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Unformatted text preview: Landscape Ecology 15: 467478, 2000. 2000 Kluwer Academic Publishers. Printed in the Netherlands. 467 Lacunarity analysis of spatial pattern: A comparison M.R.T. Dale Department of Biological Sciences, University of Alberta, Edmonton, Alberta, T6G 2E9, Canada (e-mail: firstname.lastname@example.org) Received 31 June 1998; Revised 1 June 1999; Accepted 16 July 1999 Key words: scale, patch, pattern analysis, transect Abstract Lacunarity analysis has been proposed as a general method for the analysis of spatial pattern, in particular for patterns of the dispersion of points. The method is clearly an improvement over the variance:mean ratio approach based on quadrat counts, because it examines dispersion at a range of spatial scales. This paper examines the properties of lacunarity analysis and compares it with other methods of pattern analysis. Lacunarity analysis gives different results for complementary patterns, which may be an advantage depending on circumstances. The method, however, is not precise in determining the scale or the patch size in pattern with known properties. A modification that improves the interpretability of the results of the analysis is introduced but a weakness of this approach is that it does provide clear indications of the characteristics of cases that exhibit more than one scale of pattern. Because different methods react to different features in data, it is recommended that data be analysed by more than one method and the results compared for greater insight into their characteristics. Introduction Spatial pattern is a universal feature of natural sys- tems and, as a result, a number of different approaches have been developed to characterize and to quantify different aspects of the phenomenon. One theme in the analysis of spatial pattern has been the distinction between point patterns which are random (complete spatial randomness, CSR) and those that are under- dispersed (clumped or aggregated) or overdispersed (spaced or regular) by comparison. A second theme is to visualize spatial pattern as the alternation of regions of high density (patches) with regions of low density (gaps). In this view, the important characteristics of the pattern are its scale and its intensity. The scale of pattern is the average distance between the centres of adjacent patches and gaps. It is possible, and common in plant communities, for pattern to exhibit more than one scale. The intensity of pattern can have several definitions, but it refers to the difference or degree of contrast between the two phases of the pattern (patches vs. gaps) (Hill 1973; Dale and MacIsaac 1989). These two themes have given rise to two contrast- ing approaches to the analysis of pattern. Given a spatial point pattern, it seems to be a basic question to ask whether the points are random, overdispersed, or underdispersed. Many textbooks describe a method to answer this question based on the counts of points in randomly placed or regular quadrats of a constant size. The frequency distribution of points per quadratsize....
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