Accuracy of fractal dimension estimates for small samples of ecological distributions

Author： Kallimanis Athanasios Sgardelis Stefanos Halley John

ISSN： 0921-2973

Source： Landscape Ecology, Vol.17, Iss.3, 2002-04, pp. : 281-297

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Abstract

We carry out a simulation study of the estimation of fractal dimension in agrid-based setting typical of ecological species distributions, using nulllandscape models. We calculate the box-counting dimension for samples taken invarious types of sampling geometry. Sampler geometries include simple blocks,Cantor grids and line transects. This method may be used to measure fractaldimension of a species distribution, but the accuracy depends on a number ofcriteria. The most important is sampling effort: any estimate will beinaccurateif the sampling effort is low. We also find the geometry of the sampler to beimportant. For a given sampling effort, schemes based on the Cantor gridsperformed better than either line transects or simple blocks. Sampling effortcan be improved either by using a bigger sampler over a larger area or byrepeated sampling of a smaller area: optimum performance is often a trade-offbetween these two mechanisms. However, performance is also highly sensitive tothe type of fractal object being sampled, with certain types of objectrequiringa much greater effort for an accurate estimate of fractal dimension. Theseresults raise the possibilities of using novel sampling techniques to estimatefractal dimension, when confronted with limited resources and time, butunderline also the need for an understanding of the “type” offractality expected in ecological situations.