Concepts of spatial scale, such as extent, grain, resolution, range, footprint, support and cartographic ratio are not interchangeable. Because of the potential confusion among the definitions of these terms, we suggest that authors avoid the term “scale” and instead refer to specific concepts. In particular, we are careful to discriminate between observation scales, scales of ecological phenomena and scales used in spatial statistical analysis. When scales of observation or analysis change, that is, when the unit size, shape, spacing or extent are altered, statistical results are expected to change. The kinds of results that may change include estimates of the population mean and variance, the strength and character of spatial autocorrelation and spatial anisotropy, patch and gap sizes and multivariate relationships. The first three of these results (precision of the mean, variance and spatial autocorrelation) can sometimes be estimated using geostatistical support‐effect models. We present four case studies of organism abundance and cover illustrating some of these changes and how conclusions about ecological phenomena (process and structure) may be affected. We identify the influence of observational scale on statistical results as a subset of what geographers call the Modifiable Area Unit Problem (MAUP). The way to avoid the MAUP is by careful construction of sampling design and analysis. We recommend a set of considerations for sampling design to allow useful tests for specific scales of a phenomenon under study. We further recommend that ecological studies completely report all components of observation and analysis scales to increase the possibility of cross‐study comparisons.
Pousty, S. 2002. Illustrations and guidelines for selecting statistical methods for quantifying spatial pattern in ecological data. -Ecography 25: 578-600. This paper aims to provide guidance to ecologists with limited experience in spatial analysis to help in their choice of techniques. It uses examples to compare methods of spatial analysis for ecological field data. A taxonomy of different data types is presented, including point-and area-referenced data, with and without attributes. Spatially and non-spatially explicit data are distinguished. The effects of sampling and other transformations that convert one data type to another are discussed; the possible loss of spatial information is considered. Techniques for analyzing spatial pattern, developed in plant ecology, animal ecology, landscape ecology, geostatistics and applied statistics are reviewed briefly and their overlap in methodology and philosophy noted. The techniques are categorized according to their output and the inferences that may be drawn from them, in a discursive style without formulae. Methods are compared for four case studies with field data covering a range of types. These are: 1) percentage cover of three shrubs along a line transect; 2) locations and volume of a desert plant in a 1 ha area; 3) a remotely-sensed spectral index and elevation from 10 5 km 2 of a mountainous region; and 4) land cover from three rangeland types within 800 km 2 of a coastal region. Initial approaches utilize mapping, frequency distributions and variance-mean indices. Analysis techniques we compare include: local quadrat variance, block quadrat variance, correlograms, variograms, angular correlation, directional variograms, wavelets, SADIE, nearest neighbour methods, Ripley's L . (t), and various landscape ecology metrics. Our advice to ecologists is to use simple visualization techniques for initial analysis, and subsequently to select methods that are appropriate for the data type and that answer their specific questions of interest. It is usually prudent to employ several different techniques.
Chlorophyll is a key indicator of the physiological status of a forest canopy. However, its distribution may vary greatly in time and space, so that the estimation of chlorophyll content of canopies or branches by extrapolation from leaf values obtained by destructive sampling is labor intensive and potentially inaccurate. Chlorophyll content is related positively to the point of maximum slope in vegetation reflectance spectra which occurs at wavelengths between 690-740 nm and is known as the "red edge." The red edge of needles on individual slash pine (Pinus elliottii Engelm.) branches and in whole forest canopies was measured with a spectroradiometer. Branches were measured on the ground against a spectrally flat reflectance target and canopies were measured from observation towers against a spectrally variable understory and forest floor. There was a linear relationship between red edge and chlorophyll content of branches (R(2) = 0.91). Measurements of the red edge and this relationship were used to estimate the chlorophyll content of other branches with an error that was lower than that associated with the calorimetric (laboratory) method. There was no relationship between the red edge and the chlorophyll content of whole canopies. This can be explained by the overriding influence of the understory and forest floor, an influence that was illustrated by spectral mixture modeling. The results suggest that the red edge could be used to estimate the chlorophyll content in branches, but it is unlikely to be of value for the estimation of chlorophyll content in canopies unless the canopy cover is high.
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