Illustrations and guidelines for selecting statistical methods for quantifying spatial pattern in ecological data

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 I 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 km2 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.