Measuring the fractal geometry of landscapes

Abstract

Kilometers-wide landscapes are spatially complex. Often, the consequences of spatial heterogeneity on the flow of organisms and energy is unknown, primarily due to a lack of quantitative tools appropriate for patterns which vary consistently across a range of length scales. Methods are described for quantifying perimeter, area, frequency, density, and diversity relationships for the patches composing fractal mosaics. A methodology is also introduced for applications where analyses based on the statistical association of patches are preferable to independent analyses of the patches. Determinations of the range of length scales over which systems exhibit self-similarity provide a means of identifying the scales at which fine-scale processes create "global" scale patterns. Together, these methods provide tools for the analysis of fractal patterns in landscapes, with implications for the use of predictive models at many scales, the comparison of diversity measurements from different studies, and the possible enumeration of processes affecting a system.