
Feoli, E., G. Ferro and P. Ganis. 2006. Validation of phytosociological classifications based on a fuzzy set approach. Community Ecol. 7: 99–108.
Fortin, M.J., G.M. Jacquez and B. Shipley. 2002. Computer-intensive methods. In: A.H. El-Shaarawi and W.W. Piegorsch (eds.), Encyclopedia of Environmetrics. John Wiley and Sons, Ltd, Chichester. Vol. 1, pp. 399–402.
Gamon, J.A., C.B. Field, M.L. Goulden, K.L. Griffin, A.E. Hartley, G. Joel, J. Penuelas and R. Valentini. 1995. Relationships between NDVI, canopy structure, and photosynthesis in three Californian vegetation types. Ecol. Appl. 5(1): 28–41.
Hill, J., and D. Peter. 1996. The Use of Remote Sensing for Land Degradation and Desertification Monitoring in the Mediterranean Basin - State of the Art and Future Research. Luxembourg, European Commission. p. 235.
Hill, J., S. Sommer, W. Mehl and J. Mégier. 1996. A conceptual framework for mapping and monitoring the degradation of Mediterranean ecosystems with remote sensing. In: J. Hill and D. Peter (eds.), The Use of Remote Sensing for Land Degradation and Desertification Monitoring in the Mediterranean Basin - State of the Art and Future Research. Luxembourg, European Commission, pp. 23–44.
Hurcom, S.J. and A.R. Harrison. 1998. The NDVI and spectral decomposition for semi-arid vegetation abundance estimation. Int. J. Remote Sens. 19: 3109–3125.
Hurni, H. 1985. Erosion, productivity and conservation systems in Ethiopia. Paper presented at the 4th International Conference on Soil Conservation at Maracay, Venezuela, pp. 3–9.
Hurni, H. 1990. Degradation and conservation ofsoil resourcesin the Ethiopian Highlands. In: B. Messerli and H. Hurni (eds.), African Mountains and Highlands. Problems and Perspectives. African Mountains Association (AMA), Marceline, Missouri. pp. 51–63.
Kaufman, L. and P.J. Rousseeuw. 1990. Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.
Kong, A. and D.L. Nicolae. 2000. On a randomization procedure. Am. J. Human Genet. 7:1352–1355.
Lacaze, B. 1996. Spectral characterization of vegetation communities and practical approached to vegetation cover changes monitoring. In: J. Hill and D. Peter (eds.), The Use of Remote Sensing for Land Degradation and Desertification Monitoring in the Mediterranean Basin - State of the Art and Future Research. Luxembourg, European Commission. pp. 149–166.
Legendre, P. 2000. Comparison of permutation methods for the partial correlation and partial mantel tests. J. Statist. Comput. Simul. 67: 37–73.
Legendre, P. and L. Legendre. 1998. Numerical Ecology. Second English edition. Elsevier, Amsterdam.
Longley, A., Goodchild, M.F., Paul, D.J. Maguire and D.W. Rhind. 2001. Geographic Information Systems and Science. Wiley, Baffins Land, England.
Lyon, J.G., D. Yuan, R.S. Lunetta and C.D. Elvidge. 1998. A change detection experiment using vegetation indices. Photogramm. Engineer. Remote Sens. 64: 143–150.
Manly, B.F.J. 1997. Randomization, Bootstrap and Monte Carlo Methods in Biology. 2nd ed., Chapman and Hall, London.
Mantel, N. 1967. The detection of disease clustering and a generalized regression approach. Cancer Res. 27: 209–220.
Mantel, N. and R.S. Valand. 1970. A technique of nonparametric multivariate analysis. Biometrics 26: 547–558.
McDougall, I., W.H. Morton and N.A.U. Williams. 1975. Age and rate of trap series basalts at Blue Nile Gorge, Ethiopia. Nature 254: 207–208.
Miklós, I., I. Somodi and J. Podani. 2005. Rearrangement of ecological data matrices via Markov chain Monte Carlo simulation. Ecology 86: 3398–3410.
Myneni, R.B. and G. Asrar. 1994. Atmospheric effects and spectral vegetation indices. Remote Sens. Environ. 47: 390–402.
Opdum, P., R. Foppen and C. Vos. 2002. Bridging the gap between ecology and spatial planning in landscape ecology. Landscape Ecol. 16:767–799.
Pausas, J.C. and E. Feoli. 1996. Environment-vegetation relationships in the understorey of Pyrenean Pinus sylvestris forest. II. A classification approach. Coenoses 11:45–51.
Peñuelas, J.P. and I. Filella. 1998. Visible and near-infrared reflectance techniques for diagnosing plant physiological status. Trends in Plant Science 3(4): 151–156.
Peres–Neto, P.R. and J.D. Olden. 2001. Assessing the robustness of randomization tests: examples from behavioural studies. Animal Behav. 61: 79–86.
Pesarin, F. 1999. Permutation Testing of Multidimensional Hypotheses by nOnparametric Combination of Dependent Tests. CLEUP, Padua.
Pickup, G. and V.H. Chewings. 1996. Identifying and measuring land degradation processes using remote sensing. In: J. Hill and D. Peter (eds.), The Use of Remote Sensing for Land Degradation and Desertification Monitoring in the Mediterranean Basin - State of the Art and Future Research. Luxembourg, European Commission. pp. 135–145.
Pillar, V.D. 1996. A randomization-based solution for vegetation classification and homogeneity testing. Coenoses 11: 29–36.
Pillar, V.D. 1999. How sharp are classifications? Ecology 80: 2508–2516.
Pillar, V.D. and L. Orlóci. 1996. On randomization testing in vegetation science: multifactor comparisons of relevé groups. J. Veg. Sci. 7:585–592.
Podani, J. 1994. Multivariate Data Analysis in Ecology and Systematics. A Methodological Guide to the SYN-TAX 5.0 package. SPB Academic Publishing bv, The Hague.
Podani, J. 2000. Introduction to the Exploration of Multivariate Biological Data. Backhuys Publishers, Leiden.
Podani, J. and E. Feoli. 1991. A general strategy for the simultaneous classification of variables and objects in ecological data tables. J. Veg. Sci. 2:435–444.
Price, J.P. 1992. Estimating vegetation amount from visible and near infrared reflectances. Remote Sens. Environ. 41: 29–34.
Purevdorj, Ts., R. Tateishi, T. Ishiyama and Y. Honda. 1998. Relationships between percent vegetation cover and vegetation indices. Int. J.Remote Sens. 19: 3519–3535.
Sagri, M. 1998. Land Resources inventory, environmental changes in the Abaya lake region (Ethiopia). Final report STD3 project. Contract no. TS3-CT92-0076.
Thornes, J.B. 1996. Introduction. In: C.J. Brandt and J.B. Thornes, (eds.), Mediterranean Desertification and Land Use. Wiley, New York. pp. 1–11.
Tobisch, T. and T. Standovár. 2005. A comparison of vegetation patterns in the tree and herb layers of a hardwood forest. Community Ecol. 6: 29–37.
Tucker, C.J., C. Vanpraet, E. Boerwinkel and A. Gastn. 1983. Satellite remote sensing of total dry matter production in the Senegalese Sahel. Remote Sens. Environ. 13: 461–474.
Virgo, J.R. and R.N. Munro. 1977. Soil and erosion features of the central plateau regions of Tigray. Geoderma 20: 131–157.
Wischmeier, W.H. and D.D. Smith. 1978. Predicting Rainfall Erosion Losses – A Guide to Conservation Planning. U.S. Department of Agriculture, Agriculture Handbook, n. 537.
Zerihun, Woldu and Mesfin Tadesse. 1990. The status of the vegetation in the Lake regions of the Rift Valley of Ethiopia and the possibilities of its recovery. Sinet: Ethiop. J. Sci. 13(2): 97–120.
Zhao, S.X. 1986. Discussion on fuzzy clustering. 8th int. Conf. On Pattern Recognition, IEEE Press, New York. pp. 612–614.
Zimmerman, H.G. 1996. Fuzzy Set Theory and its Applications. 3rd ed. Kluwer Academic Publishers, Dordrecht.
About this article
Cite this article
Feoli, E., Gallizia-Vuerich, L., Ganis, P. et al. A classificatory approach integrating fuzzy set theory and permutation techniques for land cover analysis: a case study on a degrading area of the Rift Valley (Ethiopia). COMMUNITY ECOLOGY 10, 53–64 (2009). https://doi.org/10.1556/ComEc.10.2009.1.7
- Fuzzy sets
- Land degradation
- Permutation tests
- Rift valley