Multiscale sources of variation in ecological variables: modeling spatial dispersion, elaborating sampling designs
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
Detection of structured spatial variation and identification of spatial scales are important aspects of ecological studies. Spatial structures can correspond to physical features of the environment or to intrinsic characteristics of ecological processes and phenomena. Spatial variability has been approached through several techniques such as classical analysis of variance, or the calculation of fractal dimensions, correlograms or variograms. Under certain assumptions, these techniques are all closely related to one another and represent equivalent tools to characterize spatial structures.
Our perception of ecological variables and processes depends on the scale at which variables are measured. We propose simple nested sampling designs enabling the detection of a wide range of spatial structures that show the relationships among nested spatial scales. When it is known that the phenomenon under study is structured as a nested series of spatial scales, this provides useful information to estimate suitable sampling intervals, which are essential to establish the relationships between spatial patterns and ecological phenomena. The use of nested sampling designs helps in choosing the most suitable solutions to reduce the amount of random variation resulting from a survey. These designs are obtained by increasing the sampling intensity to detect a wider spectrum of frequencies, or by revisiting the sampling technique to select more representative sampling units.
- Bellehumeur, C., P. Legendre and D. Marcotte. 1997. Variance and spatial scales in a tropical rain forest: changing the size of sampling units. Plant Ecology 130: 89–98.
- Bolviken, B., P.R. Stokke, J. Feder, T. Jossang. 1992. The fractal nature of geochemical landscapes. J. Geochem. Explor. 43: 91–109.
- Borcard, D. and P. Legendre. 1994. Environmental control and spatial structure in ecological communities: an example using oribatid mites (Acari, Oribatei). Environmental and Ecological Statistics 1: 37–61.
- Burrough, P.A. 1981. Fractal dimensions of landscapes and other environmental data. Nature 294: 240–242.
- Burrough, P.A. 1987. Spatial aspects of ecological data. In Data Analysis in Community and Landscape Ecology. pp. 213–251. Edited by R.H.G. Jongman, C.J.F. ter Braak and O.F.R. van Tongeren. Pudoc, Wageningen.
- Carr, J.R. and W.B. Benzer. 1991. On the practice of estimating fractal dimension. Math. Geol. 23: 945–958.
- Cliff, A.D. and J.K. Ord. 1981. Spatial processes: models and applications. Pion, London.
- Cressie, N.A.C. 1991. Statistics for spatial data. JohnWiley & Sons, New York.
- David, M. 1977. Geostatistical ore reserve estimation. Elsevier, Amsterdam.
- Dutilleul, P. 1993. Spatial heterogeneity and the design of ecological field experiments. Ecology 74: 1646–1658.
- Dutilleul, P. and P. Legendre. 1993. Spatial heterogeneity against heterocedasticity: an ecological paradigm versus a statistical concept. Oikos 66: 152–171.
- Fortin, M.-J., P. Drapeau and P. Legendre. 1989. Spatial autocorrelation and sampling design in plant ecology. Vegetatio 83: 209–222.
- Gardner, R.H. 1997. Pattern, process and the analysis of spatial scales. In Ecological Scale: Theory and Applications. Edited by D.L. Peterson and V.T. Parker. Columbia University Press, New York.
- Garrett, R.G. 1983. Sampling methodology. In Handbook of Exploration Geochemistry. Vol. 2. pp. 83–110. Edited by R.J. Howarth. Elsevier, Amsterdam.
- Geary, R.C. 1954. The contiguity ratio and statistical mapping. The Incorporated Statistician 5: 115–145.
- Gower, J.C. 1962. Variance component estimation for unbalanced hierarchical classification. Biometrics 18: 537–542.
- Greig-Smith, P. 1952. The use of random and contiguous quadrats in the study of the structure of plant communities. Ann. Bot. New Series 16: 293–316.
- He, F., P. Legendre, C. Bellehumeur, J.V. LaFrankie. 1994. Diversity pattern and spatial scale: a study of a tropical rain forest of Malaysia. Environmental and Ecological Statistics 1: 265–286.
- He, F., P. Legendre and J.V. LaFrankie. 1996. Spatial pattern of diversity in a tropical rain forest of Malaysia. Journal of Biogeography 23: 57–74.
- He, F., P. Legendre and J.V. LaFrankie. 1997. Distribution patterns of tree species in a Malaysian tropical rain forest. J. Veget. Sci. 8: 105–114.
- Hewitt, J.E., P. Legendre, B.H. McArdle, S.F. Thrush, C. Bellehumeur and S.M. Lawrie. 1997. Identifying relationships between adult and juvenile bivalves at different spatial scales. J. Exp. Mar. Biol. Ecol. (in press).
- Journel, A.G. and Ch.J. Huijbregts. 1978. Mining geostatistics. Academic Press, London.
- Kochummen, K. M., J.V. LaFrankie and N. Manokaran. 1991. Floristic composition of Pasoh forest Reserve, a lowland rain forest in Peninsular Malaysia. Journal of Tropical Forest Science 3: 1–13.
- Legendre, P. and M.-J. Fortin. 1989. Spatial pattern and ecological analysis. Vegetatio 80: 107–138.
- Levin, S.A. 1992. The problem of pattern and scales in ecology. Ecology 73: 1943–1967.
- Lewis, W.M., Jr. 1978. Comparison of temporal and spatial variation in the zooplancton of a lake by means of variance components. Ecology 59: 666–671.
- Ludwig, J.A. and D.W. Goodall. 1978. A comparison of paired-with blocked-quadrat variance methods for the analysis of spatial pattern. Vegetatio 38: 49–59.
- Mandelbrot, B.B. 1983. The fractal geometry of nature. Freeman, San Francisco.
- Matheron, G. 1965. Les variables régionalisées et leur estimation; une application de la théorie des fonctions aléatoires aux sciences de la nature. Masson, Paris.
- Miesch, A.T. 1975. Variograms and variance components in geochemistry and ore evaluation. Geological Society of America, Memoirs, 142: 333–340.
- Milne, B.T. 1991. Heterogeneity as a multiscale characteristic of landscapes. In Ecological Heterogeneity. pp. 69–84. Edited by J. Kolasa and S.T.A. Pickett. Springer-Verlag, New York.
- Moran, P.A.P. 1950. Notes on continuous stochastic phenomena. Biometrika 37: 17–23.
- Nortcliff, S. 1978. Soil variability and reconnaissance soil mapping: a statistical study in Norfolk. J. Soil Sci. 29: 403–418.
- Oliver, M.A. and R. Webster. 1986. Combining nested and linear sampling for determining the scale and form of spatial variation of regionalized variables. Geogr. Analysis 18: 227–242.
- Palmer, M.W. 1988. Fractal geometry: a tool for describing spatial patterns of plant communities. Vegetatio 75: 91–102.
- Pinel-Alloul, B., J.A. Downing, M. Pérusse and G. Codin-Blumer. 1988. Spatial heterogeneity in freshwater zooplankton: variation with body size, depth, and scale. Ecology 69: 1393–1400.
- Platt, T. and C. Filion. 1973. Spatial variability of the productivity: biomass ratio for phytoplankton in small marine basin. Limnol. Oceanogr. 18: 743–749.
- Renshaw, E. and E.D. Ford. 1984. The description of spatial pattern using two-dimensional spectral analysis. Vegetatio 56: 75–85.
- Rossi, R.E., D.J. Mulla, A.G. Journel and E.H. Franz. 1992. Geostatistical tools for modeling and interpreting ecological spatial dependence. Ecol. Monogr. 62: 277–314.
- Shaw, R.G. and T. Mitchell-Olds. 1993. Anova for unbalanced data: an overview. Ecology 74: 1638–1645.
- Sokal, R.R. and N.L. Oden. 1978a. Spatial autocorrelation in biology, 1. Methodology. Biological Journal of the Linnean Society 10: 199–228.
- Sokal, R.R. and N.L. Oden. 1978b. Spatial autocorrelation in biology, 2. Some biological implications and four applications of evolutionary and ecological interest. Biological Journal of the Linnean Society 10: 229–249.
- Sokal, R.R. and F.J. Rohlf. 1995. Biometry, 3rd ed. W.H. Freeman and Co., San Francisco.
- Troussellier, M., A. Maul and B. Baleux. 1989. Stratégies d'échantillonnage. In Microorganismes dans les Écosystèmes Océaniques. pp. 27–62. Edited by M. Bianchi, D. Marty, J.-C. Bertrand, P. Caumette and M. Gauthier. Masson, Paris.
- Ver Hoef, J.M, N.A.C. Cressie and D.C. Glenn-Lewin. 1993. Spatial models for spatial statistics: some unification. J. Veg. Sci. 4: 441–452.
- Multiscale sources of variation in ecological variables: modeling spatial dispersion, elaborating sampling designs
Volume 13, Issue 1 , pp 15-25
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- spatial pattern
- sampling design
- analysis of variance