Species rarefaction curves have long been used for estimating the expected number of species as a function of sampling effort and they represent a powerful tool for quantifying the diversity of an area from local (α-diversity) to regional scale (β- and γ-diversity). Nonetheless, sampling species based on standard plant inventories represents a cost expensive approach. In this view, remotely sensed information may be straightforwardly used for predicting species rich sites. In this paper, we present spectral rarefaction, i.e., the rarefaction of reflectance values derived from satellite imagery, as an effective manner for predicting bio-diverse sites. We tested this approach in ten biogeographical subregions in Switzerland. Plant species data were derived from the Swiss ‘Biodiversity Monitoring’ programme (BDM), which represents species richness of Switzerland at the landscape scale by a systematic sample of 520 quadrats of 1 km × 1 km. Seven Landsat ETM+ images covering the whole study area were acquired. Species and spectral rarefaction were built and results were compared by Pearson correlation coefficient considering several sampling efforts (as measured by the number of sampled quadrats). Local α-diversity showed a similar pattern considering the ten biogeographical subregions while β- and γ-diversity showed higher values for regions in the Alpine arc and lower values for plateau regions and Jura mountains on the strength of the higher ecological (and spectral) variability of the former areas. Meanwhile, positive correlations between species and spectral richness values were significant only after a certain amount of area was accumulated, thus indicating a scale dependence of the fit of satellite and species data. With this paper, we introduce spectral rarefaction as an effective tool in quantifying diversity at a range of spatial scales. Obviously, the achieved results should be viewed as an aid to plan field survey rather than to replace it. We propose to use worldwide available remotely sensed information as a driver for field sampling design strategies.
Baffetta, F., G. Bacaro, L. Fattorini, D. Rocchini and A. Chiarucci. 2007. Multi-stage cluster sampling for estimating average species richness at different spatial grains. Community Ecol. 8: 119–127.
Chiarucci A. , 'Multi-stage cluster sampling for estimating average species richness at different spatial grains ' (2007 ) 8 Community Ecol. : 119 -127 .
BFS (1992/1997) Arealstatistik . Bundesamt für Statistik, Servicestelle GEOSTAT, Neuchâtel, Switzerland.
'', in Arealstatistik , (1992 ) -.
Chavez, P.S. Jr. 1988. An improved dark object subtraction technique for atmospheric scattering correction of multispectral data. Remote Sensing of Environment 24: 459–479.
Chavez P.S. , 'An improved dark object subtraction technique for atmospheric scattering correction of multispectral data ' (1988 ) 24 Remote Sensing of Environment : 459 -479 .
Chavez, P.S. Jr. 1996. Image based calibration revisited and improved. Photogrammetric Engineering & Remote Sensing 62: 1025–1036.
Chavez P.S. , 'Image based calibration revisited and improved ' (1996 ) 62 Photogrammetric Engineering & Remote Sensing : 1025 -1036 .
Chiarucci, A., G. Bacaro, D. Rocchini and L. Fattorini. 2008. Discovering and rediscovering the sample-based rarefaction formula in the ecological literature. Community Ecol. 9: 121–123.
Fattorini L. , 'Discovering and rediscovering the sample-based rarefaction formula in the ecological literature ' (2008 ) 9 Community Ecol. : 121 -123 .
Chiarucci, A. and I. Bonini. 2005. Quantitative floristics as a tool for the assessment of plant diversity in Tuscan forests. Forest Ecol. Manage. 212: 160–170.
Bonini I. , 'Quantitative floristics as a tool for the assessment of plant diversity in Tuscan forests ' (2005 ) 212 Forest Ecol. Manage. : 160 -170 .
Chiarucci, A., N.J. Enright, G.L.W. Perry, B.P. Miller and B.B. Lamont. 2003. Performance of nonparametric species richness estimators in a high diversity plant community. Diversity and Distributions 9: 283–295.
Lamont B.B. , 'Performance of nonparametric species richness estimators in a high diversity plant community ' (2003 ) 9 Diversity and Distributions : 283 -295 .
Chiarucci, A., S. Maccherini and V. De Dominicis. 2001. Evaluation and monitoring of the flora in a nature reserve by estimation methods. Biol. Conserv. 101: 305–314.
Dominicis V. , 'Evaluation and monitoring of the flora in a nature reserve by estimation methods ' (2001 ) 101 Biol. Conserv. : 305 -314 .
Crist, T.O. and J.A. Veech. 2006. Additive partitioning of rarefaction curves and species-area relationships: unifying alpha-, beta- and gamma-diversity with sample size and habitat area. Ecol. Lett. 9: 923–932.
Veech J.A. , 'Additive partitioning of rarefaction curves and species-area relationships: unifying alpha-, beta- and gamma-diversity with sample size and habitat area ' (2006 ) 9 Ecol. Lett. : 923 -932 .
D’Alessandro, L. and L. Fattorini. 2002. Resampling estimators of species richness from presence-absence data: why they don’t work. Metron 61: 5–19.
Fattorini L. , 'Resampling estimators of species richness from presence-absence data: why they don’t work ' (2002 ) 61 Metron : 5 -19 .
Fairbanks, D.H.K. and K.C. McGwire. 2004. Patterns of floristic richness in vegetation communities of California: regional scale analysis with multi-temporal NDVI. Global Ecol. Biogeogr. 13: 221–235.
McGwire K.C. , 'Patterns of floristic richness in vegetation communities of California: regional scale analysis with multi-temporal NDVI ' (2004 ) 13 Global Ecol. Biogeogr. : 221 -235 .
Ferretti, M. and A. Chiarucci. 2003. Design concepts adopted in long-term forest monitoring programs in Europg: problems for the future? The Science of the Total Environment 310: 171–178.
Chiarucci A. , 'Design concepts adopted in long-term forest monitoring programs in Europg: problems for the future? ' (2003 ) 310 The Science of the Total Environment : 171 -178 .
Fisher, P. 1997. The pixel: a snare and a delusion. International J. Remote Sensing 18: 679–685
Fisher P. , 'The pixel: a snare and a delusion ' (1997 ) 18 International J. Remote Sensing : 679 -685 .
Foody, G.M. 1996. Fuzzy modelling of vegetation from remotely sensed imagery. Ecol. Model. 85: 3–12.
Foody G.M. , 'Fuzzy modelling of vegetation from remotely sensed imagery ' (1996 ) 85 Ecol. Model. : 3 -12 .
Foody, G.M. and M.E.J. Cutler. 2003. Tree biodiversity in protected and logged Bornean tropical rain forests and its measurement by satellite remote sensing. J. Biogeogr. 30: 1053–1066.
Cutler M.E.J. , 'Tree biodiversity in protected and logged Bornean tropical rain forests and its measurement by satellite remote sensing ' (2003 ) 30 J. Biogeogr. : 1053 -1066 .
Foody, G.M. and M.E.J. Cutler. 2006. Mapping the species richness and composition of tropical forests from remotely sensed data with neural networks. Ecol. Model. 195: 37–42.
Cutler M.E.J. , 'Mapping the species richness and composition of tropical forests from remotely sensed data with neural networks ' (2006 ) 195 Ecol. Model. : 37 -42 .
Fox, J., M. Ash, T. Boye, S. Calza, A. Chang, P. Grosjean, R. Heiberger, G.J. Kerns, R. Lancelot, M. Lesnoff, S. Messad, M. Maechler, D. Putler, M. Ristic, and P. Wolf. 2007. Rcmdr: R Commander . R package version 1.2-9. http://www.r-project.org , http://socserv.socsci.mcmaster.ca/jfox/Misc/Rcmdr/
Gaston, K.J. 2000. Global patterns in biodiversity. Nature 405: 220–227.
Gaston K.J. , 'Global patterns in biodiversity ' (2000 ) 405 Nature : 220 -227 .
Gering, J.C., T.O. Crist and J.A. Veech. 2003. Additive partitioning of species diversity across multiple spatial scales: implications for regional conservation of biodiversity. Conserv. Biol. 17: 488–499.
Veech J.A. , 'Additive partitioning of species diversity across multiple spatial scales: implications for regional conservation of biodiversity ' (2003 ) 17 Conserv. Biol. : 488 -499 .
Gillespie, T.W., G.M. Foody, D. Rocchini, A.P. Giorgi and S. Saatchi. 2008. Measuring and modeling biodiversity from space. Progress in Physical Geography , in press.
Gillison, A.N. and K.R.W. Brewer. 1985. The use of gradient directed transects or gradsects in natural resource surveys. J. Environmental Manage. 20: 103–127.
Brewer K.R.W. , 'The use of gradient directed transects or gradsects in natural resource surveys ' (1985 ) 20 J. Environmental Manage. : 103 -127 .
Gonseth, Y., T. Wohlgemuth, B. Sansonnens and A. Buttler. 2001. Die Biogeographischen Regionen der Schweiz. Erläuterungen und Einteilungsstandard / Les régions biogéographiques de la Suisse. Explications et division standard. Umwelt Materialien / Cahiers de l’environment 137: 47 S.
Gotelli, N.J. and R.K. Colwell. 2001. Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness. Ecol. Lett. 4: 379–391.
Colwell R.K. , 'Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness ' (2001 ) 4 Ecol. Lett. : 379 -391 .
Gould, W. 2000. Remote Sensing of vegetation, plant species richness, and regional biodiversity hot spots. Ecol. App. 10: 1861–1870.
Gould W. , 'Remote Sensing of vegetation, plant species richness, and regional biodiversity hot spots ' (2000 ) 10 Ecol. App. : 1861 -1870 .
Hintermann, U., D. Weber and A. Zangger. 2000. Biodiversity monitoring in Switzerland. Schriftenreihe für Landschaftspflege und Naturschutz 62: 47–58.
Zangger A. , 'Biodiversity monitoring in Switzerland ' (2000 ) 62 Schriftenreihe für Landschaftspflege und Naturschutz : 47 -58 .
Kalkhan, M.A., E.J. Stafford and T.J. Stohlgren. 2007. Rapid plant diversity assessment using a pixel nested plot design: A case study in Beaver Meadows, Rocky Mountain National Park, Colorado, USA. Diversity and Distributions 13: 379–388.
Stohlgren T.J. , 'Rapid plant diversity assessment using a pixel nested plot design: A case study in Beaver Meadows, Rocky Mountain National Park, Colorado, USA ' (2007 ) 13 Diversity and Distributions : 379 -388 .
Kirby, K.J. and R.C. Thomas. 2000. Changes in the ground flora in Wytham Woods, southern England from 1974 to 1991 — implications for nature conservation. J. Veg. Sci. 11: 871–880.
Thomas R.C. , 'Changes in the ground flora in Wytham Woods, southern England from 1974 to 1991 — implications for nature conservation ' (2000 ) 11 J. Veg. Sci. : 871 -880 .
Kobayashi, S. 1974. The species-area relation I. A model for discrete sampling. Res. Popul. Ecol. 15: 223–237.
Kobayashi S. , 'The species-area relation I. A model for discrete sampling ' (1974 ) 15 Res. Popul. Ecol. : 223 -237 .
Koellner, T., A.M. Hersperger and T. Wohlgemuth. 2004. Rarefaction method for assessing plant species diversity on a regional scale. Ecography 27: 532–544.
Wohlgemuth T. , 'Rarefaction method for assessing plant species diversity on a regional scale ' (2004 ) 27 Ecography : 532 -544 .
Kumar, S., T.J. Stohlgren and G.W. Chong. 2006. Spatial heterogeneity influences native and nonnative plant species richness. Ecology 87: 3186–3199.
Chong G.W. , 'Spatial heterogeneity influences native and nonnative plant species richness ' (2006 ) 87 Ecology : 3186 -3199 .
Lande, R. 1996. Statistics and partitioning of species diversity, and similarity among multiple communities. Oikos 76: 5–13.
Lande R. , 'Statistics and partitioning of species diversity, and similarity among multiple communities ' (1996 ) 76 Oikos : 5 -13 .
Le Hégarat-Mascle, S., D. Vidal-Madjar, O. Taconet and M. Zribi. 1997. Application of Shannon information theory to a comparison between L- and C-band SIR-C polarimetric data versus incidence angle. Remote Sensing of Environment 60: 121–130.
Zribi M. , 'Application of Shannon information theory to a comparison between L- and C-band SIR-C polarimetric data versus incidence angle ' (1997 ) 60 Remote Sensing of Environment : 121 -130 .
Magurran, E.M. 1983. Ecological Diversity and its Measurement . Chapman and Hall, London.
Magurran E.M. , '', in Ecological Diversity and its Measurement , (1983 ) -.
McCollin, D., L. Moore and T. Sparks. 2000. The flora of a cultural landscape: environmental determinants of change using archival sources. Biol. Conserv. 92: 249–263.
Sparks T. , 'The flora of a cultural landscape: environmental determinants of change using archival sources ' (2000 ) 92 Biol. Conserv. : 249 -263 .
Moreno, C.E. and G. Halffter. 2001. On the measure of sampling effort used in species accumulation curves. J. App. Ecol. 38: 487–490.
Halffter G. , 'On the measure of sampling effort used in species accumulation curves ' (2001 ) 38 J. App. Ecol. : 487 -490 .
Nichol, J. and M.S. Wong. 2007. Remote sensing of urban vegetation life form by spectral mixture analysis of high-resolution IKONOS satellite images. International Journal of Remote Sensing 28: 985–1000.
Wong M.S. , 'Remote sensing of urban vegetation life form by spectral mixture analysis of high-resolution IKONOS satellite images ' (2007 ) 28 International Journal of Remote Sensing : 985 -1000 .
Oindo, B.O. and A.K. Skidmore. 2002. Interannual variability of NDVI and species richness in Kenya. International Journal of Remote Sensing 23: 285–298.
Skidmore A.K. , 'Interannual variability of NDVI and species richness in Kenya ' (2002 ) 23 International Journal of Remote Sensing : 285 -298 .
Okeke, F. and A. Karnieli. 2006. Methods for fuzzy classification and accuracy assessment of historical aerial photographs for vegetation change analyses. Part I: Algorithm development. International Journal of Remote Sensing 27: 153–176.
Karnieli A. , 'Methods for fuzzy classification and accuracy assessment of historical aerial photographs for vegetation change analyses. Part I: Algorithm development ' (2006 ) 27 International Journal of Remote Sensing : 153 -176 .
Oksanen, J., R. Kindt, P. Legendre and R.B. O’Hara. 2007. Vegan: Community Ecology Package version 1.8-6 . http://cran.r-project.org/
Palmer, M.W. 1995. How should one count species? Natural Areas Journal 15: 124–135.
Palmer M.W. , 'How should one count species? ' (1995 ) 15 Natural Areas Journal : 124 -135 .
Palmer, M.W., P. Earls, B.W. Hoagland, P.S. White and T. Wohlgemuth. 2002. Quantitative tools for perfecting species lists. Environmetrics 13: 121–137.
Wohlgemuth T. , 'Quantitative tools for perfecting species lists ' (2002 ) 13 Environmetrics : 121 -137 .
Pelissier, R. and P. Couteron. 2007. An operational, additive framework for species diversity partitioning and beta-diversity analysis. J. Ecol. 95: 294–300.
Couteron P. , 'An operational, additive framework for species diversity partitioning and beta-diversity analysis ' (2007 ) 95 J. Ecol. : 294 -300 .
Plattner, M., S. Birrer and D. Weber. 2004. Data quality in monitoring plant species richness in Switzerland. Community Ecol. 5: 135–143.
Weber D. , 'Data quality in monitoring plant species richness in Switzerland ' (2004 ) 5 Community Ecol. : 135 -143 .
Ricotta, C. 2005. Additive partitioning of Rao’s quadratic diversity: a hierarchical approach. Ecol. Model. 183: 365–371.
Ricotta C. , 'Additive partitioning of Rao’s quadratic diversity: a hierarchical approach ' (2005 ) 183 Ecol. Model. : 365 -371 .
Robinson, G.R., M.E. Yurlina and S.N. Handel. 1994. A century of change in the Staten island flora: ecological correlates of species losses and invasions. Bull. Torrey Bot. Club 121: 119–129.
Handel S.N. , 'A century of change in the Staten island flora: ecological correlates of species losses and invasions ' (1994 ) 121 Bull. Torrey Bot. Club : 119 -129 .
Rocchini, D. 2007a. Distance decay in spectral space in analysing ecosystem β-diversity. International Journal of Remote Sensing 28: 2635–2644.
Rocchini D. , 'Distance decay in spectral space in analysing ecosystem β-diversity ' (2007 ) 28 International Journal of Remote Sensing : 2635 -2644 .
Rocchini, D. 2007b. Effects of spatial and spectral resolution in estimating ecosystem α-diversity by satellite imagery. Remote Sensing of Environment 111: 423–434.
Rocchini D. , 'Effects of spatial and spectral resolution in estimating ecosystem α-diversity by satellite imagery ' (2007 ) 111 Remote Sensing of Environment : 423 -434 .
Rocchini, D., S. Andreini Butini and A. Chiarucci. 2005. Maximizing plant species inventory efficiency by means of remotely sensed spectral distances. Global Ecol. Biogeogr. 14: 431–437.
Chiarucci A. , 'Maximizing plant species inventory efficiency by means of remotely sensed spectral distances ' (2005 ) 14 Global Ecol. Biogeogr. : 431 -437 .
Rocchini, D. and B. Cade. in press. Quantile regression applied to spectral distance decay. IEEE Geoscience and Remote Sensing Letters . doi: 10.1109/LGRS.2008.2001767.
Rocchini, D., A. Chiarucci and S.A. Loiselle. 2004. Testing the spectral variation hypothesis by using satellite multispectral images. Acta Oecol. 26: 117–120.
Loiselle S.A. , 'Testing the spectral variation hypothesis by using satellite multispectral images ' (2004 ) 26 Acta Oecol. : 117 -120 .
Rocchini, D. and C. Ricotta. 2007. Are landscapes as crisp as we may think? Ecol. Model. 204: 535–539.
Ricotta C. , 'Are landscapes as crisp as we may think? ' (2007 ) 204 Ecol. Model. : 535 -539 .
Rodrigues, A.S.L., S.J. Andelman, M.I. Bakarr, L. Boitani, T.M. Brooks, R.M. Cowling, L.D.C. Fishpool, G.A.B. da Fonseca, K.J. Gaston, M. Hoffmann, J.S. Long, P.A. Marquet, J.D. Pilgrim, R.L. Pressey, J. Schipper, W. Sechrest, S.N. Stuart, L.G. Underhill, R.W. Waller, M.E.J. Watts and X. Yan. 2004. Effectiveness of the global protected area network in representing species diversity. Nature 428: 640–643.
Yan X. , 'Effectiveness of the global protected area network in representing species diversity ' (2004 ) 428 Nature : 640 -643 .
Schwarz, M. and N.E. Zimmermann. 2005. A new GLM-based method for mapping tree cover continuous fields using regional MODIS reflectance data. Remote Sensing of Environment 95: 428–443.
Zimmermann N.E. , 'A new GLM-based method for mapping tree cover continuous fields using regional MODIS reflectance data ' (2005 ) 95 Remote Sensing of Environment : 428 -443 .
Shanmugam, P., Y.H. Ahn and S. Sanjeevi. 2006. A comparison of the classification of wetland characteristics by linear spectral mixture modelling and traditional hard classifiers on multispectral remotely sensed imagery in southern India. Ecol. Model. 194: 379–394.
Sanjeevi S. , 'A comparison of the classification of wetland characteristics by linear spectral mixture modelling and traditional hard classifiers on multispectral remotely sensed imagery in southern India ' (2006 ) 194 Ecol. Model. : 379 -394 .
Small, C. 2004. The Landsat ETM+ spectral mixing space. Remote Sensing of Environment 93: 1–17.
Small C. , 'The Landsat ETM+ spectral mixing space ' (2004 ) 93 Remote Sensing of Environment : 1 -17 .
Small, C. 2005. A global analysis of urban reflectance. International Journal of Remote Sensing 26: 661–681.
Small C. , 'A global analysis of urban reflectance ' (2005 ) 26 International Journal of Remote Sensing : 661 -681 .
Stohlgren, T.J. 2007. Measuring Plant Diversity: Lessons from the Field . Oxford University Press, New York, USA.
Stohlgren T.J. , '', in Measuring Plant Diversity: Lessons from the Field , (2007 ) -.
Stohlgren, T.J., G.W. Chong, M.A. Kalkhan and L.D. Schell. 1997a. Multiscale sampling of plant diversity: effects of minimum mapping unit size. Ecol. App. 7: 1064–1074.
Schell L.D. , 'Multiscale sampling of plant diversity: effects of minimum mapping unit size ' (1997 ) 7 Ecol. App. : 1064 -1074 .
Stohlgren, T.J., M.B. Coughenour, G.W. Chong, D. Binkley, M.A. Kalkhan, L.D. Schell, D.J. Buckley and J.K. Berry. 1997b. Landscape analysis of plant diversity. Landsc. Ecol. 12: 155–170.
Berry J.K. , 'Landscape analysis of plant diversity ' (1997 ) 12 Landsc. Ecol. : 155 -170 .
Stoms, D.M. and J.E. Estes. 1993. A remote sensing research agenda for mapping and monitoring biodiversity. International Journal of Remote Sensing 14: 1839–1860.
Estes J.E. , 'A remote sensing research agenda for mapping and monitoring biodiversity ' (1993 ) 14 International Journal of Remote Sensing : 1839 -1860 .
Tang, X.M., W. Kainz and Y. Fang. 2005. Reasoning about changes of land covers with fuzzy settings. International Journal of Remote Sensing 26: 3025–3046.
Fang Y. , 'Reasoning about changes of land covers with fuzzy settings ' (2005 ) 26 International Journal of Remote Sensing : 3025 -3046 .
Townshend, J.R.G., C. Huang, S.N.V. Kalluri, R.S. Defries, S. Liang and K. Yang. 2004. Beware of per-pixel characterization of land cover. International Journal of Remote Sensing 21: 839–843.
Yang K. , 'Beware of per-pixel characterization of land cover ' (2004 ) 21 International Journal of Remote Sensing : 839 -843 .
Tuomisto, H., A.D. Poulsen, K. Ruokolainen, R.C. Moran, C. Quintana, J. Celi and G. Cañas. 2003. Linking floristic patterns with soil heterogeneity and satellite imagery in Ecuadorian Amazonia. Ecol. App. 13: 352–371.
Cañas G. , 'Linking floristic patterns with soil heterogeneity and satellite imagery in Ecuadorian Amazonia ' (2003 ) 13 Ecol. App. : 352 -371 .
Veech, J.A. and T.O. Crist. 2007. Habitat and climate heterogeneity maintain beta-diversity of birds among landscapes within ecoregions. Global Ecol. Biogeogr. 16: 650–656.
Crist T.O. , 'Habitat and climate heterogeneity maintain beta-diversity of birds among landscapes within ecoregions ' (2007 ) 16 Global Ecol. Biogeogr. : 650 -656 .
Wagner, H.H., O. Wildi and K.C. Ewald. 2000. Additive partitioning of plant species diversity in an agricultural mosaic landscape. Landsc. Ecol. 15: 219–227.
Ewald K.C. , 'Additive partitioning of plant species diversity in an agricultural mosaic landscape ' (2000 ) 15 Landsc. Ecol. : 219 -227 .
Waser, L.T., S. Stofer, M. Schwarz, M. Küchler, E. Ivits and C.H. Scheidegger. 2004. Prediction of biodiversity: regression of lichen species richness on remote sensing data. Community Ecol. 5: 121–134.
Scheidegger C.H. , 'Prediction of biodiversity: regression of lichen species richness on remote sensing data ' (2004 ) 5 Community Ecol. : 121 -134 .
Wohlgemuth, T. 1993. The distribution atlas of pteridophytes and phanerograms of Switzerland (Welten and Sutter 1982) in a relational database — species number per mapping unit and its dependence on various factors. Bot. Helv. 103: 55–71.
Wohlgemuth T. , 'The distribution atlas of pteridophytes and phanerograms of Switzerland (Welten and Sutter 1982) in a relational database — species number per mapping unit and its dependence on various factors ' (1993 ) 103 Bot. Helv. : 55 -71 .
Wohlgemuth, T. 1998. Modelling floristic species richness on a regional scale: A case study in Switzerland. Biodiversity and Conservation 7: 159–177.
Wohlgemuth T. , 'Modelling floristic species richness on a regional scale: A case study in Switzerland ' (1998 ) 7 Biodiversity and Conservation : 159 -177 .
Wohlgemuth, T., M. Nobis, F. Kienast and M. Plattner. 2008. Modelling vascular plant diversity at the landscape scale using systematic samples. J. Biogeogr. 35: 1226–1240.
Plattner M. , 'Modelling vascular plant diversity at the landscape scale using systematic samples ' (2008 ) 35 J. Biogeogr. : 1226 -1240 .
Woodcock, C.E. and S. Gopal. 2000. Fuzzy set theory and thematic maps: accuracy assessment and area estimation. International Journal of Geographical Information Science 14: 153–172.
Gopal S. , 'Fuzzy set theory and thematic maps: accuracy assessment and area estimation ' (2000 ) 14 International Journal of Geographical Information Science : 153 -172 .
Wu, J., D.E. Jelinski, M. Luck and P.T. Tueller. 2000. Multiscale analysis of landscape heterogeneity: scale variance and pattern metrics. Geographic Information Sciences 6: 6–19.
Tueller P.T. , 'Multiscale analysis of landscape heterogeneity: scale variance and pattern metrics ' (2000 ) 6 Geographic Information Sciences : 6 -19 .